A. I. GUSEV e t al. : Magnetic Susceptibility and Atomic Ordering in TaC, 459

phys. stat. sol. (a) IOG, 459 (1988)

Subject classification: 64.60; 75.30; S1.61

Institute of Chemistry, Academy of Sciences of the USSR, Sverdlovskl)

Magnetic Susceptibility and Atomic Ordering in Tantalum Carbide BY A. I. GUSEV, A. A. REMPEL, and V. N. LIPATNIKOV

A neutron diffraction and magnetic susceptibility study is made of the ordering of carbon atoms and vacancies in nonstoichiometric tantalum carbide TaC,. The magnetic susceptibility of tanta- lum carbide is found to decrease when this compound passes into an ordered state. From experi- mental magnetic susceptibility data, the short-range order parameters are calculated of the non- metallic sublattice of ordered tantalum carbide.

Die Anordnung der Kohlenstoffatome und Leerstellen im nichtstochiometrischen Tantalkarbid TaC, wird mittels Neutronenbeugung und magnetischer Suszeptibilitat untersucht. Es wird ge- funden, daR die magnetische Suszeptibilitat von Tantalkarbid abnimmt, wenn diese Verbindung in den geordneten Zustand ubergeht. Aus den experimentellen Werten der magnetischen Suszepti- bilitit werden die Nahordnungsparameter im nichtmetallischen Untergitter des geordneten Tantal- karbids berechnet.

1. Introduction

The physical properties of the nonstoichiometric transition metal carbides are known to be very sensitive to their structural state [l t o 71. Of these compounds, the non- stoichiometric tantalum carbide TaC, (1.0 >= y 2 0.74) with B1 structure has been studied recently. The wide region of homogeneity and the presence of a large number of structural vacancies in TaC, create (as a function of external conditions) pre- requisites for a statistical or ordered distribution of carbon atoms in the sites of the nonmetallic face-centered cubic (f.c.c.) sublattice. However, no experimental evidence has thus far been available for the ordering and its effect on the properties of tantalum carbide.

I n the present paper the ordering of carbon atoms and vacancies in the nonmetallic sublattice of TaC, is studied for the first time by magnetic susceptibility and neutron diffraction analysis methods.

Disregarding possible ordering, the magnetic susceptibility of tantalum carbide within its region of homogeneity was investigated earlier in [8 to 101. According to their data, the magnetic susceptibility of TaC, decreases with increase in structural vacancy concentration, passing from the paramagnetic t o the diamagnetic region, reaches a minimum corresponding to the carbide and then rises as the lower boundary of the homogeneity region is approached. Studies of the temperature dependence x (T) in the tantalum carbide TaC, have shown that the magnetic SUS-

ceptibility x varies with temperature in a nonlinear fashion and that its behaviour depends largely on carbide composition [9, 101. It should be noted that the suscepti- bility measurement technique (specifically prior to prolonged annealing of samples a t 1200 t o 1300 K) employed in [9] could promote a transition of TaC, from disordered

l) Pervomaiskaya 91, 620219 Sverdlovsk, USSR.

460 A. I. GUSEV, A. A. REMPEL, and V. N. LIPATNIKOV

t o ordered state and therefore some features of the x(T) relations obtained in [9] could arise from the ordering or disordering processes that occurred during the measurements.

2. Experimental

To investigate the influence of atomic ordering on the magnetic susceptibility of tantalum carbide, samples of TaC, with different carbon contents (y =- 0.98, 0.90, 0.85, 0.83, 0.82, 0.76) were synthesized. The synthesis was done by solid-phase sinter- ing of metallic tantalum and carbon powders a t a temperature of 2500 K during 20 h in a vacuum not worse than 0.0013 Pa (lo-, Torr). The homogeneity of the samples as well as their phase and chemical composition were verified by X-ray and chemical analyses. Two regimes of heat treatment were used t o produce samples of tantalum carbide in different structural states. Disordered tantalum carbide samples were produced by quenching from 1900 K a t a cooling rate of 2000 Kmin-l (regime “a”); prolonged annealing a t a temperature of 1600 K followed by slow (0.2 Kmin-l) cooling t o 750 K (regime “c”) was employed t o produce ordered carbide samples. Neutron diffraction patterns confirmed the presence of an ordered phase in TaC, (0.81 5 y 5 5 0.89) samples treated in regime “c”. The neutron diffraction patterns of other TaC, samples (y 5 0.80 and y 2 0.90) exhibited no superstructural reflections.

Magnetic susceptibility measurements were made on a high-sensitivity magnetic balance in the temperature interval 300 to 1300 K with a holding time a t each temper- ature for the susceptibility x to reach a steady-state value.

I n investigating x of quenched tantalum carbide over the composition range TaC,,,, to TaC,,,, under conditions of slow heating, we observed an up to now unnoted irreversible decrease in susceptibility (Fig. 1) a t a temperature of 960 to 1OOOK. The temperature T::::: a t which the susceptibility x decreases abruptly is apparently the temperature of incipient diffusion of carbon atoms in TaC, and corresponds to a transition from quenched nonequilibrium disordered state t o equilibrium ordered state. This is borne out by neutron diffraction data according to which the anneal taking place during susceptibility measurements up to T < 1100 K, in fact, leads t o the appearance, on the neutron diffraction patterns of TaC,,,,, Taco,,,, and of a set of superstructural reflections that testify to the formation of an ordered phase.

As the temperature was elevated further, a t T > T ~ ~ ~ ~ ~ , the quantity x first increased smoothly and then an abrupt increase in x occurred a t a temperature equal to 1090, 1130, and 1150 K for TaC,,,,, and respectively. Magnetic suseptibility measurements for the same samples when the temperature was lowered revealed the presense of a thermal susceptibility hysteresis in the interval 1070 to 1090, 1100 to 11.30, arid 1120 to 1150 K for TaCo.8B, TaC0.83, and Taco,,,, respectively (Fig. 1). The reversible susceptibility jump corresponding to the region of temper- ature hysteresis on the x versus T curves is associated with the equilibrium structural order-disorder phase transition that occurs a t temperature T&,. The presence of a hysteresis, i.e. a two-phase region, indicates that the order-disorder transition is a first-order phase transition. With the temperature lowered below T&,, the sus- ceptibility of these tantalum carbide samples decreased ; in the temperature range T < Tt:::: the susceptibility x of the carbide TaC, (0.82 5 y 5 0.85) annealed during the measurements was smaller in magnitude than the counterpart for the quenched disordered sample of the same composition (Fig. 1). Measurements showed also that the temperature dependences of the susceptibility for the tantalum carbide samples annealed under regime “c” practically coincided with those for the samples annealed during the measurement of x.

Magnetic Susceptibility and Atomic Ordering in Tantalum Carbide 461

300 500 700 900 1100 1300

Fig. 1. Effect of ordering on the mag- netic susceptibility of tantalum car- bide TaC,: o disordered state; ord- ered state; Q transient state (arrows show the sense of temperature varia- tion)

, TIIO -

The x versus T curves of the TaC, carbide (y 50.80 and y 2 0.90) exhibited no peculiarities since these tantalum carbide compositions lie outside the TaC,.,, t o TaC,,,, range in which, according to neutron diffraction data, an ordered phase is formed.

3. Discussion

Measurements have shown the ordering to be accompanied by a decrease in the sus- ceptibility of tantalum carbide (Fig. 2), the difference of the susceptibilities of TaC, in the disordered and ordered states, Ax = xdisord - xor&, being most pronounced for the carbide TaC,,,,. Earlier a similar lowering of the susceptibility occurred during ordering in the niobium carbide NbC, [3 t o 51. It might be well pointed ou t that for niobium carbide the effect of ordering on x is appreciably larger than that for a tantalum carbide with the same carbon content : e.g., a t 300 K for NbC,,,, and TaC,,,, the dif- ference Ax is 7.6 x and 3.9 x 10-6 e.m.u./mol, and for NbC,,,, and TaC,,,, the quantity Ax is 9.7 x 10-6 and 2.2 x 10-6 e.m.u./mol, respectively.

Which are the causes for the variation of the magnetic susceptibility in tantalum carbide as a function of its composition ? It is known [Ill that the measured magnetic

462 A. I. GUSEV, A. A. REMPEL, and V. N. LIPATNIKOV

Fig. 2. Dependence of the magnetic suscep- tibility on the composition of tantalum car- bide TaC, a t 300 K in disordered (1) and ordered (2) states and the difference of the susceptibilities in these states, A x =

values for Taco,,, and Taco,,, are taken from [9]) - - p*isora - p d (the suseptibility

susceptibility of the nonstoichiometric carbides is a sum of several contributions :

= X i + x i + xp f xz + Xorb 7 (1) where ~ " p and ~2 stand for the para- and diamagnetism of atomic cores (xi = 0; the quantity x i for Tab+ and C4+ is equal to - 14 x and -0.15 x e.m.u./mol, respectively), xp is the Pauli paramagnetism of conduction electrons, ~d the Landau diamagnetism of conduetion electrons, and %orb the Van Vleck orbital paramagnetism. If one extrapolates the measured susceptibility to 0 K arid introduces corrections for the para- arid diamagnetism of atomic cores, the resulting quantity x$ will be a sum of two paramagnetic contributions and one diamagnetic contribution : x$ = xP(0) + + x;(O) + xorb. A t 0 K the Pauli paramagnetism depends immediately only on the density of electron states a t the Fermi level, N(E,,) , and the Landau diamagnetism is proportional to xp and equal t o XI = -[(m,/m*)'] xJ3, with m, being the free electron mass and wb* the effective mass. AS the carbon content decreases the magnetic susceptibility of TaC, is lowered, reaching a minimum for TaC,,,, (Fig. 2) ; the quantity xt varies as a function of tantalum carbide composition in a similar fashion. Since the orbital paramagnetism xort, is positive and, with the composition of the disordered carbide TaC, departing from stoichiometry, may only increase due to the symmetry distortion of the nearest environment of metallic atoms, the observed decrease in susceptibility arid the reversal of i ts sign in going from TaC,,,, to TaC,,,, can be ex- plained only by the variation of xp and ~2.

The electron energy spectrum of group V transition metal carbides forms two over- lapping bands which correspond to Me-C and Me-Me interactions. The high-energy Me-Me band is less than half-filled even in a stoichiometric carbide. As the composition of the carbide deviates from stoichiometry the degree of filling of the Me-Me band varies, the density of electron states a t the Fermi level, N(E,! , decreasing 1111. As a consequence, when the composition of the tantalum carbide is varied from TaC,,,, t o Taco,,, the quantity xp decreases. As the lower boundary of the homogeneity region is approached the Me-Me band turns out to be nearly empty. According t o [lZ], the itinerant electron effective mass decreases rapidly when the occupancy of the energy band, which is less than half-filled, changes; this certainly leads t o an increase in diamagnetism. I n the case under consideration the change in Me-Me band occupancy, as the composition of the carbides departs from stoichiometry, is ac- companied also by a decrease in conduction electron effective mass and, as a conse- quence, by a rapid enhancement of the diamagnetism of the electron gas. When

Magnetic Susceptibility and Atomic Ordering in Tantalum Carbide 463

empty electronic levels appear in the overlap region of the Me-C and Me-Me bands the electron effective mass starts increasing, therefore the diamagnetic contribution decreases. A result of this variation of m* is the presence of a susceptibility minimum which corresponds to the overlap region of the Me-C and Me-Me bands. It should be noted that the quantity x$ = + xd is less than zero for a disordered TaC, carbide (0.76 < y < 0.83). This is possible if and only if the Landau diamagnetism ~2 of conduction electrons exceeds in magnitude the Pauli paramagnetism xi. Since X; =

= - [ (mo/m*)2] xJ3, then 1x21 > xp if m,/m* > 1/3. Thus the appreciable diamagnet- ism of a disordered nonstoichiometric tantalum carbide is due to the small conduction electron effective mass. On the whole, the variation of the magnetic susceptibility in the region of homogeneity of tantalum carbide is due to the variation of the para- and diamagnetism of conduction electrons. The dependence of the magnetic suscepti- bility on the composition of cubic carbides of other transition metals can be explained simpilarly .

What may be responsible for the decrease of the magnetic susceptibility of tantalum carbide during ordering ? A lowering of x during ordering is possible if m f d < mTisord. But if the change in conduction electron effective mass during ordering is small, the decrease of the susceptibility may come from the variation of the density of electron states a t the Fermi level. However, according to [6], the quantity N ( E , ) varies little or does not vary a t all during ordering in niobium carbide. If this holds good for tantalum carbide as well, then the afore-mentioned reason for the decrease of ;5 during the disorder-order transition may be excluded.

A possible and most probable cause for the decrease of the susceptibility owing t o ordering may be the variation of the contribution made by the orbital paramagnetism, for this contribution depends sensibly on the symmetry of the nearest surroundings of the metallic atom. I n a disordered nonstoichiometric carbide the nearest environ- ment of metallic atoms may have different symmetry, whereas in an ordered carbide such as Me&, the nearest environment of all the atoms is identical. Since the sym- metry of the nearest environment of metallic atoms in an ordered carbide is higher than that in a disordered one, the orbital paramagnetism for an ordered carbide is smaller in magnitude than the counterpart for a disordered one. A consequence of this is the observed lowering of the susceptibility a t the disorder-order transition.

Support for the effect of the nearest-environment symmetry on the magnetic susceptibility of tantalum carbide may come from a calculation of the short-range order parameters from the experimental data obtained. A substantiation and the technique of such a calculation have been proposed in [3 , 41.

The temperature dependences of the magnetic susceptibility for all the TaC, samples investigated in the 300 K to Tf:::: temperature range (for quenched dis- ordered samples) or in the interval from 300 K to T&, (for annealed samples contain- ing an ordered phase) are described with adequate accuracy by the function

The values of the coefficients a and b for tantalum carbides TaC, of different compo- sition in disordered and ordered states are summarized in Table 1. If the crystal is viewed as a collection of noninteracting clusters, then, according to [3, 41, its sus- ceptibility x may be expressed in terms of the susceptibility xi of individual clusters,

where Pi@) is the probability that an i-configuration cluster exists in the crystal, and i l i the multiplicity (number of equivalent configurations) of an i-configuration

464 A. I. GUSEV. A. A. REMPEL, and V. N. LIPATKIKOV

d

d"

h

M .

Magnetic Susceptibility and Atomic Ordering in Tantalum Carbide 465

cluster. To describe nonstoichiometric compounds with basis structure B1, the authors of 13, 41 have suggested as a basis cluster an octahedron (a metallic atom surrounded by six nonmetallic sublattice sites). Allowing for (2), (3) may be represented as

x(y, T ) = C (ai + biT2)AiPdy) , (4) a

whence

To correctly describe the tantalum carbide in the TaC,,,, t o TaC,,,, range, i t suffices to take into consideration four configurations of the basis cluster: a cluster with a tantalum atom completely surrounded by six carbon atoms, having the susceptibility xo and the probability Po (2, = 1); a cluster with one vacancy in the octahedral environment of the tantalum atom, having the susceptibility xI and the probability Pl ( I l = 6); clusters with two nonadjacent and adjacent vacancies, having the suscepti- bilities and probabilities xz, Pz(& = 3) and x3, P3 ( I 3 = 12), respectively.

In a disordered compound the interstitial atoms and vacancies in the nonmetallic sublattice are distributed statistically and therefore the cluster probabilities Pi can be found with the help of a binomial distribution. To determine the susceptibility of the clusters chosen, i.e. the coefficients ag and bi, it suffices, by using the experimental values of a ( y ) and b(y) and the calculated values of P;'"(y), t o solve two systems each of which consists of four linear equations of the form (5) (one for calculating a,, the other for calculating b%). The values of ag and b, thus found were used to calculate the probabilities Pyd(y) for TaC, containing an ordered phase. The calculation of the solution for Pyd(y) reduced to a system of equations that involved (5), the probability normalization condition C Itpi = 1, and the equation coupling the probabilities t o

1

the composition of TaC,: C liAiPi = y, where li is the fraction of sites occupied by 1.

carbon atoms in an i-configuration cluster. A basis cluster in form of an octahedron comprises two coordination spheres of the

nonmetallic sublattice. According to [3,4], the short-range order parameters for these spheres are

where Pc-o is the probability that a carbon-vacancy pair (C-0 ) will form. I n the present case the quantities P&, P e D , and Pg?o can be found from the equations

(7) bin Jc-apc-• = 2Y(l - Y) ,

with the multiplicity IC-o = 2. The calculation performed has shown that for the tantalum carbide samples ordered

during magnetic susceptibility measurements the values of the short-range order parameters for the first and second coordination spheres are negative and differ appreciably from zero: e.g., for TaC,,,, 0 1 ~ = -0.063 and aZ = -0.080 (Table 1). On the assumption that the structure of ordered tantalum carbide is similar t o that of 30 physiea (a) l 06 /2

466 A. I. GUSEV et al. : Magnetic Susceptibility and Atomic Ordering in TaC,

Nb,C, [3], t h e limiting values of t h e short-range order parameters for an ideal, ordered phase Ta,C, (TaC,,,,) a re equal t o a1 = a2 = -0.20. The difference of t h e calculated values of a1 a n d a2 from t h e limiting values indicates t h a t when annealing taritalum carbide during measure merit^ no complete ordering was attained.

Thus i t may he assumed t h a t t h e lowering of t h e magnetic susceptibility in nori- stoichiometric tau ta lum carbide during ordering is due t o a change in t h e oharacter of t h e nearest environment of tan ta lum atoms, as a result of which t h e orbital para- magnetic contribution t o t h e susceptibility of TaC, decreases.

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[4] A. I. GUSEV and A. A. REMPEL, phys. stat. sol. (a) 84, 527 (1984). [ 3 ] A. I. GUSEV and A. A. REMPEL, Piz. tverd. Tela 2 i , 1528 (1985). [6] A. A. REMPEL, 9. I. GUSEV, E. M. GOLOBOV, N. A. PRYTKOVA, and ZH. M. TOMILO, Fiz.

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[ l l] G. P. SHVEIKIN, S. I. ALYAMOVSKII, Yu. G. ZAINULIN, A. I. GUSEV, V. A. GUBAROV. and E. Z. KURMAEV, Nonstoichiometric Compounds and Their Solid Solutions, Ural Scientific Centre, Sverdlovsk 1984 (in Russian).

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(Received October 27, 1987)