ISSN 00213640, JETP Letters, 2009, Vol. 90, No. 3, pp. 191–196. © 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. 3, pp. 210–215.

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The VCy vanadium carbide with a basic cubic structure B1 belongs to the group of strongly nonstoichiometric compounds [1, 2]. Disordered VCy (VCy1 – y)vanadium carbide has a wide homogeneity region fromVC0.65 to VC0.875 in which carbon atoms C and structure vacancies form a substitution solution in thenonmetallic sublattice. A high concentration of structure vacancies promotes the ordering of the VCy carbide. The cubic VCy vanadium carbide was the first ofthe nonstoichiometric carbides of transition metals inwhich an ordered phase was found [3]; this was a phaseof the M8C7 type. The superstructure of the M2C typewas slightly later found in cubic TiCy titanium carbide[4] and the superstructure of the M6C5 type was foundin the VCy vanadium carbide [5, 6].

Atom–vacancy ordering noticeably affects theelectrokinetic properties of the strongly nonstoichiometric MCy carbides, but early works on the investigation of the electric resistivity of the nonstoichiometriccarbides were performed disregarding the structure(disordered or ordered) state of these carbides.

The resistivity of nine vanadium carbide samplesfrom VC0.755 to VC0.884 was measured at a temperatureof 300 K in [7]. The samples were obtained by carbidizing a vanadium wire 0.25 mm in diameter in amethane atmosphere at a temperature of 1773 K for8 h. According to the synthesis conditions, the studiedVCy carbides were disordered.

Borukhovich and Volkova [8] measured the electricresistivity ρ of the cubic VC0.72, VC0.76, VC0.84, andVC0.88 carbides at temperatures from 77 to 1200 K. Theporosity of the VCy samples exceeded 15%, informa

tion on their structural state is absent, but indirect dataon the synthesis method imply that they were disordered. Although porosity was taken into account, theabsolute values of ρ of all samples except for VC0.88

were evidently overestimated.The effects associated with the ordering of the VCy

carbide were studied in [9–12].The decrease in the electric resistivity by ~14% due

to the disorder–order transition VC0.833 V6C5 at atemperature of 1530 or 1548 ± 8 K and the increase inρ under the disordering of the vanadium carbide withthe hysteresis of the ρ(T) dependence near the transition temperature were found in [9, 10]. In [10], thestepwise change in the electric resistivity by ~4% nearthe temperature of the VC0.875 V8C7 transition wasestablished, which is equal to 1397 ± 15 K, which issimilar to a change in the VC0.833 V6C5 transition.In [9], it was noted that the studied vanadium carbidehad a structure of the V6C5 type, but no experimentalevidence was given; in [10], the crystal structure of theVC0.833 and VC0.875 carbides was not investigated andthere is no structural experimental evidence that somesamples were ordered and contained the V6C5 or V8C7

phase and other were disordered.The resistivity of the singlecrystal samples of the

VCy vanadium carbide (0.79 < y < 0.88) obtained byzone melting was measured at temperatures of 4.2 and298 K in [11]. The electric resistivity of the disorderedand ordered samples of the VC0.66, VC0.79, VC0.83, andVC0.87 vanadium carbides was measured at a temperature of 300 K in [12, 13], where it was found that theordering leads to an increase in the electroconductivity (or to a decrease in the electric resistivity). The

Effect of Carbon Vacancies on the Electric Resistivityof Nonstoichiometric VCy Vanadium Carbide

A. I. GusevInstitute of Solid State Chemistry, Ural Division, Russian Academy of Sciences, Yekaterinburg, 620219 Russia

email: gusev@ihim.uran.ruReceived June 25, 2009

The influence of the temperature, concentration, and distribution of structure vacancies of the carbon sublattice on the electric resistivity ρ of nonstoichiometric VCy vanadium carbide (0.66 ≤ y ≤ 0.875) has beenstudied in the temperature range of 300–1200 K. The symmetry and structure characteristics of the orderedV6C5 and V8C7 phases formed owing to lowtemperature annealing on various sections of the homogeneityregion of the VCy carbide. The dependence of the residual electric resistivity on the content of the disorderedvanadium carbide is explained by the atom–vacancy interaction and the change in the carrier concentrationin the homogeneity region of VCy.

PACS numbers: 61.50.Ks, 61.66.Fn, 61.72.Ji, 72.15.Eb

DOI: 10.1134/S0021364009150077

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structure of the ordered phases was determined by theXray diffraction method in [11–13].

Experimental investigations [3, 5, 6, 11, 13] andcalculations by the orderparameter functionalmethod [1] show that the ordering of the VCy carbidecan be accompanied by the appearance of the V6C5

and V8C7 superstructures with the transition temperatures 1400–1500 K.

Taking into account the above introduction, thecrystal structure of the VCy carbides in the quenchedand annealed ordered states, as well as the electricresistivity, which is very sensitive to the structure phasetransition, is investigated in this work in the homogeneity region of the VCy vanadium carbide.

Samples of the nonstoichiometric VCy carbideswith various relative carbon contents (y = 0.66, 0.79,0.83, and 0.875) were obtained by hot pressing of themixture of the powders of the VC0.875 vanadium carbide (Treibacher Powdermet, Austria) and metallicvanadium. The initial powder mixtures after mixing ina planetary ball mill were pressed at temperatures of2173–2273 K and a pressure of 35 MPa in an atmosphere of extremely pure Ar for 30 min; graphitefoilgaskets preventing the spalling of a sample were placedbetween the powder mixture and the graphite mold.The cooling of the samples to 600–700 K occurred in15 min with an average cooling rate of 100 K/min. Theporosity of the VCy samples was 1–2%.

The structure certification of the vanadium carbidesamples and the determination of the unitcell parameters of the disordered and ordered phases were performed by the Xray diffraction method in CuKα1, 2

radiation in the 2θ angular range from 14° to 120° witha step of ∆2θ = 0.02°. The Xray diffraction patterns ofthe quenched disordered VCy samples were detectedwith a scanning time of 2 s at a point by the Bragg–Brentano method using a Siemens D500 diffractometer and the measurements of the annealed vanadium carbides were carried out with an increased scanning time of 10 s at a point. The final refinement of thestructure of the phases was performed using the X’PertPlus program package [14].

The preliminary structure certification showed thatthe synthesized samples VC0.66, VC0.79, and VC0.83 werehomogeneous and contained only the cubic disordered phase VCy with the B1 structure; the periods aB1

of the unit cells of these samples are 0.41305, 0.41548,and 0.41596 nm, respectively. The Xray diffractionpattern of the sintered hotpressed VC0.875 sample contains very weak superstructure reflections, indicatingthat the cooling rate of the synthesized VC0.875 sampleis insufficiently high for holding the hightemperaturedisordered state. For this reason, the disorderedVC0.875 carbide was obtained by additional quenching:the synthesized sample was annealed at 1500 K for15 min in a quartz ampoule evacuated to 10–3 Pa and

the ampoule was dropped into water; the quenchingrate was 100 K/s.

To obtain vanadium carbides in the disorderedstate, the synthesized compact samples were annealedin sealed optical quartz ampoules evacuated to10⎯3 Pa; before annealing, the ampoules were washedby argon. The samples were annealed for 20 h at1173 K, then for 20 h at 1073 K, and finally for 60 h at973 K. The presence or absence of the ordered phaseswas controlled by Xray phase analysis.

The electric resistivity ρ was measured by the fourterminal method on 1.5 × 1.5 × 10mm VCy samplesobtained by hot pressing and quenched or annealedaccording to the mentioned temperature regimes. Themeasurements were performed in a vacuum of noworse than 10–3 Pa (10–5 mercury mm) in the temperature range of 300–1200 K with a step of about 1 K;the currents flowing through the samples were 20 and100 mA. To ensure a reliable electric contact, the sample surfaces were coated by In–Ga paste. The stabilityof the temperature in the measurements was maintained with an accuracy of 0.2 K and the average heating rate was 1 K/min. The porosity of the samples wasless than 2%; for this reason, the correction to theporosity was not introduced when determining ρ. Therelative error of the measurement of the electric resistivity was no more than 0.5%.

The Xray diffraction patterns of the quenched andannealed samples of the VC0.66, VC0.79, VC0.83, andVC0.875 vanadium carbides are shown in Fig. 1. As seenin this figure, the Xray diffraction patterns of theannealed VC0.66 sample and the same carbide afterquenching are almost the same and contain only thestructure reflections of the basic cubic phase with theB1 structure. In addition to the structure reflections,weak superstructure reflections appear on the Xraydiffraction patterns of the VC0.79, VC0.83, and VC0.875

carbides after their annealing.

Let us first discuss the diffraction data that allowedfor the determination of the structure of the orderedphases of the nonstoichiometric VCy vanadium carbide. The performed analysis shows that the Xray diffraction pattern of the annealed VC0.79 carbide contains superstructure reflections of only the monoclinic(space group C2/m) ordered phase of the V6C5 type(see Fig. 1). Sites at the 2(a) crystallographic positionsof the nonmetallic sublattice of the ideal monoclinic(space group C2/m) structure V6C5 are vacant,whereas sites at the 2(d), 4(g), and 4(h) positions areoccupied by carbon atoms C [15]. The maximumlongrange order parameter η depends on the composition of the MXy compound and the type of theformed superstructure M2tX2t – 1 [1]:

(1)ηmax y t,( )2t 1 y–( ) if y 2t 1–( )/2t,≥

2ty/ 2t 1–( ) if y 2t 1–( )/2t.<⎩⎨⎧

=

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EFFECT OF CARBON VACANCIES ON THE ELECTRIC RESISTIVITY 193

According to Eq. (1), when the V6C5 (t = 3) superstructure is formed in the VC0.79 carbide, the maximum longrange order parameter is ηmax = 2ty/(2t –1) = 0.95. The quantitative minimization of the Xraydiffraction pattern of the annealed VC0.79 carbideshows that the filling factor of 2(a) positions is a nonzero value of 0.04 and the filling factors of the 2(d),4(g), and 4(h) positions by C atoms are 0.94. Thesefilling factors correspond to the longrange orderparameter η = 0.90, which is very close to ηmax = 0.95.Thus, the annealing conditions make it possible toobtain the VC0.79 carbide in the state with almost themaximum possible longrange order parameter. Theunit cell parameters of the V6C5type ordered phaseformed in the VC0.79 carbide are a = 0.50940(2) nm,b = 0.88140(3) nm, c = 0.50991(2) nm, and β =109.342°; the period aB1 of the basic cubic lattice is0.41607 nm. The small difference between the periodsa and c indicates the distortion of the crystal lattice ofthe V6C5type superstructure.

The minimization of the Xray diffraction patternof the VC0.83 sample (see Fig. 1) annealed in 100 h from1170 to 970 K shows that it contains ~70 wt % of themonoclinic V6C5 phase (space group C2/m) and~30 wt % of the cubic V8C7 phase (space group P4332)with the lattice period a = 0.83402 nm. The presenceof two ordered phases in the annealed VC0.83 vanadiumcarbide was previously mentioned in [13]. The unitcell parameters of the V6C5 monoclinic superstructureformed in the annealed VC0.83 vanadium carbide area = 0.51093(2) nm, b = 0.88454(3) nm, c =0.50897(2) nm, and β = 109.436°. The period aB1 ofthe basic cubic lattice of the annealed VC0.83 carbide is0.41657 nm. The quantitative minimization of theXray diffraction pattern of the annealed VC0.83 carbide shows that the filling factor of vacant 2(a) positions by carbon atoms in the ordered V6C5 phase is 0and the filling factor of the 2(d), 4(g), and 4(h) positions are 1, which corresponds to the longrange orderparameter η = 1.0.

The analysis of the position and intensity of superstructure reflections observed on the Xray diffractionpattern of the annealed VC0.875 carbide (see Fig. 1)shows that this carbide contains only the ordered cubic(space group P4332) phase V8C7 with the unit cellperiod a = 0.83362(7) nm and with a longrange orderparameter of 1.0. The period aB1 of the basic cubic lattice of the annealed VC0.875 carbide is 0.41681 nm. Theminimization of the Xray diffraction pattern of theannealed VC0.875 carbide revealed large displacementsof V atoms in the ordered cubic phase V8C7, leading tothe appearance of additional weak diffraction reflections , , and at 2θ =

30.30°, 32.12°, and 44.70°, respectively, which areabsent on the theoretical Xray diffraction pattern ofthe ideal V8C7 superstructure. Large atomic displace

220( )V8C7221( )V8C7

410( )V8C7

ments in the V8C7 superstructure were previouslyrevealed in [16].

Careful analysis of the Xray diffraction pattern ofthe quenched VC0.875 sample (see Fig. 1) indicatestraces of the smeared weak superstructure reflections

and of the V8C7 phase at the angles

2θ ~ 18.5° and 23.9°, respectively. The Xray diffraction patterns of the quenched VC0.79 and VC0.83 carbides contain a smeared weak superstructure reflection at 2θ ≈ 23.6°.

111( )V8C7210( )V8C7

11 1–( )V6C5

Fig. 1. Xray diffraction patterns of quenched andannealed samples of the nonstoichiometric VC0.66, VC0.79,VC0.83, and VC0.875 vanadium carbides obtained inCuKα1, 2 radiation. For the VC0.66 carbide, only the Xraydiffraction pattern of the annealed sample is shown; theXray diffraction pattern of the quenched sample has thesame form. The indices of the structure reflections of thebasic disordered phase with the B1 structure are given inthe upper part of the figure. The long and short dashes inthe lower part of the figure correspond to the diffractionreflections of the ordered monoclinic (space group C2/m)V6C5 phase and ordered cubic (space group P4332) V8C7phase. The annealed VC0.83 carbide contains ~70 wt % ofthe monoclinic (space group C2/m) V6C5 phase and~30 wt % of the cubic (space group P4332) V8C7 phase.

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Thus, the longterm annealing of the VC0.79 andVC0.875 carbides resulted in the formation of orderedV6C5 and V8C7 phases, respectively. The annealedVC0.83 carbide contains not only the ordered V6C5

phase, but also the ordered V8C7 phase. The presenceof two ordered phases in the annealed VC0.83 carbide isin agreement with the phase diagram of the V–C system [17] and experimental data [13, 18]. The longrange order parameter in the ordered phases of theannealed VC0.79, VC0.83, and VC0.875 carbides is close tothe maximum possible value. After any thermal treatment, the VC0.66 carbide contains only the disorderedcubic phase with the B1 structure. The presence oftraces of smeared superstructure reflections on the Xray diffraction patterns of the quenched VC0.79, VC0.83,and VC0.875 carbides indicates that a small longrangeorder parameter exists despite quenching. The periodsof the basic cubic phase with the B1 structure in the

annealed ordered VC0.79, VC0.83, and VC0.875 carbidesare larger than those in the respective quenched carbides: 0.41607 and 0.41548, 0.41657 and 0.41596, and0.41681 and 0.41638 nm, respectively. This is indirectevidence that the VCy V6C5 and VCy V8C7

transitions are firstorder transitions. The conclusionthat these transitions are firstorder transitions waspreviously made in [15] on the basis of the symmetrygrouptheoretical analysis of the VCy V6C5 andVCy V8C7 disorder–order transitions and in [10,13, 19, 20] on the basis of the experimental data.

The measured temperature dependences of theelectric resistivity ρ(T) of the quenched and annealedVC0.66, VC0.79, VC0.83, and VC0.875 carbides are shown inFig. 2. Over the entire temperature range, the electricresistivities of the quenched disordered VC0.79, VC0.83,and VC0.875 carbides are larger than the electric resistivities of the respective annealed carbides. The measured ρ(T) dependences are noticeably lower than the

Fig. 2. Temperature dependences of the electric resistivityρ(T) of the VC0.66, VC0.79, VC0.83, and VC0.875 vanadiumcarbides in the () quenched and () annealed states. Theelectric resistivities of the quenched and annealed VC0.66samples coincide with each other within the measurementerror. Only every sixth experimental point of the measuredρ(T) dependences are shown for all of the curves. For comparison, the ρ(T) dependences measured in [10] for theordered V6C5 and V8C7 carbides and the disordered VC0.83and VC0.875 carbides are shown in the same temperaturerange.

Fig. 3. The effect of ordering on the electric resistivity ρ ofVCy VC: 1 and 2 are the electric resistivities of thequenched and annealed VCy samples, respectively, at300 K according to the data of this work (the arrows markchange in the electric resistivity of the VCy carbide afterordering annealing); 3 and 4 are the electric resistivities ofVCy single crystals at temperatures of 298 and 4.2 K,respectively, according to the data from [11]; 5 and 6 arethe electric resistivity of the disordered VCy carbides at atemperature of 300 K according to the data from [7] and[8], respectively. The dash–dotted line is the dependenceof the electric resistivity on the composition of the disordered VCy carbide at ~300 K estimated in [11]. The regionsof the existence of the ordered V6C5 and V8C7 phases areindicated in the homogeneity region of the cubic VCy carbide.

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EFFECT OF CARBON VACANCIES ON THE ELECTRIC RESISTIVITY 195

corresponding dependences obtained for the disordered VCy carbides in [8] and the dependences for theordered and disordered VC0.83 carbide presented in[10]. The temperature coefficients of the electric resistivity of the quenched disordered and annealedordered VC0.83 and VC0.875 carbides investigated in thiswork are from 0.026 to 0.047 µΩ cm K–1 and areapproximately one third of the values measured in[10]. The absolute values of the electric resistivity ofthe quenched and annealed VC0.66, VC0.79, VC0.83, andVC0.875 carbides at 300 K are close to the valuesobtained in [12, 13].

Figure 3 shows the measured electric resistivities ofthe VC0.66, VC0.79, VC0.83, and VC0.875 carbides in thequenched disordered and annealed ordered states at atemperature of 300 K. It is clearly seen that the electricresistivities of the VC0.79, VC0.83, and VC0.875 carbidesdecrease owing to annealing and the resulting ordering; the largest change in the electric resistivity ρ isobserved for the VC0.875 carbide in which the cubic(space group P4332) ordered V8C7 phase is formed.

With an increase in the relative content of carbon,the electric resistivity ρ(y) of the VCy carbides at T =300 K in the quenched disordered and annealedordered states decreases. The observed variation of theelectric resistivity is caused by a decrease in the scattering of carriers on the structure vacancies whoseconcentration decreases when the composition of theVCy carbide approaches the upper boundary of thehomogeneity region.

These results can be compared to the data [11]obtained when measuring the resistivity ρ of singlecrystal VCy samples (0.75 ≤ y ≤ 0.88) at temperaturesof 4.2 and 300 K. The dependence of the electric resistivity ρ(T = 4.2 K) on the relative carbon content inthe VCy carbide (see Fig. 3) exhibits pronounced minima corresponding to the stoichiometric compositionsof the ordered phases V6C5 (VC0.83) and V8C7 (VC0.875).The dash–dotted line in Fig. 3 is the dependence ofthe electric resistivity on the relative carbon content inthe disordered VCy carbide at ~300 K theoreticallyestimated in [11]. The measured resistivity of the disordered vanadium carbides is smaller than the valuesobtained in [11] because a certain longrange orderexists in these samples. Indeed, it is difficult to obtaincompletely disordered vanadium carbides by means ofquenching from a high temperature. This particularlyconcerns the V8C7 phase: weak superstructure reflections remain on the diffraction pattern of thequenched VC0.875 carbide even after quenching from atemperature of 1500 K with a high cooling rate (seeFig. 2).

Conductivity in the vanadium carbide is predominantly electronic and the dependence of the electricresistivity on the composition VCy indicates thedependence of the carrier concentration on the content of structure vacancies and the scattering of elec

trons on them. The residual electric resistivity ρres(y)of the disordered VCy carbide can be described using amodified Nordheim’s rule (taking into account theatom–vacancy and electron–vacancy interactions) inthe form ρres(y) = Ay(1 – y)/n(y), where A is the normalization factor and n is the carrier concentration(conduction electrons). In the first approximation, thecarrier concentration n is proportional to [N(EF)]3,where N(EF) is the density of electronic states at theFermi level. Therefore, the dependence of the residualelectric resistivity on the composition of the disordered VCy carbide is given by the expression

(2)

The calculation [21] of the electronic structure ofthe nonstoichiometric disordered vanadium carbideby the Korringa–Kon–Rostoker method in thecoherentpotential approximation (KKR–CPA)shows that when the carbide composition changesfrom VC0.875 to VC0.65, the density of electronic statesat the Fermi level N(EF) per unit cell changes from~17.5 to ~20.7 Ry–1, passing through a pronouncedminimum of ~14.2 Ry–1 for the VC0.78 carbide.

The approximation of the results of this work on theresidual resistivity of the disordered VCy carbides byfunction (2) taking into account the data from [21] onthe density of states N(EF) of the disordered VCy carbides makes it possible to calculate the concentrationdependence ρres(y) (see line 1 in Fig. 4). For comparison, the resistivities of the disordered VCy carbides

ρres y( ) Ay 1 y–( )/ N EF( ) y( )[ ]3.∼

Fig. 4. (1) Residual electric resistivity ρres(y) and (2) density of electronic states at the Fermi level N(EF) [21] versusthe relative carbon content in the disordered VCy vanadium carbide. Line 1 is approximation (2) of the experimental results that are obtained in this work and are shownby closed circles 3. For comparison, squares 4 are the electric resistivities of the disordered VCy carbides measured ata temperature of 4.2 K in [11] and closed triangles 5 are theresidual electric resistivities of the disordered VC0.83 andVC0.875 carbides according to the data from [10].

N(E

F)

N(E

F)

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measured at a temperature of 4.2 K in [11] and theresidual electric resistivities of the disordered VC0.83

and VC0.875 carbides according to the data from [10]are shown in Fig. 4. The normalization factor A inEq. (2) is 2.55 × 106 µΩ cm Ry–3 (or 16 µΩ cm eV–3

form. units–3). As is seen, the calculated ρres(y) dependence is in satisfactory agreement with the experimental data.

The analysis of the structure and electric resistivityof the nonstoichiometric VCy vanadium carbide(0.65 < y ≤ 0.875) has shown that the ordering of VCy

with the formation of the monoclinic (space groupC2/m) and cubic (space group P4332) V6C5 and V8C7

superstructures is accompanied by a decrease in theresistivity. The dependence of the resistivity on thecomposition of the disordered VCy carbide appearsdue to the scattering of electrons from structure vacancies of the carbon sublattice and the dependence of thecarrier concentration on the vacancy concentration inthe carbide.

I am grateful to V.N. Lipatnikov for the vanadiumcarbide samples.

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Translated by R. Tyapaev