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Intermetallic Compounds and the Use of Atomic Radii in Their DescriptionЧReply.

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mon's Fig. 6, cf. [I1). These slopes vary from ca. 2.5 for lanthanoidlmanganese phases to - 0.4 for nonlanthanoid/
gold phases.
Even when the unit-cell dimensions have been adjusted
to ideal stoichiometry and the data-set appears to be extremely homogeneous as in Simon's Figure 17['], which reproduces Waterstrat's data for MN3 phases with the cubic
SiCr3 structure, the delusion may originate from the low
precision or poor selection of the components in the plot.
Indeed, Simon is not alone in this respect. Recently,
but for different and justifiable reasons, Villars, Girgis,
and H ~ l l i g e r obtained
[~~
a linear relation between d M N =
a . 6 / 4 and K = (RM 3RN)/4-essentially a versus DM if
N is fixed-calculated for 91 phases with a linear regression factor of 0.989; this would certainly be interpreted as
indicating a homogeneous data-set. Nevertheless, with
plots of much higher precision obtained using Waterstrat's
cell dimensions (i.e. the same data as Simon) P e ~ r s o nar[~~
rived at a different conclusion.
In these compounds the component N is a transition
metal and M may either be a transition metal (T-T phases)
or a nontransition metal (B-T phases). When these two
groups are considered separately and a is plotted against
DM varying M and the phases of each component N are
considered separately then:
+
The slopes of a versus DM for the B-T and T-T phases
of the same N components are not exactly the same;
and
for both groups of phases the slope of a versus DM decreases approximately linearly with increasing diameter
of component N and is proportional to - 0.4 ( f 0.1) DN.
Conclusions: Taking two structural types as examples
analyzed by Simon, we have shown that when the data are
examined much more precisely and attention is paid both
to the choice of the group and period of the components of
the phases they may not form an overall homogeneous
data-set in terms of dimensional behavior. The recognition
of such inhomogeneities requires analytical methods to determine their causes: Indeed, for phases with the MgCu,
structure inhomogeneities in dimensional behavior have
long been
but since the analyses were conducted using radius ratios no interpretation was possible.
-
-
-
For phases of medium complexity and/or symmetry
lower than cubic, the study of atomic volumes provides
little more than overall energy considerations.
Even plots of cell-dimensions a (b, c) against the diameters of the component atoms DM or DN are insufficiently diagnostic.
However, plots of individual interatomic distances relative to the corresponding sums of the atomic diameters
(for C N = 12 regardless of the atomic coordination
number in the structure["') against the atomic diameters
DM or DN indicate the basic causes of the different dimensional behavior for specific groups of phases with a
given structure. These differences do not result per se
from the various diameters of the component atoms but
from the different interatomic contacts, or combinations thereof, which control the cell dimensions of
groups of phases exhibiting different dimensional behaviors. Such information, which is quantitative in nature, should be amenable to firm theoretical analysis
(see e.g. data in ["I and [I3]).
Angew. Chem. Int. Ed. Engl. 23 (1984) No. 4
Our studies also show that in three-dimensional space
with DM and DN for CN 12 as abscissae and the cell dimension as ordinate all phases with a given structure lie on
a planar surface. One exception to this rule has been
noted-phases with the SiCr3 structure discussed previously. These phases lie on a curved surface in DM,DN,a-space;
nevertheless, this surface has the property that phases
formed by the same component N and T or B as components M lie along straight lines on it.
Finally, we draw attention to potential difficulties in
analyzing near-neighbor diagrams sketched with high precisi~n['~].
Received: December 7, 1983 [Z 649a IE]
German version: Angew. Chem. 96 (1984) 302
[I] A. Simon, Angew. Chem. 95 (1983) 94; Angew. Chem. Int. Ed. Engl. 22
(1983) 95.
[2] W. B. Pearson, Acta Crystallogr. 8 3 7 (1981) 1174.
[3] E. Hellner, W. B. Pearson, Z . KristaNogr. 163 (1983) 197.
141 W. B. Pearson, J. Less-Common Met. 81 (1981) 161.
[5] W. B. Pearson, Acta Crystallogr. 8 2 4 (1968) 1, 1415.
[6] E. Hellner, A.C.A. Meeting, Snowmass, Colorado, August 1983.
[7] P. Villars, K. Girgis, F. Hulliger, J Solid State Chem. 42 (1982) 89.
[8] R. L. Berry, G. V. Raynor, Acra Crystallogr. 6 (1953) 178.
[9] M. V. Nevitt in P. A. Beck: Electronic Structure and Alloy Chemistry of
Transition Metals. Wiley-Interscience, New York 1963, p. 101.
[lo] A. E. Dwight, Trans. Am. SOC.Met. 53 (1961) 479.
[ l l ] W. B. Pearson, Philos. Trans. Roy. Soc. London 298 (1980) 415.
[12] W. B. Pearson, J. Less-Common Met. 97 (1984) 119.
[13] W. B. Pearson, Acta Crystallogr. A36 (1980) 724.
[14] W. B. Pearson, Z . Kristallogr. 158 (1982) 181.
Intermetallic Compounds and the Use of Atomic
Radii in Their Description-Reply
By Arndt Simon*
The important remark made by Hellner and Pearson"'
that phases of one structure type to not represent a homogeneous set is further supported by the occurrence of (1st
order) phase transitions which do not involve a change of
With this in mind, I stated in my restructure
viewf4]"that it is not very meaningful to start an analysis of
packing effects in a particular structure type on the basis
of all known representatives". The Laves phases KNa,,
CsNa, and CsK, offer a model system-metallic bonding
without significant heteropolarity-to study packing effects. The analysis yields a kind of Vegard rule, i.e. the distances between the atoms are proportional to the sum of
atomic radii weighted according to the composition. On
this basis, by means of a general approach for the adaption
of atomic sizes to coordinations, the interatomic distances
in the three phases can be calculated with high accuracy
(3%0).
According to Churcher and HeinerS1,such a Vegard-type
law can only be plausible when certain assumptions about
the interatomic potentials are made; but these assumptions
are consistent with the relation between distances and
force constants, according to Badger's rulef6].It must therefore be expected that many intermetallic compounds with
topologically close packed structures obey such a Vegardtype law reasonably well. The alkali metal compounds
mentioned follow this law extremely well, but all Laves
phases of the MgZn, and MgCuz type are also reasonably
well described by it (Fig. 6 in [41), at least better than by a
[*I Prof. Dr. A. Simon
Max-Planck-Institut fur Festkorperforschung
Heisenbergstrasse 1, D-7000 Stuttgart 80 (FRG)
0 Verlag Chemie GmbH, 0-6940 Weinheim, 1984
OS70-0833/84/0404-0325 $ 0 2 . 5 0 / 0
325
simple sum of atomic radii (rM+rN). Nevertheless, the deviations and scatter of the data are significant. In part, they
were discussed and by no means were they taken to arise
from a “general experimental scatter of data collected
from various sources”. On the contrary, it is repeatedly
pointed outEBthat this scatter is due to interesting influences of chemical bonding. One cannot expect compounds like CaRh,, SrIr2, AuBi,, or NaAu, to exhibit the
same dimensional behavior as KNa,. A subdivision of
compounds into single families as shown in Figure 1[11and
their analysis according to Hellner and Pearson provides
hope of gaining insight into the chemical bonding in these
compounds; more precisely, into interatomic potentials
and mutual influences of atomic sizes. The same insight
might hopefully be gathered from analysis of the deviations of real compounds from Vegard-type behavior, which
can be formulated quantitatively.
What does “radius ratios ... are intractable” mean? Radius ratios (rM/rN;since 2r=D, also DM/DN) are as good
(or bad) as the anticipated atomic sizes DM and DN, respectively. These depend on the structure and on the bonding partner. This is clear if the transition of a metal from
body centered cubic to face centered cubic packing, on the
one hand, and the different sizes of the Cs atoms in CsF
and CsK,, on the other, are considered. Therefore, all representatives in [’], but also in [41 are based on normalized
values DMrDN for the close-packed elements. We are left
with the problem of using near-neighbor diagrams for the
representation of all compounds belonging to one structure typer4].Hellner and Pearson prefer plots of the lattice
constants against DMor DN, and they use the experimental
distances d M M , d”, dMN (relative to the normalized values
DM, DN,or 0.5 (DM DN), e.g., (DM -dMM)) instead of the
lattice constants for structures with free parameters. The
representation (DM -dMM)/(DN= f(DM/DN)chosen in E41,
of course, corresponds to the representation of the linear
relationships in Figure 1[”, but with a different scale since
DN is a constant for each of these relationships. The problem lies not in the use of near-neighbour diagrams, but in
the interpretation of the plot of experimental data. The interpretation given in [41 has a distinctly different basis than
previous interpretations”].
+
Received: December 29, 1983 [Z 649b IE]
German version: Angew. Chem. 96 (1984) 204
111 E. Hellner, W. B. Pearson, Angew. Chem. 96 (1984) 302; Angew. Chem.
I n f . Ed. Engl. 23 (1984) 324.
121 A. Jayaraman, V. Narayananiurti, E. Bucher, R. G. Mains, Phys. Re”.
Lett. 25 (1970) 1430.
[3] D. Weber, H. G. von Schnering, Z . Krisfullogr. 162 (1983) 230.
[4] A. Simon, Angew. Chem. 95 (1983) 94; Angew. Chem. Int. Ed. Engl. 22
(1983) 95.
[S] C. D. Churcher, V. Heine, Ac/u CrystaNogr., in print.
[6] R. M. Badger, J. Chem. Phys. 2 (IY34) 128.
[7] W. B. Pearson, Actu Crystullogqr. 8 2 4 (1968) 1415.
BOOK R E V I E W S
Ozonation in Organic Chemistry. Vol. 2: Nonolefinic Compounds. By P. S . Bailey. Academic Press, New York
1982. xx, 497 pp., bound, $ 28.50.
“The saga of the many-faceted, many-splendored reactions of ozone with organic groupings is the purpose of
this volume”. Four years after Vol. l[*],which deals with
the ozonation of olefins, the author presents Vol. 2, which
covers the literature until 1980 with 1249 citations.
A small chapter on the still underdeveloped ozonation
of the CC triple bond-lo4 times slower than that of similarly substituted double bonds-is followed by four chapters dedicated to aromatic compounds. The author distinguishes between “bond attack” (0, as 1,3-dipole) and
“atom attack” (0, as electrophile). The justification for applying the Criegee mechanism of olefinic ozonation to the
aromatic compounds stems, inter alia, from the interception of the intermediate carbonyl oxides by methanol or
acetic acid. These trapping reactions offer preparative access to dialdehydes starting from condensed aromatic systems.
The interaction of ozone with nucleophiles (amines,
phosphites, thioethers and polysulfides) is the topic of a
major chapter. The oxidation of the side chain as well as
the oxide formation at the nucleophilic center are interpreted via the same 0, adduct.
326
The reaction of ozone with CH and CH, groups is comparatively slower than with 71 systems, providing tert-alcohols and ketones, respectively. The initiating step of this
important method (235 lit. ref.) is supposed to be a 1,3-dipolar CH insertion with partial carbonium character in the
transition state; in superacid medium this insertion is ascribed to the species HO :.
The technique of ozonation has made progress. The use
of nitrogen as a carrier gas combined with the measurement of 0, generation is an important analytical tool. In
this operation, the ozone adsorbed on silica,gel at - 78 “C
is driven out by N2. The “dry ozonation” on silica gel is likewise applied with increasing frequency. Quite justly the
author pleads that most synthetic chemists are not sufficiently aware of the advantages of ozone as a reagent. The
sewage purification with ozone and the contrmersy about
the stratospheric ozone layer are briefly outlined.
The concluding chapter “Ozonation of Olefins Revisited” reports on the progress achieved (120 lit. ref.) since
publication of Volume 1. Among other things, it is noteworthy that an ozonide has been found as a natural product in a fern. Dioxiranes, i.e., the cyclic isomers of carbonyl oxides, have been established at low temperature. The
trump card that quantum chemists have predicted this species, is perhaps not so impressive; according to all MO or
Angew. Chem. Int. Ed. Engl. 23 (1984) No. 4
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