Oct. 20, 1961
MAGKETIC SUSCEPTIBILITIES IN THE TUNGSTEN -OXYGENSYSTE~I
[CONTRIBUTION FROM THE
BAKERLABORATORY O F CHEAIISTRY,
4149
CORNELL UNIVERSITY, IT€IACA, KEW YORK]
Studies in Non-stoichiometry : Magnetic Susceptibilities in the Tungsten-Oxygen System1 BY &I. J. SIENKO AND BIRESWAR BRNERJEE RECEIVED APRIL17, 1961 Magnetic susceptibilities have been measured by the Gouy method for several tungsten oxides oE the series WO,. At from -0.65 X lope to +0.46 X 10-o as 297.5”K. the susceptibility per unit volume is found t o increase n~o~~otonically x in WO, decreases from 3 to 2. Results are interpretable in terms of a defect structure in which 3 x oxygen atoms have been removed from a host WO, lattice leaving 2(3 - x ) rlectrons iii the conduction band of the host. Quantitative agreement with a Pauli-Peierls calcrrlation is surprisingly good. The model may be applicable to other non-stoichiometric oxides for which “mixetl-oxidation-state” structures have been postulated.
-
Like most or’ the other transition elements, tungsten can form a series of oxides which do not conform to simple Daltonian stoichiometry. Traditionally, these non-stoichiometric oxides have been interpreted as mixtures of several oxidation states. Magneli, however, has shown2 that the crystal structures of the tungsten-oxygen series are rather simply related and are differentiated from each other principally in the relative number of WOa octahedra. that are mutually corner-linked or edgelinked. In WOa, the Woe octahedra are joined through sharing of comer oxygen atoms only; in WO?, the Woe octahedra share edges so as to give the extended chains of the rutile structure. Between these terminal compounds, Magneli finds a series of oxides \V;V,Oe++-1in which there are “slabs” of WO6 octahedra connected through corner-sharing but with the “slabs” joined to each other by edge-sharing. As n increases, the size of the “slabs” is believed to be larger. In a series of extended solid state structures such as WnOEn- 1, the concept of pentavalent and tetravalent tungsten loses utility since the local symmetry about each tungsten atom is identically octahedral. A similar problem with the alkali metal-tungsten bronzes was resolved successfully3 by replacing hypothetical pentavalent tungsten in xMWVO3. (l--x)WvxO.l by an electron gas formed from the valence electrons of ionized nil atoms in M,WV103. In investigating the properties of WOZ doped with various metals we speculated on the possibility that the non-stoichiometric oxides WO, might also be interpretable in ternis of an electron gasspecifically, that they are defect structures in which 3 - x oxygen atoms have been removed from a W 0 3 host lattice leaving 2 ( 3 - x ) electrons in the host conduction band. In this communication we report some magnetic measurements and their interpretation by such a model. Electrical characteristics, more difficult to determine since they require single crystals for unambiguous interpretation, are currently under investigation in this Laboratory and, although the work is by 110 means complete, a t least the results are not inconsistent with the model used in this paper. (1) This research was supported by the United States Air Force under Contract No. AF 49 (638)-191 and was monitored by the Air Force Office of Scientific Research and Development Command through its Directorate of Solid State Sciences, (2) A. Magnhli, N m a Acta Reg. Soc. Sci., Upsala, 1949, Ser. IV, 14, No. 8 ; Acfa C r y s f . , 6,495 (1953); J . Inorg. Nuclear Chem., 2, 330 (1956); Acla Chem. Scand., 9, 1382 (1955). (3) L. E. Conroy and M. .l Sienko, . J . A m . Chem. Soc., 74, 3520 (1032); F. Kupku aucl M. J. Sienko, J . Chem. P h r s . , 18. 1280 (1950)
Experimental Procedure and Results Preparation of Samples .-Tungsten powder and tungsten trioxide powder of a t least 99.9% purity were thoroughly ground up as mixtur? corresponding to WOz.m, WOIPO, WOg76, and W02.~;--2.t-., n = I, 2, 4 and 8 in the series W n 0 8 n - l . They were fired for 40 hr. under argonat 1000D until X-ray analys,is showed complete absence of tungsten or 8-tungsten lines. Longer heating with and without subsequent regrinding gave no change in the X-ray pattern. Chemical composition was checked by firing aliquots in oxygen to complete oxidation to WOs. The weight increase due to oxygen up-take was within 1% of that calculated assuming complete conversion of the starting mixtures to homogeneous WO,. In the case of WOZ, an additional check was made by comparing our observed X-ray spacings with the interplanar distances calculated from the data of Magn6L4 Agreement was very good. Densities.-Densities were determined pycnometrically using water as the immersion liquid. Within the limits of experimental error, f 0.01 g./cc., there was no difference in the density measured on powder portions or chunks of the products. The measured densities in g./cc. are: WOzo,, 11.15; W02.60,8.26; WOZT ~ 7.74; , and WO2.87, 7.30. Magnetic Measurements.-Magnetic susceptibilities were determined using theGouy technique with semi-micro balance and electromagnet as previously described.6 Because of changes in the design of the power supply to the magnetic field, i t was necessary to re-calibrate the field using a 30% “special low cobalt” nickel chloride solution. A check on powdered NaCl gave a measured molar susceptibility of -28.5 X 10-O compared to the best literature value of -30.2 X 10-E. Calibration and the measurements were all carried out a t 24.5’, except for one sample of WOz which in addition was taken down to liquid nitrogen temperature but without sensible effect. For each oxide composition, three samples were selected from different, independent preparations and measured nine times, corresponding to three packings each a t three realignments in the field. Results are quoted in Table I as volume susceptibilities. They are true volume susceptibilities in the sense that they are calculated from an “apparent volume susceptibility,” obtained from the measured weight change, by multiplying it with the ratio “true density/apparent density of powder.” The apparent density of the powder was figured from the cathetometrically measured height of powder in the precision-bore sample tube. Probable errors, which were calculated from a statistical analysis of the 27 measurements on the 3 samples, are rather high because the forces iuvolved here are extremely small. In all cases, measurements were checked a t both 3500 and 5000 gauss to monitor independence of field strength and to ensure absence of trace ferromagnetic impurities. The last column in Table I gives the susceptibility per gram-formula weight for the simplest formulas ns given.
Discussion The magnetic susceptibilities of the tungsten oxides show two features of special interest: (a) the susceptibilities are extraordinarily low, much lower than one would normally anticipate for mixtures of W+6 with or W+5 and (b) the (4) A. Magnai, Arkio Kemi, Mi,. Geol., 24A, 1 (1947). ( 5 ) J. L. Kernahan and M. J. Sienko, J . A m . Chcm. Suc., 17, 1978 (1!ls55).
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11.J. S I E N K O
AND
VOl. 83
BIRESKARBA4NERJER
integrals for structures that place so many parameters a t our disposal, not the least of which is the variation in chemical composition. Furthermore, l the mechanisin by which “exchange demagnetiza6 I tion” is set up is still not certain and may call for I ferromagnetic ordering a t least as frequently as I the antiferromagnetic ordering that would inI 5 tuitively €ollo.cvfrom a “covalent bonding” model. I In this paper, although we considered exchange I demagnetization as a possible explanation of our I 4 results, we quickly gave it up because it did not I allow us to calculate in closed form the magnetic I susceptibility of tungsten oxide a t any compoI sition and also because i t seemed to predict a 3 I dependence on concentration that was directly I opposite to the experimentally observed. I Two extreme models can be proposed for the I 2 tungsten oxides. In one, which we call the I I Langevin model, the lower oxides are viewed as I containing W+5 or 1V+4--i.e., with one or two, I respectively, electrons bound to local centers and giving rise to magnetic moments appropriate to dl or d 2 configurations. I n the alternate model, which we call the Pauli-Peierls model, the lower 0 oxides are viewed as containing essentially free electrons in a 1 1 - 0 8 l a t t i c e i . e . , a collective electron u x m b l y in which only tlie electrons at the top of -1 the distribution can orient in a magnetic field and thereby contribute to the moment. Figure 1 2.0 2.5 3.0 shows as a function of tungsten oxide composition a comparison o€ the volume susceptibilities as x in WO,. calculated by these two models with the experiE 1.-Magnetic susceptibility per cc. as a function of inentally observed values. The dashed curve tungsten oxide composition: --------- , localized electrons represents inagnetic susceptibilities calculated on -__ , quasi-free the Langevin model; the solid curve represents the without exchange demagnetization; electrons; 0, observed susceptibilities. susceptibilities assuming quasi-free electrons as in the Pauli-Peierls calculation ; the circles represent maximum a t W 0 2 . 5 0 in the molar susceptibility is the observed susceptibilities. The agreement is not duplicated in the volume susceptibility. This much better with the Pauli-Peierls model and, concombination of features along with low electrical sidering the simplicity of the calculation, is truly resistivities as reported by Glemser and Sauer6 reniarkable. strongly suggest that a model based on delocalized In calculating predicted susceptibilities we have electrons, perhaps like the degenerate electron gas had to face two problems: (1) 1Vhat is an apused for the tungsten bronzes, is more appropriate propriate value for the diamagnetic susceptibility for describing the tungsten oxides than is the tradi- correction of the oxide anion in the structure and, tional “mixed-oxidation-state” model. With a concomitantly, what is an appropriate value for the tcniperature-independent paramagnetism of the TABLE I tungsten cation? ( 2 ) \%-hatis an appropriate value EXPERIMESTAL MAGNETIC SUSCEPTIBILITIES OF TUNGSTES for the effective mass of an electron if it is “quasiOXIDES bound” in an oxide host of variable composition? XII, susceptibility Probable susceptibility The diniagnetic increment of oxide anion ranges per cc. error per mole Oxide from -4.6 X as rccorninended by Pascal7 5 0 026 i 1 0 - 6 8 . 8 3 x io-$ ~o~~~ 0.456 x 1 0 - 6 in his remarkably successful scheme for organic =k ,032 X 10-8 11.0 X 10-0 w02.m ,405 X 10-6 compounds to -20 X 10-6 as quoted by Klemm* i ,016 x 10-6 4.06 x 1 0 - 6 W02.76 .i3s x 1 0 - 6 W02.a7 - , 2 2 6 X 10-6 f ,024 X 10-6 - 7.11 X 10-6 for gaseous oxide ion. 1lre have selected -9.8 X WOa.ou - ,649 X 10-8 = , 0 5 4 X 10-8 - 2 1 . 0 X 10-8 on the basis of a graphical extrapolation of the mixture of oxidation states, one would have to isoelectronic sequence I\lg++, Xa+, F-, 0--. attribute observed low magnetic susceptibilities to The Brindley and Hoare diamagnetic increments exchange demagnetization. However, exchange for Q+-, hTa+ and F- (based 011 their additivity demagnetization has not proved particularly fruit- analyses of crystalsq) were plotted as a function of ful as a way of accounting panbitatively for ob- the square of the ionic radii and extrapolated to served electric, magnetic and chemical properties (7) See, for esarnple, P. Selwood, Xagnetochemistry,” 2nd Ed., of non-stoichiometric compounds. In general, Interscience Publishers, Inc., New York, X. Y . , 1956. ( 8 ) Landolt-Bdrnstein, “Zahlenwerte und Funktionen,” Band I , a searching quantitative test has not been possible p . 306. because there are difficulties in calculating exchange Teil(9)1,See tlie reviem paper of W, R. Myers, Rcri. M o d . P h y s . , 2 4 , 15 HX
IO6
I(
“
(6) 0. Glemser and H. Saner, Z .
OnOYg.
Chem., 252, 144 (1943).
(1952), for a comparison of diamagnetic increments.
Oct. 20, 1961
MAGNETIC SUSCEPTIBILITIES IN THE TUNGSTEXOXYGEXSYSTEM
4151
TABLE I11 the ionic radius of O=. The justification for this procedure is that the diamagnetic moment is proCALCULATED MACSETIC SUSCEPTIBILITIES O N PAULIportional to the electron density as r 2 with the PEIERLSMODEL major contribution coming from the outermost lIoles per cc.----Susceptibility per cc. ( X 106)reaches of the ion. A somewhat better fit between TungsOxy Elec- TungsOxyElecten gen trons ten gen trons Total experiment and the Pauli-Peierls calculation can W 0 z . w 0.0517 0,103 0.103 0.43 -1.01 1.51 0.93 be obtained using the Pascal value of -4.6 X ,0369 ,0923 ,0869 .31 -0.91 1.07 .47 for Os. (However] there is an almost limitless W02.m W0z.n ,0340 ,0935 ,0170 .29 - .92 0.83 .20 number of combinations, many of which would WO2.87 ,0318 ,0913 . 0 0 8 2 i .27 - .90 0 . 6 5 .02 .26 - .91 .. - .65 improve the fit with experiment, but the choice W03.0: ,0309 ,0927 . . . . . of diamagnetic increment would have to be justified a posteriori, perhaps validly only for the tung- electrons, we have used the Pauli-Peierls equationlo sten-oxygen system.) Using -9.8 X for 0-and -21.0 X as the best value for the molar susceptibility of WOs, we calculate $8.4 X as the combined diamagnetic increment and where rn” is the effective mass of the electrons, high-frequency, temperature-independent paramag- p0 is the Bohr magneton, n is the electron density netism of W7+. In Table I1 we show the break- per cc., rn is the rest mass of the electron and h is down of a Langevin type calculation assuming the the Planck constant. For the effective mass of tungsten oxides are appropriate mixtures of the electrons, we have used 1.9 times the rest mass, W+4, or W i 6 . For LV+4 we have used 1100 this being a mean of the experimental values X for the molar susceptibility; for W+5,found in the alkali tungsten bronzes.” Because 1020 X These values are for d 2 and d1 con- the tungsten oxides are not cubic, whereas the figurations] respectively, and are little changed if derived effective mass was deduced for cubic we were to go over to a spin-only calculation or if structures, one could argue that the single scalar we consider octahedral field-splitting of a 3F(d2)or effective mass should be replaced by a tensor, a 2D(d1) configuration. It is evident from com- which would mean that the electronic contribution parison of the last column of Table I1 with the first to the magnetic susceptibility would not be isocolumn of Table I that a simple bound-electron- tropic. However, any anisotropy would not have model will not work for the tungsten oxides unless been detected in the powder measurements. exchange demagnetization is essentially complete. Comparison of the last column of Table I11 with In the latter event, we need to face the question the first column of Table I shows satisfying agreeas to how there can be any rise in K a t all in going ment. The agreement can be made even better by from WO, to W02. We would expect more perfect making other choices for the magnetic increments demagnetization as we decrease average inter- of 0-and Furthermore, it is quite probable atomic spacing between magnetic centers with that one single value of the effective electron mass perhaps incipient ferromagnetic ordering near should not be used for the whole range of composiWOS, not near MiOs. tion possible with WO,. As discussed for the alkali tungsten bronzes M,WOS there is theoretical and TABLEI1 experimental justification1’ for believing that the CALCULATED MAGNETIC SUSCEPTIBILITIES O N LANGEVIN effective mass of the electrons increases as states MODEL are removed from the conduction band by local Calculated x, polarization of tungsten atoms by M + ions. In Equivalent composition per cc. WO,, when x is near 3, any oxygen defect probably W’VO2 4-56.2 X puts electrons into the conduction band with fairly wvo2.s $37.0 X low effective mass, though there may be a finite ( 0 .5WV02.5)(0.5WV10a) $16. 7 X trapping energy a t the site of the oxygen defect. (0.26~v~~.~)(0.74Wf y 1 7~. ~ 8 )X lo-’ As the deviation from W03stoichiometry increases, W‘O3 - 0.65 X lo-’ there is probably increase in the electron effective mass a t least until the trapping sites effectively The Pauli-Peierls calculation, which incidentally has a built-in exchange demagnetization in the begin to overlap. On the basis of arguments preelectron-pairing that exists in all states except those viously given for MxIJT03,we might expect overlap near the top of the Fermi distribution, is shown in of the trapped electrons to begin to occur when 0.26 breakdown in Table 111. The columns headed moles of oxygen have been removed, corresponding “moles per cc.” are calculated from the observed to W02.74. With x less than 2.74 we would expect densities and the gram-formula-weights of the local polarization to be reduced and the effective various oxides. The “moles per cc.” of electrons mass to be decreased nearer to the free electron are calculable as twice the difference between theo- value. Such behavior would effectively pull down retical oxygen as if the material were WOS and the two extremes of the solid curve shown in Fig. 1. Other transition metal oxides, particularly V0,l2 actual oxygen per cc. of material. It amounts to and NbO,, l 3 show higher magnetic susceptibilities pulling neutral oxygen atoms out of a WOs lattice, leaving behind two electrons per oxygen, until the (10) See, for example, A. H. Wilson, ” T h e Theory of Metals,” composition WO, is attained. The columns headed 2nd Ed., Cambridge University Press, Cambridge, 1954, p. 155. M. J. Sienko and T h u Ba Nguyen Truong, J . A m . C h e n . Soc., “susceptibility per cc.” are calculated applying 83,(11) 3939 (1961). f 8.4 X per mole of tungsten atoms and (12) E. Hoschek and W. Klemm, Z. anoug. Chent., 242, 63 (1939). -9.8 x per mole of oxygen atoms. For the (13) G. Brauer, ibid., 256, 10 (1948). r -
DAVIDJ. MACDONALD AKD
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s. G A R N E R
Vol. 53
and also maxima in their molar susceptibilities as x is decreased below 2.5. These maxima may be symptomatic of the occurrence of electron trapping sites a t oxygen defects. The greater the trapping energy, the more firmly bound the electron and the bigger its contribution to the paramagnetic susceptibility. The sketchy data that are available, particularly for the series V O X ,KbO,, TaO, and CrO,, MoOx, WO,? suggest a decreasing maximum
in the susceptibility us. composition curves near 2.4 and 2.8, respectively. Otherwise, the susceptibiiities can be interpreted a t least qualitatively in terms of a partially-delocalized-electron model on either side of the maxima. It would be most useful to have additional magnetic data on other non-stoichiometric oxides and also electrical conductivity measurements over the range of coniposition.
[cONTRXI?iiTIONFROM
UNIVERSITY OS
THE
DEPARTMEXT O F CHEXISTRY OF THE
CALIFOKSIA, h S
.‘!iNGELEJ
24, CALIPORNIA]
Kinetics and Products of Aquation of cis- and tuansDichlorobis- (ethylenediamine) -chromium (111) Cations la,’ BY DAVIDj. MACDONALD~~ AND CLIFFORD S. GAXYBR RECEIVED MARCH 25, 1961 The products of the first-stage aquation of tians-[Cr(enj~Ci2] + in 0.lO.f HKOa a t 35.@’ in the absence of light were found , lcisy[Cr(en)2(0H2)C1] +2 2nd a dichloro complex tentatively identified as trans-[Cr(en)t o be t r ~ n s - [ C r ( e n ) ~ ( O H ~+)2 C ] cation). These previously unisolated or unre(OH2)2C12]+ ( i . e . , 1,6-dichloro-2,3-d~aquo-ethylened1amine-chromium(III) ported chloroaquo comp!exes have been isolated in solution and their visible absorption spectra determined. Pseudo first(1.12 C 0.40)X 10-6 and (0.78 & 0.05) X order rate constants for formation of these products are (6.90 & 0.41) X sec. -l, respectively. The only detectable first-stage aquation product of cis- [Cr(en)2Ci2]+ in 0.10 f HCi a t 35.0’ in sec.-l. the dark was cis-[Cr(en)p(OHz)Cl]+2, formed directly with a pseudo first-order rate constant of (1.11 f 0.02) X +z to the trans isomers was not detected, conservative upper Isomerization of cis-[Cr(en)2Clz]+ and of ci~-[Cr(en)~(OHz)Cl] limits thus established for the cis-to-tmns isomerization rate constants being 5 X 10-fi and 2 X 10-6 set.-', respectively. The possibility of trans-to-cis isomerization of these two complexes could be neither confirmed nor ruled out, but k < 1.12 X 10-6 see.-’ for isomerization of trans-[Cr(en)rC12]+ and k < 1 X sec.-l for isomerization of tr~irs-[Cr(en)~(OH?)CI] +z.
This investigation began in a study of the kinetics of production of ionic chloride from trans - dichlorobis - (ethylenediamine) - chromium(111) cation in acidic aqueous solution,2 as part of a program of comparing the reaction kinetics of analogous chromium(II1) and cobalt(II1) complexes. At first it was thought that a simple twostep process such as trans-[Cr(en)zClz]
+
+ H2O +
tr.ens-[Cr(en)p(OIin!Cr] +* -tCit r ~ n s - [ C r ( e n ) ~ ( O H ~+)2 Cfl ] H 2 0 -+ t r ~ n s - [ C r ( e n ) ~ ( O I I ~ -4-) ~ ]Cl-
proach can provide a knowledge of the steric course of the aquation, needed for a full understanding of the reaction mechanism, and can lead to the discovery of reaction paths which are not revealed by studies of the rate of production of ionic chloride alone. Earlier kinetic studies3s4 of the aquation of trans- and cis-[Cr(en)<] +, including our own,2 mere based solely on measurement of the rate of chloride-ion release, and as is true of many previous kinetic studies of the aquation of coordination complexes, did not include identification of the product complexes.
Experimental
might account for the production of ionic chloride (ix., chloride ions displaced from the complex) during aquation, but the experimental kinetic data on the secondary aquation soon revealed that the actual process must be more complicated. Therefore we undertook to separate and identify the reaction products a t various reaction times during the aquation of both trans- and cis-[Cr(en)zClz]+. Combination of the chromatographic separation data with determinations of the total rate of loss of the reactant complex ion and the rate of production of ionic chloride, together with spectral observations, have enabled us to evaluate or place upper limits on nine rate constants for reactions occurring in the primary aquation of tmns- and cis- [Cr(en)zClz]+ and the rearrangements of these two cations and their first-stage aquation products. I n favorable cases, this ap-
trans-Dichlorobis-(ethylenediamine )-chromium( 111) Nitrate.-This compound was prepared and characterized as described in a previous paper.2 cis-Dichlorobis-(ethylenediamine)-chromium(II1) Chloride Hydrate.-Violet powdered anhydrous chromium( 111) chloride. donated by the Diamond Alkali Company, was suspended in technical ethyl ether and mixed with a 2070 excess (in 20% ethereal soiution) of Eastman Kodak “White Label” ethylenediamine (dried by distillation from sodium hydroxide). -4fter -2 hr. on the steam-bath, the mixture formed yeiloiv-brown flufTy tris-(ethylenediamine)-chrornium(II1) chloride, which mas washed with ethyl ether and yield-100%. This crude dried overnight at - 1 0 0 O : product was recrystallized with half its weight of ammonium chloride from 1 f HCl. The crystals were filtered, rinsed with ethyl ether, then thermally decomposed6 in an Abderhalden drier a t the temperature of refluxing methyl salicylate (b.p. 220-224’); concd. H2SOI was used to absorb the ethylenediamine eroivcd. The resulting crude cis-dichlorobis-(ethylenediamine)-chromium(II1) chloride was recrystallized twice from 3-6 f HCl solution; yield -2070.
(1) (a) Based on a portion of the doctoral dissertation of D. J. MacDonald, University of California, Los Angeles. January, 1960. (b) Work partly supported under Contract AT(l1-1)-34, Project S o . 12. between the U. S. Atomic EneTgy Commission and the University. ( c ) California Research Corp., Richmond, Calif. (2) D. J. AlacDonald and C . S. Garner, J . I?:orZ. Nlcclear Chenz 18, 310 ( i N l ) .
(3) J. Selbin and J . C . Eaiia:, Jr.. J. Ant. C h i t . Soc., 79, 4285 (1957). (4) R. G. Pearson, R . A, Ailur.son ond F . Basolo, i b i d . , 8 0 , 504 (195s). (6) C. L. Rollinson and J. C. Baiiar, Jr., “Inorganic Syntheses.” Vol. 11, W. C. Fernelius, ed.. McGraw-Hill Book Co., Inc., New York, h-.Y . , 194G. p. ‘201.
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