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An Investigation of the Effect of Processing Variables on Magnetic Permeability of Some Materials produced By Powder Metallurgy

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AH IHVESTIGATIOF OF THE EFFECT OF PHOCESSIITG VARIABLES Oft KAGIIETIC
PERMEABILITY OF SQUB kATERIALS PRODUCED BY POWDER
METALLURGY
A Thesis
Presented to
the Faculty of the Department of Metallurgy
Montana School of Mines
•75
In P a r t i a l
Fulfillment
of the Requizjemeirtk rfOr #*kg Degree
•••
*••'/
Master of Sqltpifee* i n Metallurgical Engineering
* **•*-***•*
Donald q. Cole
May 20, 1941
LiBRARY-MOKTAXATECI
Byn£4 mmimk
UMI Number: EP33373
All rights reserved
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TABLE OF CONTENTS
CHAPTER
I.
PAGE
INTRODUCTION
The problem
.........
1
.••••
. •..
..............
Investigations ••.....•....••........•
...........
2
....
5
.
4
••...•.•..•.••••••...
4
Outline of thesis ..........
II.
.
PREVIOUS INVESTIGATIONS AND PRESENT lETHODS OF
PRODUCING MAGNETS BY POWDER METALLURGY .....
Early developments
Compacted Permalloy •••.••••......••
"2-81 Molybdenum Permalloy" •
•
.....
Alni co
III*
1
5
..
6
.... •
7
POWDER METALLURGY .....
9
Definition
10
History
11
Advantages and limitations
Mature of the bond
IV. MAGNETISM
••«.••...••..•
•••..•••••••....•••.
.
13
16
......
23
magnetic properties ••••••••••...••.......*.•.••.••
24
Early theories of magnetism •.••.•».••••••••••••......
25
The magnetic field
28
Bozorthfs theory of magnetism ••••....••••.•....••.••.
29
Correlation of physical characteristics with
CHAPTER
PAGE
Theory of alloying ferromagnetics with
V.
paramagnetic materials ..»...••••.*••*•....•.
36
Magnetic permeability and susceptibility .......
38
Effect of separating magnetic poles •
43
FACTORS WHICH AFFECT THE PHYSICAL AND MAGNETIC
PROPERTIES OF COMPACTED POWDERS
VL.
47
Effect of pressure
47
Effect of heat treatment
49
Effect of particle size
50
Effect of impurities
51
DESCRIPTION OF THE EQUIPMENT
53
Weighing and mixing apparatus
Pressing apparatus •
53
•
55
Heat treating devices
68
Permeameters
•
70
Metal powders, lubricants, etc.
VII.
83
PRODUCING THE HSJAL COITACTS ABB MEASURING
THEIR MAGNETIC PERMEABILITY
Weighing and mixing
84
•••.••••••••
84
Reducing the oxide coating of metal powders ....
85
The pressing operation ••••••••
87
Heat treating •
•••••
t
•
•
Magnetic measurements ••
•
•
90
91
CHAPTER
PAGE
VIII.
IX.
EXPERIMENTAL RESULTS
93
Preliminaries
93
Effect of pressure
96
Effect of pressing temperature
100
Effect of heat treatment
102
Effect of composition
106
Diffusion
Ill
CONCLUSIONS AND SUGGESTIONS FOR FURTffiJR
RESEARCH
114
Conclusions
114
Suggestions for further research
115
APPENDIX A.
Pressure conversions from gage readings
of hydraulic jack to actual applied pressure ... 117
APPENDIX B.
Weight of powder required to give a
pellet of the correct size
118
APPENDIX C.
Reduction of metallic oxides ............ 119
APPENDIX D.
To measure the constant, k , of a
ballistic galvanometer
120
ACKNO?/LEDGEI!ENTS *
APPROVAL SHEET
121
.•*
122
LIST OF FIGURES
FIGURE
PAGE
1.
Electron Shells in an Atom of Iron ................
2.
Apparatus for Mixing Metal Powders and General
View of Equipment
3#
54
Component Parts of Pressing Mold and Assembled
Pressing Mold
4.
31
56
Pressing Mold Showing Reducing Chamber and
Heating Unit
57
5. Atmosphere Control Apparatus .«••••.••••••....•••.•
65
6.
Atmosphere Control Apparatus for Pressing Mold ....
66
7.
Heat Treating Apparatus
69
8*
Circuit for Making Magnetic Measurements ........ ••
9*
Device for Making Magnetic Measurements
•
•••••...••••.«
(For Soft Iron Standard) *.•....
71
77
10*
Equipment Used for Making Magnetic Measurements ...
80
11.
Circuit for Measuring Magnetic Susceptibility (K) «
81
12.
Equipment Ready for Pressing Operation ••••..••....
88
14.
Effect of Pressure, With and Without the Application
of Heat, on Ma-Ttetic Permeability of Compacted
Metal Powders
15.
98
Typical Curves Showing the Effect of Pressii g
Temperature on Magnetic Permeability of
Compacted Metals ...............................
101
FIGURE
16.
PAGE
Equal Permeability Curves for the Fe-Co«Al
Series
17•
109
Equal Permeability Curves for the Fe-Co-Al
Series (Heat Treated) ....•
...»
110
LIST OF TABLES
TABLE
PAGE
I. Typical Table Showing the Effect of Heat
Treatment on Magnetic Permeability of
Compacted Metals
II.
....#........».•**
Effect of Quenc^xiig on the Magnetic
Permeability of Compacted Metals .............
III.
104
105
Effect of Annealing Time (or Diffusion)
on the Magnetic Permeability of 75Fe^25Al
Compact s
113
CHAPTER I
INTRODUCTION
The field of powder metallurgy has expanded rapidly in recent
years because of the interest aroused by the great volume of successful research which has been accomplished. Until very recently, however, most of the research was confined to practical problems dealing with the fabrication of materials from metal powders, with the
commercial aspects in view.
In short, the theories connected with
powder metallurgy have been somewhat neglected.
I.
THE PROBLEM
Although magnetic materials made by powder methods have been
in use for several years, it is extremely difficult to find any published papers on the theories behind them.
A better understanding
of the connection of the theories of magnetism to magnetic materials
produced by powder metallurgy might lead to urforseen results which
will vitally affect the manufacture of such materials. With this in
view, the work of this investigation was conducted.
Permeability, one of the magnetic properties of a substance,
is a function of many of the same characteristics which influence
its physical and chemical properties. Among these characteristics
are the atomic structure, the regularity of the space lattice, impurities, aging, cavities, grain-size, and grain orientation.
2
Burrows has shown that for any set of physical and chemical
properties there is one and only one set of magnetic properties.-1*
Since permeability is probably the easiest of the magnetic properties to measure accurately, this was tar en as the basis for all magnetic measurements in this investigation, and is designated by the
Greek letter [a.
II.
INVESTIGATIONS
The physical characteristics of compacted metal powders, in
general, are dependent on the purity and characteristics of the constituent powders; the pressing variables such as applied pressure,
pressing temperature and atmosphere; and subsequent heat treatment
including heat treating atmosphere.
The first part of this work con-
sisted of preparation of the equipment and an investigation of the
effect of some of the above variables on the magnetic properties,
(and thus the physical properties) of some compacted specimens of
powders in different magnetic classes, including:
1. Paramagnetic powders
a. Heusler Alloy
2. Ferromagnetic powders
a. Permalloy
b. 1040 Alloy
c. Fe, Co, Mo Alloy
bulletin of the Bureau of Standards, 1916, Vol 13, (Washington D.C., United States Government Printing Office), p.207.
3
3. Mixtures of paramagnetic and ferromagnetic powders
a. Fe, Co, Al Series
The major part
of the experimental work consisted of a study
of the effect of various compositions, in the Fe, Co, Al Series,
upon the magnetic properties. Some work was also done on diffusion.
III. OUTLINE OF THESIS
This thesis contains, in general (l) a review of production
of magnetic materials by powder methods, (2) a brief discussion of
the principles of powder metallurgy together with some of the interesting aspects of it, (3) a discussion of some of the theories of magnetism and their possible relation to the magnetic material produced in
powder metallurgy, (4) a summary of the factors which affect the magnetic properties of compacted metals, (5) experimental procedure including a description of the apparatus as well as the technique used
in obtaining the experimental data, (6) graphical and tabular representation of the data acquired, (7) an interpretation of the data, and
(8) conclusions with suggestions for further research.
Throughout the entire text an attempt was made to correlate
the magnetic theories with magnetic materials produced by powder
methods.
CHAPTER II
PREVIOUS INVESTIGATIONS AND PRESFNT METHODS
OF PRODUCING MAGNETS BY POrtDER kETiiLLURGY
Theories of magnetism in connection with powder metallurgy
have probably not been extensively investigated, and certainly the
lacr of publication on this subject is notable. However, commercial production of magnets from powders has been quite extensive,
and some published material on their fabrication is available.
This chapter contains a short description of the origin of
research in the production of magnets fron compressed powders.
Some of the commercial magnets along with a discussion of methods
of their manufacture are also included.
I. EARLY DEVBLOPdEfcT
Prior to 1925 magnetic materials made from corpressed powders were rare, and literature on their production is extremely
meager. The Bell Telephone and Telegraph Company became pioneers
in this field about 1915. They were stimulated along this line by
the necessity of more satisfactory loading coils and network coils.
This need was augmented by the extension of telephone circuits to
transcontinental length.
It was necessary to find a material for
these coils which would have high magnetic stability with time,
5
temperature, and accidental magnetization, so considerable research
was instigated. This stability was first acquired by using iron
wire cores in which there were many air gaps. However, these were
not satisfactory for various reasons. A core of compressed, insulated powders was the next product of "this research.
This core
was mechannically stable; it introduced the required air gaps and
avoided undesirable leakage fields; and it subdivided the magnetic
material so as to reduce eddy current losses.^*
II.
COMPACTED PERMALLOY
Electrolytic iron powder, pressed into cores, gave the required stability, but due to the low permeability they were large
and costly.
discovered.^
In 1925 Permalloy fabricated from magnetic powders was
Cores tuade from these powders had the required stabil-
ity and low hysteresis loss, and were economical. Other electrical
industries, as well as the telephone and telegraph companies, found
widespread use for small magnets of Permalloy produced by powder
methods, and this material is still used when its specific magnetic
properties are desired.
2
W.C. Ellis and Earle E. Schuuacher,
Metals and Alloys, 5:275, December 1934.
"Magnetic Materials",
^V.E. Legg and F.J. Given, "New Magnetic Alloy of Powdered
Metal", Metals Progress, 38:284, September 1940.
6
III.
"2-81 MOLYBDENUM PftteiALLOY"
Subsequent to the discovery of permalloy from powders, there
was a great amount of research along this line, and in 1940 a new
material known as"2-81 molybdenum permalloy" was made available.^
The composition is 2% molybdenum 81^ nickel and 17$ iron. The
chief advantages of this core material over permalloy is thet it has
a higher permeability and electrical resistivity with smaller losses
from eddy currents and hysteresis.
The method of manufacture of "2-81 molybdenum permalloy" is
unique.^ The raw materials and necessary embrittling agents are
melted together and cast into ingots, which are rolled to develop
the desired grain structure. The ingot is then pulverized to the
desired particle size, and then annealed to soften the particles
and to give them better pressing properties. The alloy powder is
then coated with a minimum thickness of insulating material which
will not breav away during pressing operations and which will not
fuse and flux with the magnetic material.
If low permeability is desired, some non-magnetic powder is
added to dilute the magnetic material. After insulating and diluting
3
.V.E. Legg and F.J. Given, "Compressed Powdered Molybdenum
Permalloy for High Quality Inductance Coils", Bell System Technical
Journal, 19:386, July 1940.
4 Legg and Given, "New Magnetic Alloy of Powdered Metal",
Metals Progress, 38:384, September 1940.
7
to the desired value, the mixture is pressed at about 100 tons per
square inch, or at such a pressure as to give the maximum strength
and proper density. Ihen the non-magnetic substance added is a
plastic material the pressure need not be so high, since the plastic
powder will act as a binder to give the compact strength when lower pressures are used.
The compressel core is then annealed in hydrogen at such a
temperature as to remove the strains incident to pressing.
Permeability shift, due to accidental strong magnetization
is found to be less than 0.2/5 even Yd.thin a few seconds after the
magnetization is released.
1'his material is a decided improvement
over permalloy, and will prob&bly find wide application in the field
of communications.
IV. ALNICO
Alnico, which is 20°^ nickel, 12j£ aluminum, 5% cobalt, balance
iron, is another magnetic alloy that has special properties which
warrant its commercial exploitation.
This alioy is made with balanced
values of coercive force and residual magnetism in order to develop
the maximum energy value.5
Due to the nature of these alloys they
cannot be machined, rolled, or drilled, and can only be finished by
grinding.
5
For this reason they must be cast or made by powder methods.
Edwin F. Cone, "Alnico and Related Alloys", Metals and Alloys,
10:293, October 1939.
8
Small sizes used in telephone cuxcuits are difficult to cast, and
the even smaller sizes used in microphones, etc, cannot be produced
by casting alone. These sraall sizes could be Jiade by casting accompanied by expensive grinding, but powder methods, in general, are
more economical. Magnets .aade by powder methods do not need a finishing operation to give accurate size or clean cut appearance, while
casting's invariably require a costly grinding operation to obtain
these characteristics.
It is also true that the powder method produces a fine grained structure which has considerably higher mechanical strength than
the coarse grained magnets formed by casting.
9
CHAPTER III
POWDER METALLURGY
Existing definitions of powder metallurgy do not distinguish between cases in which a molten constituent is present
and those in which none of the constituents are molten. In the
first part of this chapter products of powder metallurgy are divided into two classes based on the heat treatment.
In the first
class are those which contain no molten constituent at any stage
in their production.
The other class includes those which receive
heat treatment at temperatures high enough to produce one or more
molten constituents, but which retain their outward appearance
of solidity.
There are, of course, other classifications of the
products of powder metallurgy, but this one might have some
significance.
Next in the chapter is presented a brief history of powder metallurgy followed by some of the important advantages and
limitations, some of which have direct bearing on the work of
this thesis.
Finally a rather detailed description of the nature or
the bond, as conceived by eminent powder metallurgists, is offered along with remarks as to the connection of these theories,
especially those of diffusion, with the magnetic phenomena exhibited by magnetic materials of compressed powders.
10
I. DEFINITION
Powder metallurgy is defined by Hardy and Balke1 as the art
of making objects by heat treatment of compressed metallic powders
with or without the addition of non-metallic substances.
respects this definition is quite satisfactory.
tures of powders as well as nono-elemental
x
t
In most
covers mix-
powders and it can be
interpreted to include pressing at ordinary or at elevated temperatures. The definition is vague, however, in one respect: the term
heat treatment is not limited
A commonly accepted definition of
heat treatment includes an operation or combination of operations
involving phe heating and cooling ox1 a metal in the solid state for
the purpose of obtaining certain desirable conditions or properties.
Although this definition of heat treatment excludes operations at
temperatures at which the metal or alloy is actually molten, it is
not certain whether or not the term heat treatment would apply to
an operation at a temperature at which one of the constituents is
in the fluid state while the object as a whole remains as a solid.
It seems to be common practice among powder metallurgists to include the production of this semi-molten condition under the definition of heat treatment, and to limit treatment of compacted
powders only to those temperatures below the melting point of the
^#
^e"fc&ls handbook, 1959 Edition, (Cleveland, 0hio: American
Society for Metals, 1939), page 104.
11
major constituent. However, it would be expedient to relegate
those products obtained by treatment of compacted metal powders
at such temperatures at which a molten constituent is present
to a classification midway between those products of powder
metallurgy treated at temperature at which no molten constituent
is present, and those produced by casting.
In this work the definition of heat treatment, as applied
to powder metallurgy, was assumed to exclude any operation at a
temperature at which any of the components are in the molten state,
i. e., at temperatures at or above the melting point of the component
which has the lowest melting point.
It was because of this de-
finition that work on Heusler Alloys was abandoned.
These alloys
were found to be non-magnetic unless the compacted powders were
treated at temperatures above 656°C, the melting point of aluminum.
Although the compacts showed no external signs of melting when
heated at 800°C, it is certain that some melting must have occured.
II. JilSTORY
The art of making solid objects from metal powders is over
a hundred years old.2
The first report of endeavor in this field
is that of Wollaston who, in 1828, described a method of producing
platinum powder and pressing this in a mold followed by heat treatment.
2. Clark, °. Carpenter, "Powder Metallurgy A Review of
its Literature" Quarterly of the Colorado School of Mines.
(Golden, Colorado) 35:5, October 1940.
12
His methods were crude, however, and little came of his work.
Sir Henry Bessemer revived interest in powder metallurgy in the
1880fs when he developed a method of producing bronze powders,
but since he kept his method secret, little was accomplished until
1915.
In 1915 the production of objects from the powders of such
refractory metals as tungsten, tantalum, and molybdenum really
stimulated the industry. Most of the work was carried out by
electrical companies, and the production of tungsten wire *>y
powder metallurgy may be said to be the first application of
commercial importance. After 1915 there followed a period of
rapid development in manufacturing procedure which found new
applications in production. The electrical industry has developed
a host of materials made by powder methods, including contactors
and welding electrodes combining the high arcing temperatures
of such metals as tungsten, molybdenum and nickel. Current collector
brushes wherein copper and graphite powders are combined to give
high conductivity with minimum weight are also in wide use.
"Powder" magnets of various compo sit ions and small shapes are
manufactured by electrical companies. The varied and numerous propsrties
of the products of powder metallurgy are not within the scope of
this thesis but some the advantages and limitations should be
considered.
13
III.
ADVANTAGES AND LIMITATIONS
The physical and chemical properties of a compacted powder
are not in general, reproductions of the physical and chemical
properties of its cast composition equivalent. It is true that
some of the properties may be similar, but other of the properties
can be relegated only to that one produced by a given method.
A
great many compacted powders are brittle and porous, or hard with
low tensile strength, or of high density, while their cast composition equivalents have none of these properties. Other products of powder metallurgy may have electrical or magnetic properties impossible to obtain by casting.
In short, highly special-
ized properties may be obtained in materials fabricated from powders.
Although many advantages of powder metallurgy have been expounded, and perhaps exaggerated, in the past few years, -chere have
been some which have withstood the test of time.
It has been
authentically established that, while it will never completely
replace casting methods, powder metallurgy does have a definite
place in the field of science. Some of the points khich have won
this branch of science its place in the field of metallurgy are^:
1.
Special structures can be obtained by regulating the
compacting va riables. This regulation is easily accomplished siidTce
high temperatures are usually not necessary and the product is
quite small. Special
structures, of course give rise to special
3. Metals Handbook, 1939 Edition, (Cleveland, Ohio: American
Society for Petals) p. 104
14
properties, and this is probably one of the most important of the
advantages.
2.
Composition of the exact proportion of each constituent
can be assured. This is practically an impossibility in common
foundry practice.
3. Products can be made of metals which have widely divergent melting points, or which are immiscible in the liquid state.
Examples are lead and copper, copper and chromium, copper and
tungsten, and copper and molybdenum.
4.
Only by this method has it oeen possible to manufacture
useful articles of high refractory materials, such as tungsten,
tantalum, and molybdenum.
Examples are lamp filaments of tungsten
and the cemented carbides used as cutting tools.
5. Purity can easily be attained. Metal powders of high
purity are e& sily secured, and this purity may be Maintained by
careful processing of the compact.
6.
It is possible to produce metal in * ich non-metals such
as graphite is uniformly distributed.
Current collectors of copper
and graphite, bearings and bushings are some examples.
7.
Dimensions of the finished product may be accurately con-
trolled, providing no subsequent heat treatment is necessary.
Change of dimensions * after heat treatment may be remedied by coining but this is usually not feasible since coining cannot usually
be done in the same mold in which the object was originally pressed.
8. Less scrap is produced by this method than by any other
15
method.
9.
Low temperatures can be used in the production of some
materials such as refractory metals and the iron nickel-cobalt
alloys.
10.
A controlled atmosphere is possible in work by this
method.
There are obviously some distinct limitations^ to powder
metallurgy, some of which might be overcome in the future. At
present the limitaions are:
1. Unless it is possible to press hot, the excessive pressure necessary to cause cohesion seriously limits the type of mold
which can be used.
It is usually not possible to press large ob-
jects for the same reason.
2.
Because
some powders have a tendency to stick to the
sides of the mold, this causes uneven pressure throughout the
compact. Thus the depth of the compact is seriously limited.
However this disadva ntage may be overcome, in some cases, by the
use of lubricants.
3.
powders.
It is difficult to control the particle size of the
This defect is not at all serious since it can be con-
trolled within the limits of necessity.
4.
compounds.
Air and moisture often combine with some powders to form
This action is facilitated by the large exposed surface
of the finely divided powder.
Compounds formed by oxidation or hy-
dration may, in a great many instances, can be eliminated by heating
4.
Ibid., p. 105.
16
and reducing with hydrogen or natural gas.
5.
The theory has been so neglected that a great
research is necessary to produce a new product.
amount of
This is being
speedily remedied because of the wide interest in this field at
the present time.
Summarizing, the advantages are:
special structures and
properties, controlle d composition, purity, combination of metals
not possible by melting, manufacture of products from high refractory
metals, combimtions of metals and non-metals, controlled dimensions,
and more economical in some cases.
The serious disadvantages are:
limitation of the type of
mold due to high pressures, inability to press large objects,
and inability to remove oxide coatings from some metals.
IV. NATURE OF THE BOND
If two slabs of silver are placed together and heated for
a short time at a temperature below the melting point, they will
adhere to one another at their points of contact; if they are
pressed tightly together, thus increasing the contact surface,
and then heated, the bonding is stronger.
It has further been
shown that tv/o metals which have no affinity for each other, that
is, those which are practically immiscible in the molten state as
well as in the solid, will be strongly bonded by pressing them together and heating below the melting points. Examples are ironsilver and silver-carbon.
In cases of this type the bonding is
17
due to the formation of a network of the silver particles which
are cemented together, holding the particles of iron or carbon
within it as inclusions. "When two metals which are miscible in
all proportions, such as silver and copper, are pressed together
and heat treated, the bonding material is found to consist of the
eutectic.
The above are examples of diffusion in the solid state,
cr more correctly, , in the plastic sta~e. The temperature at
w iich a metal is plastic varies for different metals. Some
metals such as tin, lead, and cadmium are plastic at room tempertures; others such as iron, cobalt, and manganese requires high
temperatures in order to attain the plastic state. The rate of
diffusion is directly dependent upon the plasticity of the solvent.
Plasticity is really a poor term to designate increased atomic
mobility, but a better word has not been coined. The temperature
of plasticity is definitely connected with the recrystallization
temperature. Recrystallization takes place only at temperatures
at which the atoms are mobile enough to rearrange themselves,
eliminating strains and forming new crystals in the grain boundaries.
Diffusion operates on the principle of concentration equilibrium, that is, when there is concentration gradient there is a
tendency to attain uniformity of concentration by migration of
ions or atoms from portion of high concentration to the portion of
low concentration until equilibrium is established.
The rate of
diffusion is, of course, dependent on the ease with which the par-
18
tides can move through the medium of the lower concentration.
For convenience the migrating particles will be called solute
and the medium of lower concentration will be referred to as the
solvent, although these terms are not meant to apply in any
sense to the solubility of the materials.
The ease of movement of the atoms of solute will depend
on the amount of "loosening" of the crystal lattice of the solvent.
"Loosening" of the lattice occurs at temperatures at which plasticity occurs, or at temperatures at which the thermal energy of
the atom is increased sufficiently to neutralize part of the energy which holds the atoms together.
Thus plasticity designates
a state of limited atomic mobility.
As the temperature increases
to the poinipf recrystallization the atoms become more mobile,
the crystal lattice is "loosened", the solvent metal becomes
more plastic, and the rate of diffusion increases. Diffusion does
take place, however, at temperatures below recrystallization, but
the time required increases with decreasing temperatures.
'/fliether or not the solute is miscible with the solvent
in the solid state, diffusion will occur.
In fact, some work has
shown that the rate of diffusion increases with decreasing solubility.
Examples of this are iron in silver and carbon in silver.
The migrating particles of solute are always atomic, and
the part they play in the final structure depends entirely upon
their chemical (or atomic) relations to the chemical (or atomic)
properties of the solvent.
Solid solutions or compounds of
varying composition might form, or perhaps the crystals of solute
19
will remain in the interstices of crystals of solvent.
In the
iron, cobalt, aluminum system several compounds are formed, including AI3C03, Al5Co£f AICo, and AlgFeg, and a large number of
solid solutions are solid solutions are possible.5
Therefore it is
impossible to predict the structure of this system as a result of
diffusion. However, it i s certain that there will be a close association of aluminum atoms with the atoms of cobalt and iron. This
fact is extreme importance in the interpretation of properties
exhibited by this system.
Metallurgists have not yet unanimously accepted any particular theory concerning,the mechanics by which metal powders are held
together when they have been compressed and subjected to heat treatment.
Some theories advanced by Comstock, Hardy, and others are how-
ever, still in good standing. Comstock believes that both pressure and heat are necessary for true bonding in metal compacts.
Pressure is especially important in the type of bonding where no
molten constituent is formed, ^articles which have been subjected
to pressure at temperatures below there recrystallization point
will acquire strains due to the deformation of the particle. It
has been shown conclusively that recrystallization temperatures,
in general, are lowered proportionally with the degree of cold deformation.
If surface recrystallization ot inter-particle recry-
5. Internation Critical Tables, 1927, Vol. II, (National
Reserach Council, by mcGraw Hill Book Co., Inc., N. Y. 1927) pages
402, 403, 450.
6. Gregory J. Comstock, "Nature of Bonding in Metal Compacts11,
Metals Progress, 35: 576-81: June 1939
20
stallization be factors in particle to particle bonding, pressure
affects bonding to the degree it influences the recrystallization
temperature. Comstock has also shown that pressure affects bonding by increasing the particle to particle surface contact, and
thus allovfing, upon heat treatment, a type of bonding similar to
inter crystalline bonding in a cast material.
Temperature, according to Comstock, affects bonding by
producing a plastic state in the metals in which the atomic mobility is sufficient to allow production of intercrystalline bonds
to become affected.
Intercrystalline bonds are initially produced
by cooling from the liquid, through the plastic, to the solid state.
Apparently, however, cooling from the plastic state to the solid
state is sufficient to develop atomic bonds between contacting
surfaces,ftiobonding occurs below recrystallization temperatures.
Thus true bonding, of the sort where no molten constituent is present, should take place at ordinary temperatures for those metals
which have low recrystallization temperatures, at high temperatures
only for metals with high recrystallization temperatures, and
should not take place at all between metals with widely divergent
recrystallization temperatures. Experimentally this has been
verified.
Gold powders may be "cold-welded", tungsten powders re-
quire high temperatures for bonding, and graphite and silver do not
form bonds of this nature at all.
Summarizing, Comstock proposed that the bond between properly compressed and heat-treated powders is the same as the intercrystalline bond in cast metals. The effect of pressure is to give
21
a greater particle to particle surface of contact and to reduce
the recrystallization temperatures by developing strains by cold
pressing. Hot pressing at temperatures above the recrystallization point merely allows a better contact of surfaces at lower
pressures and simultaneous development of the bond because of
the plastic condition of the metals. *ieat propagates the
development of the bond between particles by causing plasticity
and thus increased atomic mobility (facilitating diffusion).
Coo'ing from the plastic state forms the intercrystalline bond
just as does cooling from the liquid to the solid state in cast
metals.
W. D# tones' attributes the binding of compacted metal
powders to "cohesional forces" between particles. The exact
nature of these forces is not escplained, but their magnitude is
dependent on the total particle to particb surface contact. The
plastic state is necessary for the creation of maximum surface
contact at temperatures above the recrystallization point. Pressure creates a particle to particle contact to an extent depending upon the deformation of the particles. ,as the metal becomes
more plastic additional surfa^ es are pulled together by some force.
Thus pressure is necessary to obtain the initial contact surfaces,
and these are held together by "cohesional" forces. Proper heat
treatment increases the contact surfaces and thus gives better
binding.
7. W. D. Jones, Principles .of Powder Metallurgy, (London:
Edward Arnold and Co., 1937) p. 1-16.
22
A third theory for the mechanism of bonding was suggested
by Hardy.^
The structure of powders made by electrolysis is ir-
regular or angular, and under pressure these particles interlock.
Surfaces of powders are usually quite clean if care is taken.
Applied pressure creates heat sufficient to weld the particles
at the surface.
Friction may cause Enough heat to promote al-
loying.
The theory of "atomic welding" was advanced by ^ardy in 1936,
and was confirmed by subsequent work of F. r. Bowder and Hardy
and was reported before the British Institue of Metals in the autumn of 1937. This work showed that the temperatures created when
two metal particles were rubbed together, even lightly, could be
measured electrically.
At sufficient pressures the temperature
quickly rose vhe melting points of the metals, and by no increase of load or rubbing speed could they be made to rise higher.
They also showed that initial bonding during compression facilitates full diffusion during subsequent heat treatment.
8.
Charles Hardy, "Nature of* the Bond in Powder &etal Com-
pacts", Metals Progress,, 35:
171-2, 1939.
23
CHAPTER IV
MAGNETISM
Magnetism, like light, is one of the natural phenomena
whose basic principles are not completely understood.
This is
not at all surprising since it has been shown that magnetism is
closely connected with the constitution of matter and physical
theory, involving v/aves or small particles of matter called quanta,
whose nature is little know. The physical exhibition of magnetic
phenomena has given rise to many superstitions and the extent to
which they still exist is surprising. However, during the last
century men of science have made great progress in advancing theories which at least offer some explanation of magnetism.
Since
these theories are not widely known, and because they are usually
wrilten in a highly technical manner, it is the purpose of this
chapter to present the most plausible of the theories in as simple
a form as possible, and to attempt to correlate them with the
phenomena exhibited in experimental results obtained from laboratory
work on this thesis.
This chapter contains, first of all, the criterion of correlation of physical characteristics with magnetic properties,
along with a brief history of the work done on magnetic theory.
Next follows an outline of the principles of a theory advanced by Sir J. A. Ewing in collaboration with work by others.
The quantum theory and Einstein's explanation of the magnetic
field are briefly considered.
24
The principles of magnetism as propounded by R. M. Bozorth
are discussed in considerable detail, since this is the most
recent and probably, in many respects, the most plausible to theories attempting to explain magnetic phenomena. An effort is
made to correlate this theory with thesis work.
Next the magnetic properties including especially permeability, \x, and susceptibility, K, are treated.
Finally the eflect of increasing the distance between
poles of magnet is discussed, along with its effect in powder
metallurgy of magnetic substances.
I. CORRELATION OF PHYSICAL CHARACTERISTICS
MITE jAGhhTlQ
PROPERTIES
$hen a substance is exposed to the influence of magnetic
field it behaves in various ways, depending on its physical and
chemicals properties. Based on investigation of magnetic phenomem
exhibited by various materials, Burrows1 advanced the theory that
for any set of mechanical characteristics, there is only one set
of magnetic characteristics and conversely, there is one and
only one set of magnetic characteristic corresponding to a
given set of mechanical characteristics. This theory has been
1. Charles W. Burrows, "Correlation of Magnetic Mechanical Properties of Steel", Bulletin of the Bureau of Standards,
(Washington D. C* U. S. Government Printing Office, 1916) 13:207
August 1916.
25
expanded to include all characteristics of a substance, so that it
now reads: There is one and only one set of physical and chemical
properties corresponding to a given set of magnetic characteristics,
and conversely, there is one and only one set of magnetic properties,
corresponding to a given set of physical and chemical characteristics.
The absolute truth of the above statement has not been conclusively
proven, but much evidence has been accumulated to justify its
acceptance until it is either confirmed or disproven. On the basis
of this line of thought it seems that the atomic theory and magnetism are closely related.
II.
EARLY THEORIES OF MAGNETISM
It is not the purpose of this paper to deal with the
simpler concepts of magnetism which can be found in almost any
text book of college physics. Probably more important to this
work are the theories ofmagnetism which might offer an explanation of the correlation of the magnetic characteristics of a substance to its physical and chemical properties.
The nature of the ultimate particle which will not yield
two like magnets when broken into equal parts is one of the most
serious questions relating to magnetism.
The answer to this
question would probably clear up a great number of problems in
the field of magneto-magnetics. However, for convenience this
particle is called the magneton.
A great many theories have been
advanced as to what the magneton is and on the formation of a
magnet. Possibly the mas t widely accepted theory, until very
26
recently, is that the magneton is due to atomic currents. The
basis for this theory is simply that an electric current always
produces a magnetic field, and that poles are formed only where
the distribution of electric circuits become non-uniform. ^
3
Yvork which led to the development of this theory correlating the atomic structure to magnetism was done by Poisson who was
inspired by the work of Coulomb. Oersted, Ampere and Faraday advanced the theory which supposed minute currents flowing in molecules.
Ctirie, Langevin, and Tieiss developed the following important
equation:
K- M 2 N
"5ST
where K « susceptibility
M * magnetic moment
N ~ number of molecules per cubic centimeter
R - constant
T - absolute temperature
Upon calculation it was found that, for each element, M is a
multiple of a definite number. This number for iron and nickel,
according to Currie, Langevin, and leiss, was found to be 1.85x
—21
—21
10" e.m.u. The magnetic moment for iron is 11 (1.85x10
) , while
nickel has a magnetic moment of 3 (1.85*10"" ) based on these
2. Samuel R. "Williams, Magnetic Phenomena, (Hew York:
McGraw-Hill Book uorapany, Inc., 1938) p. g.
5
*
Ibid., pp. 7-10.
27
calculations. However, experiments by Bohr^ showed the value of
the magneton to be 9.2xiO""^Ie.m.u., and the quantum theory favors
this value.
Weber, in conjunction with Rowland and Maxwell, set up a
model to explain magnetic phenomena, his theory, in short, was
that the molecules of a magnetic substance are permanent magnets,
and that during magnetization they are turned into the direction of
the field. He explained the resistance to saturation by weak fieBs
by mechanical resistance which supposedly opposes rotation of the
molecular magnets so that their axes are parallel to the magnetizing field. A neutral of unmagnetized body was assumed to consist
of a collection of molecular magnets which are oriented to oppose
each other.
In a magnetic field these elemental magnets rotate
in the direction of the field to an extent which increases with
the strength of the field. The resistance to saturation by weak
fields was explained on the basis of restoring couples which resemble strains in a solid substance. Hysteresis loss he explained
by assuming that for strains beyond the elastic limit the recovery
is imperfect and loss occurs.
Sir J. A. Ewing changed Weber s theory with respect to the
resistance to, saturation by weak fields. This restraint to the
arrangement of the axes of all of the elemental magnets parallel
to the magnetizing
was now explained by the magnetic interaction
between the molecules themselves.^
^. Williams, op.cit., p. 12.
5. Sidney G. Starling, Electricity and Magnetism £New York
Longman, Green and Company, 1937} p. 294.
28
His model which is very simple accounts for a great many magnetic
manifestations •
III.
THE MAGNETIC FIELD
The field produced by a magnet is not thoroughly understood, and there are two important theories as to its constitution.
Both theories start with the postulate that a field is composed
of lines of force. Exactly what is meant by "lines of force" is
debatable. Proponents of the wave theory maintain that the lines
of force are similar to waves produced by sound, and that the energy
is thus transmitted. However, more widely accepted is the theory
that magnetic fields are produced by the emmission of quanta of ene
? gy by certain of the atoms when they are excited by some external
agent. Einstein
supports the quantum theory with the statement
that, "there is a certain probability that an atom in an excited
state will radiate by the emmission of the quantum of energy in time,
dt, which is dependent only on the nature of the atom." More generally it is stated7 that an electromagnetic field is a physical
condition which is propagated throughout space with a finite velocity in accordance with the laws expressed by Maxwell's equation,
often called the first fundamental equation of the electromagnetic
6. Condon and Morse, quantum Mechanics, (New York: McGrawHill Book Company, Inc., 1929, page jJW.
7. W. F. Lenzen, The Nature of Physical Theory, (New York:
John Wiley and Sons, In4., 1931) page X7T.
29
field,8
c u r l H-
4 7T
K
»
4
c
if
c
j
+
1
<3 D
4 7T d)T
Where i= a stationary current in a closed conducting circuit
c= velocity of light
_i
Q* ~
» density of the displaced current
In short the magnetic field is thought to consist of quanta
of energy emitted by atoms which have been externally excited.
This energy is propagated by waves and has the ability to influence
certain other atoms or groups of atoms.
III.
B O O T H ' S THEORY OF M A G N E T I S M
Explanations of magnetism by assuming the rotations of electrons around the nucleus of an atom in such a manner as to produce
polarity have met with disapproval and are not satisfactory in many
respects.
Experimental data have been obtained which tends to show that
polarity is produced by the spin of electrons about their own axes,
and magnetism is a result of such an unbalanced magnetic moment within the atom. A theory based on this principle has been advanced by
R. M. Bozorth9 who substantiates some of the aspects of Ewingl theory
and most of those of Weiss.
8.
Following is a summary of Bozorth1 s theoryi
Ibid, page 129.
9. R. M. Bozorth, wThe Physical Basis of Ferromagnetism,"
Bell System Technical Journal, 19: 1-40, January 1940.
30
1. A magnetic field is created by the spin of electrons
about their own axis, not by the motion of the electrons in their
orbital path around the nucleus of the atom.
2.
The amount of magnetism or strength of the field is re-
lative to the excess of electrons spinning in one direction over
the electrons spinning in the opposite direction.
3.
Ferromagnetic materials are those which have a large excess
of electrons in the "3d" orbit (see Fig. l) spinning in a given
direction.
4.
"Domains" consist of groups of atomic magnets which align
themselves in one direction, due to an internal field.
shown that there are from 1©
to 10
It has been
atoms per domain, and that a
single crystal of iron contains 100,000 domains. The
crystals are
of such size that there are 10,000 crystals to a cubic inch.
5. Magnetism is caused by alignment of the domains. In an
unmagnetized sample the domains are oriented in such a manner that
the fields produced by each domain are annulled and the total effective
field is zero.
6.
The Curie point is the temperature at which the forces
of thermal vibration overcome the forces which hold the atomic magnets in a domain in alignment.
7.
Alloying ferromagnetics with paramagnetic substances de-
creases the magnetization due to the fact that more or less free
electrons in the "4s" orbit of the paramagnetic atoms go into
the "3d" orbit of the ferromagnetic atoms, and cause a smaller
excess of the electrons spinning in one direction and thus lessens
the total magnetic moment of the atom.
Figure 1
ELECTRON SHELLS IN AN ATOM OF IRON*
(The arrow indicates the incomplete sub-shell that is responsible for ferromagnetism. The numbers specify how
many electrons with each snin are in the corresponding
sub-shells.)
•Bosorth, op. cit., p.2,
32
These principles will be explained in detail in the folJ owing
pages and an attempt will be made to correlate these princ^pl&s with
properties exhibited by compacts fabricated from ferromagnetic powders
or mixtures of ferromagnetic and paramagnetic powders.
The spin of electrons is now thought to be the explanation
of magnetism.
The substantiating evidence which tends to prove
this theory is the fact that when the magnetization is altered,
the only atomic change is the direction of spin of the electrons;
the orbital motions remain practically unchanged.
In the ferromagnetic
metals, iron, cobalt, and nickel, the
electrons which are responsible for the magnetic properties are in
the third shell of electrons (see Fig. l). Those electrons in
the third shell are responsible for ferromagnetism because the magnetic moment produced by those spinning in one direction is not
wholly annulled by those spinning in the
opposite direction. This
magnetic moment caTuses each atom to act as a permanent magnet.
The fact that these atomic magnets align themselves or point
in the same direction when subjected to the proper external field
can only be explained by an internal force wiiich holds these magnets
in the same direction in spite of the disrupting energy of thermal
agitation. This force has been called "exchange interaction" by
atomic-structure experts. This force is sufficient to hold groups
of atomic magnets in alignment when
the energy which tends to dis-
rupt the alignment, causing vibrating and rotating of the indlvidua 1^ *
is not excessive, uhen this energy is increased by increased
temperature, however, disruption does occur because the "exchange
interaction," force is not
sufficient to overcome the forces of
33
thermal agitation. This temperature above which the substance is
no longer magnetic is called the Curie point.
There is one phenomena ifthich cannot be explained at present.
The force which holds the atomic magnets in alignment acts only in
localized portions of a solid. These volumes are very small on the
order of 10
or 10~ 9 cubic centimeters, which however contain
approximately lO1^ atoms. These volumes in which the atomic magnets are aligned are called "domains". The magnetic moments of
neighboring domains are not necessarily parallel at room temperature.
When the
solid is "demagnetized" it is thought that the magnetic
moments of neighboring domains annul each other and the net magnetic effect is zero, /vhen the solid is subjected to an external
magnetizing force it is thought that the direction of magnetization
of domains change direction until, with a sufficient external force,
the solid is said to be saturated or the directions of magnetization
of all the domains are parallel, The vector sum of the magnetizations of all the domains at
any time is the total magnetization.
The magnetic forces of the atom are much smaller than the force
holding the atoms together.
It has been calculated that the
magnetic forces are about lO"* of the electrostatic forces. This
is best shown by a comparison of the boiling points with the Curie
points.
The best estimate of the energy of magnetization is that
it is equal to the energy of thermal agitation at the Curie point,
l/2 KO. For iron 0= 1943° K, which gives the energy of magnetization
as 7 x 10"*
ergs per atom.
34
Probably the most important equation in the theory of magnetism which supports the "domain" principle as proposed by Weiss is:
1
- tanhsYA
where
(H
+ NI)
j - ,
1 Q
I = intensity of magnetization
I0= intensity of magnetization at saturation
* 1740 for iron
YA25 magnetic moment
-20
= 2.04 x 10
erg per gauss for iron
H = applied field
NI35 molecular field of influence of neighboring atoms.
k - constant » 14 x 10" 1 7
T = Curie temperature (°K)
This equation shows that there is considerable magnetization
even when there is no applied field, provided the temperature is
not too high.
It may be show that at all temperatures below the
Curie point, the intensity of magnetization las a definite value
even ?tihen no field is applied.
This might lead one to believe that a ferromagnetic substance could not be demagnetized, but Yveiss answers it by explaining that below the
Curie point all parts of the ferromagnetic
material are magnetized, but that they are magnetized in different
directions and so oppose each other so that the net effect is zero.
The atomic structure of the ferromagnetics are responsible
for their magnetic properties. The atom, as conceived by Bohr,
consists of a nucleus around which "shells" of electrons are rotating. The number of electrons in each shell are dependent upon the
35
atom itself but there is always a definite pattern to be followed.
The maximum number of electrons in the first shell is two, in the
second eight, eighteen in the third and thirty-two in the fourth.
However each shell is not always completely filled before the next
shell is started.
The number of electrons in the third shell iden-
tifies the ferromagnetics. Bozarth believes that the direction of
spin of the electrons about an axis thru their center is responsible
for the magnetic properties. In the iron atom, he has attempted to
prove, there is an excess of four electrons spinning in one direction over those spinning in the opposite direction and the magnetization is the vector sum of the magnetic moments of these electrons.
It is thought that the orbital motion of the electrons aground the
nucleus does affect the magnetic moment of the free atom, but when
an atom is in a solid the orbits are too firmly fixed to be changed
by a magnetic field. As proof it is pointed out that the magnetic
moments produced by the orbital rotations do not change with in10
tensity of magnetization as shown by experimentation.
It is
assumed that the orbital moments of the electrons of neighboring
atoms neutralize each other.
10.
Bozorth, p. 31.
36
IV.
THEORY OF ALLOYING FERROMAGNETIC
WITH PARAMAGNETIC MATERIALS
When there is one more electron spinning in a given direction, it has been shown that the magnetic moment of the atom is one
Bohr magneton (\iB = 9.2 x 10 " " erg per gauss), and thus the number
of Bohr magnetons (equivalent to the excess of electrons spinning
in one direction) can be calculated from the atomic weight, A, and
the density, d, :
Bohr magnetons per atom = B = 1^ A
Where I Q - saturation intensity of magnetization at absolute
zero.
The force which holds the electrons in the outer shell of an
atom are comparatively weak and these electrons are often called
the "free" electrons or the electrons which conduct an electric
current. Calculations have shown thax the incomplete "3d" shell
of the atom is the lowest energy level.11
A "free electron" will
seek the lowest energy level. Thus when an atom such as Cu, Al,
Si, Sn, or Sb, becomes alloyed with an atom of one of the ferromagnetics, the free electrons of these paramagnetic substances will
tend to fill the incomplete "3d" shell of the ferromagnetic atom.
Each additional atom added to the "3d" shellwill lower the magnetic
saturation of the alloy one Bohr magneton. Thus the magnetic
saturation of a ferromagnetic may be reduced to zero by the addition
11.
J. C. Slater, Physical Review, 49:
537-45 (1936) .
37
of the proper number of electrons to the "3d" shell so that the
number of electrons rotating in each direction are equal, and the
resultant magnetic moment is zeit> at 0°K. Marion1^ proved this to
be true for the addition of various metals to nickel. It was shown
that the magnetic saturation at 0°K of a nickel alloy containing 60
atomic per cent copper is zero. Since zinc has two "4s" electrons
it will fill up the "3d" shell of nickel twice as fast as will
copper and will fill up the shell of twice as many atoins. An atom
of aluminum, which has three "4s" electrons, will fill up the "3d"
band of nickel three times as fast as will copper, and will render
three times as many atoms of n ickel non-magnetic.
Thus an aluminum-
nickel alloy of 20 atomic per cent aluminum will be non-magnetic.
Since the excess of electrons in the "3d" shell of iron is
m
£z
.01
times as much as for nickel, it requires 3.64 times as many atoms
of aluminum to render it non-magnetic.
On this basis 20 x -*|f
=
72.8 atomic per cent or 72.8 x ~~ - 16*9% by weight, of aluminum
will render an alloy of iron and aluminum non-magnetic.
This holds for alloys which are1 fabricated from the molten
constituents where there is atomic dispersion but the case for
metals compacted from ferromagnetic powders is different. The
particles of the paramagnetic and ferromagnetic powder only come in
contact at the surface, and the exchange of electrons probably takes
place only among the atoms which actually come in close contact,
leaving the atoms within the grains of the ferromagnetic powder
12.
*. Marion, Ann de Physique, 11, 7:
459-527, 1937.
38
unaltered.
This is substantiated by the fact that compacts of the
Fe, Co, Al system were magnetic with as high as ninety-five percent aluminum. This is not true of cast specimens of the Fe, Ni,
Al series, which are very similar, as shown in Metals Handbook, *^
where it is seen from the diagram that alloys of this system become non-magnetic when the amount of aluminum exceeds twenty percent by weight. This conforms closely to theory. This is proof of
the exchange of electrons between atoms of paramagnetic and ferromagnetic materials.
¥.
MAGNETIC PERMEABILITY AND SUSCEPTIBILITY
On the basis that the lines of force emitted by a magnet are
in reality a flow of particles or quanta, the concept of permeability may be explained.
It is easily seen that these lines of
force will pass more easily through some media than others (just
as an electric current will flow more easily through some conductors
than others),will not flow at all through some materials, and will
actually be deflected by other materials. The degree to which a
substance will allow magnetic lines of force to pass through it is
called permeabili y of the substance represented by the Greek letter
[x.
The basis for comparison is conventionally taken as the permea-
bility of a vacuuir*
field strengths.
This value was designated as unity for all
However, the p ermeability of air is found to be
only slightly different than unity (1.000005), and so for ordinary
13. Metals Handbook, op. cit., p. 417.
39
work it is considered to be unity.
If ^ is greater than unity the
substance is called a paramagnetic body; when it is less than one
it is said to be diamagnetic.
At all ordinary field intensities,
[A is a constant for most substances. However, there is a group of
paramagnetics for which this is not true.
Iron, nickel, cobalt, and
manganese, and some of their alloys constitute the major portion of
this class, and they are called the ferromagnetics.
A physical concept of permeability may be visualized by considering ^t to be the ra tio of the number of lines of force which
are allowed to pass through a unit or area of the substance as compared to the number of lines of force which pass through a unit of
area of vacuum, or air, the field remaining the same for both cases.
If N is the number of lines per square centimeter in a vacuum and
N
is the number of lines in the same area when it is filled with
another substance, then the permeability of the substance is N / N ^ .
On the basis of the foregoing principles of the mechanics
of magnetism and the concept of a magnetic field and permeability,
it will now be attempted to show how magnetization may be induced
by a field created by the flow ofanelectric current through solenoid •
Before developing the formulas it might be well to define
some of the terms.
1. A unit pole is that pole which will, in a vacuum, exprt
a dyne of force on an equal pole one centimeter away. The pole
strength is designated by the letter m.
The force exerted between
two poles of strength m^ and mo * F * M O , where d is the distance
between the poles.
40
2.
A unit field will exert a force of one dyne on a unit
pole in that field.
The unit of magnetic field is the oersted and
its dimensions are dynes per unit pole. H = _F
m
vector sum of J& p
or H equals the
'
3. The magnetic moment is defined as the torque necessary
to hold a magnet perpendicular to a unit magnetic field.
Torque = 2 m 1 H
4.
An abampere is that current, flowing through a wire or
any length one cm of which is bent in an arc of one centimeter
radius, and which establishes a unit magnetic field intensity at
the center of the arc.
H =11
r
where i = current in abamperes
1 =
length of arc
4 - radius of arc
It may be shown that the magnetic field produced by a
sclenoid which has $ turns on the primary coil of length, L, is,
H = 4<nrNp i
L
=
.4* N p I
L
where I - current i n amperes.
This f i e l d produced by passinga current through a solenoid
w i l l produce magnetic induction, B, i n a specimen of permeability
\x i s placed in t h e f i e l d , H, of the amount,
B = {JtH
The specimen which is now magnetized exerts a magnetic
field of Its own. This field will tend to oppose the magnetizing
41
field to some extent but the net effect is to add to the lines
of force by the amount: 13
B-H= 4-7Tm
A
1/Khere m = pole strength of induced magnet
A = cross section of magnet
The quantity m is called the intensity of magnetization, I.
A
I s J « specific intensity of magnetization.
When J is multiplied by the molecular or atomic weight of
the substance, -che products are called the molecular or atomic
intensities of magnetization, respectively.
Now, B-H - 4 7T I
a n d , B=H + 4 7T I
d i v i d i n g b y H,
+. i
+^P-
.
or
[x « 1 + 4 rt K
Magnetic susceptibility, K « ^
m a y
b e interpreted as the
intensity of magnetization per unit of applied field strength.
K
- X = specific susceptibility or susceptibility per unit
mass.
'When X is multiplied by its atomic or molecular weight the
products are called the atomic or molecular susceptibilites, respectively.
13. S. R. Williams, Magnetic Phenomena, (New York: McGrawHill Book Co., Inc. 1931) p.
42
The intensity of magnetization of an unknown specimen
may be measured as a function of the permeability or susceptibility providing the permeability or susceptibility of a sample
of the same dimensions is known for given applied field strength.
This measurement is based on the fact that the specimen which
magnetized and which has pole strength, m, will exert an effective
field strength of 4 if m
A
+ 4 7T l #
It is a well iaiown fact "Chat a changing field will induce
a current in a conductor which is proportional to the number of
lines of force which are cut per unit time. This means that the
induced current is a function of the rate of change of flux. The
induced EMF is given by the equation:
E =
d
" JL
10
8
& # and I « -_N
dt
*£
10°R dt
From this equation it is easily seen that the current produced in the secondary circuit is dependent upon the amount of
change of flux, which in turn is dependent upon the permeability
of the substance. The change in flux is also dependent upon the
magnetizing field, the dimensions of the specimen, and the rate
at wh ch the lines of force are cut. These factors, however, can
be made constant by using the same field, specimens of the same
dimensions, and by cutting the lines of force at approximately the
same rate.
These principles were used in making permeability and susceptibility tests on magnetic compacts of powdered met&ls. 1'he
apparatus used will be described in a subsequent chapter.
43
VI.
THE EFFECT OF SEPARATING MAGNETIC POLES
The magnetic field at a distance, d, from the poles of a
bar magnet varies inversely as the square of the distance, as may
be seen from the equation:
H =
m
~
Since the total induced magnetism of an object is the vector
sum of magnetization of the component particles which act as units
of magnetization or "domains", the distance between the particles
is important. Also the medium or material separating the particles
will have a decided effect depending upon the number of lines of
force which may be transmitted through it, which of course is a
function of the permeability.
If the domains are separated by
dimensions on the atomic order the total magnetization is a
maximum,because the induced field as well as the magnetizing
field are easily transmitted.
As the distance between the domains
increases, the effective magnetic field of each unit becomes
less, and the total magnetization is reduced because the vectorial
sum of the fields of the component is reduced. This effect is
probably influenced by two factors. First, the effective magnetizing field which passes through the specimen is reduced due to the
lower permeability of the specimen as a whole, and since the magnetization of ferromagnetic materials is seriously affected by
the magnetizing field, this factor is of considerable importance.
Secondly, the total field produced by the magnetized specimen is
less due to the dissipation of the induced field of each unit or
44
or domain in the separating medium, as has been intimated before.
The effective induced field is the vector sum of the effective
field of each domain. Since the effective field at a distance,
d, is a function of the square of the distance, the thickness of
the separating material between each domain is of prime importance.
In the first position of gauss, or the position in which the
poirrtof consideration is on the same line as the horizontal axis
of the magnet, the effective field strength at that point varies
inversely as the cube of the distance between the poles of the
magnet and the point.
where M = magnetic moment of the magnet
D = distance of the point from the center of
the magnet
2L = length of the magnet
In the second position of gauss, where the point lies on
a line which represents the perpendicular bisector of the horizontal axis of the magnet, the field strength is represented by
•che equation:
Instead of considering a point in relation to a bar magnet, the effect of two adjacent magnets should be anali&ed.
If
D now represents the distance between the centers of the magnets,
the effective force for the first gauss position is,
45
F = m2(
— T~D
1
- 2 )
+ 1
^—ZE) 2 (TJmf 2
T&)
^rom this equation is may be seen that, if L is small in
comparison with D, the net effect is attraction. As L increase
the force changes from attraction to repulsion, and when D - 2L,
the net force is repulsion,
"hen L is large in comparison with
D, the resultant force is again attraction.
This has been found
to be true up to a certain point. However, it seems that there xs
a point where the magnets are too close together (the ratio of
L
is very large) and the force is repulsion.
This might account for the higher permeabilities of com-
pacts made from powdered iron and cobalt to which small percentage of aluminum has been added.
Since the surface contact of
the grains of aluminum with the grains of iron and cobalt is very
small with such small percentages of aluminum, the exchange of
electrons, lessening the total magnetization is probably negligible.
Whereas it is possible the separation of iron and cobalt grains
might eliminate some repulsive effects and thus actually increase
the manifested magnetization.
Thus the addition of small amounts
of aluminum to powdered iron and cobalt in fabricating magnetic
materials is not only advantageous as a binder, but also probably
actually improves the magnetic properties if properly controlled.
There are, of course?many other relative positions of the
magnetized domains in an object. It would be impossible to consider them all, however, so two special cases are chosen as the
representative positions, l/hen a magnet shows polarity, it is
46
an outward manifestation that the effective magnetic fields of a
majority of the domains are parallel.
If this is the case it is
fitting that the case where the axes of two magnets are parallel
and separated by a distance, D, be considered. Using the same
notation as in the previous case, it may be shown the net force
is one of repulsion, as may be seen from the equation developed
for this position:
P-
Si2
2 m2 D
" ? " WZZ?) 3/2
A rotating torque would be the resultant force between
two magnets in the third position, where the axes of the magnets
are perpendicular, unless the forces were in such perfect balance
that there would be no resultant force.
47
CHAPTER V
FACTORSttHICHAFFECT THE PHYSICAL AND MAGNETIC
PROPERTIES OF COMPACTED POWDERS
Permeability, as one of the magnetic properties, is a
function of the lattice distortion and lattice orientation.1
Anything that affects the regularity of the space lattice will
affect the permeability.
Factors which markedly affect the re-
gularity of the lattice in powder compacts are:
1. Pressure
2. Heat treatment
3.
4.
Particle size
Impurities
It is the purpose of this chapter to discuss these factors«
I.
EFFECT OF PRESbTJRE
High pressures perform two closely allied funtions in improving the magnetic properties of compacted powders, and also
ha^a detrimental effect.
Porosity of the compact is intimately connected with the
pressure applied. At low pressures the particles of most metal
powders are not deformed and thus the products are soft and will
1. H. E. Cleaves and J. G. Thompson, The Metal-Iron,
(New York: McGraw-Hill Book Co., In., 1935). page 267.
48
easily crumble due to the loosely connected individual grains
with their inter-granular or air spaces. These cavities probably
give rise to interference by eddy current losses and otherwise
render the substance less permeability. Higher pressures, on the
other hand, cause deformation on the grains making a greater surface of contact and decreasing the porosity. Decreased porosity
increases the permeability,and the greater surface contact of the
individual grains allows better bonding and grain growth upon subsequent heat treatment. Porosity may be desired, however, in some
cases such as to increase the magnetic stability of the material.
In this case the percentage of cavities can be accurately controlled after a little reserach has been done with the particular
magnetic powder or combination of powders.
By hot pressing then umber and size of cavities may be reduced to a minimum.
The temperature should be high enough to
render at least one of the metals plastic, and the pressure should
be sufficient to cause maximum grain deformation at that particular temperature.
A reduction in the number of cavities obviously means that
the particle to particle contact surface will be increased. This
larger contact surface aids bonding, as previously stated, 2 and
thus facilitates grain boundaries, the fewer the grain boundaries
the better the magnetic properties.3
2.
Cf. ante, page 19.
3. Metals Handbook, 1959 Edition, (Cleveland, Ohio: Amer
ican Society for Metals), page 104*
49
Pressure also introduces a factor which has a detrimental
effect on the magnetic properties. If the pressing is done cold,
the grains are deformed and have received the equivalent of cold
work. The effect of cold work is usually to harden the object
due to the internal stresses set up by the deformation. At temperatures well below the recrystallization point these stresses remain in the object. It is thought that these stresses, which are,
in reality, forces, oppose the lines of force of the elementary
magnets of magnetic material and thus substantially reduce the
total magnetization of the object. Such stresses may be removed
by proper heat treatment as will be euqplained under the section
on heat treatment in this work.
The majority of internal stresses
may also be eliminated by hot pressing at or near recrystallization temperatures.
II.
EFFECT OFHEAT TREATMENT
Grain growth is commonly brought about by heat treatment
at the proper temperature. Magnetic permeability, as a rule,
increa ses with grain growth because distrubances at the grain
boundaries are lessened by the decrease in grain boundary surface. A total elimination of the grain boundary surfaces would
be ideal. Grain growth and internal structure are not only dependent on the temperature but also upon the rate of heating and
cooling and the time of heat treatment. If the specimen is heated
rapidly so that the outside becomes hot while the center remains
50
cold, stresses will be introduced.
If this condition is preserved
by quenching then the internal stresses will affect the permeability.
A long period of heat treatment facilitates grain growth
and thus obviously improves the permeability.
Besides promoting
grain growth, a slow heating to temperature and a long period of
holding at temperature followed by slow cooling, will remove
stresses introduced by cold work and thus will always increase
the permeability to an extent depending on the amount of stresses
removed. This phenomena'was observed in the heat treatment of
compacts of magnetic material.
Heat treatment may influence the magnetic properties in
still another way. Under the proper conditions precipitation
hardening will occur. This effect is usually to increase the
permeability, but in some cases may actually cause a decrease.
The increase of permeability with precipitation hardening may be
explained by Bozorth1 s theory of magnetism.
During the precip-
itation atoms of elements which exchange, or share, electrons
with atoms of the magnetic material are removed from the crystal
lattice, thus render the specimen as a ^hole more permeaole.
III.
EFFECT OF PARTICLE SIZE
The magnetic properties of compacted powders are substantially affected by at least three factors dependent on the
particle size of the powders used.
51
Particle size is a controlling factor, along with heat
treatment, in the resultant grain size and grain boundary surfaces. I*arge particles reduce the amount of grain boundary surface, but cause a greater number of cavities than do small particles.
Thesr cavities are hard to eliminate. Small particle
size allows more surface contact with lower pressures than does
large particle size, but the total grain boundary surface is
enormously increased.
Small grain size also introduces more oxide
impurities because of the greater surface exposed to the atmosphere.
w
xides may be removed by reducing with hydrogen, carbon mon-
oxide, natural gas, or some other reducing agent A
Grain size
may be increased by suitable heat treatment. Thus powders of
small particle size result in better compacts when all factors
are considered.
IV. EFFECT OF IMPURITIES
Impurities in products of powder metallurgy are few and
are easily avoided by careful processiiig. Only two impurities
are of any importance, and these are oxide films and carbonaceous
matter.
w
f these oxide film is most prevalent.
Carbonaceous
matter, while detrimental to the physical and magentic properties
of the compact, can be, for the most part, eliminated by careful
selection of the component powders and meticulous operation
methods in producing the compact. "Very pure metal powders pro-
4. J. W. Mellor, A Comprehensive Treatise on Inorganic
and Theoretical Chemistry, Vol. I, jfliew York: Eongmans, Green
and Company, 1932), page 328.
52
duced by a number of leading concerns are readily available.
Effect of some other impurities will be discussed in later sections.
53
CHAPTER VI
DESCRIPTION OF THE EQUIMENT
In general the equipment used for the experimental work of
this thesis consisted of (l) weighing and mixing appartus, (2)
pressing
equipment, (3) heat treating devices, (4) permeameters,
and (5) such materials as metal powders, lubricants, natural gas,
and hydrogen gas.
(See Figure 2).
It is the purpose of this chapter to describe in some detail the materials and apparatus used in obtaining the experimental results.
I. "rtEIGHIH&AHD MIXING APPARATUS
l*or weighing the powder charges an analytical balance with
a sensitivity of one one-hundredth was used.
In order to disaggregate the constituent powders they were
ground in a porcelain motar, which had been glazed with sillimanite, and a glass pestle.
Thorough mixing of the powders for compacts of various compositions was accomplished by the use of a tumbler mixer, (Figure
2a).
A cubical box, one and three quarters inches on an edge, with
a removable cover served as the tumbler or mixing chamber. Both
the box and its cover were fabricated from corrosion resistant
metal#
A steel rod three-sixteenth of an inch in diameter solder-
ed through the middle of two opposite edges of the box acted as
the axis of rotation, and since it occupied a position through the
Figure 2a
APPARATUS FOR MIXING METAL POWDERS
Figure 2b
GENERAL VIEW OF EQUIPMENT
55
middle of the box it also facilitated mixing.
A solid rubber gasket was placed inside the cover of the
box so that, when the mixing operation proceeded, the powders, some
of which were as fine as 300 mesh, cottld not leak out of the chamber, thus endangering accurate composition control.
The motion of the tumbler was provided by a small electric
motor operating on 110 volts A. C. in combination with a set of
reducing gears. The motor traveled normally at 1750 ©evolutions
per
minute. This speed, due to centrifugal force, is of course
many times too great to allow mixing to take place. To overcome
this obstacle two reducing gears were placed between the motor
and the tumbler. By proper combination, the tumbler was made to
rotate at 60 revolutions per minute at which speed very satisfactory
mixing took place.
II.
PRESSING EQUIPMENT
A mold with its accessories, a hydraulic jack, a frame
for the mold and jae-c, and a reducing atmosphere comprised the
pressing equipment, (Figure 2b).
The mold and its accessories (Figures 3 and 4 included (l)
the mold proper comprised of the pressing chamber, the reducing
chamber with its gas inlet and outlet, the cap with its bolts and
gasket, the plug, and the ram (not shown), (2) the heating element
and insulation, and (3) the thermocouple and millivoltmeter.
*«Jt *
i. - ,
COMPONENT PARTS OF PHSSSIHG MOLD
Figure i/b
ASS3SHLKD PBBSSIBG MOLD
Thermocouple
Gas
Scale - actual site
Figure 4
PRESSING MOLD SHOWING DEDUCING
NIT
58
The mold proper was essentially a cylinder machined from
a chrome steel shaft and accurately bored for pressing and reducing chambers.
The largest outside diameter of the cylinder was three inches.
One inch from the top a groove, three-eighthsof an inch deep and
two and one-half inches long, was cut for the heating element.
In the center at the top a conical shaped reducing chamber was
machined out. The larger diameter was one inch and the diameter
of the bottom was one-half inch, the slant height being approximately one inch.
Into the bottom of the chamber was tapped a
gas inlet of three-thirtyjbeconds of an inch in diameter. At the
top of the chamber a gas outlet of the same diameter was drilled.
To the inlet was connected a copper tube coming from the reducing
gas sources, while the outlet was connected to a burning jet.
Concentrically in the bottom of the reducing chamber a
bore one-half inch in diameter was carefully drilled through to
the bottom of the mold proper.
From the bottom this bore was
enlarged to seven-eighths of an inch in diameterfor a distance
of one and one-half inches toward the center. This was done to
accomodate the shoulder on the ram.
i'hus the pressing chamber
of one-half inch in diameter extended from the bottom of the reducing chamber to the top of the bore drilled to accomodate the
ram shoulder, making a total length of two and one-quarter inches.
In the top of the mold proper a hole one eighth of an inch in
diameter was drilled one quarter of an inch from the rim of the
reducing chamber for the thermocouple. Two holes were tapped to
59
accomodate the five-sixteenths inch bolts which held up the mold
proper.
The cap was made to fit on the top of the mold proper and
produce gas tight seal for the gas chamber.
suspend the plug during the reducing period.
It also served to
The outside diameter
of the cap was the same as that of the mold, namely three inches,
and was maclined from the same material. Thru the center of the
center of the cap, which was two inches higii, a hole seven-eighths
of an inch indiameter was first drilled.
This was then threaded
on the inside with standard pipe threads to a depth of two thirds
its length from the top. These threads were then reamed out from
the top to a depth of one-half inch and from the bottom one inch,
leaving one-half inch of threads at a distance of one-half inch
from the top. Two holes one-quarter inch in diameter for the
bolts wh. ch held the cap to the mold proper were drilled opposite
each other at a distance of one-half inch from the outside surface of the cap. A groove was cut in the bottom of the cap so
that the wires of the thermocouple would' not be flattened when the
cap was tightened in place.
The plug, which wa,s made of the same chrome-steel as were
the cap and the mold proper, had an overall length of three and
three-quarters inches. At the top a flange one-half inch thick
was left whose diameter was one and one-quarter inches. This
flange gave a larger surface over which the pressure against the
top plate of the frame was exerted during pressing.
Below this
flange for one and one-half inches the plug was machined to a
60
seven-eighths inch diameter. At this point the plug was threaded
so as to screw in the threads of the cap and produce a gas tight
seal.
These threads were one-half inch long and the diameter of
the plug across these threads was one inch. Below these threads
the diameter of the plug was again reduced to seven-eighths inch,
below which point a tapered portion was machined which would exactly fit into the tapered reducing chamber. That is, the slope
of the tapered part of the plug was exactly the same as the slope
of the walls of the reducing chamber in the mold proper, so that
when the plug was jut tightly into place for presang, none of the
powder could escape around the plug.
portion of the plug was one-half inch,
The length of this tapered
ht the bottom of the taper
was a short cylindrical portion, one-quarter inch long and onehalf inch in diameter. This part, in reality, was the actual plug,
for it fits tightly into the top of the pressing chamber, and
against its bottom surface the powders were actually pressed.
The ram which had a total le ngth of ten and one-half inches
was also machined from a rod of chrome steel. The part of the ram
which entered the reducing chamber was very carefully cut to a
diameter of one-half inch.
±he machining had to be done very
accurate so that this portion of the ram fit perfectly into the
bore of the pressing chamber so that the fine powders would not
flow between the ram and the walls of the pressing chamber when
high pressures were applied.
If the powders became lodged in this
position due to some imperfection in the macining or due to excessively high pressures on metal in the plastic state, the ram
61
would stick and could not be removed without destroying the bore
of the pressing e: amber or the ram itself. The rest of the ram,
seven and three-quarters inches, was made of a larger diameter,
seven eighths or an inch, in order to eive greater strength.
A one-thousand watt heating element was wrapped around the
mold proper in the groove provided for it. This element was well
insulated with asbestos and encased in a metal tube to prevent any
damage to it by mechanical agents. The ends of the element were
connected to a standard plug so that a cord to the A. ^. source
could be easily removed.
0 v e r the metal encased element a re-
fractory mixture of alundum and fireclay was placed to provide
heat insulation. This insulation was built up to a thickness of
approximately one inch. After the mixture of fireclay and alundum
was thoroughly dried, the whole was encased with a thin sheet of
rolled steel to prevent the insulation from cracking away. A
special porcelain cement was used on the top and bottom of the
insulation where the metal plate did not cover it. This porcelain cement was very hard and did not crack upon drying. Thus
the heat insulation wt s held securely held in place, safe from
cracking when used with ordinary precautions. Iftith this heating element and insulation it was possible to attain temperatures
much higher than the safe working temperatures for the material
of which the mold was constructed.
A chrome 1-alumel thermocouple in connection with a WilsonMaulen millivoltmeter was used to measure the pressing temperature.
The thermocouple junction was placed in the hole bored in the
62
mold proper to a depth of approximately one and one-half inches.
Thus the junction was very close to the portion where the powders
were actually pressed.
The thermocouple wires were insulated in
the conventional manner. A calibiration chart was made for the
thermocouple by correlating the reading on the millivoltmeter at
different temperatures with the actual temperature as measured by
a standardized platniumxVplatinum + 10°l rhodium thermocouple in
connection with a Leeds and Northrup high precision potentiometer.
The pressure was furnished by a Blaekhawic 20-ton hydraulic
jack, i'he jack was equipped with a gage calibrated to register
the applied pressure in pounds on the surface of a circle
/$iose
diameter is 2.562 inches. On the basis the safe working pressure
was 40,0u0 pounds and the maximum pressure 50,000 pounds. The
diameter of the ram, however, at the point where the pressure was
apflied was only one-half inch, so that the actual applied pressure
in pounds per square inch was found by multiplying the gage reading bv the factor 6.67. (See appendix).
A heavy steltl frame, which actually received the force of
the pressure exerted by the jack, held the mold and the jack in
such a manner that pressing was accomplished easily and efficiently. The top and bottom plates were;made of mild steel and
were one inch thick and one foot square. These plates were held
together by four steel rods each beingjpne inch in diameter and
three feet long. These rods were strongly welded to the bottom
plate and threaded at the top and also at a distance of one foot
from the top. The top plate of the same dimensions as the bottom
63
plate was drilled at each corner so that the rods could be passed
through it. The plate was held in place by three one inch nuts
on each rod:
one nut below and two on top in order to withstand
the high pressure without stripping the threads on the rods or
on the nuts.
A second steel plate, one-half inch thick, was held
in place one foot from the top plate at the position on the rods
where they had been threaded, by half inch nuts.
The mold itself
rested on this plate, A third guide plate was fastened to the rods
six inches below the second plate by set screws. The purpose of
this plate was to hold the ram in the correct position. This was
accomplished by drillinra hole only slightly larger than the
diameter of the ram in such a position that the ram was securely
held vertically, thus eliminating components of force tending
to bend the ram.
The three plates were all bored in a position near
the
center of the plate so that when an imaginary line was passed
through the center of the pressing chamber of the mold proper,
it would also pass through the center of the hole in the plates.
The holes in the lower plates were large enough to allow the
passage of the ram.
The hole in the top plate was threaded
so that a rod could be screwed down through it in order to
push the ram out of the pressing chamber of the mold if necessary.
The mold, properly centered over the holes in the plates,
was fastened to the plate second from the top with quarter inch
cap screws. The ram, extending from the mold through the holes
in the guide plates was kept from dropping out by a sleeve fas-
64
tened to the ram by set screws and resting on the lower plate.
Since the mold was designed with a reducing chamber and a
heating element, the pov/ders could be pressed in practically any
atmosphere desired and at any temperature up to 450 C.
A great
many metals will oxidize at room temperatures with sufiicient time
especially if they are in a finely divided state so as to provide
a very large surface for reaction with constituents of the atmosphere. i&etal powders, some ofWhich are as fine as 300 mesh,
are likely to become oxidized when exposed to the atmosphere for
any length of time, If the stable oxide is formed. (See Appendix).
For this reason reducing atmospheres were preferred in pressing
operations in order to remove the oxide film and facilitate bonding.
Equipment was so arranged that an atmosphere of natural gas
or hydrogen could be maintained (Figures 5 and &).
The natural gas consists, essentially, oi methane with some
ethane, nitrogen, and water vapor. The water vapor must be removed because at elevated temperatures it is likely to react with
the metal powders forming a compound.
This water is eliminated
by passing the gas first through concentrated sulfuric acid. The
acid also removes the odor of the gas. After the acid a tube of
calcium chloride is placed to further dehydrate the gas. A third
tube containing calcium sulfate stained with cobalt chloride is
used as an indicator for the completeness of dehydration.
Normally the color of cobalt chloride is blue but when it becomes
xydrated it changes to a bright pink.
Figure 5
ATMOSPHSRiS CONTROL APPAHATUS
Burning
Jet
jatural Gas Source
f Trap \
(H 2 SO 4 J
I Water J
(c.S04 j
Reducing
Chamber
Figure 6
ATMOSPHERE CONTROL APPARATUS FOR PRESSING MOLD
67
Hydrogen was produced in a specially designed generator.
This generator was made from a liter side ana flasx. Dilute
sulfuric acid was placed in the bottom of the flask, kossy zinc
was introduced by lowering a perforated lead bucket containing
the zinc into the acid without removing the stopper. The hydrogen
was drawn off through a rubber tube connected to the side arm of
the flask. As can be seen from the flow sheet, the hydrogen
train contained first of all a surge bottle to catch any acid
that might be forced backward by accidental reversed pressure.
The hydrogen next bubbled through alkaline pyrogallic acid to
remove any oxygen present.
It then passed through another surge
bottle and a bottle containing concentrated sulfuric acid which
removed moisture. Next the hydrogen passed through calcium chloride ana calcium sulfate stained with cobalt chloride to indicate
whether or not the hydrogen was completely dry.
Stop coci£s at the beginning of each line and also at the
end of each line at the "T- connection maae it possible to shut
off either or both lines. ^ith such an arrangement it was possible to run natural gas through the mold while the powder was
being heated, then switch over to hydrogen to reduce the oxide
film on the powder, and then reverse to natural gas to that the
hydrogen would be removed before pressing which allowed air to
enter the mold to some extent. At elevated temperatures hydrogen
might explode upon the introduction of air and thus natural gas
was used to sweep hydrogen from the mold.
A common exit train was used for conducting both gases
68
from the mold to the jet where -they were burned.
After leaving
the mold they first passed into a surge wh-uch caused the gas to
become more steady in its flow. Secondly it passed through a water
trap to prevent back burn, and finally through another surge
bottle which again tended to make the pressure more uniform and
thus allowed the gas to be burned at the jet.
III. HEAT TREATING DEVICES
Heat treating was done in a multiple unit electric combustion furnace and an auxiliary combustion furnace. The furnaces were connected in the same type circuit and both operated
on 110 volts A. C#
Figure 7 shows the multiple unit furnace with
its resistances. The maximum operating temperature of these furnaces was 1000°C. with a safe operating temperature of 800 to
900°C.
Current was supplied by an A. 0. Source of 110 volts.
The amperage f lowing {Though the furnace, and thus the temperature
was regulated by two variable resistances connected in series.
The current was indicated on an A. 0. ammeter with a range of ten
amperes.
Iron-constantan thermocouples, connected to millivoltmeters,
were calibrated to indicate the temperature of the furnaces. The
portion of each couple which entered the furnace was properly
insulated and encased in a fused silica tube to protect the couple
from reaction with the atmosphere.
The natural gas atmosphere for the furn8.ces was supplied by
Figure 7
HEAT TREATING APPARATUS
70
the same source as for the mold.
Before entering the furnace the
gas was dried by bubbling it through concentrated sulfuric acid
followed by a long tube of anhydrous calcium chloride. After
passing through the furnace the gas was burned at a jet provided
for this purpose.
IV.
PERMEAMETEKS
Accurate measurement of magnet permeability of the compacted specimens, made with the equipment previously described, was
complicated by the unavoidably limited length of the specimen,
due to the unequal distribution of applied pressure throughout
the compact. Pressed specimens longer than one-half inch were
in most cases so mechanically weak that they could not be conveniently handled in order to make the required measurements.
Three special devices for making magnetic measurements were
assembled and tried before any logical results were obtained.
It
might be well to describe these devices even though two of them
f&iled in their purpose.
Figure 8 shows the circuit for the first method used in
an attempt to make these magnetic measurements.
circuit consisted of four parts:
In reality the
(l) the primary circuit, (2)
the secondary circuit, (3) the demagnetizing circuit, and (4) the
iron ring.
The primary, or magnetizing circuit, contained a 12 volt
lead storage cell in series with a variable resistance box and an
Variable Resistance
> >:
§
>>>}
o
o-
Q
9
P
Figure 8
Variac
Transformer
CIRCUIT FOR MArING MAGNETIC I^EASUREkEKTS
72;
ammeter. This series circuit was connecxed to the primary winding
of the solenoid by a reversing switch by means of which the current
could be made to flow in either direction through the primary windings.
The secondary windings of the solenoid was connected in
series with a ballistic galvanometer and a resistance box. The
resistance was so adjusted as to give the proper deflection of
the galvanometer according to the material on which the measurement was being made.
The demagnetizing circuit contained a Variac transformer
with an A. C. source of 110 volts connected to a high resistance
and an ammeter bv a double throw switch.
x
his circuit was so con-
nected bv the same reversing switch used for the primary circuit
•chat the solenoid with its unknown sample could be completely demagnetized by causing the alternating current flowing through the
primary coil to be reduced from approximately four amperes to zero.
The iron ring, which was wound with a primary coil of 80
turns of copper wire and a secondary coil of 75 turns, was accurately cut so that a section of exactly three-eighths of an inch
was removed.
Ihe faces of this cut were polished smooth so that
a pellet of unknown permeability could be placed in this slot insuring minimum air gap between the surfaces of the pellet and the
facts of the slot, thus eliminatin^nagnetic losses as much as
possible.
A standard pellet of the same soft iron as that of the
ring was machined to exactly fit into the slotcut from the ring.
The diameter of the rod from which the ringwas made was one-half
inch as was the diameterbf all pellets of compacted powders. The
73
rod from which the ring was made was originally six inches long.
Howerer, after cutting out the three^eighths inch slot, the axial
circumference of the iron was five and five-eighths inches, while
the length of the slot, or the length of the pellet was threeeighths of an inch. On the basis of these measurements and utilizing the principles concerning magnetic permeability as outlined in
this thesis^- in the chapter on magnetism a formula was developed
with which the permeability of the pellet could be calculated
from measurements obtained by this device.
The field, H, produced by the flow of a current , I, in a
primary coil of N p turns and of length, L, is expressed by the
eqqation;
H - .47TNp I
T ^ -
(I)
This field produces an induction, B, in the magnetic material of cross section A. This induction exerts a magnetic
flux, jzf, given by the expression:
ft - BA
(2)
A changing flux with time, T, induces a current in the
secondary coil of N
turns whose potential, E , is expressed by
the equation:
s
iSPt
10*t
(3)
The current in the secondary circuit of total resistance
(R+g) is:
1. Cf. Ante pages 38-43.
74
T
= Es
= N s BA
s (R-+TTJ
l§8t
(4)
The deflection of the ga lvanometer, d, is proportional
to the change, Qs, which given by the expression:
y„« I t - KSBA
- kd
(5)
where k - constant of the galvanometer
then,
„ 10 8 (R+g)k
NSA
' d
(6)
and,
108L(R+g)K .d
(7)
.4irMjr A
I
P s
The value of the resistance of the secondary circuit must
B
H
=
be so chosen that the deflection of the galvanometer, at its maximum, is practically full scale. The constant, k, of the galvanometer changes with the resistance of this circuit and may be
found for various values of (R+g) by the method as outlined in
the appendix of this work,
"hen a pellet of the same soft iron
as the rest of the ring was used, it was found that an optimum
deflection was the value of (R+g) was 40u0 ohms.
The corre-
sponding value of the galvanometer constant was found to be
.202 times 16~ • Substituting these values, alondarith those
given above in the equation (7), the permeability of the iron
was given as:
Pi = 130 d
(8)
I
This equation was used for the calculations of the permeability of the iron when a pellet of the same material as the iron
ring was used.
7*
Vftien a p e l l e t of m a t e r i a l whose p e r m e a b i l i t y i s
different
t h a n t h e p e r m e a b i l i t y of t h e i r o n a s p e c i a l e q u a t i o n must be used
t h e magnetic f l u x i s now shown t o be i n v e r s e l y p r o p o r t i o n a l t o t h e
r e l u c t a n c e , R e , given by t h e e q u a t i o n :
Re = IA j( Hi I^ + .i£)
up)
and,
. 4 T * Kp
*
Re *
I
TtXT^A
1
P P
(9)
also from equations (2) and (6),
d « R A = 108 (R+g)kd
*
(10)
5^
and from e q u a t i o n s (9) and ( 1 0 ) ,
Id
+ _ L Q _ , .40-nr N„ I N s
* P
»
^VP"
.4 7TNp I K s
10°(R+g) k a
-
L*
JvTTT
thus,
L
(i "
P
JL
*p
1
.4!TN p K s
1U W ^ g )
I
*
—
_ Li
"tx i A t
S u b s t i t u t i n g t h e proper v a l u e s i n t h i s e q u a t i o n and choosi n g t h e v a l u e of (R+ g) as 4000 ohms and k as .202 t i m e s 10" ,
reduces t o :
Up -
iZ5Z
.0922
\
d
- H«35
•*!
it
76
or
.121
I *
15
~
(12)
i
Using this equation to sadve for the permeability of air,
that is leaving the slot in the iron ring unfilled, it was found
that the method was not accurate. This was shown by the fact that
the permeability of air, by these calculations, was five to ten
times too high. This was thought to be due to leakage or magnetic
lines across the air gap due to the short distance between the
faces of the slot in the ring.
For this reason the method was
abandoned.
A second device, illustrated by Figure 9, was tried with
little more success. The primary and secondary circuits were
identical with those used in the first method.
i'he demagnetizing
device, however, was entirely separate, and consisted of a coil
of copper wire of large diameter \^hich contained 135 turns. J-his
coil was connected to a 110 volt A. C. source.
Demagnetization
was accomplished merely by introducing the specimen into the
field and slowly -vithdrawing it,
The device itself consisted of a large soft iron core,
which also acted as a frame. A hole in the center of the top
part of this core, or return path, allowed a rod five-eighths
of an inch in diameter to pass through it.
-the minimum length of
rod 7/hich could be used was four inches. Such soft iron rod was
tapered to one-half inch diameter at one end, and the face of
1
1
I
1
1
I
1
1"
>
\
\
t'
>
(
Primary
(
<
i
i Circuit
>
>
|i
i
1
<
>
{D.C.j
ft
>
1
r
'
;
4
l
>
•
Figure 9
DEVICE FOR MArUMG MAGNETIC
(FOR SOFT' IRON STANDARD)
Secondary
Circuit
with
— ballistic
Galvanometer
'
HTS
re
this end waspolished to insure good contact with a pellet placed
beneath it. Two hundred turns of Number 18 enamelled copper wire
was wound on a wooden spool four and one-half centimeters and whose
inside diameter was five-eigh-frs of an inch, and placed around the
the rod as shown in Fibure 9.
One hundred and twenty five turns
of Number 28 B. S. wrapped copper wire was wound on a wooden spool
four millimeters long and having an inside diameter of one-half
inch. 1'his was placed a round the pellet as shown and constituted
the secondary coil.
The same equations developed for the first method hold for
calculations of permeability by this method.
Choosing the value
of (R+g) as 4000 and hence the value of k as 20.2 times 10~
these equations reduce to:
|i4« 19.15 d
T
(IS)
and
u
h?
=
1.032
1—c 67.9
o.389 ^ . ^rr-
(14)
Again upon trial, these method was found to be inaccurate
as shown by the values obtained for the permeability which were,
this time, three to fives times too high.
It was thought that
leakage of magnetic lines across the gap was responsible for the
inaccuracy and thus this set-up as a device for measuring the
permeability of small pellets was also abandoned. However, it
was found that the permeability of a continuous iron rod could be
measured with high accuracy.
Thus the method was used to obtain
the permeability of a specimen of iron bo be used as a standard
?9
in measurements made by the third tend final method.
This was
done by machining a soft iron rod to the required dimensions an 3
placing it in the device so that it was encircled by both coils
and measuring its permeability at various field strengths, ftiow
a portion of the rod was cut off and machined to the exact size
of the compacted specimens.
The third and final method of making magnetic measurements
was based on cutting the lines of force of the field produced by
magnetizing a specimen of permeability, p, in an applied field,
H.
The change of field which is equal to the difference of the
induced field and the applied field will induce an hmF in a conductor which cuts this field. The resultant field is expressed
by the equations
B-H - 47T K H
(15)
and since,
B = pH
p « 1+47TK
(16)
Thus if the permeability of a standard specimen is known,
the deflection of the galvanometer may be calibrated to read in
terms of permeability for any given field strength.
Figure 10 shows the apparatus used for this third method,
and the wiring diagram is shown in Figure 11. The primary circuit is exactly the same as that used in the first two methods
except that no reversing switch was used, and that the D. C. Source
was a series circuit of twelve lead storage batteries. The secondary circuit contained only a pointer type Weston galvanometer and
Figure 10
EQUIPMENT USED FOR MAKII7G 11AGKETIC KEA^REMENTS
6
6
9
Q
110 volts
A.C.
Demagnetising Circuit
-o o-
9
-o o-
D.C»
Source
Variable Resistance
Figure 11
CIRCUIT FOR MEASURING MAGNETIC SUSCEPTIBILITY (R)
&2
a tap key.
The solenoid itself consisted of one thousand turns of
each the primary and secondary coils, properly insulated, on the
same wooden spool. A brass pipe about one foot long, whose inside
diameter Was tiust large enough to allow a pellet of one-half inch
diameter to fall freely through it, was fitted tightly into the
center of the wooden spool containing the coils. One end of this
brass tube extended about six inches above the top of the Suool so
that the pellet, when dropped from the top,weula tend to reach
a fairly uniform velocity by the time it entered the field created
by the priiaary windings. A wooden stick was so placed in the tube
through the bottom that the pellet was allowed to travel only half
way through the windings. Upon removing this wooden obstruction
the ^ellet fell the remainder of the way through the windings and
out of the brass tube, \ftiile the pellet is traveling through the
first half of the windings, lines of force are cut in one direction causing a current to flow in a given direction in the secondary. Upon removal of the wooden obstruction allowing the pellet
to fall through the field created by the lower half of tie coils,
the lines of force are cut in such a manner as to cause a current
to flow in the opposite direction. Thus the obstruction is necessary
in order to allow indication of the full magnitude of each current
on the galvanometer.
83
Y.
M E T A L JPO>»DEKS,
LUBRICANTS, ETC.
Metal powders used in this experiment were manufactured by
the Metals Disintegrating Company of Elizabeth, New Jersey,
of them wer
^st
approximately 300 mesh and were of high purity, ex-
cluding the oxide coatings formed on soine of them.
The walls of the pressing chamber and the ram were lubricated first with a thin film of a special lubricant, called Lubriplate 310 manufactured by Fiske Brothers Refining Company of
Newark, New Jersey. This lubricant did not decompose to an appreciable extent at 400°0 and the pressures used.
In addition
to Lubriplate a small amount of powdered graphite was used to
insure against sticking of the pellet or the ram in the pressing
chamber of the mold.
With this combination of Lubriplate and
powdered graphite very satisfactory results were obtained with
respect to "Che often serious problem of lubrication in powder
metallurgy.
Hydrogen, for reducing the oxide coating of some of the
metal powders, was produced by adding mossy zinc to dilute
sulfuric adid.
^atural gas used for neutral atmospheres was approximately
85% methane, 5% carbon dioxide, 9% ethane, and the remainder
water vapor and nitrogen, experience
in working with this gas
o
showed that decomposition occured at approximately 70U C which
is slightly lower than the theoretical decomposition temperature
of methane. The gas was dried as previously described.
84
CHAPTER VII
PRODUCING THE idETnL OD^PACTb AND MEASURING
THEIR MAGNETIC PER&dEitBILlTY
Production of the compacted metal powders involved (l)
obtaining the require compositions and mixing thoroughly in'
order to attain homogeneity, (2) reducing the oxide coatings of
powders, (3) pressing operations, and (4) heat treating.
This chapter presents the general procedure followed in
producing the metal compacts as well as the method used in making
magnetic measurements and the required calculations.
I. WEIGHING AND M X H G
All powders were weighed on the analytical balance to the
nearest tenth of a milligram.
This accuracy was entirely sufficient
for it was found that in most cases a variation in composition as
high as 0.5% in one of the constituents made no appreciable difference in the magnetic permeability of the compact. Thus in a ten
gram charge an error of fifty milligrams in the weight on one of
the constituents was not serious. The weight of oxygen in the
oxide coating of some of the powders was not taken into account in
weighing, since the percentage of oxide was found to be very small,
thus bringing the error introduced by the oxygen within the practical limit.
The powders, now in their proper proportion, were placed in
85
the porcelain mortar and disaggregated by careful manipulation
with the glass pestle.
From the porcelain mortar the powders
were charged to the tumbler of the mixing device designed especially for this purpose.
The lid ofjthe tumbler was fastened
securely in place and the motor was started, causing the tumbler
to rotate at a speed of sixty revolutions per minute. This process was allowed to continue for aporoximately fifteen minutes,
after which the constituents of the powder were found to be
thoroughly mixed.
The contents of the tumbler were transferred
to a pyrex beaker, and from this, a portion was weighed to be
charged to the reducing chamber of the mold.
The amount of
powder to be charged to the reducing chamber was calculated from
the density so as to produce a compact approximately one-half
inch long upon pressing.
II.
REDUC1NGTHE OXIDE COATING OF METiiL x^vDERS.
The special reducing chamber in the mold was so constructed
that the incoming gas entered at the bottom of the chamber, passed
through the powder charged into the chamber, and passed out through
the exit tube at the top of the chamber. Thus the gas actually
contacted the surfaces of the metal powders without depending on
diffusion. The actual amount of reduction was not determined by
analysis, but it was assumed that reactions occurred in accord
with theory and with experiments by others. (See appendix.)
After the proper amount of powder of the desired composition
86
was charged into the reducing chamber, the ram was raised to such
a position to prevent the powder from entering the reducing chamber.
The cap, with the plug in the position shown in the diagram of the
mold, (page 56), was bolted into place. A copper encased asbestos
gasket formed a gas proof seal between the top of the mold and
the bottom of the cap. The treads of the plug, screwed into the
treads in the cap and properly lubricated with Lubriplate No. 310,
prevented gas from escaping in this direction. Thus the reducing
chamber was rendered air tight.
^atural gas, passing through the train as shown in Figure 6**
was introduced into the gas chamber.
The temperature desired was
now reached by closing the circuit connected to the heating element of the mold, and varying its resistance until the proper
temperature was maintained.
After the temperature of the powder was thus raised, in a
neutral atmosphere, bo the desired point, the natural gas was shut
off and a stream of dry hydrogen was introduced into the chamber.
Hydrogen was ordinarily allowed to pass through the powder, at the
proper temperature, for one-half hour.
This time was deemed suffi-
cient for oxides which could be reduced at ordinary temperatures.
It was not possible to raise the temperature of reduction above
450 C since the safe working temperature of thepold was limited
by the recrystallization point of the iron.
After the reduction period, the supply of hydrogen was disconnected and a stream of natural gas was again introduced into the
chamber long enough to clear the residual hydrogen out of the mold.
> 87
This was done to avoid possible explosions due to introduction of
air in preparation for pressing.
The ram was dropped to its proper position in the pressing
chamber allowing the powder to slide down the smooth inclined walls
of the reducing chamber into the pressing chamber.
natural gas through the chamber was stopped.
The flow of
After lowering the
plug to its pressing position and properly blocking it against
the top plate of the frame, as shown in Figure 12, everything was
in readiness for the pressing operation.
III.
THE PRESSING! OPERATION
To press.the excape valve was closed and the handle of the
jack manipulated until the gage indicated the proper pressure.
Thms
pressure was maintained for approximately two minutes since it was
found by previous research
that any limited extension of this press-
ing time had practically no effect on the properties of the compact.
At the end of two minutes the pressure w^s released; the
steel blocks under "Che top plate removed; the plug raised to its
proper position; and the cap was removed from the top of the mold
proper.
This being done, additional blocks were placed between
the top of the mold proper and the top plate of the frame.
The
purpose of these were to take the pressure, preventing the bolts
1. J. E. Shaw, Production of ^etal Compacts by the Powder
Method, with bpecial Reference to Copper-Tin Alloys, (Unpublished
Master's +>»*•*•-. ontana School of Mines,1940) p. 44.
I»p^
F i g u r e IS
EQUIHCTT READY FOR PRESSING OPERATION
w %
89
holding the mold to the second plate from the frame from being
snapped off when the pellet was ejected from the pressing cnamber.
Ejection was accomplished by again applying pressure on the ram
when the bolts holding the mold were protected as above. Pressure
was necessary to eject the pellet, because, in spite of adequate
lubrication, there was in most cases a slight tendency for the
pellet to stick to the walls of the pressing chamber, especially
when pressing was done at elevated temperatures. Excessive pressures and pressing temperatures were, for the most part, avoi-aed
in order to prevent this sticking, for, if thee pellet should
seriously adhere to the molu walls, ejection was difficult, and
in many cases a film of the pressed material, which remained on
the walls after ejection, become lodged between the ram and the
mold walls causing serious trouble.
After ejecting the pellet it was allowed to cool in air
to room temperature.
It was then sized by placing it into a set of holes bored
in a steel plate, v/hieh were of the proper depth and of the same
diameter as the pellet, and filing off the excess material of the
pellet until it was exactly three-eighths of an inch long. This
device was very convenient because it eliminated the inaccurate
measuring method, insuring the same length for all pellets prepared, and at the aame time acted as a vice to hold the pellet
while they were being reduced to the proper size.
Ordinarily magnetic measurements were made at this stage.
The method of these measurements will be described presently.
90
Ihe first magnetic measurements were commonly followed by
heat treatment.
IV. HEAT TREATING
Heat treatment was accomplished in the apparatus as described in Chapter VI. The temperature and time of heat treatment, of course, was dependent on the material being heat treated
and the results desired.
In general the treatment, designed to
relieve strains and stresses induced by pressing,was carried out
at a temperature just above the highest recrystallization temperature of the constituents of the specimen, and this temperature
was maintained for one or two hours, followed by slow cooling.
If
the object was to cause precipitation hardening, the temperature
was raised considerably above the recrystallization temperatures,
and the specimen was quenched in air.
In order to promote grain
growth and diffusion the temperature was maintained a few degrees
above the recrystallization temperature for considerable periods.
The atmosphere, at all time§,was natural gas. This substance is not ideal for a neutral atmosphere in a heat-treating
furnace because the principal* constituent, methane, decomposes
at approximately 740°C under ordinary conditions and probably at
lower temperatures in the presence of a catalyst. This decomposition of methane leaves a residue of carbon in the furnace and
on the object being treated which mifht lead to detrimental effects.
91
Thus it is not feasible to heat treat in an atmosphere of natural
gas above 740°G. Heat treatment was followed by magnetic measurements.
V.
MAGNETIC JUIASUREMENTS
After trying the first two methods of making magnetic
measurements without success, the third method was devised and
used for obtaining all magnetic measurements for the experimental
data.
For sketches and description of these methods see Chapter VI.
In order to obtain a standard for comparison, the iron
pellet of kiown permeability which was machined to the same size
as the compacted pellets, was dropped through the brass tube inside the solenoid (in the third method) and the deflection of the
galvometer was noted. This deflection was recorded for various
fields produced by currents flowing through the primary coil of
the solenoid.
This done, the deflections caused by the compacted
pellets were notea and recorded for the same currents as used for
the standard iron pellet.
From this data various graphs were
plotted as will b^ shown in the next chapter. The standard
pellet was not at all necessary except to give a basis for
com-
parison and also to assign numerical values to the measurements
for the various pellets.
In reality susceptibilities, K, were compared but since the
permeability, p, is a more common expression, the values were put
into this form.
92
Knowing the permeability of the standard iron pellet and the
deflection of the galvanometer caused by it at a given field strength,
the permeability of the unknown compact may be calculated from a
direct proportion provided the measurements are made at the same
field strength.
For example assume that the permeability of the
iron was found to be 286 by the method as outlined on page 77,
when a current of one ampere is passed through the primary coil
of the solenoid.
This pellet, when dropped through the brass tube
of the solenoid accepted for all measurements, caused a deflection
of l4t divisions when a current of one ampere flowed through the
primary coil.
A pelJe t of unknown permeability caused a deflection
of 11 divisions on the galvanometer when the same current flowed
through the priiaary. The permeability of the pellet, p , is
XT
calculated from a direct proportion:
J±B_ =
m
-
14
TT
or
u
P
= 286 14
TT
'
This proportion was used for all calculations, and the
results do not represent the absolute permeability of the specimens but offers merely a basis for comparison of the permeabilities
of the various specimens.
93
CHAPTER VIII
EXPERIMENTAL RESULTS
After some preliminary work the effect of processing variables on the magnetic properties was studied for some compacted
powders.
These variables included pressing conditions, heat treat-
ment, and composition.
Suitable graphs were drawn to show the ef-
fect of the3e variables.
Some work was also done with iron-aluminum alloys on a
method of determining diffusion of magnetic means.
I. PRELIMINARIES
Some preliminary studies were made in order to determine
such operating factors as the size of the powder charge of various metals to give a pellet of the proper size, the ti:ne of
mixing in the tumbler needed to obtain homogenity, the amount
of oxide film on so ue metal powders and its reduction, the time
of pressing and many other minor details.
For the weight in grams of various metal powders required
to give a pellet three-eighths of an inch long and one-half inch
in diameter see the table on pageHTof the appendix. The data
for this table was obtained partly by experiment and partly by
calculations.
94
The time of mixing in the apparatus and by the method already described was determined by trial.
In soiu.e cases a period
of fifteen minutes was more than adequate, but in no case was it
insufficient; thus it was adopted as the standard mixing period
for all powders. The mixtures were examined for homogeneity
with a Leitz binocular microscope.
Investigation showed that oxygen of the oxide film of most
of the metal powders used amounted to less than one-tenth of one
per cent of the total weight.
Since this was well within the
allowable error, the weight of the
oxygen was neglected in mail-
ing up the charges.
Natural gas containing 85% methane was used to reduce the
powders investigated for oxide content. At temperatures used
(from 400f to 600^0, depending upon the powder)
the reducing pow-
er of natural gas was almost identical with that of hydrogen.
The great disadvantage of hydrogen for operations of tnis sort,
when elevated- temperatures are used and where air cannot be
entirely excluded, is the danger of violent explosions. On the
other hand natural gas can be used safely at high temperatures
with almost the same efficiency. However the decomposition of
methane limits its use to temperatures below 740 C when the presence of carbon is detrimental.
In the reducing chamber of the mold
hydrogen was used exclusively for reducing because of its efficiency at the lower temperatures necessitated by the chromesteel of which the mold was constructed.
95
Time of maintaining the pressure on the*compact was not
sufficiently studied. However, it waspound that the magnetic
properties were not iniproved by maintaining the pressure more
than one minute during cold pressing.
In all work in this inves-
tigation the pressure waaheld at the desired point for two minutes.
The effect of maintaing the pressure for longer periods when
'
the pressing temperatures was above the recrystallization points
of the constituents of the compact was not studied.
An inves-
tigation along these lines might prove valuable since it is known
that pressure lowers the recrystallization temperatures and thus
might promote diffusion.
A great amount of work was done in an attempt to render
magnetic Heusler alloy (61 copper, 13 aluminum, 26 manganesej made
from metal powders. The applied pressure was varied from twentyfive to fifty tons per square inch; the pressing temperature
ranged from room (20°C) to 300°C; and heat treatment consisted of
annealing at veTrious temperatures in oil, water, and air. No measurable results were obtained.
The alloy remained nonmagnetic
as long as the processing temperatures remained below the melting
point of aluminum.
A specimen which had been annealed eight hours
&fe 700°C gave a permeability value at saturation of approximately one hundred.
A molten constituent, however, was Know to be
present as evidenced by small globules of metal on the surface of
the pellet.
Specimens of cast Heusler alloy showed a permeability at
saturation, with no subsequent heat treatment, of about one hundred and fifty.
96
Since no magnetic measurements could be obtained on this
alloy unless the aluminum had melted, work along this line was
abandoned as the conditions necessary to produce a magnetic specimen were not considered consistent with powder metallurgy.
II.
THE EFFECT OF PRESSURE
The effect of pressure from the standpoint of the magnetic
properties was investigated as the first; of the series, and the
results were expressed in terms of magnetic permeability.
Tests
with tnis object in view were performed on specimens of the same
composition as Permalloy and 1040 Alloy and on samples containing
72% iron, 16% molybedenum, and 12% cobalt. The mixture of powders
of the above compositions were pressed cold as well as at various
temperatures, and received, inp.ll cases, some form of heat treatment.
The magnetic measurements obtained as described on p£ge 90
were plotted on coordinate paper with .aagnetic permeability as the
ordinate and pressure in pounds per square inch as the abscissa.
Metal powders mixed in such proportions as to give compacts
of the same composition as Permalloy (d0% nickel, 205S iron) were
pressed cold at pressures up to sixty tons per square inch. At
pressures belo# fifteen tons per square inch the bonding of the
particles was so weak that the compacts could not be handled without serious breakage, and thus no measurements were made at pressures lower than fifteen pounds per square inch. The curve
plotted from magnetic measurements without and with subsequent
97
heat treatment is shown in Figure 14a, and indicates that pressures above fifty tons per square inch improve the magnetic properties but slightly. Or, in other words the optimum pressure
for cold pressing is fifty tons per S4uare inch for specimens of
this composition.
An explanation for the existence of an optimum pressure
may be offered in an equilibrium relation between the greater
magnetic forces due to reduction of losses caused by cavities and
the opposing forces set up by increased strains induced by cold
work. This is brought out more clearly by comparing the curves
(1) and (2) in Figure 14a. Curve (2) shows the permeabilities obtained when the same samples were annealed at 800 C.
The fact that
the wide divergence of the curves become approximately parallel
indicates that when the inherent strains of pressing are relieved, the beneficial effect of high pressure becomes apparent.
The permeability of specimens pressed at 300°C and receiving no subsequent heat treatment becomes constant, reaching its
maximum at low pressures. No divergence, as the pressure increases,
is shown between this curve and the curve obtained by heat treating the same specimens at 800°C. A possible explanation of this
fact might also lie in the idea of an equilibrium between magnetic
forces and the stresses of cold work. At temperatures above the
recrystallization point, the strains are removed. Pressure, it
has been show, lowers this recrystallization temperature. Since
the tempeaature of pressing was fairly close to the recrystallization point of many of the metals, it is possible that a great part
1040 ALLOY
40
Fig. 14a
PERMALLOY
72Fe-16Mo-12Co
60 0
20
40
60 0
Pressure in tons par square inch
>•
Fig. 14b
20
40
Fig. 14c
EFFECT OF PRESSURE, WITH AND WITHOUT THE APPLICATION OF HEAT, ON MAGNETIC
PERMEABILITY OF COMPACTED METAL POWDERS
(1)
(2)
(5)
(4)
Cold pressed; no subsequent heat treatment.
Cold pressed; annealed at 800°C for one hour.
Pressed at 3008C; no subsequent heat treatment.
Pressed at 300°C; annealed at 800°C for one hour.
60
99
of the stresses were removed as fast as they were set up, or the .
they were not set up at all due to the plastic conditions of the
metals.
It is quite possible that such a state existed in the
compacts of 800/,. nickel and 20% iron under pressure because the recrystallization temperature under ordinary conditions is 449°C for
iron and 599°C for nickel. If the temperature employed allowed for
plasticity, some of the increase in magnetic permeability was undoubtedly due to the fact that the cavities were closed and disturbances in the interstices of the particles were at fe ast partially
removed.
Similar tests were made and curves drawn for compacts of
72% nickel 14% copper, 11% iron, and 3% molybedenum (1040 Alloy)
and for specimens of 72% iron, 16% molyoedenum, and 12% cobalt.
Those for the 1040 Alloy were almost identical with those obtained
for Permalloy.
This fact may be interpreted to show that for
small amounts of impurities the magnetic properties of materials
produced by powder metallurgy are not drastically affected. This
may be seen by comjaring Figure 14a with Figure 14b.
The curve obtained for compacts of 72a/? iron, 16% molybedenum,
and 12% cobalt, as shown in Figure 14c, follow the general plan of
those obtained for Permalloy and 1040 Alloy except that their relative positions are quite different,
^t may be seen that neither
pressure, heat treatment nor pressing temperature have any marked
effect on the magnetic properties. Thus magnets of this composition
made by powder methods are stable under these conditions. Further
investigation showed that their permeability was practically con-
100
stant in spite of changes in the magnetic field. No attempt was
made to explain these properties.
III.
THE EFFECT OF PRESSING TEkPERATURE
Figure 15 shows typical results obtained on investigations c£
the pressing temperature on the magnetic properties. The same
procedure was followed asin obtaining and recordin^data in the
effect of pressure on the permeability, except that in this case
the pressure was kept constant for any given series, and the pr essing temperatures was varied.
The purpose of these curves is to
show that the same results may be obtained in ir.ost instances by
substituting moderate pressing temperatures for higher pressures.
In other words, hot pressing serves as well in improving the magnetic properties as pressing cold at very high pressures. Plasticity of the particles at moderate temperatures while under pressure
is thought to be the cause. Cavities are closed more easily thus
resulting in fewer interference losses. If the temperatures are
high enough, elimination of stresses induced by cold work is partially
responsible for the improvement in the magnetic permeability.
1040 ALLOY
300
250
200
200
150
100
100
200
300
400
Pressing temperature (°C)
Figure 15
TYPICAL CURVES SHOWING THE EFFECT OF PRESSING TEMPERATURE
ON MAGNETIC PERMEABILITY OF COMPACTED METALS
(1} Pressed
(2) Pressed
13) Pressed
(4) Pressed
at
at
at
at
25
25
40
40
T/in§;
T/in?;
T/inS;
T/inf;
S3275
no subsequent heat treatment.
annealed 1 hr. at 800°C.
no subsequent heat treatment.
annealed 1 hr. at 800°C.
102
IV. EFFECT 0J? hEAT TREATMENT
Heat treament is very important in production of magnetic
materials. Various properties may be obtained by special heat
treatment alone. The effect may be to increase the permeability
or might; actually lower it, although in powder metallurgy the latter is seldom the case, -^eat treatments which increase the permeability are, in general, those which relieve stresses set up by
mechanical work, those which might promote grain growth and recrystallizaion, or those which cause
precipitation of impurities
from "Che crystal lattice. The most important heat treatment which
casues decrease in pe rmeability is that ^/hich causes diffusion
and the formation of new phases vmich are non magnetic.
Of those &rhich cause an increase in the permeability the moat
important is, perhaps, the heat treatment which relieves stresses
caused by cold work.
Compacted metal particles are deformed under
pressure, and even if the pressing is done at moderate temperatures some of the forces exerted by this strained conditio"^. remain in the product after the pressing operation. Kemoval of these
stresses is best accomplished by annealing at a temperature just
above the recrystallization points of the constituents. Only a
short time is re iiired for this rearrangement of intercrystalline
forces, but cooling should be slow so that internal stresses will
not be set up due to differential cooling. Results of annealing
are shown in Figures 14 and 15. The slope of the curves obtained
by plotting the data obtained on annealed specimens follows very
103
closely the slope of the curves obtained by plotting the data for
unannealed specimens. The increase of permeability is due to removal of stresses.
A study was made .on the effect of grain growth on the magnetic properties of 1040 Alloy.
Specimens which had been prepared
by pr essing at various temperatures and pressures were first heated to 700°C for one hour to remove strains and then drawn at 500 C
for four hours. At these temperatures grain growth within the
particles should occur and thus improve the magnetic properties.
In this case copper was present in small amounts and some diffusion might have taken place causing an exchange of electrons between the copper and the atoms of iron and nickel, thus rendering
the specimens as a whole less magnetic. However, as 3a ter tests
showed, it is unlikely that diffusion to any great degree occured
in such a short time and thus the permeability was not affected
to a measurable extent by diffusion. However, grain growth did
occur and caused an increase in the permeability however slight as
shown in Table I.
Quenching has decided effect on the magnetic permeability.
It was found that by beating specimens of 1040 Alloy to 700°^, and
quenching in air, a considerable increase in the permeability occured. These results are shown in Table II. A satisfactory explanation of this phenomenon wasfoot found, although it is quite possible
that some changes such as pr ecipitation hardening or a change of
crystallographic structure is responsible.
Figure 16
EQUAL PERMEABILITY OntVBS
FOR THE Fe-Co-Al SERI2S
(All specimens pressed
at 300°C and 40 T/in£;
no subsequent hoat
treatment)
i ruing ,
figure IU
EQUAL PERMEABILITY CURVES
FOR THE Fe-Co-Al SERIES
(All specimen* pressed at 300°C and 40T/
annealed 1 hour at
350°C„)
106
V.
EFFECT OF COMPOSITION
Obviously changes in composition will affect the magnetic
properties, but to what extent, cannot be predicted on the same
basis as for cast specimens, ^t was seen that the permeability
of compacts of Permalloy and of 1040 Alloy powders were practicaljr
the same, provided they were formed under the same conditions.
Cast alloys of^^hese same compositions have widely different
magnetic properties, because, as it has been show, small amounts
of some impurities
have a very marked effect. Considering the
copper of the 1040 Alloy as an impurity, it was concluded that
impurities have little bearing in the properties of pellets produced by powder metallurgy.
The percentage of impurities (14:%
copper) was probably not high enough to cause serious dilution of
the magnetic field, nor had diffusion taken place in such an
amount as to cause any quantitative effects due to* the exchange
of electrons between the atoms of copper and those of nickel.
In order to further study the effects of changing composition a series wasjchosen in which it would be possible to study
J
the effects of magnetic dilution and at the same time study exchange of electrons between a paramagnetic substance and a
ferromagnetic. The iron-cobalt-aluminum series seemed ideal
for this study because It contains a paramagnetic substance
(aluminum), a strongly ferromagnetic material (iron), and a
weaker ferromagnetic (cobalt). An increase in the percentage
of aluminum in the mixture should weaken the effective magnetic
107
field of the iron and cobalt due to dilution. Also, u^on proper
heat treatment aluminum should decrease the magnetic properties
of a given compact due to exchange of electrons in the M 4s"
orbit of the paramagnetic with the "3d" orbit of the ferromagnetic.
Experiments on the latter phenomenon will be discussed
under diffusion.
Studies of the permeabilities of the specimens of this
system revealed, principally, two important facts. Additions of
aluminum do nox so markedly affect the magnetic properties of compacted powders as in cast alloys of the same system.
As stated
before it has been proven that any cast alloys of a similar system become non-magnetic when the aluminum constitutes over 20%
of the alloy by weight. This is satisfactorily explained on pages
3b, 37, and 38 of Chapter IV. Wien pressed iron-cob alt-aluminum
powders containing as high as 9b% aluminum give evidence of being
ferromagnetic,
it appears that the only effect of additions of
aluminum is dilution, or, in other words, separating the magnetic
domains \A th a less permeable substance, thus reducing the total
effective magnetic moment by an amount directly proportional to
the square of the separatingjdistance.
Because specimens contain-
ing such high percentages of aluminum remained magnetic, it seems
feasible to assume that electron exchange is at a minimum due to
the relatively small number of atoms of aluminum which actually
contact atoms of iron and cobalt.
Over one hundred specimens of the series irere pressed a.t
applied pressures ranging from 25 to 40 tons per square inch and
109
at temperatures from 300° to 400°C, depending on the percentage of
aluminum in the powder.
It was found that samples high in aluminum
could not be pr essed, without injury to the mold, at temperatures
and pressures higher than 300°C and 25 tons per square inch, respectively.
Compacts with high percentages of cobalt required high
pressures and temperatures (400°C and 40 tons per square inch) in
order to obtain the necessary mechanical strength. All specimens
were measured for magnetic permeability immediately after pressingthat is, before any subsequent heat treatment was given.
Equal permeability curves, as obtained by interpolation cf
this data, are shown in Figure 16. No startling variations from
theory are observed in these curves, except, possibly in the corner
of theternary diagram with high percentages, or iron. This variation from normal, an unwarranted rise in the permeability in this
region, might be explained by the fact that the magnetic domains,
or particles, are separated by such a distance as to eliminate repulsion, as developed on pages 43-46 in Chapter IY.
The data for the curves in Figure 16 were obtained from
specimens which had received no heot treatment subsequent to pressing.
As shown before in the section of this chapter entitled
"Effect or ^eat Treatment11, it is evident that the only effect
of annealing at low temperatures is to relieve internal stresses
set up by the mechanical work of pressing.
Figure 17 shows curves
drawn from data obtained by annealing, at a low temperature, the
same specimens used to obtain the curves of Figure 16. The specimens were annealed at 500°0 for one hour and cooled in air. These
TABLE I
TYPICAL TABLE SHOWING THE EFFECT OF HEAT TREATMENT ON
MAGNETIC PERMEABILITY OF COMPACTED METALS
Composition
Pressure
Pressing
Temp.
1040 Alloy
25 T/in?
20°C
tt
tt
tf
n
n
ft
n
H
1040 Alloy
n
N
n
1040 Alloy
Heat
Treatment
None
H
132
Annealed 1 hr., QOdb 154
Annealed 2 hr., 800 C 204
Drawn at 350°C, 4 hrs ,214
40 T/in!
tl
tt
tt
40 T/in?
20°C
None
175
ti
Annealed 1 hr., 800°C 242
ti
Annealed 2 hr., 800°C 245
ti
Drawn at 350 C, 4 hrs- 250
300°C
n
ti
n
tt
it
it
w
tt
«
None
198
Annealed 1 hr., 800°C
264
Annealed 2 hr., 800°C
276
Drawn at 350°C, 4 hrs. 276
/
TABLE II
EFFECT OF QUENCHING ON THE MAGNETIC PERMEABILITY OF
COMPACTED METALS
Composition
Pressure
Pressing
Temp.
1040 Alloy
25 T/in?
20°C
«
tt
1040 Alloy
40 T/ in.
20 C
t!
1040 Alloy
50 T/in.
n
1040 Alloy
ii
1040 Alloy
tt
1040 Alloy
tt
20 C
40 T/in.
ft
50 T/in.
ft
300 C
n
300 C
it
300 C
n
H
Annealed 1 hr., 800°C 154
Q. air from 700°C
210
Annealed 1 hr., 800 C 175
Q. air from 700 C.
11
25 T/in.
Heat Treatment
225
Annealed 1 hr., 800 C .198
Q. air from 700 C.
264
Annealed 1 hr., 800 C ,198
Q.air from 700 C.
274
Annealed 1 hr., 800 C 205
Q. air from 700 C.
274
Annealed 1 hr., 800 C 205
Q. air from 700 C.
276
Ill
curves merely substantiate the statement that a mild anneal removes internal stresses only.
Annealing at higher temperatures
for a Ion er time should cause diffusion.
V.
DIFFUSION
From the standpoint of powder metallurgy, diffusion has been
a debatable circumstance for some tLue.
If it does occur, it is
to such a minute amount that it cannot be measured satisfactorily
b;y ordinary quantitative methods. Thus, this portion or the work
of this thesis was devoted to an attempt to determine whether or
not diffusion could be measured quantitatively by magnetic methods•
With this in view a first trial to make such ne asurements
teas performed on specimens of 75°? iron and 25^ aluminum powders
compacted at 400°C and 40 tons per square inch. Difficulty was
encountered in obtaining annealing temperatures high enough to
cause diffusion without causing a serious expansion of the compact.
It was noted that at temperatures between 5O0O and 600°J
a drastic
change in the dimensions and appearance of the compact occurred.
Probably this wasdue to a chemical reaction between the aluminum
and the iron and iron oxide (if oxides could be present after such
care was taken in their reduction), or to melting of the aluminum
at this temperature, caused by the depression of its melting point
by iron or some impurity. At any event no magnetic measurements
were possible on specimens treated at this temperature.
At 450°0, which is slightly above the recrystallization
112
temperature of both aluminium and iron some results were obtained.
These results are shown in Table III. The rate of diffusion increases
proportionally with increases of temperature above the recrystallization points. Since the highest possible annealing temperature
for these specimens was only a few degrees above the recrystallization points the rate was slow and the difference in permeability
very small. It is also known that the rate of diffusion decreases
with time so that after a long period of annealing the effect on
the permeability wc-s hardly noticeable.
TABLE III
EFFECT OF ANNEALING TIME (OR DIFFUSION) ON THE
MAGNETIC PERMEABILITY OF 75Fe~25Al
COMPACTS
Composition
Annealing Temp.
75Fe-25Al
(pressed at
300°C and
40 T/in?)
450°C
Annealing Time
n
0 hours
204
1 hour
225
n
24 hours
204
tt
H
48 hours
184
ft
tt
72 hours
184
n
ft
120 hours
164
tt
Y
ll£
CHAPTJSK
IX
CONCLUSIONS AND SUGGESTIONS FOR FURTHEit RESEARCH
I.
CONCLUSIONS
Magnetic permeability might be used as the basis for determining some of the physical properties of compressed metal
powders.
-4; is a direct function of porosity, or percentage
of cavities, vvhieh so vitally afreets physical properties. This
relation is shown by the curves obtained by plotting pressure and
pressing temperature against permeability.
Both of "Chese vari-
ables greatly influence the porosity in accord with the principles
of plasticity.
Of course other variables such as the nature of the
constituent powders themselves and minor processing details influence porosity and therefore permeability.
The degree of bond-
ing which is practically analogous with porosity must also be intimately connected with magnetic properties.
Paramagnetic powders in compacted mixtures with ferromagnetic powders tend, principally, to dilute the total magnetic
field rather than to render the atoms of the ferromagnetic ponder
non-magnetic by exchange or sharing ox electrons. Evidence of
this dilution was shown by plotting equal permeability curves on
a ternary diagram for specimens compacted from mixtures of iron,
cobalt, and aluminum.
From these curves it waslseen that specimens
115
of this series retained magnetic properties with as high as ninetyfive per cent aluminum.
Assuming atomic dispersion,as in cast specimens, manifestations of magnetic properties should disappear when the sample
contains slightly less than twenty per cent aluminum.
On the
basis that electrons of aluminum atoms render atoms of iron less
magnetic, some experiments were conducted in an attempt to measure
diffusion by magnetic means. Compacts of 75$' iron and 25$ aluminum were annealed above their recrystallizati on temperatures
for various periods. Since diffusion is atomic some exchange or
sharing of electrons, proportional to the amount of diffusion,
should occur, thus rendering the specimens less magnetic. Experimental #ork confirmed this theory to some degree, but certain limiting factors hindered entirely satisfactory results.
II.
SUGGESTIONS FOR FURTHER RESEARCH
The study of the amount of diffusion in powder compacts
might be furthered by annealing compacts of mixtures of powders
containing 13 atomic per cent antimony, remainder nickel.
It is
possible that there would be no expansion of the compact on annealing at temperatures close to the melting point of antimony (630°C)
as in compacts containing aluminum.
Theroetically, as diffusion
proceeds, these specimens should become less magnetic until, with
atomic dispersion of the antimony in the nickel, no magnetic pro-
116
perties would be exhibited.
Measurements of magnetic permeability of compacted powders
at very low field strengths, that is, in fields below which che
saturation value of magnetization occurs, is a second suggestion
for further research.
It might also be interesting and worth
while to determine the maximum permeability of these products of
powder metallurgy, since the maximum permeability is often startling while the saturation value is quite low.
A considerable amount of research might be done on correlation
of such physical properties as hardness, density and others with
magnetic permeability.
APPENDIX
117
APPENDIX
A
PR2SSUBS CQEnnBHSIOSS FHOM GAGE BLADINGS OF HYDRAULIC JACK
TO ACTUAL APPLIED PRESSURE
The following equation was used to obtain actual applied
pressure, P, (in tone per square inch) on the rata of cross sectional
area, A, (in square inches) from gage readings, G, (in pounds,
total):
P =
2000 A
Following is a list of gage readings converted to actual
applied pressures:
Gage readings
(pounds)
Applied pre133.
(tons/sq. in.)
Gage readings
(poinds)
Applied press.
(tons/se* in.)
2500
8.35
1,500
5
5000
16.7
3,750
12.5
7500
25.0
7,500
25
10,000
33.3
12,000
40
12,000
40.0
15,000
50
14,000
46."
18,000
60
50,000
100
16,000
53.4
18,000
6Q*0
20,000
.66.7
25,000
.-83.5
30,000
100
118
APPMDIX
B
fEIOHT OF POSIMR REQUIRED TO GIVE A PELLET OF THE COBBECT
SIZE
Based on the apparent specific gravity of the following
metals, the weight of each required to give a pellet 3/8 inch
long and one-half inch in diameter was calculated.
was taken as the standard*
Copper powder
It was found experimentally that ten
grams of copper powder gave a pellet of very nearly the correct
size.
Calculations of the weight of the given powder, x, were
made from a direct proportion.
'owder
Sp, Gr.
X
Powder
Sp. Gr.
z
Cu
8.93
10.0
Fe
7.86
6.61
Al
2.70
3.04
Mo
10.2
8.58
3D
6.67
5.62 .
Cd
8.60
7.24
Cr
7.10
5.98
PI)
11.3
15.1
Hi
8.90
7.48
Sn
7.31
6.15
Zn
7.14
6.01
Co
8.90
7.48
Mn
7.20
6.06
119
APP3KDIX
C
RSKJCTIOH OF METALLIC OXIDES
According to Mellor* some metallic oxides may be reduced to
the metal by heating for fifteen minutes at the proper temperature
in an atmosphere of dry hydrogen. The equation of the reduction,
stated generally, is:
II 0 •+ H g - H 2 0
-f- M
Following is a list of some of these oxides with the temperature at which the reduction occurs j
Oxides of Ag and Pd
.• Boom Temp.
Cupric oxide
••• 150°C.
Ferric oxide
• 22G°C.
Magnetic oxide
290<>C*
Ferrous oxide
Manganese dioxide ••••
Pyrolusite
Cobalt sesquioxide
Cobalt monoxide
Hickel sesquioxide
Fickel monoxide
l
*».• 505°0.
•
145°C.
190<>C.
....•••*»• 110°C*
...•••••*»•».« 165°C.
?0°C.
225°C»
J. S. Mellor, A Comprehensive Treatise on Inorganic and
Theoretical Chemistry, (Longmans, Green and Co.t H.Y., 1932}
Tol. I, p,328.
120
APPENDIX
D
TO MEASURE THE CONSTANT, k, OF A BALLISTIC GALVAROMETSR
The charge causing a deflection of a galvanometer is proportional to the deflection.
In order to obtain the actual value
of this charge it is necessary to multiply the deflection by a
constant, k.
Following is a method of determining this constant.
A dry cell battery (1.3 volts) is connected in series with
a condenser, a resistance, and a ballistic galvanometer which is
suitably damped. An arrangement is so ma.de that the condenser
may be charged, noting the galvanometer deflection, then shunted
out, discharging the condenser and again noting the deflection of
the galvanometer.
The constant, k, will of course be dependent
on the damping resistance of the galvanometer.
The following equations express these relations:
Qc - C E
CL. m
k «
R
Qc
a
2
CE S k d
B O B
(R+g) ~ T ~
Example:
A s s i s t a n c e of c i r c u i t , B » 1850 ohms
Damping r e s i s t a n c e , ( B ^ - g ) - 4000 ohms
Average d e f l e c t i o n , d » 2 . 1 5
Charge of condenser, C B « 1C186 x 10~ 6
k a
1850 1.0186 x 10~ 6
wm—£TT5
-
0.219 x 10~ 6
121
ACEIIOIILEDGSI^SFTS
I wish to express ray sincere thanks to all who so kindly
offered their advice or assistance in this work.
Thanks are
especially due to the following members of the faculty at the
Montana School of Mines: Dr. Curtis L. Wilson, Professor of
Metallurgy,
matics,
Dr. George L. Shue, Professor of Physics and Mathe-
and Robert Wilson, Assistant in Mneral Dressing*
122
Mr. Donald Quincy Cole has satisfactorily completed this
15th day of May, 1941, all the requirements prescribed "by the
Montana School of Mines for the degree of Master of Science in
Metallurgical Engineering.
BADUATE COMMITTEE
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