ISSN 0021�3640, JETP Letters, 2009, Vol. 90, No. 5, pp. 376–381. © Pleiades Publishing, Ltd., 2009.Original Russian Text © A.I. Gusev, 2009, published in Pis’ma v Zhurnal Éksperimental’noі i Teoreticheskoі Fiziki, 2009, Vol. 90, No. 5, pp. 418–423.

376

In strongly nonstoichiometric cubic carbides,nitrides, and oxides MXy (X = C, N, O), structuralvacancies are analogs of nonmetallic interstitial atomsX and form a substitution solution, forming a condi�tion for atom–vacancy ordering. Structural vacanciesin most of these compounds exist only in the nonme�tallic sublattice. However, two nonstoichiometriccompounds, cubic titanium and vanadium monox�ides, contain up to 10–15 at % of structural vacanciesin both sublattices [1]. The cubic VOy vanadium mon�oxide (Vx�1 – xOz�1 – x ≡ VxOz, where y = z/x and � and� are the structural vacancies in the fcc vanadium andoxygen sublattices, respectively) at a temperature of1600 K has a wide homogeneity interval VO0.90–VO1.30

[2] and has a capability of ordering.

One ordered phase with the tetragonal symmetrywas observed in cubic VOy vanadium monoxide [3–6].According to [7], it has a very narrow homogeneityinterval and exists in the region VO1.22–VO1.24 at970 K, i.e., is formed in the VxO monoxide containingvacancies only in the vanadium sublattice. The sam�ples are two�phase and contain not only the V52O64

phase, but also the V2O3 oxide or the disordered VOy

monoxide at a larger or smaller oxygen content,respectively. The feature of the structure of V52O64 isthat 4 out of 52 vanadium atoms occupy unnaturalpositions in tetrahedral interstices of the basic cubiclattice with the B1 structure. The nearest environmentof these vanadium atoms Vtetr is formed by four oxygen

atoms and four vacant sites of the fcc vanadium sublat�tice, i.e., four � vacancies. In strongly nonstoichio�metric MXy compounds with the B1 structure, the Mmetal atoms occupy 4(a) positions with the coordi�nates (0 0 0) and nonmetallic atoms X occupy 4(b)positions with the coordinates (1/2 1/2 1/2) [1, 8].Nonmetallic atoms X are located in the octahedralinterstices of the fcc metal sublattice. Tetrahedralinterstices, i.e., crystallographic positions 8(c) withthe coordinates (1/4 1/4 1/4) in disordered nonsto�ichiometric compounds with the B1 structure are notoccupied by any atoms. Moreover, in all of the knownsuperstructures of nonstoichiometric compounds,atoms and vacancies are redistributed only over the4(b) (or 4(a)) positions of the basic disordered lattice.For this reason, the question arises of whether the dis�ordered VxO monoxide with vacancies only in thevanadium sublattice on the basis of which the V52O64

superstructure is formed has the B1 structure or thismonoxide has another cubic structure, but with the

same space group Fm m.

The problem of the second cubic phase has alreadyarisen in published works. In particular, Vol’f et al. [9]reported on the stepwise change in the lattice periodnear the composition VO1.05–VO1.06, which can beattributed to the presence of the phase interfacebetween two cubic phases close in structure in thisplace. Reuther and Brauer [10] arrived at a similarconclusion on the presence of two similar cubic phases

3

Atomic Displacements in the V52O64 Superstructureand the Short�Range Order in Superstoichiometric Cubic VOy

Vanadium Monoxide with Metal VacanciesA. I. Gusev

Institute of Solid State Chemistry, Ural Division, Russian Academy of Sciences, Yekaterinburg, 620990 Russiae�mail: gusev@ihim.uran.ru

Received July 28, 2009

Atomic displacements in the lattice of the tetragonal V52O64 superstructure have been experimentally deter�mined. It has been found that atomic displacement waves, which are attributed to the formation of the short�range displacement order, appear in the vanadium and oxygen sublattices of this superstructure. It has beenshown that the V52O64 superstructure is formed on the basis of disordered superstoichiometric cubic vana�dium monoxide with the short�range order in the metallic sublattice. The character of the short�range orderis such that vanadium atoms occupying tetrahedral positions are in the environment of four vacant sites of thevanadium sublattice. This means that the superstoichiometric VO>1.0 vanadium monoxide has a cubic struc�ture differing from the B1�type structure characteristic of most of the strongly nonstoichiometric cubic com�pounds MXy (X = C, N, O) of transition metals.

PACS numbers: 61.50.Ks, 61.66.Fn, 61.72.Dd, 64.70.Kb

DOI: 10.1134/S0021364009170135

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ATOMIC DISPLACEMENTS 377

in the region VO0.970–VO1.011, but they did not proposethe structures of the phases. Pointing to the nonmono�tonic variation of the lattice period, density, and defec�tivenesses of the oxygen and vanadium sublattices ofthe VOy vanadium monoxide near the equiatomiccomposition VO, Davydov and Rempel [11] also men�tioned the possibility of the existence of two cubicphases.

The presence of nonvacancy defects, namely, vana�dium atoms, which are present in a small amount inthe tetrahedral interstices of the cubic lattice can be animportant factor affecting the structure of the vana�dium monoxide [12, 13]. In this case, the vanadiummonoxide has the short�range order. Indeed, Ansers�son et al. [12] assumed that the superstoichiometricVO>1.0 vanadium monoxide contains tetrahedral clus�ters of the vacancies of the metallic sublattice; thevanadium atoms located in the tetrahedral intersticesof the cubic lattice are the centers of these clusters.Using the electron diffraction method, Ansersson [14]demonstrated that the disordered VO1.23 vanadiummonoxide has not only the short�range substitutionorder, but also significant atomic displacements. Inthe 51V NMR spectrum of the VO1.25 monoxide at atemperature below 5 K, Takagi et al. [15] detected aline corresponding to the V3+ ions occupying tetrahe�dral interstices.

The above background makes it possible to supposethat vanadium atoms in the tetrahedral environment,i.e., in the environment consisting of four sites of theoxygen sublattice and four sites of the vanadium sub�lattice, appear in superstoichiometric cubic vanadiummonoxides in addition to vanadium atoms in the octa�hedral environment consisting of oxygen atoms andoxygen vacancies �. In essence, this means the transi�tion from the cubic phase with the B1 structure, wherethe 8(c) positions are free of any atoms, to a new cubicphase, where the 8(c) positions are partially occupiedby vanadium atoms; note that both phases belong to

the same space group Fm m.In view of this circumstance, the atomic displace�

ments in the lattice of the tetragonal V52O64 super�structure are experimentally determined and somestatements are given concerning the short�range orderin this superstructure and in the superstoichiometricdisordered vanadium monoxide containing vacanciesonly in the metallic sublattice.

This investigation was performed with the VO1.29

(V0.775O) sample that has a composition near the upperboundary of the homogeneity interval of the cubic VOy

vanadium monoxide and contains vacancies only inthe metallic sublattice. The synthesis of the sampleand its certification were previously described in detailin [6].

The phase content and parameters of the crystallattice of various phases were determined through theX�ray diffraction measurements by the Bragg–Bren�

3

tano method in the CuKα1, 2 radiation in the 2θ angu�lar range from 10° to 140° with a step of Δ2θ = 0.03°with a scanning time of 10 s at a point. The final refine�ment of the structures was performed using the GSASsoftware package [16]. The background and profile ofthe diffraction reflections were described by the fifth�order Chebyshev polynomial and pseudo�Voigt func�tion, respectively.

The X�ray diffraction pattern shows that the freshlysynthesized VO1.29 sample contains only cubic vana�

dium monoxide (space group Fm m). The minimiza�tion of the X�ray diffraction pattern of the VO1.29

(V0.775O) sample annealed for 1000 h at 970 K indi�cates that it contains ~85 wt % of the tetragonal

ordered V52O64 phase (space group I41/amd( )) and~15 wt % of the rhombohedral V2O3 oxide (space

group R c( )). The refinement of the X�ray patternusing the GSAS software package [16] provides thefollowing results: the real ordered phase has the com�position V51.6O64, unit cell parameters at = bt =1.1746(1) nm and ct = 0.82527(8) nm, which are ingood agreement with the data reported in [3, 4]. Theordered V51.6O64 phase in the composition correspondsto the disordered cubic VO1.24 monoxide with a latticeperiod of a ≅ 0.412 nm. Taking into account the perioda of the basic disordered cubic VO1.24 monoxide andthe geometry of the ideal tetragonal phase V52O64, thetranslation vectors of the unit cell of the V52O64 phaseare at = [2 –2 0]cub, bt = [2 2 0]cub, and ct = [0 0 2]cub.In the ideal tetragonal structure V52O64, vanadiumatoms occupy the 16(h) position with the coordinates(0 1/8 1/4), two 16( f) positions with the coordinates(1/8 0 0) and (5/8 0 0), and the 4(a) position with thecoordinates (0 3/4 1/8); oxygen atoms are in two 16(h)positions with the coordinates (0 1/8 1/2) and (0 7/8 0)and in the 32(i) position with the coordinates (1/8 0 1/4).The 16(h) position with the coordinates (0 1/8 1/4) inthe metallic sublattice is vacant.

The refinement of the crystal structure shows thatall of the 16(h) sites with the coordinates (0 5/8 1/4) inthe tetragonal V52O64 superstructure observed in theannealed VO1.29 sample are vacant. Moreover, some16( f) sites of the metallic sublattice with the coordi�nates (5/8 0 0) are also vacant: the filling factor of thesepositions in the tetragonal phase of the annealed VO1.29

sample is 0.975 (see table). These sites in the perfectV52O64 superstructure are completely occupied byvanadium atoms.

The real structure of the ordered tetragonal V52O64

phase (space group I41/amd) exhibits noticeableatomic displacements shown in the table. The absolutevalues of the displacements of the oxygen and vana�dium atoms are related as ΔO2 > ΔO3 > ΔO1 > ΔV4 > ΔV2;i.e., the oxygen atoms O2 and vanadium atoms V2undergo the largest and least displacements, respec�

3

D4h19

3 D3d6

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GUSEV

tively. Figure 1 shows the directions of the displace�ments of the vanadium and oxygen atoms in the (0 0 z)planes, where z = 0, 1/4, 1/2, and 3/4, of the V52O64

superstructure. The lengths of the vectors indicatingthe displacement directions are proportional to thedisplacement magnitudes, but are increased by a fac�tor of 20.

As is seen, vanadium atoms V2 occupying the 16(h)positions with the coordinates (0 y z), where y = 1/8and z = 1/4, in the ideal V52O64 structure are shifted inthe (0 0 z) planes in the real ordered phase from eachother to the nearest vanadium vacancy �. In any(0 0 z) plane, the V2–V2 distance increases from0.29365 nm in the ideal structure to 0.29647 nm in thereal structure; the shortest distance between the atomsV2 in the neighboring planes increases to 0.29414 nm.Vanadium atoms V4 in the 16(f) positions with thecoordinates (x 0 0), where x = 5/8, in the real orderedphase are shifted in the (0 0 z) planes towards eachother. In any plane, the V4–V4 distance between themdecreases from 0.29365 nm in the ideal structure to0.28778 nm in the real structure; the shortest distancebetween the same V4 atoms in the neighboring planesincreases to 0.29568 nm. As a result, the atomic dis�placement waves of the V2 and V4 atoms appear in themetallic sublattice of the real ordered V52O64 phase(see Fig. 1). The V3 vanadium atoms in the 16(f) posi�tions with the coordinates (x 0 0), where x = 1/8, arenot shifted according to our data. The V5 vanadiumatoms that occupy the tetrahedral interstices and arelocated above and below the (0 0 z) planes by z = 1/8are in fixed 4(a) positions.

The O1 oxygen atoms occupying the 16(h) posi�tions with the coordinates (0 y z), where y = 1/8 andz = 1/2, are shifted in the (0 0 z) plane towards eachother, approaching the V2 vanadium atoms occupyingthe 16(h) positions with the coordinates (0 y – Δ z),

where y = 1/8, and shifting away from the V4 vana�dium atoms occupying the 16( f) positions with thecoordinates (x – Δ 0 0), where x = 5/8. The O2 oxygenatoms occupying the 16(h) positions with the coordi�nates (0 y 0), where y = 7/8, are shifted in the (0 0 z)plane towards each other, moving away from the vana�dium vacancies and approaching the V3 vanadiumatoms. In the planes under consideration, the O1–O1and O2–O2 distances between the nearest atomsdecrease to 0.28449 and 0.27768 nm, respectively; thedistances between the O1 atoms located in the neigh�boring atomic planes decrease to 0.28816 nm and thedistances between the nearest O2 atoms located in theneighboring atomic planes (the edges of the oxygentetrahedron) increase to 0.30084 nm. The O3 oxygenatoms occupying the 32(i) positions in the real orderedphase are shifted in the (0 0 z) planes towards eachother, approaching the nearest V4 atom and movingaway from the nearest vanadium vacancy � (seeFig. 1); the O3–V4 and O3–O3 distances between thenearest atoms in the (0 0 z) planes under considerationdecrease to 0.20302 and 0.28238 nm, respectively.Thus, the atomic displacement waves of the O1, O2,and O3 atoms exist in the oxygen sublattice of the realV52O64 superstructure.

The found displacement directions of the vana�dium and oxygen atoms predominantly coincide withthe displacement directions found in [17]. However, incontrast to [17], the atomic displacements along the zaxis are almost absent according to our data.

Each Vtetr atom in the ideal V52O64 superstructurehas the first coordination sphere that consists of fourO2 oxygen atoms and four vacancies of the vanadium

sublattice and has the radius R1 = a/4, where a isthe lattice period of the disordered cubic monoxide.The second coordination sphere with the radius R2 =

3

Ideal and real (taking into account the displacements of V and O atoms) structures of the tetragonal ordered V51.6O64 phase

(space group no. 141, i.e., I41/amd ( )) with at = bt = 1.1746(1) nm, ct = 0.82527(8) nm

AtomPosition

and multi�plicity

Atomic coordinatesFillingfactorin the ideal superstructure taking into account displacements

x/at y/bt z/ct x/at y/bt z/ct

V1 (vacancy �) 16(h) 0 0.625 0.25 0 0.625 0.25 0

V2 16(h) 0 0.125 0.25 0 0.1238 0.25 1

V3 16(f) 0.125 0 0 0.125 0 0 1

V4 16(f) 0.625 0 0 0.6225 0 0 0.975

V5 (V(t)) *4(a) 0 0.75 0.125 0 0.75 0.125 1

O1 16(h) 0 0.125 0.5 0 0.1289 0.5 1

O2 16(h) 0 0.875 0 0 0.8818 0 1

O3 32(i) 0.125 0 0.25 0.1298 0.0033 0.25 1

* The tetrahedral interstice is the 8(c) position of the basic disordered cubic structure.

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ATOMIC DISPLACEMENTS 379

a/4 consists of 24 atoms: 4 V2 atoms, 8 V3 atoms,4 O1 atoms, and 8 O3 atoms. The radius of the firstcoordination sphere in the real V52O64 superstructure,i.e., the shortest interatomic distance V5–O2, is0.18604 nm. Owing to atomic displacements, the sec�ond coordination sphere in the real V52O64 superstruc�

11 ture is split into four coordination spheres formed onlyby the O1, V2, V3, or O3 atoms with close radii0.34060, 0.34315, 0.34414, and 0.34987 nm, respec�tively (see Fig. 2).

Thus, the presence of atomic displacements in thereal V52O64 superstructure results in the formation of

Fig. 1. Directions of the displacements of the vanadium and oxygen atoms in the (0 0 0), (0 0 1/4), (0 0 1/2), and (0 0 3/4) planesof the V52O64 superstructure: (1) vanadium atoms V in the 16(h) and 16( f) positions, (2) vanadium atoms V(t) in the tetrahedralinterstices, 4(a) positions, (3) vacancies of the vanadium sublattice, and (4) oxygen atoms O. The displacement directions areindicated by arrows; the vector lengths are proportional to the displacement magnitudes and are increased by a factor of 20 (thedisplacement scale in the units of 0.005at is given below, where at is the unit cell parameter of the tetragonal V52O64 superstruc�ture). The contour of the unit cell of the V52O64 superstructure is shown by the solid line; and dashed line is the basic cubic lattice.The displacement waves of the V2 and V4 vanadium atoms are shown; displacement waves of oxygen atoms are not shown. TheV and O atoms are enumerated according to the table; the sign + or – in front of the tetrahedral symbols V5 means that the cor�responding atom is above or below the plane under consideration by a value of z = 1/8.

t

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GUSEV

the short�range displacement order. As a result, theelectron diffraction patterns should exhibit extendedplanar regions of diffusion scattering that do not passthrough the structural sites of the reciprocal lattice[18]. This is in agreement with the experimentalresults reported in [5], where the short�range order inthe ordered VO1.23 vanadium monoxide was revealedby the diffusion electron scattering method.

The investigation shows that some V atoms in theV52O64 superstructure are regularly located in tetrahedralinterstices. What is the probability that vanadium atomsare in tetrahedral interstices of the disordered cubicvanadium monoxide? Let us represent the compositionof the cubic VxOz vanadium monoxide taking intoaccount the presence of vacancies in the metallic and

nonmetallic fcc sublattices as Vx – t �1 – x + tOz�1 – z,

where t is the relative fraction of V(t) vanadium atomsin the tetrahedral interstices. Each V(t) atom in the dis�ordered monoxide has the nearest environment con�sisting of four sites of the metallic sublattice and foursites of the oxygen sublattice; each site can be occu�pied by an atom of its kind or be vacant. For the statis�tical distribution of the atoms and vacancies, the prob�ability PnV/mO that the nearest environment of the V(t)

atom contains n vacancies of the metallic sublatticeand m vacancies of the oxygen sublattice is given by theexpression

Vtt( )

(1)

The disordered cubic monoxide corresponding to theV52O64 superstructure does not contain oxygen vacan�cies and has the composition ~V0.8O (V13/16O). For�mula (1) with z = 1 and m = 0 has the form

(2)

According to this expression, the probability P0V/0O isthe maximum probability at 1 > x > 0.7 and t � x. Inother words, the environment consisting of four vana�dium atoms should formally be the most probablenearest environment of the V(t) atoms in the com�pletely disordered V0.8O monoxide. However, this isphysically excluded, because the radius of the tetrahe�dral interstice formed by the vanadium atoms is given

by the expression RtetrV = a/4 – RV � RV, which isclose to the vanadium atomic radius RV. Under thesame conditions, the radius of the tetrahedral inter�stice formed by four oxygen atoms is given by the

expression RtetrO = a/4 – RO ≤ RV, which is muchsmaller than the vanadium atomic radius RV. Thus, theprobability P0V/0O is zero due to the sizes of the vana�dium atoms. This is satisfied if short�range order existsat least in the first coordination sphere of V(t) atomsformed by the sites of the vanadium sublattice in the

PnV/mO C4nC4

m x t–( )4 n– 1 x– t+( )

nz4 m– 1 z–( )m

.=

PnV/0O C4n x t–( )

4 n– 1 x– t+( )n.=

3

3

Fig. 2. (a) The first and (b) second coordination spheres of the vanadium atom V(t) (V5) in the V52O64 superstructure: (1) vana�

dium atoms V occupying the 16(h) and 16( f) positions, (2) V(t) (V5) vanadium atoms in tetrahedral interstices, (3) vacancies ofthe vanadium sublattice, and (4) oxygen atoms O. The V and O atoms are enumerated according to the table. Twenty four O andV atoms forming the second coordination sphere of the V(t) (V5) atom in the ideal V52O64 superstructure are in the vertices of thedistorted small rhombicuboctahedron, which is a convex semiregular Archimedes body with point symmetry Oh. Owing to theindicated atomic displacements, the second coordination sphere in the real V52O64 superstructure is split into four spheres withclose radii 0.34060, 0.34315, 0.34414, and 0.34987 nm.

JETP LETTERS Vol. 90 No. 5 2009

ATOMIC DISPLACEMENTS 381

absence of the long�range order. In this case, the num�ber of vacant sites of the vanadium sublattice in thefirst coordination sphere of any V(t) atom is

(3)

where α1 and z1 = 4 is the short�range order parameterand coordination number of the first coordinationsphere of the V(t) atom, respectively. When consideringthe metallic sublattice, the V(t) atom in the disorderedmonoxide can only be in the environment of fourvacancies of the vanadium sublattice, i.e., n = 4.According to Eq. (3) with this number, the short�rangeorder parameter is α1 = –x/(1 – x).

The above analysis indicates that the disorderedsuperstoichiometric VxO vanadium monoxide withvacancies only in the vanadium sublattice has the

cubic structure (space group Fm m) with a partial fill�ing of tetrahedral 8(c) positions by vanadium atoms.This structure is characterized by the presence of theshort�range order in the metallic sublattice, whichappears because vanadium atoms in the 8(c) positionsare always in the environment of four vacancies � ofthe vanadium sublattice. Taking into account the pub�lished data, it can be assumed that the disorderedsuperstoichiometric vanadium monoxide VxOz

(Vx�1 ⎯ xOz�1 – x, z > x) with the minimum content ofoxygen vacancies � has the same short�range order inthe metallic sublattice. The disordered VxOz vanadiummonoxide with z ≅ x or z < x, i.e., with approximatelythe same contents of oxygen and metallic vacancies,has the B1 cubic structure usual for strongly nonsto�ichiometric compounds.

This work was supported by the Ural Division,Russian Academy of Sciences (interdisciplinaryproject “Short and Long�Range Orders in Nonsto�ichiometric Carbides, Carbon Hydrides, and Oxidesof Transition Metals”).

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14. B. Andersson, Acta Cryst. A 35, 718 (1979).15. S. Takagi, Y. Kitaoka, H. Yasuoka, et al., J. Phys. Soc.

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Translated by R. Tyapaev

n z1 1 α1–( ) 1 x–( ),=

3