A. I. GUSEV and A. A. REMPEL: The Atomic Ordering in the n'iobium Carbide 527

phys. stat. sol. (a) 84, 527 (1984)

Subject classification: 1.3; 18.1; 22

Institute of Chemistry, Academy of Sciences of the USSR, Gral Scientific Centre, Sverdloosk' j

A Study of the Atomic Ordering in the Niobium Carbide Using the Magnetic Susceptibility Method

BY A. I. GUSEV and A. A. KEMPEL

The magnetic susceptibility of a nonstoicliiometric niobium carbide in the ordered and disordered state in the region of homogeneity of the Nb,C, phase is measured. It is for the first time that the magnetic susceptibility method is employed to analyse the atomic distribution in the crystal and to determine the short-range order parameters. In terms of the clustcr approach proposed, a short- range parameter calculation is carried out which shows that the variation of the magnetic suscepti- bility due to ordering in the niobium carbide is associated with, chiefly, the formation of short- range order rather than with the formation of long-range order. A considerable increase in the diamagnetism of an ordered niobium carbide compared to that of a disordered one is noted.

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1. Introduction

Magnetic susceptibility is one of the few properties of a crystalline material which is determined by the electronic subsystem alone. Therefore, a magnetic susceptibility study of the atomic ordering in the niobium carbide permits ascertaining the features peculiar to the effect of the formation of short-range and long-range order on changes in the electronic structure of the compound.

The magnetic susceptibility x of a cubic (NaC1-structure) niobium carbide NbC, within its region of homogeneity (0.72 < y < 1.0) was studied in [l to 31. According to those papers, with increasing vacancy concentration of the carbon sublattice in NbC, the magnetic susceptibility decreases quickly, passing from the paramagnetic to the diamagnetic region and reaching a niinimuni near the conipositions NbCo 79 [I], NbC0,80 [2], or NbCo,82 [3], and then rises again up to paramagnetic values. A study of the dependence x ( T ) of the niobium carbide in the region of homogeneity a t tern- peratures above 300 K has revealed that the magnetic susceptibility varies nonlinearly with temperature, this behaviour depending substantially on coinposition [2]. It should be noted that the above work was effected with NbC, specimens synthesized under different heat treatment conditions without taking into account the possible

j Prrvomaiskaya 91, 620219 Sverdlovsk, USSR.

528 A. I. GUSEV and A. A. REMPEL

ordering of carbon atoms and structural vacancies in the nonmetallic sublattice. It is known that an Nb,C,-type phase possessing a region of homogeneity in the NbCO,sl to NbCoss coniposition range is produced as a result of annealing at a temperature below the order-disorder transition teniperature ( Ttrarls = 1258, 1304, and 1355 K for NbCo 81, NbCo 83, and NbCo 88 respectively) [4, 51. Therefore, some peculiarities in the teniperature dependence of x in the niobium carbide, obtained in [2], could arise from the order-disorder transition occurring during measurements. In this context the purpose of the present investigation was to t ry to reveal the effect of atomic order- ing on the magnetic susceptibility of NbC, by measuring x of niobium carbide speci- mens in both ordered and disordered states over a wide temperature interval.

Niobium carbide NbC, in the region of homogeneity was synthesized by caking powders of metallic niobium and carbon in vacuum a t 2300 K. The chemical and phase compositions as well as the homogeneity of the speclinens were checked by chemical and X-ray analyses. To produce NbC, specimens possessing states with different de- grees of ordering three thermal treatment regimes were employed. specimens contain- ing only a disordered phase were produced by quenching from 2300 K. Niobium carbide specimens containing an ordered and a disordered phase a t a tinie were syn- thesized as a result of additional annealing a t 1300 K followed by fast cooling. NbC, specimens containing only an ordered phase were produced as a result of annealing at 1300 K followed by slow (0.5 K/min) cooling. Magnetic susceptibility measurements were made following the technique described in [2]. The magnetic susceptibility was measured in the temperature interval between 300 and 1300 K with the specimens being soaked a t each measurement tcmperatiire until a constant value of x not varying with tinie was reached.

2. Results and Discussion

Within measurement accuracy, the temperature dependence of the magnetic suscepti- bility for the NbC, specimens invest>igated (Fig. 1 , 2 ) in the interval from 300 K to the

2 0 t I , I , j 300 500 700 000 1100 1300

TiKi -~ -+ T(K) ---A

Fig. 1 Fig. 2 Fig. 1. Ordering influence on the magnetic susceptihility of NbC0.83: 1 quenched disordered car- bide NbC0.83; 2 carbide NbCos3 (a = -0.132) ordered during measurement of x ; 3 annealed ordered carbide NbC0.83 (a = -0.135)

Pig. 2. Ordering influence on the magnetic susceptibility of NbC,: x NbCl.00, o NbCo.88,. NbCo 81 ; {a) quenched disordered carbide NbC,; (c) annealed ordered carbide NbC,

Study of Atomic Ordering in Xiobiurn Carbide from Magnetic Susceptibility 529

incipient order-disorder transition temperature (for ordered specimens) or disorder- order transition temperature (for quenched disordered specimens) is described as

The values of the coefficients 11 and b are tabulatcd. Typical x versus T curves for specimens of niobium carbide KbC, in ordered and

disordered states are presented in Fig. 1. When measured, t,he suscept,ibility of iYbCo,8s specimens quenched from temperatures exceeding appreciably Ttrans, whose neutron diffraction patterns display no superst'ructural reflexes, drops abrupt'ly (curve 1) down to the susceptibilit'y of ordered specimens (curve 2 ) of the same composition (Fig. 1). The neutron diffraction patterns obt,ained for NhC, (0.81 5 y 5 0.88) speci- niens after measuring the temperature dependencc of the magnetic susceptibilit; exhibit siiperstrnctnral reflexes test'ifying to ordering which takes place during rrieasure- ment. It' should he noted that the observed t,ransit,ion teniperat'ure TZ,,,, from a quench- ed nonequilihriuni disordered state to an ordered stmate (see Table 1) must8 he distin- guished from the t,eiiiperature corresponding to the transition from an equilibriuiii dis- ordered state to an ordered one. The atomic ordering in NbC, occurs t,hrough diffusion nirchanisnis. Therefore, the inception of diffusion for NbC0,R3 a t a smaller T&,, value (Table 1) as compared mit,h carbides of other compositions indicates that t8he dif- ference between the energies of specimens of this composition in disordered and ordered states i s largest. In other words, when NbC0.83 is being ordered the decrease in free energy is higher than t'hat of other KhC, conipositions. As Ttralls is approached the riiagnetic suscept'ihility of ordered PibC, specimens increases quickly, but the absence of a pronounced step on the x (T) curve (Fig. 1, 2 ) does not allow the order-disorder transition teinperat'ure to be determined from these dat'a. The teniperature dependences of the susceptibility for niobium carbide specimens of ot,her compositions in states wit'h different degrees of ordering (Fig. 2 ) can he explained in tmhe same way as those for KthCo,8S.

Magnetic susceptibility nieasiireiiients have shown tha t the minima of 71 for speci- mens of NbC, in disordered and ordered states occur for the conipositions NbCo.hu and NhCo.xl, respectively (Fig. 3) . This permits the differcnce in experimental evidence of 12, 31 t o be accounted for by the fact that the susceptibility measurements in t,hose papers were carried out, on niobiuni carbide specinicns in states wit'h different degrees of order.

If the variation of x at tfhe t,ransition from a disordered state to an ordered one is assumed to be associated with only the formation of long-range order, the srisceptibil- ity of speeiniens containing a disordered and an ordercd phase a t a time should be 1)ro- portional to the content of t,hose phases. However, measurements have shown that' the uiagnitude of the susceptibility of two-phase specimens practically coincides with the susceptibility of ordered speciniens having the same composition, i.e. does not, depend on the ordered-phase content. The establishment, of long-range order is acconlpanied by the formation of short-range order, therefore t,hc susceptibility x being independent, of ordered-phase content t,estifies that the iiiagnetic suscept,ibilit,y is det'eruiined mainly by the format'ion of short-range order rather than by long-trange order. I n this case the coincidence of the quantities 3~ for specimens containing an ordered and a disorder- ed phase and containing an ordered phase only stenis from the fact t'hat, t'hose speci- mens were annealed a t t8he sanie temperature, as a result of which they have approxi- mately equal shohrange order parameters. I n specimens annealed at, a teniperat,ure well above Ttrarlh and then quenched, t'he short-range order parallleter is appreciably smaller than that in specimens annealed near Ttrans, therefore, t.heir snsceptibilit'ies differ considerably. The decrease of x a t the disorder-order transition results from the 35 pliysim (a) 81/Y

530 A. I. GUSEV and A. B.REMPEL

quick increase of the short-range order parameter during ordering, and the increase of x a t the order-disorder transition is due to the decrease of the short-range order par- ameter during disordering. The concept concerning the decisive effect of short-range order on the magnitude of the magnetic susceptibility may be corroborated by a calculation of the short-range order parameters from the experimental data obtained.

If the equivalent disordered lattice sites are occupied by particles of two species, A and B, the probability of detecting a particle of a given sort, A or B, in any Ising lattice site coincides with the relative share of sites occupied by particles of species A or B, i.e. coincides with the concentrations C, and C, and C, + C, = 1 (what is im- plied by particles is both atoms and structural vacancies). I n case of a statistical distri- bution of N particles in the lattice i t is possible, for any coordination sphere j , to find the total number of AA, AB, and BB particle pairs as their sum N, = N,, + N g g f + N B , ~ or, according to the binonrinal distribution,

where E , is the coordination number of the j-th sphere. In the presence of short-rango order a particle of a given species will be surrounded preferentially by either particles of the same species or particles of the other species, depending on the relation between interparticle interaction energies. Obviously, the short-range order parameter for any coordination sphere j here is the deviation of the number of pairs of unlike particles N i B in a crystal with a certain degree of order from the number of pairs of unlike par- ticles Ny{ in the same crystal in the case of statistical (absolutely disordered) particle distribution in lattice sites,

or, proceeding to the probabilities of A B pairs (pi, = NiB/N,, p!?;: = N E l x j = = 2ilrk1c*c,/Nk, = 2c,cu),

The ordering in the niobium carbide is associated with the redistribution of carbon atoms and structural vacancies in the carbon sublattice. To estimate the short-range order parameter 01 is therefore required to determine the real probability of the forma- tion of a “carbon atom-vacancy” (C-0 ) pair. The binomial probability of the forma- tion of a C-n pair, which corresponds to the disordered state, depends on composition only and, for NbC,, is equal to PF2n = 2 y ( l - y) for any coordination sphere.

If the crystal is represented as a set of noninteracting clusters, its magnetic sus- ceptibility x may be expressed in terms of the susceptibility x t of individual clusters,

where Pl (y ) stands for the probability of an i-configuration cluster in the crystal and C Pt(y) = 1. It follows from expression (4) that as clusters such sets of atoms should be selected the susceptibilities of which do not depend, in a first approximation, on coniposition and degree of order, since only in this case the susceptibility of the crystal, ~ ( y ) , changes only when the cluster probabilities P,(y) vary. The magnetic susceptibil- i ty of NaC1-structure interstitial compounds is determined mainly by metallic atom electrons, each of the metallic atoms being in the octahedral environment of six occu- pied or vacant nonmetallic sublattice sites. The analysis of NMR spectra [4, 51 has

Study of Atomic Ordering in Niobium Carbide from Magnetic Susceptibility 53 1

Fig. 3. Concentration dependence of magnetic susceptibility of NbC, at T = 300 K: 1 disordered carbide NbC,; 2 order- ed carbid? XbC,

--?

07 08 09 10 Y --

shown tha t with the variation of the number of vacancies in the nearest coordination sphere of a nietallic atom the electron density of the niobium nucleus varies. It hence follows tha t when the number of vacancies in the first coordination sphere varies due to the variation of the niobium electron density, the magnetic susceptibility will vary, too. For NaC1-structure interstitial compounds it is thus physically reasonable to select a cluster in the form of an octahedron with a iiietallic atom in the centre. The suscep- tibility of such a cluster does not depend on the coniposition and the degree of order in the carbide investigated, but is determined by only the niiinber of vacancies in the environment of a metallic a t o m Therefore, the crystal of a nonstoichionretric niobium carbide niay be regarded as a set of clusters in the form of cotahedra with different niobium atom environments - from complete, Po, to entirely defective, P, (Fig. 4). The relation between the numbers of such clusters with different vacancy content, i.e. their probabilities P,(y) will vary both with the coniposition of the compound and with the degree of order, thereby causing a variation of the magnetic susceptibility of the compound according to (4).

The real probability of the forination of a C-• pair for the first coordination sphere can be expressed in terms of the cluster probability

P c - p = c %PL(Y) 2 (5) where n, is the relative share of C-m pairs in the first coordination sphere of an i-con- figuration cluster.

I n order to describe correctly the niobium carbide NbC, (1.0 > y > 0.80) it suffices to consider four types of clusters: a cluster, in which the niobium atom is surrounded hy six carbon atonis, with the susceptibility xo and the probability Po: a cluster with one vacancy In the octahedral environment of a niobium atom, which has the sus-

$@@@@ \

Fig. tion 4. of Set NaC1-structure of clusters for intersti- descrip-

tial compounds such as MeXV J 6 4 5 6 (X = C, N) ; o Me, 0 C, vacancy

\

3 5 *

532 A. I. GLJSEV and 9. A. R,EMPEL

ceptibility x1 and the probability Pl; clusters with two nonadjacent and two adjacent vacancies with the susceptibilities and probabilities xz, P2 and x3, P3, respectively (only these four types of clusters are liable to occur in an ordered niobium carbide [5]; the probabilities of the existence of clusters with three and more vacancies in a disordered crystal are very sniall and can therefore be neglected). I n the case of a statistical distri- bution of vacancies in a disordered crystal the probabilities of the occurrence of clus- ters are determined by the binomial distribution

where n is the number of vacancies in a cluster. For vacancy-free and one-vacancy clusters Po = P(0) and Pi = P(1). For a cluster possessing two vacancies two versions of vacancy location are possible : either in nonadjacent positions or in adjacent posi- tions, therefore P, + P3 = P(2) and, allowing for the number of ways, I. , in which each of these two clusters can be obtained (A2 = 3, I., = 12),

In view of (1), (4) niay be writtcn as

3 3

i-0 i = O a(y) = c %P,(Y)l b(Y) = c b iP i (Y ) . (9)

For quenched disordercd specinlens t'he values of P,(y) should coincide with the prob- abilities for t'he case of statistical vacancy distribution, i.c. with the binomial values of P?"(y) determined according to (B), ( 7 ) . To find the magnetic susceptibility of the clust,ers chosen, i.e. to determine the coefficients ai and bi, two systems of linear eqna- t'ions, each comprising four equations, were set up. Solving these systems of equations wit,h t'he use of t,he values of Pyri(y) and the values of u(y) and b(y) obtained from ex- perimental data for disordered NbC, specimens of four compositions (see Table 1) allowed us to find the coefficients ai and bi for each of t'he four clusters select>ed, i.e. to determine their susceptibility. The a i and bi values thus found were used t'o calculate the probabilities of t'hese clusters in niohinni carbide NbC, specimens annealed a t a temperature close to Ttrans, i.e. in specinlens with a cert'ain degree of short-range order. The calculation reduced t o solving a systcni of equations in PYder(y) which involved (9) the probabilit8y normalization condition c Pi (y ) = 1, and the equation relating the cluster probability to the composition of PibC,: c ZiPi(y) = y, where Z i is the relative share of occupied carbon site in the rioniiiet'allic sublattice in an i-configurat'ion cluster. The values of Pyder(y) found for the ordered niobium carbide specimens studied are tabulated.

I n accordance wit'h (3), the short-range order parameter for the first coordinat'ion sphere may bc determined from t'he relation between t'he real and t,he binomial prob- abilit'y of the formation of C - 0 pairs. I n the case under consideration, according t,o ( 5 ) , the real probabilit'y Pc-n = Pl /3 + 2P,/3 + P3/3 and the binomial probabihy

c-u = 2 y ( l - y). For disordered niobiiini carbide specimens the values of a are close t.0 zero, whereas for specinlens annealed a t a temperature near Ttrans the values of t'he short-range order parameter are negative and differ appreciably from zero (Table 1). The negative value of a iridicat'es t'he niut~nal repulsion of hot'h vacancies and

pbiri

Study of Atomir Ordering in Niobium Carbide from Magnetic Susceptibility 533

534 A. I. GUSEV and A. A. REDIPEL: The Atomic Ordering in the Niobium Carbide

carbon atonis. It is this repulsion which determines the charmter of short-range order. For a completely ordered Nb,C, phase the probability of a one-vacancy cluster PI = 1 and the short-range order parameter LX = -0.20, which is in good agreement with the value of 01 = -0.132, obtained for NbCo 85 (Table 1). Some difference of the parameter 01 = -0.132 from the highest possible value for this composition indicates that no coniplete ordering was attained in the specimens investigated.

The decrease of the magnetic susceptibility in nonstoichionietric niobium carbide due to ordering may be accounted for as follows. The magnetic susceptibility of NbC, re- presents a sum of several contributions, of which the conduction electron para- and diamagnetism and the orbital Van Vleck paramagnetism are the major ones. The or- bital contribution to the magnetic susceptibility depends negligibly weakly on tem- perature, the temperature dependence dXjdT of the measured magnetic susceptibility is actually determined by that of the conduction electron spin paramagnetism. As evidenced by results of measurements of the temperature dependence of the suscepti- bility (Fig. 1 ,2 ) , the quantityd dXjdT derreases somewhat a t the transition from dis- ordered to ordered niobium carbide. This indicates that the contribution of the Pauli susceptibility of conduction electrons to the magnetic susceptibility decreases due to ordering. The orbital Van Vleck paramagnetism depends considerably on the sym- metry of the nearest neighbourhood of the metallic atom, therefore this contribution to the susceptibility for clusters with one or two vacancies should be larger than that for a complete cluster. The considerable diamagnetic susceptibility of a nonstoichio- metric niobium carbide cannot be accounted for by only the diamagnetism of atomic cores. Apparently, the high diamagnetic susceptibility of NbC, results mainly from the Landau diamagnetisni of conduction electrons which should be larger in absolute mag- nitude than the Pauli paramagnetism. This is possible if the effective mass of conduc- tion electrons is small. Thus, the decrease of the magnetic susceptibility in the nio- bium carbide during ordering may be conditioned by two causes, viz. the decrease of the paramagnetism of conduction electrons and the increase of the relative number of I; clusters possessing the lowest magnetic susceptibility compared to other clusters.

The present paper is a first attempt, by applying magnetic susceptibility measure- ments, to analyse the distribution of atoms in the crystal and to determine the short- range order parameters. This has become possible owing to the fact that the metallic sublattice in interstitial compounds serves as a matrix for all kinds of atonis penetrating into its interstitial space and, as a result, the magnetic susceptibility of such com- pounds, including niobium carbide, is mainly determined by the character of the nearest neighbourhood of metallic atonis, i.e. by short-range order.

References

[l] H. BITTNER and H. GORETZKI, Mh. Chem. 93, 1000 (1962). [2] I. I. MATVEENKO, L. B. DUBROVRKAYA, P. V. GELD, and M. G. TRETNIKOVA, Izv. Akad. Nauk

[3] Ya. E. GENKIN, I. A. MILOVANOVA, and A. V. LYAKUTKIN, Izv. Akad. Naiik Kaz. SSR, Ser.

[4] A. A. REMPEL and A. 1. GUSEV, Fiz. tverd. Tela 25, 3169 (1983). [ 5 ] A. A. REMPEL and A. I. GUSEV, Ordering in Nonstoichiometric Niobium Monocarbide, Preprint

SSSR, Ser. neorg. Mater. 1, 1062 (1965).

fis.-mat. 2, 12 (1976).

of Institute of Chemistry No. 76 (83), Sverdlovsk 1983 (in Russian).

(Received February 22, 1984)