TARLE I\'
11 Y l ~ l U l ~ ~ l C N , 4 l ' l O0N1 ' '
lit:ihRrv C,. F:. I < i n ~ l ~ i.I. ~ l lClrcm. , /'h!,s., 8 , I88 (I!M).
ion disttril)iitJionis M ~ i ~ - f [ M n ~ ~ i+n +which j O ~ ~t,lip MnZ+ions have all t h o d orbit,als half filled and are siipposetl to form sp3 crnptjy hyl)rid orI)it,uls. The tetragonal distortion is produc!cd because of d4 configuration of M i l 3 + ions at. oct8ahcrlrnlposit,ions and which can forni sqriare bonds. However, as pointed out above, tJheions a t tetrahedral positions do not form regular t,etrahedrons, as far as the angles are concerned, which is not likely with sp3 hybridization. Furt!hermore, Goodenough and IJoct~12 have suggestcd that i n y-Mn203all tJhe vacancies are i n tet,ralirdrnl sib; a concliision which conflicts with the magnetic data. [n what follows a gcneralized model of bonding, consistniit with I)ot,li magnet,ic and diffraction d:\tn, for hllldh and y-h4nz03 is presented and which siiggcst,s the I)rot)aliln tlist,rihution of vacancies. Moore, Ellis and Sclwood'" havc mensurd t,he magnetfir: susccptibilitics of all the oxides of manganese a t t)emperntures 25, -80 and -185". Using their d a h t,lie effective ningrieton nunil)crs, p e ~per , mmgancse ion for Mn304and y-M1i103were calculated from (I)
where X M is the molar susceptibility, k the Boltzmann constant, T the a1)solute temperattiire,0 the Weiss molecular field constant', N o Avogadro's number and p the Bohr magneton. The 0 values for MnaOd and y-MnzOa were ascertained by plot,t8ingthe reciprocal suscept,ihility against tJemperat,ure and extrapolating for 0 t80* / x h I = 0. Since the orbital magnetic moments are qr~ttnched for transi tfion metal ions, the niiml)er n of unpaired electJronswas nalculnted from = t'$G722)
Pelf
(2)
The calculated data are Set out in Table I. It is evident that the tiuinber of unpaired electrons in y-Mnz03per formula unit,, h4na/,04,is 8.64 or about 69.12 per spinel unit cell. This suggests that a t least two electrons per fortniiln unit arc paired, TABLE I ~ J N P A I R E D ELECTRONS PER M A N ~ A NIONS ESE IN y-Mii2O3 AND Rln3O4
EFECTIVF: N u m R E R O F
CiiritWeisu
Substance
Strricfiirn
r-MnzOa
Dcfert pwidn-
~ 1 ~ 5 0 0.24
Mn3O4
spinel Pseiitln-spinel
-160
8
(OK.)
n(oxptl.)
3.02
TABLIT I1 UNITC E I J ~DIMENSIONS oi'~ROME ~~ANCIANITES Siilistanae
CdRln204" MnaO4
in A . 8.22 8.15 8.15 8.07 8.10
n
cin
A.
C/a
9.87 1.20 0.44 1.16 -y-R4II203 9.44 1.16 MgM11~04' 9.28 1.15 ZnMii2O4 0.25 1.14 A . P. B. Sinlia, N. R.. 8:injnna and A . 73. Biswas, A&. Crust., in prcm.
which nffortls a cliie t,o t,he nat)iire of the vacancy
I(. P. SINHAAND A. P.B. SINHA
760
distribution. No electronic configuration of cations and with vacancies a t tetrahedral sites can possibly lead to theoretical spin values consistent with the observed inngnctic value of 8.64 unpaired elcctroris per Mna/,Od molecule. If we picture the oation configuration a t octahedral sites as':M , a t tetrahedral sites as
m]
M!' atid keeps11 thecation vacancies a t octdiedral sites, the number of unpaired 8 x 2 = electrons comes out to be 13'/a x 4 69.3 per unit cell or 8.66 per formula unit. Thus, since this postulated arrangement is consistent with magnetic data, it may reasonably be concluded that there are no vacancies at tetrahedral sites, as has been suggested by Goodenough and Loebla but that, on the contrary, these are distributed among the octahedral sites, the correct formula thus being Mn3+[Mn3+~/,0 1/,]04*-~ X-Ray data also support this conclusion and, since additional reflections are absent, there does not seem to be an ordered distribution of vacancies a t octahedral sites. Furthermore, the ions at these sites maintain their coplanar square bond formation
+
ds p2
tion, the ions a t tetrahedral sites will by virtue of their changed electronic configuration give rise to a sort of irregular tetrahedral empty hybrid bond dasp depicteda,s Since
~ z 1' -
--T-d SP the tetrahedrons in y-MnzOaare irregular this view may be regarded as more plausible than the sfsump-. tion of spa bonding. For MnaO4, Table I indicates that the number of unpaired elect,rons per molecule is about 9. If in hlnP+[Mn2a+]O42-all the manganese ions had unpaired electrons, the total number would be 13. It follows that four electrons per molecule are paired. Since in view of the tetragonality of the structure, the Mn3+ions a t octahedral sites must take part in covalent sauare-bond formation, its electronic configuration should remain ~ 8 ' The pairing would therefore occur in Mn2+ at tetrahedral sites giving ':M The two empty d orbitals would again take part in the d*sp tetrahedral empty hybrid bond formation. Thus it appears that the same coordinate covalent bonding mechanism is present in both y-Mnp08and Mn@4, i.e., dsp2 square bonds at octahedral sites and d%p irregular tetrahedral bonds at tetrahedral sites. Furthermore, the tendency for empty d%phybrid bond formation in these compounds seems t o be so strong that some of the electrons of ions at tetrahedral sites get paired to give two empty d orbitals. Examples of such pairing of 3d electrons, in apparent violation of Hund's rule, are found in some nicke1,complexes having square bonds" and in antiferromagnetic stiperexchange coupling in Bome
Im] .
.1-
Vol. 61
rhombohedral sesquioxides.16m16 Thus the crystal electric field also seems to influence this distribution of electrons over the 3d orbitals. The ideal condition of bonding giving rise to tetragonal distortion seems to be attained when all the tetrahedral cations show dzsp bonds and when octahedral cations enter into dsp2 square type bonding. Both MnaOd and y-MnzOa satisfy theae conditions and have the axial ratio c/u = 1.16, which may be taken as a standard value. The axial ratios of some of the tetragonal manganites with normal spinel type structure are given in Table 11. In the case of CdMnzOc the axial ratio is c/a = 1.20. In virtue of the large size of the Cda+ ion and its tendency to fbrm tetrahedral covalent bonds, a larger contribution of the irregular bonds (presumably spd2in this case) is to be expected with a corresponding increase in the axial ratio, For others, where the tendency for the cations a t tetrahedral sites to form d2sp tetrahedral bond is less the c/a ratio decreases accordingly. The hypothesis of Goodenough and Loeb that the axial ratio is maximum when only the octahedral cations are covalently bound, and decreases with increasing amount of covalence a t tetrahedral sites seems to be arbitrary and is a t variance with the experimental values particularly for CdMnzO,. y-CrzOa.-y-CraOa is an unstable phase of the normal a-Cr20aand is not found free in nature. It,s existence was first reported in the dehydrated products of CrOOH*7; no magnetic data are available. X-Ray data alone must therefore be relied on for asseming the vacancy distribution in this compound. The crystal structure of Y-CrzOa is cubic spinel type with a = 8.36 A. There are no forbidden reflections in the diffraction patterns; thus it would appear that the vacancies are distributed randomly, either at octahedral or tetrahedral sites, or both. The intensities of some of the important reflections were calculated for these three distributions and compared with those observed by the above workers. The results are set out in Table 111. The best fit between the observed and calculated values is for the case when all the vacancies are in octahedral positions. It is therefore concluded that, as in y-FezOs and y-MnzOs, the vacancies in y-Cr20a are predominantly distrlbuted among the octahedral sites. However, unlike y-Fez03 and like y-MnzOa there is no superstructure of vacancies and the distribution is random. Thus y-CrzOamay be assigned the formula Cr3+[Cr3+v,01/,]0:-. y-A120a.-y-AlzOs is a cubic spinel with u = 7.94 A. Various forms of aluminas obtained by dehydrating a variety of alumina hydrates at different temperatures have been reported in literature. la The differences in these aluminas noted by these authors may be due to the degree of dehydration and their order-disorder states with respect to the cation distribution. Even for -y-A120athe reported (14) K. 8. Pitrer, "Quantum Chemiatry," Prentice-Hall. N e w York, N. Y.,1958. ( 1 5 ) Y. Y. Ll, Phys. Rm.,101, 1015 (1956). (16) D. Polder, Phydca, 0 , 709 (1942); J , P h y s . Radium, 19, 174 (1961).
(17) A. W. Lauhengayer and H. W. McCune. J . Am. Chsm. Sor.. 74, 2362 (1952). (18) A, Stumpf e1 d., Ind. Enp. Chem., 49, 1398 (1950).
June, 1957
T H E R M O D Y N A M I C P R O P E R T I E S OF
NICKEL-ZINC ~ERROSPINEI23
7G1
The absence of the 111 reflection is significant and almost rules out the possibility of vacancies in tetrahedral positions. There is a fair over-all agreement between the experimental intensities and thosc calculated on the assumption of the vacancies prcdorninating a t octahedral sites. This may indi-, cate a random distribution of vacancies a t octahedral positions. Certainly, the possibility of a statistical vacancy distribution both a t octahedral and tetrahedral positions cannot be ruled out in the TABLU I11 OBSERVEDA N D CALCULATED INTENSITIESFOR VARIOUS light of the existing data. However, in view of the known distribution in other defect spinels the tentaDISTRIBUTIONS O F VACANCIES I N y-CrpOa !/2]0i-may bc astive formula A13+[R13+5/80 r-Cr20a. u = 0.383. a = 8.36 d. . signed to r-A1203. I , calcd. X-Ray Vacancies intensity Vacancies Vacancies Conclusion (visual in tet. randomly in oct. distributed impression) hk sites aites X-Ra,y, electron diffraction and magnetic data 11.7 Absent 36 llt 4.7 for defect spinel type oxides indicate that the cation W 17 27.7 220 33.8 vacancies predominate among the octahedral posi100 vs 311 100 100 tions. In 7-Fez03there is an ordered distribution Absent 8.3 4.0 222 2 4 of the vacancies a t octahedral sites probably around W 43.4 27.4 4 00 21.1 the cell center. In Y-Mn2O3,r-Cr208 and r-Al203 61 57 M 440 55.4 the vacancies are randomly distributed among the octahedral positions and an ordered superstructure TABLE IV of vacancies is apparently lacking in these oxides. OBSERVEDA N D CALCULATED INTENSITIESFOR VARIOUS The tetragonal symmetry of y-Mn203and Mn30c is to be attributed t o the ability of Mn3+ions a t ocDISTRIBUTIONS OF VACANCIES I N y-Ala08 tahedral sites to form dsp2 empty hybrid square y-A120J,a = 7.94 k,u = 0.383 bonds with the overlapping oxygen orbitals, the I , calcd. X-Ray Vacancies Vacancies VacanciPe intensity tetragonal structure being further stabilized as a i n oct. in tet. randoiiily (visual h kl si t,es sites distributed impression) result of the formation by the Mn3+and Mn2+ions of d2sp irregular tetrahedral bonds a t tetrahedral 19.4 Absent 111 10.6 45.2 positions, The ideal axial ratio of c / a = 1.16 beems M 17.7 31.9 220 38.8 to be attained when both these bonding mecha105 vs 311 I08 98 W nisms are operative. 1.8 4.8 222 6.8 Acknowledgment.-The authors wish to express 72.2 MS 400 62.5 95.1 their thanks to Professor G. I. Finch, F.R.S., 0 Absent 33 1 0.5 1.5 and Dr. A. B. Biswas for helpful discussions and 12.6 W 422 IS. 1 7.1 keen interest in the work. 100 100 VS 440 100
intensities depend much on the history of the preparation of the samples. The most reproducible form of r-A1203,as judged by X-ray and electron diffraction, was obtained by oxidizing in air thin films of aluminum a t about 800".' Similar calculations as for r-Crz03were made for this case and the calculated intensity value6 are set out in Table IV togethnr with the observed values.
~
-,
HEAT CAPACITIES A T LOW TEMPERATURES, ENTROPY AND ENTHALPY INCREMENTS OF FOUR NICKEL-ZINC FERROSPINELS' BY EDGAR F. WESTRUM, JR.,AND D. M. GRIMES Conlribulion ,from the Deparlnients of Chemistry and of Electrical Enl/ineering of the Unitlerdy of Michigan, Ann Arbor, Michigan Received December 18, 1066
Heat capacitie8 from 5" t o above 300"IC. were determined on synthetic samples of Ni,-,Zn.Fez04 with z 0.6, 0.7, 0.8 and 0.9 t o test a hypothesis of Yafet and Kittel concerning triangrilnr transformations. The normal sigmoid dependence of heat capacity on temperature is modified by ferrimagnetic contributions, and an antiferromagnetic transformation near IOOK. becomes increasingly more pronoiiinced with increasing zinc content. Thermodyiismic fiinctions have been evaluated from the data presented. =I
Spinel minerals are fairly common and include important ores. Synthetic ferrospinels (ferrit,es) possess interesting electromagnet#ic propert>iesand are technologically significant components of high frequency electrical circuits. Despite these facts, thermal data extending to liquid helium temperatures (and thereby permitting a more accurate eval(1) Presented at the Ninth Annual Calorimetry Conference in Soheneotady, New York, on September 18, 19.54. This work wns eupported by the U. 8. Army Signal Corps throixh the Engineering Reoearch Institute of the University of Michigan.
uation of the thermodynamic properties) are available probably only for zinc ferrite (ZnFe20d).2 Heat capacity data above 50°K. have, however, been published for more than twelve other^,^ and measurements on magnet,ite over tjhe range 1.8 to 4.2"K. recently have been pi11)lishcd.~ (2) E. F. Westrum, J r . , and T). M. Grimes, Phus. and Chem. of Solidb, in press. (3) E. G . King, J . Chem. Phtia., 6 0 , 410 (1950). Cf.the references
to other works contained therein. (4) J. 8. Kouvel. Phye. Reu.. 102, 1489 (1906).
