Y. S. Hong R. F. Williamson and W. 0. J. BOO' The University of Mississippi Unwersity, MS 38677
Some Lower Valence Vanadium Fluorides Their crystal distortions, domain structures, modulated structures, ferrimagnetism, and composition dependence
This paper describes some contemporary concepts that are unique to the structure of advanced solids. The number of ways in which the chemical elements can combine to form ordered solids is almost infinite. For this reason, solid state chemistry, in addition to being highly theoretical, is a descriptive science, and as it is further developed, will become increasingly so. There are compounds such as rutile ( T i 0 4 and perovskite (CaTiOs) whose structures are so basic that they occur repeatedly both in nature and in man-made materials. Analogies to simple, well behaved materials such as these is the first step toward understanding the solid state chemistry of more advanced materials. Figure l a shows VF2 ( I , 2) which is of the rutile structure. A solid solution of MgF2 and VF2 (3), represented by Figure lh, has a rutile-like structure in which Mg"+ and V2+ ions occur randomly. This compound can be represented by a stoichiometric formula (MgVF4), hut the compound itself is nonstoichiometric because the V2+ and Mg2+ ions have no ordered structure and, hence, define no unit cell. In Figure Ic, trirutile LiVzFs (3) is seen to have basically the same structure except that the Li+ ions and the vanadium ions are periodically ordered, introducing a modulation along the c direction which gives a repeating distance of 3c. Figure 2a shows a topographical view of the ideal perovskite KVF3 (4). If the monovalent ion is reduced significantly in size (i.e., K+ is replaced by Na+), the GdFeO3 structure results, which is nothing more than a "puckered" perovskite structure. The Goldschmidt radius-ratio rules (5) define a tolerance factor t = ( I * + r g ) / [ 2 ' % ~ + rx)] where r A , re, and r x are Goldschmidt radii for ions in the ideal perovskite ABXs Stabilization of the cubic phase occurs when 0.8 < t < 1.0. The tolerance factor for NaVF3 is below 0.8, which predicts distortion to lower symmetry. One layer of the structure of NaVF3 (4) is illustrated in Figure 2b. By reducing the number of K+ ions in KVF3 and replacing that same number of V2+ ions by V3+ inns, new structures having the general formula K,VX"V~-,"'F3 (K,VFd evolve. For r between 0.45 and 0.56 the structure assumes a larger unit cell with tetragonal symmetry (67).This structure is an analog of tetragonal potassium tungsten bronze, space group P4lmbm (a),and it is illustrated topographically in Figure 2c. In this structure, some of the square holeg, which were sites for K+ ions in KVF3, are converted to smaller triangular holes, while others are converted to larger pentagonal-shaped holes. Only the pentagonal and square holes are large enough to accommodate K+ ions. Furthermore, in the tetragonal tungsten bronze structure, all the pentagonal holes are occupied, hut the square holes may be partially occupied, allowing the theoretical value of x to range from 0.4-0.6. Another structure having the general formula K,VF3 also forms (9,10) which is an analog of hexagonal potassium tungsten bronze, space group P6sImcm (11). As in the te-
Presented at the ACS National Meeting, March 25, 1980, as part of the State-of-the-ArtSymposium on Solid State Chemistry in the Undergraduate Curriculum sponsored by the Division of Chemical Education. Author to whom correspondence should be addressed.
VF,-MgF, i
bi
o
. . . V*' or Mg*'
o
Li"
0 F" Figure 1. Rutile type structures. (a)The m i l e structure of VF2. (b) The rutiie-like structure MgVF4. (c) The trirutile structure of LiVzFs.
KVF,
)a?
Tetragonal K.VF, a
NaVF, I b,
c
I
Pseudo-Hexagonal
.
V-or c A+'
K.VF,
,d! V-
0 F" Figure 2. Perovskite-like structures. (a) Ideal perovskite KVFI. (b) Distorted to orihohmbic NaVF,. (c) Tetragonal Tungsten bronze-like K,VF3. (dl Hexagonal Tungsten bronze-like K.VF3.
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tragonal case, the structure consists of layers of vanadium and fluoride ions held apart by other fluoride ions ahove and below each vanadium ion. Potassium ions are located in sites hetween the layers. Figure 2d shows one layer of this structure. The vanadium ions are translated slightly in the ab dane, alternately toward and away from the hexagonal centers. Hexagonal symmetry is preserved, however, hy introducing a second layer directly below the first which is identical hut rotated 180". This total operation introduces a modulation to the structure along the hexagonal axis making the period of c two layers deep. The structure has both hexagonal and triangular holes, hut only the former can he occupied by K+ ions, making the maximum theoretical value of x 0.333. The exnerimental values of x in K,VFq - - actuallv range - from 0%-0.27. The two K,VFn structures retain a considerable amount of similarity K*~. As seen in Figure 2, all three structures can he viewed as laver structures. Although the arrangement of vanadium and fluoride ions in the ab iayers are different, the rows of vanadium and fluoride ions along the c axis are essentially the same in all three structures. One other important similarity is that all the vanadium ions are swruunded octahedrallv hv six fluoride ions. These octahedra are all corner sharkg."The result is that V-F-V bond angles are close to 180'. There are natural consequences of substituting a particular set of ions into a eiven structure. and often resulting- orooerties . . and anomalies can he predicted. The K, VF? rompounds are excellent exmoles of this. In fluoride octah~dra,the electronic and (t2g)2,respecconfigurationlof V2+ and V3+ are tively. The V2+ ion is approximately spherical, hut the V3+ ion is best described as having a tetragonal shape. Furthermore, V2+ has a nondegenerate ground state 4A2g, but V3+ should have the degenerate ground state 3Tlg. According to the Jahn-Teller theorem (1% however, orhitally degenerate ground states are not possible in an octahedral system. Furthermore, there will always be a mechanism for reducing the svmmetrv of a molecule or comolex such that its ground state will he nondegenerate. Large level splittings are expected in an octahedral environment if the ground state is u bonding or o antihonding as in Cr2+ and %+, respectively. ~ u c h smaller splittings would he expected if the ground state were a honding or a antihonding as (Sc2+, Ti2+, Ti3+, V3+) and (Fez+, Co2+,Co3+) in octahedral environments, respectively. In the K,VF3 compounds, a cooperative Jahn-Teller effect would be expected to set in a few hundred degrees ahove room temperature. This kind of order would result either in distorting the crystal lattice or imposing commensurate modulations on it. The two bronze structures have high svmmetrv (tetragonal and hexagonal). In all likelihood &st&tions or modulations would occur in the vanadium fluorides which would lower their symmetries to orthorhomhic, monoclinic, or triclinic. Because the predicted distortions are small, twinning (90° in the ab plane of the tetragonal) or trilling (120' in the ab plane of the hexagonal) are likely. In fact, the smaller the distortion the more likely it is twinning or trilling will occur. In the case of a modulation superimposed upon the parent lattice which is not accompanied by a detectable distortion, a twinning or trilling of sorts is almost a certainty. A sinele ervstal mav-he formed at hieh temoeratures with microscopic twins or trills forming wi&in its hundaries at lower temoeratures. In cases of this kind. thev are better described as oiientation domains. The effect bf these domains would he to give the crvstal the macroscooic aooearance of high svmmGry, In fact, this effect is usuaily undetected, and needless to say, single crystal structure determinations would he extremely di?ficuli. In addition to having different shapes, the V2+and V3+ions have considerably different radii andthe ratio of their charges is 3.2. l i these et'fects are supplemrntcd with the likelihuod of electron hopping between the two ions, plus the fact that K+ sites are only partially occupied in the tungsten bronze
to
-
structures, the possihility of long range ionic ordering must also be considered. In the K,VI.'? compounds, since hoth V" - \I1* telectron orderine) and K T orderin? arc mssible. the two may occur cooperakely. The effect-of idnic ordering would be the formation of suoerstructures which are suoerimposed on the host lattice.'l'his kind ofsuperstructure may also he acromoanied by small lattice distortions. That region of a crystal in ivhich a modulated structure of this kind occurs is usually stoichiometric. If the energy of a crystal is lowered sufficiently hy this kind of ordering, two or more modulated structures of different compositions may coexist within a single crystal. This situation is best described as composition domains. In this case, the formula representing the compound mav he nonstoichiometric (ratios of elements are irrational numbers), hut thc ctrmpound consists of relative amounts ot jtoichiomrtric domains, e n ~ hdomain having- a well-defined unit cell. At temperatures well below ambient, weak magnetic interactions between paramagnetic V2+ and V3+ ions should lead to further structural anomalies. In inorganic salts (as opposed to metals) these interactions are usually not direct hut involve intermediate anions. Because the anion increases the strength of the interaction by an order of magnitude or more, these are sometimes referred to as superexchange interactions. In the first row transition metal fluorides. both ierromagnetic and antiferromagnetic superexchanpe interactions are aossible as vredicterl b y the rules oiGuodenouel~ (13, and ~ & a m o r i( l j j From thew rules, the 180° V-F:'V internstion is vredicted to he antiferromacnetic. This vrediction was verified to be true for KVF3 (75).The antiferromagnetic ordered structure of KVFn is shown in Figure 3. The magnetic unit cell is a modulated structure which has eight times the volume of the crystallographic unit cell. I t should he noted that symmetry of KVF3 in its magnetically ordered state is lowered from cubic to tetragonal because the ordered spins have direction. ) the cubic perovskite KVFs, The NBel temperatures ( T N for tetragonal bronze-like Ko.soVF3,and hexagonal bronze-like G25VF3 are 130' ( 4 ) , 50" (6), and 8'K (lo), respectively. One might conclude the strengths of the V-V magnetic interaction decreases as the ratio V3+/V2+ increases. I t is probably true that magnitudes V2+- V2+ > V2+ - V3+ > V3+ - V3+:however, this explanation is an oversimplification and theke are effects of greater imoortance that must he considered. A laver of hexagonal tungsten bronze-like K,VF3 is shown in ~ i ~ u r e 2d. In this figure each pair of nearest neighboring vanadium ions has a common nearest neighbor. It isnot posiible for the magnetic moments of three metal ions arranged in a triangle to all order antiparallel to each other. This triangle then is a constraint to antiferromagnetic ordering. In the hexagonallike structure. there are three vanadium ions involved in each constraint and each vanadium ion contributes to two constraints. The number of constraints oer vanadium ion. therefore, is 0.667. It can also he shownihat the number of constraints oer vanadium ion in tetragonal K,VFR (Fig. 2c) is 0.40 per vinadium ion, and in K V F ~ ( F2;) ~ ~there . are no
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Figure 3. The magnetic structure of KVFs.
constraints per vanadium ion. Therefore, it is logical that the N6el temperature would decrease as the number of constraints per vanadium ion increases. To further support this argument, in VF2 (Fig. l a ) there are two constraints per vanadium ion and T Nis 7OK ( I , 2). In the trirutile LiV2Ffi(Fig. lc), all constraints to magnetic ordering are removed by the periodic replacement of paramagnetic vanadium ions with diamagnetic lithium ions, the result being TN = 26'K (3).In VF2, the constraints lead to an incommensurate modulated structure in which the magnetic spins lying in the ab plane form a spiral along the c axis. The period of the spiral is incommensurate with that of the crystallographic structure as it is about (hut not exactly) 28 c. In addition to lowering the temperature a t which long range magnetic ordering occurs, the constraints also influence the ordered structure. Another possible ordering feature of the KxVF3 compounds is ferrimagnetism. The first necessary condition for ferrimagnetism is that there must be two magnetic ions whose moments have different magnitudes. A second condition is that magnetic ordering must he preceded by ionic ordering (electronic ordering), and a third condition is that in the magnetically ordered state, the moments of one kind are parallel to each other but antiparallel to the moments of the second kind, giving a resultant remnant moment to the crystal. In layer structures such as the K,VF3 compounds, the possibility exists for ferrimagnetism within a given layer, but ordering between layers may he such that the resultant moments of the individual layers cancel each other. Further complications arise from factors such as (1) in tetraeonal K,VF?, the vanadium ions irccupy two different rry~tall
