phosphorus in silylphosphines or monogermylphosphines [1053. Similar contradictions can be found for organogermyl-, organostannyl-, and organoplumbylphosphines. The course of the oxidation and the unsuccessful attempts a t specific syntheses of organostannylphosphine oxides or organostannylphosphonium salts lead one to attribute the stability of the tin-phosphorus bond to a necessary (p-dx contribution, since the Sn-P bond is broken as soon as the lone pair of electrons on the phosphorus is engaged. The 1,2-dipolar additions of carbon disulfide and phenyl isocyanate also support this hypothesis, since Sn[P(C6H&]4 is accessible to these reactions, whereas no electrophilic attack of these 1,Zdipoles on [(C6H&Sn]3P is observed. This interpretation of the covalent bond appears to be opposed by the vibration spectra, which can be interpreted only in terms of a pyramidal structure of the compounds, though it should be pointed out that it is by no means certain that (p+d), double-bond components must be associated with a planar structure of [99] E . A . V. Ebsworth, Chem. Commun. 1966, 530. [lo01 E . W. Randall and J . J . Zuckerman, G e m . Commun. 1966, 132. [loll H . Schumann, I. Schumann-Ruidisch, and M. Schmidt in A . Sawyer: Organotin Chemistry. M. Dekker, New York, in press. [I021 H. Schumann, 0. Stelzer, and H . Rosch, J. organometallic Chem., in press. [lo31 H. Schumann and 0. Stelzer, unpubtished. [lo41 E . W. Abel, R . Honigschmidt-Grosich, and S . M . Illingworth, .I chem. . SOC. (London), A 1968, 2623. I1051 J . E . Drake and C . Riddle, J. chem. SOC.(London) A 1968, 1675. the molecule [99,1001. The reactions of the tris(trimethylmetal)-substituted phosphines with carbonyl compounds of the transition metals also show very clearly that it is possible to use the lone pair of electrons on the phosphorus for coordinate bonding without breaking the original P--MIV bonds. As regards the stability of compounds of elements of groups IVB and VB, the investigations carried out so far show clearly that the most stable molecules are obtained with approximately equal covalent radii of the bonding partners [84,8537,1011. In the light of our present knowledge, the hypothesis of the participation of the lone pair of electrons of phosphorus, arsenic, antimony, and bismuth in the bond with silicon, germanium, tin, or lead seems quite feasible. The final decision should be left to detailed physicochemical studies and structure analyses. The author is grateful to Dip1.-Chem. Ulrike Arbenz, Dr. H . Benda, Dr. P. Jutzi, Dr. H . KOpA U.Niederreuther, Fraulein Thea Ostermann, Dr. A . Roth, L. Rosch, Fraulein Elke Schauer, Dr. P. Schwabe, Dr. 0. Stelzer, and DipLChem. A . Yaghmai for their assistance in his own work in this field. Thanks are also due to Prof. Dr. M. Schmidt for valuable discussions, to Badische Anilin- urrd Soda-Fabrik, Farbenfabriken Bayer, Farbwerke Hoechst, Werk Gendorf, and the Union Mini2i-e du Haut Katanga for the free supply of valuable starting materials, and to the Fonds der Chemischen Industrie and the Deutsche Forschungsgemeinschaft for financial support. Received: December 18, 1968 [A 732 IE] German version: Angew. Chem. 81, 970 (1969) Translated by Express Translation Service, London Crystal Structure Analysis by Neutron Diffraction IF**] By G. Will[*] This second part of the article “Crystal Structure Analysis by Neutron Diffraction” deals with the diffraction of neutrons by magnetically ordered crystals. Neutron diffraction is at present the only reliable method for the determination of the magnitude, direction, and spatial distribution of magnetic moments in crystalline substances. Since the magnetic moments are essentially due to the unpaired electrons, the distribution of these electrons in the crystal can be measured in this way. 1. Introduction An important application of neutron diffraction is the determination of magnetic spin structures in crystals in the magnetically ordered state. The neutron, or [*I Priv.-Doz. Dr. G. Will Abteilung fur Kristallstrukturlehre und Neutronenbeugung Mineralogisch-PetrologischesInstitut und Museum der Universitat 53 Bonn, Poppelsdorfer Schloss (Germany) [**I Part 11: Neutron Diffraction and Magnetic Structures. Part I: Neutron Diffraction at Atomic Nuclei 111. 950 rather its magnetic moment, acts as a probe, by means of which the spatial electron spin distribution in the crystal can be measured in atomic dimensions. Neutron diffraction is at present the only method that allows the reliable determination of the magnetic environmental relations between the individual atoms or ions and of the long-range order of the spin. The investigation of magnetism and the use of constantly improving magnetic materials has now become so important that the chemist engaged in the preparation and analysis of such compounds must also be familiar with the magnetic properties and their investigation. Angew. Chem. internat. Edit. / Yof. 8 (1969)/ No. 12 2. Physical Principles The neutron has a magnetic moment of pn = -1.91 319 nuclear magnetons ( p ~ ) and , can therefore enter into magnetic dipole-dipole interaction with the magnetic moments of the atoms. The interaction with the magnetic moments of shell electrons that are situated in incomplete shells, and which therefore produce a resultant magnetic moment, is particularly important. The interaction with the magnetic moments of the atomic nuclei, on the other hand, is weaker by a factor of about 2000, and can be detected only under certain conditions; this interaction can be disregarded in the present connection. The elastic scattering of the thermal neutrons by crystals consists essentially of two components having approximately equal orders of magnitude (scattering lengths between 10-12 and 10-13 cm): 1. nuclear scattering due to interactions between the neutron and the atomic nuclei [I]; 2. magnetic scattering due to a classical dipole interaction between the magnetic moment of the neutron and the magnetic moments of the shell electrons. The observed intensity of a diffracted neutron beam from a crystal is made up additively from these two components. Since the intensities in general are proportional to the squares of the crystallographic structure factors, we can write q = magnetic interaction vector (see eq. (6)),F = crystallographic structure factor. Fnuc1 =, c b. e2xi(hxj 1 ' Fmagn = , e2xi(hxj = e,m pn Sj = = = 0.539 . 10--12 . Sj . f ( k )cm. charge and mass of the electron magnetic moment of the neutron (in p ~ ) spin quantum number of t h e atom j .fj(k)= corresponding magnetic form factor A E = scattering vector (unit vector) 2@ = scattering angle (0 = Bragg angle) Where t h e orbital moment cannot be neglected, eq. (4a) becomes with LJ a n d SJ, the projections of these q u a n t u m numbers on the vector J. jj(k) are now magnetic form factors, which describe the spatial distribution of the unpaired electrons. When the orbital moments are not negligible, separate form factorsfL and f S must be used for the orbital and spin moments; this is so e . g . for lanthanides. The magnetic scattering of neutrons is particularly interesting when the spins, in other words the individual magnetic moments, undergo a transition into an ordered state, i. e. when collective magnetism arises. Neutron diffraction is at present the only method by which the long-range order of the magnetic moments and their relative and absolute orientation can be determined. The neutron diffraction experiments provide information about: 1. the existence of collective magnetism; + kyi + fzj) 2. the transition temperature (Curie or Nee1 temperature, Tc or TN); + kyj + fzj) 3. the nature of the magnetism: paramagnetism, ferromagnetism, antiferromagnetism, or ferrimagnetism; 1 2 pj by TrammelIr31 and BIurnec41. According to these authors the magnetic scattering amplitude pj is given by i The structure factor in X-ray diffraction, for comparison, is 4. the size of the magnetic unit cell; 5. the distribution of the magnetic atoms (or ions) in the sublattice and their relative orientation; 6. the absolute orientation of the moments with respect to the crystal axes; where f p are the X-ray atomic scattering factors, which describe the spatial distribution of all the electrons around the atomic nuclei. The nuclear scattering amplitudes, which are independent of the scattering angle, are represented by bj; pj are the angle-dependent magnetic scattering amplitudes. The magnetic scattering of neutrons was discussed by Halpern and Johnson Q1, and later in an extended form [l] G . Will, Angew. Chem. 8Z, 307 (1969); Angew. Chem. internat. Edit. 8, 356 (1969). 121 0. Halgern and M . H. Johnson, Physic. Rev. 55, 898 (1939). Angew. Chem. internat. Edit. VoE. 8 (1969) I No. 12 7. the magnitude of the magnetic moments of the individual atoms or ions; 8. the magnitude and direction of the internal fields (by application of an external magnetic field); 9. the temperature dependence of the magnetization; 10. the local distribution of the magnetic moment density in the crystal, i. e . in the case of 3d electrons, the local distribution of the 3d electron density (covalency effects). ~- [3] G . T . Trammel/, Physic. Rev. 92, 1387 (1953). 141 M . Blume, Physic. Rev. 130,1670 (1963); 133, A 1366 (1964). 95 1 3. Examples of Applications 3.1. Antiferromagnetic Structure of MnO The method and the derivation of the results is best illustrated with the aid of examples. MnO was the first substance whose antiferromagnetic structure was established by neutron diffraction 151. This experiment provided evidence of the very existence of antiferromagnetic order. The same magnetic order as in MnO has also been found in NiO [61 and in EuTe 171.Though FeOC6l and C00[6~*1assume an order with the same spin-sign sequence as MnO, the moments have a different orientation in relation to the crystal axes (Table 1). The nuclear scattering lengths are b~~ = -3.7 f and bo = 5.77 f (1 f =: 1 fermi = 1 0 - 1 3 cm; cf. also [I]). When MnO powder is cooled in a cryostat, new reflections that point to magnetic order of the spins are observed below TN = 122°K. These new reflections can be indexed as h/2, k / 2 , 112 where all the indices h, k , I are odd. Integer Miller indices are obtained by multiplication by 2; this means that to describe the magnetic arrangement of the spins in the crystal, the unit cell dimensions must be doubled in all three directions. The dimensions of the magnetic unit cell are thus double the dimensions of the chemical unit cell (see Fig. 1): amagn = 2 . anucl bmagn = 2 - bnucl Cmagn = 2 . c n u c ~ Table 1. Magnetic properties of 3d metal oxides and Eu-chalcogenides. I MnO I FeO TN ( "K) Symmetry below 122 rhombohedral a < 60" Direction of magnetic moment (111) 1 COO 1 NiO 198 rhombohedral a > 60" 11111 I EuO I EuS 29 1 tetragonal cla < 1 1ii71 I EuSe 523 rhombohedral a < 60" (111) I EuTe Magnetic order T c resp. TN ( OK) 10 Ip73111 [a] According to G . Busch, P. Junod, R . G . Morris, and J . Muheim, Helv. physica Acta 37, 637 (1964). Considerable uncertainty still exists concerning the magnetic behavior and even the transition temperatures. Thus Busch et al. found a second transition at 3.8 OK, which could be confirmed by recent neutron diffraction experiments. Magnetic order manifests itself in the appearance of coherent scattering. Collective magnetism can therefore be recognized immediately if two neutron diffraction diagrams are recorded, one above and one below the Curie or Nee1 temperature, the difference diagram, representing the magnetic scattering, then being found by subtraction. Figure 1 shows a recent neutron diffraction diagram of MnO recorded by the author, and Figure 2 shows the antiferromagnetic structure derived from this diagram. MnO crystallizes in a face-centered cubic cell with the NaCl structure. The space group extinction rules for the nuclear scattering are therefore bo 5.77 = 2.07 f h,k,l = odd: F = b m - b o = -3.7 - 5.77 = -9.41 f h,k,l = even: F = b M n + = -3.7+ [5] C. G. Shull and J . S. S m a r t , Physic. Rev. 76, 1256 (1949). 161 C. G . ShuII, W. A. Strausser, and E. 0. Wollan, Physic. Rev. 83, 333 (1951). 171 G. Will, S. J . Pickart, H . A. Alperin, and R. Nathans, J. Physics Chem. Solids 24, 1679 (1963). 181 B. van Laar, Physic. Rev. 138, A 584 (1965); B. van Laor, J . Schweizer, and R . Lemaire, ibid. 141, 538 (1966). 20 - 30 281") 40 50 Fig. 1. Neutron-diffraction diagram of antiferrornagnetically ordered MnO recorded at 4.2 OK. Owing to the doubling of the unit cell in the magnetically ordered state, all the reflections of the magnetic scattering have odd indices; all the nuclear scattering reflections have even indices. The reflections (222) and (622) (= h, k , I odd x 2) are strong, and the reflections (400)and (440) (/?, k, I even x 2) are weak, corresponding to the intensity conditions for a face-centered cubic lattice (NaCl structure) and considering the negative sign of the nuclear scattering length of manganese. The magnetic phase transition is associated with a crystallographic phase transition. Below 122OK, in the antiferromagnetic range, MnO crystallizes with a rhombohedra1 unit cell, though the angle a-differs only very slightly from 90". At 4.2'K, anuc1 = b = c = 4.415 A and a = 90.6'. The magnetic order can now be deduced from the size of the magnetic unit cell together with the observed extinction rules for the magnetic reflections (MnO: h, k , 1 even not observed). For MnO, this gives an antiparallel orientation of the spins along the Since only the relative three crystal axes: orientation is expressed, the situation can be described by a sign sequence: +-+-+-. . .. This gives the antiferromagnetic structure as shown in Figure 2. It consists of ferromagnetic (111) planes in which all the spins are parallel, with an antiferromagnetic sequence of such (111) planes normal to the plane in the [111] direction. t-lt4T-l. The absolute orientation and the magnitude of the magnetic moments can be determined from the intensities of the individual reflections. The quantity q 2 from eq. (2) is used for this purpose. q is known as the magnetic interaction vector, and represents a relation between the direction of the Angew. Chem. internat. Edit. J Vol. 8 (1969) J No. 12 2 t absolute scale is rather easy in neutron diffraction studies, since the always-present nuclear scattering reflections can be used as an internal standard. 0 02' @ Mn2' 3.2. Investigations on Europium Chalcogenides +Y a""d > c 1173121 hag" Fig. 2. Antiferromagnetic structure MnO. The spins lie in the (111) planes, and all the spins are parallel within the same (1 11) plane. The same magnetic structure is also found in NiO and EuTe. magnetic moments, described by a unit vector x , and the orientation of the reflecting crystal plane h k 1, described by the scattering vector E (unit vector), which is normal to the plane hkl (cf. Fig. 3). q = E ( E x)-x (6) Multiplication gives q 2 = 1 - - (E . x)2 = sin*cc (7) where cc is the angle between E and x. Reflection /ted E Maonetization Scattering vector vector The special importance of the chalcogenides EuO, EuS, EuSe and EuTe is that they allow the direct study of the magnetic exchange forces as a function of the interionic distance in a series of simple compounds. They are of general interest because they represent the first ferromagnetic insulators that have been found which are optically transparent in the visible part of the spectrum. The compounds crystallize in the simple, parameter-free NaCl structure, which is particularly convenient for theoretical considerations. The magnetic properties of these compounds are shown in Table 1, and Figure 4 shows the exchange interactions as a function of the lattice constants. Since the Eu-Eu distances are directly reflected in the lattice constants, it is possible to combine the lattice constants and the magnetic behavior and estimate from them the exchange interactions. The strong ferromagnetic interaction J1 between the nearest-neighbor Eu ions in EuO and EuS is responsible for the ferromagnetic behavior of both compounds. In EuTe, the antiferromagnetic interaction 52 between next-nearest neighbors is distinctly greater than J1; EuTe therefore behaves antiferrornagnetically. Our neutron diffraction studies [7J have shown an antiferromagnetic order of the second kind in EuTe, which means that the compound has the same spin configurations as MnO (Fig. 2). beam rn Fig. 3. Vector relation between incident neutron beam. diffracted beam, orientation of the reflecting plane, and the magnetizationdirection. The scattering intensity is proportional to sin%, i.c. the intensity has a maximum when the magnetic moments lie in the reflecting plane hkl. Since the orientation of the various crystallites in a powder is random, limits are placed on the determination of the angle a from powder measurements. Thus i t can be shown = constant = 2/3, and that for cubic crystal symmetry, <q2> is thus independent of the orientation. In a cubic crystal therefore, the orientation of the spins in relation to the crystal axes cannot be determined from powder measurements. In crystals with rhombohedral, tetragonal, or hexagonal symmetry, the orientation of the spins can be given in relation to the unique axis of the crystal system, i.e. in relation to [111] in rhombohedra1 crystals and in relation to the c axis in tetragonal or hexagonal crystals. For MnO, and also for EuTe, the measured intensity ratios show that the magnetic moments lie in the (111) planes as shown in Figure 2. Within the (111) plane the orientation cannot be determined from powder data. The magnitude of the magnetic moment at the individual ions can be calculated from the absolute intensities using eq. (4a) or (4b). The determination of the Angew. Chem. inrernaf. Edit. / Vol. 8 (1969) / No. 12 4 1 e -10 5.0 5.5 6.0 Lattice constant Fig. 4. Plot of the magnetic interactions J I and genides as a function of the lattice constants. J2 181- 65 in europium chalco- The results for the magnetic properties of EuSe are contradictory. The magnetic structure may be influenced by small quantities of impurities or Eu3+ ions. A neutron diffraction study by Pickart and At- 953 showed that the sample used by these authors had a complicated antiferromagnetic structure, but that this structure could be changed into a ferromagnetic order by even a small external magnetic field of about 1700 Oe. EuSe was therefore not taken jnto account for the dependence of the exchange forces Jl and 52 in Figure 4. perinL9l 3.2.1. S u b l a t t i c e M a g n e t i z a t i o n a n d E x c h a n g e Jnteractions I n a face-centered cubic lattice, each ion has twelve nearest neighbors (nn) at a distance 1/2 /2 a0 along the face diagonals [110] and six next-nearest neighbors (nnn) at a distance a0 along the axes [loo]. In the order of the second kind, as the antiferromagnetic order observed in MnO is called, each Mn2+ ion has six parallel and six antiparallel nearest neighbors and six antiparallel next-nearest neighbors (Table 2). Table 2. Neighborhood relations in face-centered cubic lattices. Neighbois I ferromagnetic 1 antiferromagnetic 1st kind 1 2nd kind nn nnn When the magnetic order and the transition temperatures have been determined they can be used together with Weiss's molecular field theory to derive the Heisenberg exchange interactions. Heisenberg's view of ferromagnetism is based o n the idea that the exchange interactions between two atoms i and j are responsible for the orientation of the magnetic moments. The magnetic exchange energy is described by a Hamiltonian operator 8. and Sj are spin operators Ji,j is the exchange integral between the atoms i and j. Since the theory of exchange interactions is based on ad-hoc assumptions and the exchange integrals themselves cannot be calculated J must be determined experimentally if one wishes to understand the magnetic behavior of the substances. However, other interactions such as magnetic dipole-dipole coupling or the effects of anisotropy energies must generally be taken into account in addition to the exchange interactions. Measurements o n simple structures such as the parameter-free structures of the NaCl type are therefore of great interest for the theory of magnetism. The series MnO, FeO, COO, NiO and EuO, EuS, EuSe, EuTe have been extensively investigated; the oxides of the 3d transition metals are all antiferromagnetic, while a transition from ferromagnetism to antiferromagnetism is observed in theeuropiumchalcogenides (cf. Table 1). The exchange parameters J can be derived from the experimental data by means of relations from Weiss's molecular field theory 1101. The following relations are valid: T c is the ferromagnetic Curie temperature; for antiferromagnetic crystals, 0 is the paramagnetic or asymptotic Curie-Weiss temperature, which follows from the Curieand Weiss law. For EuTe it was found that 0 = -7.5'K, this together with the experimentally found Nee1 point T N= ~ 7.8OKr71 gives eq. 9a and 9b (order o f the second kind): Jz = -(0.12 i 0.01) O K ; (0.025 Jj .I 0.025)"K (Energies are obtained by multiplication by k = 1.38~10-16 erg "K-1). EuTe thus has a negative nnn exchange interaction, which is responsible for the antiferromagnetic orientation o f the spins, and which is about five times as great as the positive direct nn exchange interaction. Important information about the sublattice magnetization is obtained from the temperature behavior of the magnetic scattering. Figure 5 a shows the temperature dependence of the magnetic scattering for the (111) reflection of EuTe. I t is found from this that TN = 7.8 "K. For comparison with the temperature dependence of magnetization as given by Brillouin, the observed intensity Irel is normalized to I/Io and plotted against the normalized temperatures T/TN. These normalized values are shown in Figure 5b; i t can be seen that the experimental values do not agree with the theoretical Brillouin curve for a system having spin 7/2. Both Mnz+ (3d5) in MnO and Euzc (4f7) in EuTe are in pure S states. There are therefore no orbital moment components to be taken into account. The dipole interactions are also negligibly small in these crystals, and the magnetic anisotropy energy is large only within the (111) planes while it is small perpendicular to these planes, i.e. in the direction of the antiferromagnetic coupling. The relations are therefore simple and the deviation of the experimental points from the Brillouin curve is surprising a t first. a1 Si 0 [A iLm 0.2 06 01 TIT, 0.8 1.0 --j Fig. 5. Temperature dependence of the (strongest) magnetic reflection (1 11) in EuTe. (a) Dependence of the intensity on temperature: The ( 1 1 1 ) reflection disappears at TN = 7.8"K; EuTe is in a paramagnetic state above this temperature. 191 S. J . Pickart and H . A . Alperin, J. Physics Chem. Solids 29, 414 (1968). 1101 J . S. Smart, Physic. Rev. 86, 968 (1952). 954 (b) Intensity and temperature normalized to 10 and TN ' I = f(T) thus becomes universal, and should follow the Brillouin function for spin S = 112 (continuous curve). The observed dependence, on the other hand, corresponds to a curve (broken) that was calculated by insertion of a biquadratic term of about 1 % into the Hamiltonian exchange function. Angew. Chem. internal. Edit. 1 Vol. 8 (1969) J No. I 2 To explain the discrepancy, Rodbell, Jacobs, 0wen, and HarrisrI'l introduced a biquadratic contribution into the normally linear exchange interaction. If this biquadratic term is taken into account in the calculation of the Brillouin function, a very satisfactory agreement with the experimental point (broken curve in Fig. 5b) is obtained. Similar deviations of the experimental points from the Brillouin curve were found for MnO and NiO, and a biquadratic exchange term could also be detected for these crystals . The biquadratic component amounts to about 1 % of J, and is therefore very small(inEuTe,.j was found to be N 0.001 OK). It is only rarely of such importance as in MnO and EuTe, and is generally overshadowed by the much larger exchange contributions of the dipole interaction and the magnetic anisotropy. It would therefore be wrong to try to explain every deviation from a Brillouin function by a biquadratic component of the exchange interaction. 3.3. Ferrirnagnecic Structure of Ferrites Reference was made in the first part of this article to the important role of neutron diffraction in the investigation of ferrites having the general composition [X2+(Y3+)2(02-)4][I]. Since X and Y are normally adjacent elements in the periodic system they can be difficult or even impossible (e. g. in the case of MnFe204) to distinguish by X-rays. The neutron scattering powers of elements of adjacent atomic numbers on the other hand are generally quite distinct; neutron diffraction thus permits a definite identification of the ions. X and Y in the ferrites are usually 3d transition elements. The analysis of the magnetic scattering of neutrons below the ordering temperature TN also gives the ionization states of the ions and their distribution over the lattice sites. A classical example is the investigation of magnetite Fe304 = [Fe2+(Fe3+)2(02->4]. Fez+ and Fe3+ differ in their spin quantum numbers, S=2 and S=5/2 respectively, and consequently also have different magnetic scattering powers, p = 1.09 and 1.36~10-12cm respectively. Neutron scattering at room temperature 1121 gave an inverse spinel structure for magnetite with Fe3+ in the tetrahedral (or A) sites while the octahedral (or B) sites are uniformly occupied by Fe2+ and Fe3+. The neutron diffraction data also show that the moments of the ions in the A and B sites are antiparaIIe1 to one another, so that the resultant magnetic moment corresponds to the moment of one Fez+ ion per Fe304 formula unit. Fe304 is an example of ferrimagnetism postulated by N&eZ[131. The magnetic structure is shown in Figure 6; the magnetic unit cell has the same dimensions as the chemical unit cell. 1111 D. S. Rodbell, I. S . Jacobs, J. Owen, and E . A . Harris, Physic. Rev. Letters I 1 , 10 (1963). 1121 C. G. Shull, E. 0. Wollan, and W. C. Koehler, Physic. Rev. 84,912 (1951). [I31 L. NPel, Ann. Physik 3, 137 (1948) Angew. Chem. internat. Edit. Vol. 8 (1969) / N o . 12 A-sites ltetrahedral Fe3'l B-sites loctahedral Fe3*/Fe2'i 1173161 Fig. 6. Magnetic structure of magnetite at room temperature [Fe2+(Fe3+)2(OZ-)4].Magnetite crystallizes with the spinel structure. One quarter of the unit cell is shown. Magnetite exhibits a second magnetic phase transition, which was elucidated by an elegant experiment. Below 110-120 "K (the exact temperature depends on impurities in the crystals) the crystals exhibit a sudden change in electric conductivity and in magnetization. To explain this, Verwey et al. "41 postulated a crystallographic phase transition from the cubic spinel structure to an orthorhombic structure, combined with ordering of the Fez+/Fe3+ ions on the octahedral sites. Hunzilton[*sJ was able to confirm this hypothesis by neutron diffraction with a synthetic Fe304 single crystal. In this crystal, ordering of the iron ions on the octahedral sites (now in an orthorhombic unit cell) takes place at 119°K. The Fe3f ions form simple chains parallel to the a axis, while the Fez+ ions are arranged perpendicular to these in chains parallel to the 6 axis. The orthorhombic u and 6 axes correspond to the cubic [ l l O ] face diagonals (Fig. 7). All the magnetic moments in the structure below 119 "K are parallel or antiparallel to the orthorhombic c (= cubic) axis. The experimental detection of this order is based Fig. 7. Distribution of Fez+ ions (large spheres) and Fe3+ ions (small spheres) in magnetite on the octahedral sites below the second magnetic transition a t 119 OK. The ions, which are randomly distributed above this temperature (Fig. 6), now form mutually perpendicular ordered chains. 1141 E. J . W. Yerwej, P. W. Haayman, and 1.Ronegn, J. chern. Physics 15, 181 (1947). [15l W. Hamilton, Physic. Rev. 110, 1050 (1958). 955 on the appearance of the (002) reflection on neutron diffraction; this reflection is proportional to the difference in the scattering powers p(Fe3+)-p(Fe2+), and is forbidden for the cubic random distribution. 3.4. Magnetic Behavior of Solid Solutions in the Ternary System Fe203-Cr203-Al203 The sesquioxides u-FezO3, CrzO3, TizO3, VzO3 and A1203 all crystallize hexagonally in the corundum structure, but only the crystals of cc-FezO3 and CrzO3 exhibit magnetic long-range order of the spins; no long-range order of the magnetic moments could be detected by neutron diffraction in Ti203 and V2O3, despite the observed anomalies in the temperature dependence of the magnetic susceptibility. the sign sequence (+-+-). (When Fez03 is cooled below about -23 OC, the spins flip from the (111) plane into the [111] direction. This phase transition has not however been found in any solid solutions; if it does exist it does so only in a very narrow range around pure FezO3.) Since the oxides discussed here form solid solutions, information on the magnetic interactions, and hence on the conditions for the various magnetic structures, should be obtainable from the magnetic properties of the solid solutions. Thus Cox et al. found that in the system Fe203-V203, the magnetic structure of a-FezO3 persists up to a VzO3 content of 60 %. A particularly interesting phase in the system Fe203-Ti203 is a solid solution having the the composition FeTiO3, in which there is a completely ordered distribution of the Fez+ and Ti4+ ions over the A and B sitesr191. P cl bl Fig. 8. Crystalline and magnetic structures of some sesquioxides. a) Corundum structure - rhombohedral cell. Large circles = metal ions, small circles = oxygen ions. b) Corundum structure ions, are shown. - hexagonal representation. Only the metal c) Magnetic structure of a-FezO, at 25 “ C . d) Magnetic structure of Cr20,. dl el FeTi03 has an antiferromagnetic structure, in which ferromagnetic (111) planes form an antiparallel sequence in the [1111 direction. These ferromagnetic planes are separated by layers of non-magnetic Ti4+ ions. The sign sequence can be given purely formally as (+ 00); the spins themselves are oriented parallel and antiparalle1 to [lll]. ~ e) Magnetic structure of FeTiO,. Open circles - Fez+, shaded circles = Ti4+. a-FezO3 and CrzO3 have the same crystal structure, but quite different spin structures r16,17J (Fig. 8). In Fe203, the spins lie in the hexagonal basal plane at 25°C; the spins are parallel within a plane, and the planes are arranged in antiparallel sequence along the hexagonal c-axis. (In a rhombohedral description of the unit cell, we have ferromagnetic (111) planes in an antiferromagnetic sequence along [111I.) The structures are described by the atomic positions Al, A2, B1, and B2. The spins in these positions in a-FezO3 then have the sign sequence (+ + - -). In Cr2O3, on the other hand the spins are directed parallel to rhombohedral [llll; an antiferromagnetic ~ ., arrangement exists within the individual (111) Planes. In the rhombohedral [lll] direction, the spins have ____ [16] C. G. ShuN, W. A . Strausser, and E . 0.WuNan, Physic. Rev. 83, 333 (1951). 1171 B. N . Brockhouse, J. chem. Physics 21, 961 956 Complicated magnetic behavior is expected, and observed 1201, in the solid solutions of the system Fe203-Cr203, since here we have interaction of two magnetic structures with opposite spin directions and different orders. A neutron diffraction study showed that the magnetic structure from 100 to 35 mole- % of Fez03 is that of a-Fe203, while at 10 to 0 mole-% of Fez03 it is that of Cr2O3. The transition temperature decreases with increasing Cr content: Fe203:T~ = 965 OK; Fez03-Crz03 (40:60 mole- %): TN = 400 OK. Between 35 and 10 mole- % of Fe2O3, there is a helical structure described as an “umbrella structure”, i. e. an arrangement in which the spins lie on cones, adjacent spins being turned through an angle u that is different (1953). [18] D. E . cox, W. J . Takei, R . C. Miller, and G. Shirane, J. Physics Chem. Solids 23, 863 (1962). [19] G. Shirane, S. J . Pickart, R . Nathans, and Y . Ishikawa, J. Physics Chem. Solids 10,35 (1959). [20] D. E . Cox, W. J . Takei, and G. Shirane, J. Physics Chem. Solids 24, 405 (1963). Angew. Chem. infernat. Edit. / Vof. 8 (19691 / No. 12 by 180" in relation to one another. Both M. and the apex angle of the cone vary with the Cr content. The orientation of the axis of the cone in the crystal also changes. The axis of the cone is initially (above 35 % Fe203) perpendicular to the c axis, i.e. parallel to the collinear moments in Fe203, the (half) apex angle of the cone being 19 ". The apex angle increases to I1 at 20 % FezO3, and then decreases again. The orientation of the cone switches into the direction of the c axis at about 15 % FezO3; it then corresponds to the collinear moments in CrzO3. The investigations were recently carried on by Scharenberg [211 and extended to include the presence of non-magnetic aluminum ions. Dilution of the magnetic lattice in this way yields valuable information concerning the range of the exchange forces and the stability of the magnetic structures. The results of these measurements can be seen in the magnetic phase diagram of Fez03-Crz03-Alz03 (Fig. 9), from which the ranges of the various structure types are immediately recognizable. all doubly occupied by electrons. Only the higher antibonding orbitals are singly occupied, and are thus responsible for the magnetic behavior. We follow the procedure used by Hubbard and Marshallr221 and consider first a simple antiferromagnetic chain of p and d orbitals as shown in Figure 10. P" L" d" P d P' L M L' em + M (' Ypin tt Fig. 10. Schematic diagram of the orbitals of a n antiferromagnetic chain and the overlap of the form factors of 3d electrons. In the case of antiferromagnetic orientation of the spins, interference extinction occurs in the neutron diffraction in the region of the ligands. L = ligand ion, M - metal ion. Owing to the antiferromagnetic order, the spins, and hence also the spin densities and the form factors, have opposite signs in M and M". The magnetically active orbital of M can no longer be described simply by d orbitals, but we have to take into account the admixture of p orbitals (covalency). A are the admixture parameters and N is a normalization factor. S, is the overlap integral between p and d l/N2 = 1 -4 A . S o + 2 A2 (12) orbitals. This can be used to find the moment density D(r) around M; if overlap between p and p' is neglected, we obtain for D(r) Fig. 9. Magnetic phase diagram of the ternary system F e 2 0 ~ - C r ~ 0 ~ - A I 2 0In~ the . regions with double shading, the crystals have t w o magnetic transitions: paramagnetic state - T N ~(magnetic collinear structure) - T N ~(magnetic spiral structure). 3.5. Determination of Covalent Bond Components in Antiferromagnetic Salts from Neutron Diffraction Data In most antiferromagnetic salts of the 3d transition metals, e.g. LaCr03 or KMnF3, the 3d metal ion is surrounded octahedrally by six ligands. The orbitals of the ligands are of s or p character, and give bonding and antibonding orbitals with the five d orbitals of the central ion. Only the antibonding orbitals are of interest for the consideration of the magnetic properties. The bonding orbitals have such low energy levels in the complexes discussed here that these levels are The first term containing d2(r) is confined to the magnetic ion M. The second term describes the overlap density between p and d orbitals, and is also confined to the immediate neighborhood of M. The third term, on the other hand, describes a density distribution, which lies exclusively at the position of the ligands; the distance from L to the neighboring metal ion M" is the same as the distance from M. The analogous density due to the ion M" at the position L is roughly equal to the contribution due to M, but is of opposite sign in antiferromagnetic substances. This means that &p*(r) and Azp'z(r) cancel out with the analogous contributions from M and M". It is 1221 3. Hubbard and W. Marshall, Proc. physic. S O C . 86, 561 [21] W . Scharenberg, Dissertation, Universitat Bonn 1968. Angew. Chem. internat. Edit. 1 Vol. 8 (1969) 1 No. 12 (1 965). 957 clear therefore that in a neutron diffraction experiment on an antiferromagnetically ordered crystal, only the contributions of the first two terms in eq. (13) are observable in the Bragg maximum. Thus whereas the integration of eq. (13) gives 1, integration of eq. (14) merely gives Calculation of the magnetic moments Fobs (e.g. according to eq. (4)) from the measured diffraction intensity gives a value that is smaller by 2A2 than the true moment PO. theretore laborious and require a number of precautions to eliminate possible sources of error such as, for example, ‘942 contamination” of the neutron beam (cf. q. We have carried out neutron diffraction experiments of this type on LaCrO3, LaFe03, and LaMn03 as well as on a series of fluorites having the composition KMF3 (M = 3d transition elements), and have actually been able to detect this effect in LaCrOJ and LaFe03 [231. Figure I1 shows the neutron diffraction diagrams of LaFe03 and LaCr03. On application to the three-dimensional crystal structure, considerations analogous to those used for equations (11) to (15) lead to the following relations (A = covalency coefficient) [22J. It is therefore possible, in principle at least, to determine the covalent part in antiferromagnetic complexes of this type from neutron diffraction data. The effects are naturally very small, and the measurements are The evaluation of our measurements on powder specimens is concentrated mainly on the first magnetic reflection (111) at small scattering angles, where reliable theoretical assumptions regarding the form factor can be made. This means that the observed deviations in the values of the form factor can be entirely attributed to the covalency of the bond, and not e.g. to a possible asymmetric charge distribution. The measurements were hampered by a very small coherent nuclear scattering contribution to the magnetic scattering. This nuclear scattering component is the result of the distortion of the perovskite-like crystal structure from the ideal (cubic) perovskite structure; it must be determined separately by a crystal structure analysis 1241. However, this contribution can only increase the effect and cannot decrease it. LaCrO3 and LaFe03 crystallize in a perovskite-like structure, in which each cation is octahedrally surrounded by antiparallel oriented neighbors. The magnetic structure of LaMn03 is different: each Mn3+ ion has two parallel and four antiparallel neighbors. The unfavorable ratio 2 : 4 of parallel to antiparallel neighbors decreases the effect; we feel, that for this reason, among others, we were unable to detect the covalency parameters in LaMn03. Table 3 also shows the results of measurements on NiO 1251, MnO [261, and MnF2 1271. Results of nuclear magnetic resonance measurements 1281 are given for comparison. The values for Fe3+ and Mn2+ both of which have the 3d5 configuration are particularly interesting. It is I231 R. Nathans, G. Will, and D . E . Cox, Proc. int. Conf. Magnetism, Nottingham 1964, p. 327. [24] G. Will and D. E . Cox, Acta crystallogr., in press. [25] H . A . Alperin, Physic. Rev. Letters 6, 55 L 10 20 28 r1+ 30 LO Fig. 11. Neutron diffraction diagram of a) LaFeOz and b) LaCrO,, recorded at 4.2 “K in the antiferromagnetic state. 958 (1961). [26] G. Will, D . E. Cox, and R. Nathans, unpublished results. [27] R . Nathans, H . A . Alperin, S . J . Pickart, and P. J . Brown, J . appl. Physics 34, 1182 (1963). [28] R . G. Shulman and S. Surano, Physic. Rev. 130, 506 (1963); R. G. Shulman and K . Knox, Physic. Rev. Letters 4 , 603 (1960), T. P . P . Hall, W. Hayes, R . W . H . Stevenson, and J . Wilkens; J . chem. Physics 38,1977 (1963). Angew. Chem. internat. Edit. / Vol. 8 (1969) 1 No. 12 Table 3. Covalency parameters in some antiferromagnetic salts of 3d elements. I 1 From N M R measurements 1 Ion Compound __ Ni2+ cr3+ Fe3+ Mn2+ KNiFs K2NaCrF6 Fe3+ in KM~FJ KMnF, Covalency coefficients ( %) A& + AH = 4.32 n = 4.1 A2 A$- A$ = 3.3 A: = 0.76 A&-A$ = 0.18 A: - 0.52 Mn3i From neutron diffraction measurements NiO LaCrOa LaFeOs A& -A i : A; -1- = 6.0 A$ = 4.6 2A$ + A: A& i- 2 A k A; ~ MnF2 MnO LaMnO3 n o effect found 7 = 10.0 3.3 5.5 possible to determine A: and A: (in %) individually by a combination of N M R and neutron diffraction data Fe3 +: A& = Mn2+ in MnF2(MnO): A& = 5.4 1.2 (1.8) A& = 2.1 A:, = 1.0 (1.6) 3.6. Determination of the Local 3d Spin Density Distribution in Crystal~[~9J The magnetic form factor f c a n be deduced from the measured magnetic scattering with the aid of eq. (4). It is then possible by Fourier transformation of the diffraction data to calculate the spatial distribution of the magnetic moments in the crystal. The result is a diagram of the density distribution of the magnetic moments around the centers of the atoms similar to the electron density distribution obtained in X-ray structure analyses. If we confine our considerations to the 3d elements, where the crystal fields are strong compared with the spin-orbital coupling, so that the orbital moments are generally suppressed, then the magnetic moment density from the neutron diffraction data directly describes the spin density, and hence the density of the unpaired (outer) electrons, which are responsible for the chemical bonding. Since the outer electrons are on average farther from the nucleus than the mean total electron density that determines the X-ray diffraction, the magnetic form factor, which is a shape factor in the present example of the 3d electrons, falls off much more rapidly than the X-ray form factor. This is illustrated in Figure 12 for Mn2+ (the magnetic form factor of Gd3+ is also shown for comparison). In the lanthanides the unpaired electrons (4f electrons) are on average denser at the nucleus; the fall-off of the form factor is therefore rather less. Mn2+ and Gd3+ are in an S state with electronic configurations 3d5 and 4f7 respectively, and the electron distribution is spherically symmetrical. Whereas the electron distribution around the nucleus can be taken as spherically symmetrical on the whole in X-ray structure analysis, the distribution of the outer bonding electrons, which are “seen” by the neutrons, is generally not spherically symmetrical. Consequently, the “form factor curves” for neutron diffraction are not smooth curves; the experimental points are scattered more or less widely about an average curve. Figure 1 3 shows form factor values for 0. 0 -t 0 -0 0.2 0.6 0.4 _sine 08 1.0 1.2 ,p] _ j h Fig. 13. Experimental magnetic form factor values (circles) found for elementary iron with polarized neutrons, compared with theoretical curves for various electronic configurations. -01’ I 0 02 OL 06 08 10 12 14 h Fig. 12. Form factor curves of the 3d electrons in Mnzf and of the 4f electrons in Gd3+ for the magnetic scattering of neutrons [the farm factor curve of MnZ+(with all electrons) for the diffraction of X rays is also given for comparison]. [29] For a review see e.g. G. WiN, 2. angew. Physik 24, 260 (1 968). Angew. Chem. internat. Edit. J Vol. 8 (1969) J No. 12 elementary iron in the ferromagnetic state measured with polarized neutrons, together with the theoretical spherically symmetrical electronic configurations for comparison. The deviations of the experimental points from the spherical symmetry curves are real (e.g. outside the error limits), and are a direct measure of the asymmetric distribution of the 3d electrons (the size of the circles corresponds approximately to the experimental accuracy). 959 T h e resolution in t h e density d i a g r a m t o depend on t h e number of reflections a n d is determined b y t h e sin@/h range. A o f 1 8, corresponds roughly to sin@/?, 0.4 w - 1 (1 A 0.66 h/2 s i n e ) ; t o obtain a - is found measured, resolution = 0.3 t o resolution of 0.25 A, therefore, measurement up to sin@/), = 1.2 8,-1 is necessary. The deviations of t h e electron density distribution from spherical symmetry are particularly evident in t h e region around 0.8 A-1; on t h e o t h e r hand, t h e magnetic form factors are very small between sin@/h= 0.8 and 1.2 K-1 so’ t h a t t h e determination of t h e 3d electron distribution necessitates t h e accurate measurement of very small quantities. I t is interesting t o n o t e t h e c h a n g e in t h e sign of t h e form factor curves from +f t o - f a t a b o u t sin@/h = 0.8 8,-1 as a result of t h e limited spread of t h e 3 d electrons (the maximum is situated a b o u t 0.35 t o 0.40 8, from t h e center of t h e nucleus). The usual technique of diffraction of unpolarized neutrons is generally inadequate for t h e reliable determination of t h e form factors and hence t h e 3d electron densities. Much more a c c u r a t e measurements are possible with polarized neutrons. The neutron has a spin of 1/2, and can occur in the energetically different spin states + 1/2 and -1’2. Both spin states normally occur with equal probability in a neutron beam (unpolarized neutrons). With a suitable experimental arrangement (Fig. 14), however, it is possible to obtain a neutron beam that contains only neutrons in a single spin state (polarized neutrons). A polarized neutron beam of this type is obtained e . g . by Bragg reflection from a “polarization monochromator” (nowadays nearly always a single crystal having the composition Coo.92Feo.08 which is magnetized in an external field). Approximately 99 % of the neutrons in the resulting beam are in the same spin state. The direction of the spin vector is described by a unit vector A, which is referred to the external magnetic field. The neutron beam can be converted from one spin state into the other by superposition of a low frequency field on the polarized beam (“flipper”). \ kb. H=3kOe I H = 18 kOe H = L O Oe T ‘49 jp7311LI Fig. 14. Schematic representation of the experimental arrangement for measurements with polarized neutrons. A: Polarization monochromator (Coo.q*Feo.os); B: “flipper”; C: test crystal; D: counter. The conditions for the polarization of the neutrons are obtained by insertion of eq. (3a) and (3b) in eq. (2). The structure factor F can then be expressed in the general form 960 The vectors + A and -A are present in equal proportions in a beam of unpolarized neutrons; the scattered intensity is proportional to F* and therefore to b2 + p2; the cross term (qA) thus becomes zero [eq. 21. For polarized neutrons, o n the other hand, we have e . g . + A = 1 and -A = 0. Eq. (16) now leads to a phase dependence of the nuclear scattering on the magnetic scattering. The resultant intensity is proportional to (b + p)2: polarized neutrons: I unpolarized neutrons: I - (b + p)’ - bz+ p2 The requirement for the polarization monochromator is therefore simply b = p. In this case we have for an unpolarized neutron beam I(+x) = (b p)2 = 2b2 and I(-i) = (b- p)2 = 0. + To detect very small scattering contributions p, therefore, it would be necessary with unpolarized neutrons to measure a term p2 whose square is small and a term b2 whose square is large, whereas for polarized neutrons there is a linear relation between p and b. Another advantage of polarized neutrons lies in the measuring technique itself. For the accurate determination of p one need only determine accurately the ratio p: b; the method is therefore o n a relative scale, and is thus independent of systematic errors (such as the determination of an absolute scale or of the temperature factor, which is known to cause a decrease in the scattering intensity with increasing scattering angle, similar to the decrease in the form factor itself.) In measurements with polarized neutrons, one simply determines the polarization ratio P by recording first I+ with neutrons having A = +1, and then I - with neutrons having A = -1. This leads to very accurate values of p. and hence off: The limits of the method can also be found very readily from eq. (17). To obtain a difference between If and I - , coherent overlap of neutron scattering and magnetic scattering must occur in the reflections. Investigations so far have been concentrated on ferromagnetic crystals, where this condition is always satisfied. This is not generally the case in antiferromagnetic crystals, and measurement with polarized neutrons is fundamentally impossible for e . g . MnO or NiO, where the neutron scattering reflections and the magnetic reflections are rigorously separated because the magnetic unit cell is twice as large as the chemical unit cell, and the crystallographic extinction rules separate the two sets of reflections exactly. Detailed investigations have been carried o u t on the ferromagnetic elements iron 1301, nickel 1311, a n d hexagonal c o b a l t 1327, as well as on Pd-0.01 Fe [331, Fe3Al1341, and some Fe-Rh alloys 1351. A Fourier synthesis with t h e experimental data as amplitudes gives t h e electron density distribution of t h e unpaired electrons. If only t h e difference values of t h e experimental points from t h e spherically symmetrical average curve are used as amplitudes, the deviation of the electron distribution [30] C. G . Shull and Y. Yamada, J. physic. SOC.Japan, Suppl. B-I11 17, 1 (1962); C. G . Shull and H . A . Mook, Physic. Rev. Letters 16, 184 (7966). 1311 H . A . Mook and C.G . Shu//,J. appl. Physics 37,1034(1966). H. A . Moak, Physic. Rev. 148, 495 (1966). [32] R . M . Moon, Physic. Rev. 136, A 195 (1964). [33] W. C. Philips, Physic. Rev. 138, A 1649 (1965). 1341 S. J . Pickart and R. Nafhans, Physic. Rev. 123, 1163 (1961). [35J G . Shirane, R . Nathans, and C . W.Chen, Physic. Rev. 134, A 1547 (1964). Angew. Chein. internat. Edit. / Vol. 8 (1969)1 No. 12 from spherical symmetry is obtained directly. Figure 1 5 shows the result of such a difference Fourier synthesis using the values for iron from Figure 13. An interesting feature of this spin density distribution is the extended negative areas, which represent a density distribution of spins of opposite sign, i.e. antiferromagnetic orientation. The negative polarization is assigned to the 4s conduction electrons that uniformly fill the entire crystal with the opposite spin direction. distribution for spherical symmetry is 40% eg, 60% The electron distribution obtained by analysis of the neutron diffraction data are: 3dspin - 0 . 6 5 6 ~ ~ . 3dorblta1 = +0.055 VB; for 4s conduction electrons, one finds -0.105 p ~ . tZg). Table 4. Character of the electron distribution in some 3d elements and 3d-4d alloys. 3d configuration Composition eg (%) Fe-nucleus a0 - 2 t2g ( %) Theoretical values for spherical symmetry (cubic) 40 60 Fe (body-centered cubic) Ni (face-centered cubic) Co (doped with Fe) (body-centered cubic) V (body-centered cubic) 53 19 21 47 81 79 19 81 47 53 48 52 28 60 48 40 52 Fen.s~Rho.48 (ferromagnetic) Fen. sRho. 5 (antiferromagnetic) Fen.n13Pdn.987 Fe,AI : FeI FeII 72 Theoretical values for spherical symmetry (hexagonal) C o (hexagonal) 39.4 41.6 1 19.0 3.7. The Magnetic Structure of Oxygen 2 Fig. IS. Deviation of the spin density distribution from spherical symmetry in a n iron crystal (difference Fourier diagram). The extended negative regions are due to the negatively polarized 4s electrons which form a uniform antiferromagnetic background in the otherwise ferromagnetic crystal (3d electrons). The maxima therefore essentially denote an additional 3d electron density; a distinct concentration of the 3d electrons along the crystal axes is evident. This distribution is characteristic of the eg symmetry of the 3d electrons. The eg or tZg character of the electron distribution can be deduced from the observed concentration of the electron density in certain directions in the crystal. Iron crystallizes in a body-centered cubic lattice. The five-fold degenerate 3d energy levels are split by the crystal field into two states with eg symmetry and three states with tzg symmetry. Owing to the octahedral symmetry of the environment of the iron atoms, the energies of the eg levels are higher than those of the t Z g levels. The observed electron concentration along the cubic [loo] axes (Fig. 15) thus points to eg symmetry of the electron distribution. Careful numerical evaluation of the experimental data 1301, in which a small component of the orbital moment and 4s electron contributions were taken into account, gave +2.39 p~ for positive magnetization and -0.21 VB for negative magnetization. Assuming that Hund's rule is valid, therefore, there are 7.6 electrons in the 3d band and 0.4 electrons in the conduction band. The electronic configuration in ferromagnetic elementary iron should thus be 3d7-6 4s 0.4. Of the 7.6 electrons, 53 % are in an eg symmetry state (along the cube axes) and 47 % in a tZg symmetry state (along the cube diagonals). Exactly the opposite situation is found in nickel, which crystallizes in a face-centered cubic lattice; 1 9 % of the 3d electrons are in eg levels and 81 % in t2g levels (the Angew. Chem. internat. Edit. Vol. 8 (1969) / No. 12 Finally, brief mention should be made of a neutron diffraction study on solid oxygen, which showed an antiferromagnetic order [361. Crystalline oxygen exists in three phases: a-02 (0-24 OK); p - 0 2 (24-44 OK); y-02 (44-54 OK). T h e y phase has 8 molecules in a cubic unit cell. The p phase has one molecule in a rhombohedra1 cell, the molecule probabIy being oriented along the trigonal axis. The structure of the a phase is unknown. The symmetry is presumably monoclinic. Magnetic measurements on gaseous, liquid, and solid y oxygen indicate two unpaired electrons in a 3S1 state [371; the susceptibility indicates an anti-ferromagnetic order at low temperatures. In the neutron diffraction experiments on solid 8- and a-oxygen, the diagram of a-02 did in fact contain two additional lines at small scattering angles, which must be attributed to an antiferromagnetic order in a - 0 2 . Since the magnetically ordered spins are due to unpaired p-electrons which have a relatively large spread, the magnetic form factor falls off very rapidly, with the result that the detection of magnetic reflections become difficult (f := 0.5 for sin@/h = 0.2 k 1 ) . No magnetic longrange order was observed for P-0,. The magnetic and neutron diffraction data (maximum of the diffuse scattering at sin@/h = 0.1 kl), however, indicate an antiferromagnetic short-range order in p-02. Received: December 11, 1968 [A 731 IE] German version: Angew. Chem. 81, 984 (1969) Translated by Express Translation Service, London [36] M . F. CoNins, Proc. physic. SOC.89, 415 (1966). [37] E. Kanda, T . Hasedo, and A . Otsubo, Physica (Utrecht) 20, 131 (1954); A . S. Borovic-Roinanov, M . P. Orlova, and P. C. Strelkov, Doklady Akad. Nauk SSSR 99, 699 (1954). 961

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