Order-Disorder Phase Transition Channel in Niobium Carbide

A. I. GIJSEV and A. A. REMPEL: Order-Disorder Phase Transition Channel 71

phys. stat. sol. (a) 93, 71 (1986)

Subject classification: 64.60; S1.61

Institute of Chemistry, Academy of Sciences of the USSR, Ural Scientific Centre, Sverdlovsk')

Order-Disorder Phase Transition Channel in Niobium Carbide

By A. I. GKJSEV and A. A. ItEMrEL

Using a neutron diffraction structure analysis method it is found that an order-disorder phase transition of the first kind occurs in a nonstoichiometric niobium carbide NbC, a t a temperature of ~ 1 3 0 0 K in the composition range NbCo,sl-NbCo,ss. The phase transition channel which incorporates five nonequivalent superstructural vectors belonging to three stars is determined. A carbon atom distribution function is obtained which depends on three one-component order parameters.

~ a p 6 a a e H A O ~ H R NbC, npH TeMnepaType ~ ~ - 1 3 0 0 K B o6nac~a cocTaBoB NbCo,si-NbCo,ss ~ ~ O E ~ C X O ~ E ~ T aa30sb1B nepexon nepBoro pona Tana nop13~0~-6ecnop~no~. OnpeAeneH

MeTOAOM CTPYKTYPHOa HegTpOHOrpa@llH yCTaHOBneH0, 9 T O B HeCTeXllOMeTpHseCKOM

KaHaJl @a3OBOrO IlepeXOna, BKJIIo9aIoLWa nHTb He3KBHBaJIeHTHbIX CBePXCTPYKTYPHbIX BeKTOPOB, IIpllHaAJIe?KaI4AX TpeM 3Be3AaM. HaBAeHa (PYHK4HII paCnpeJXeJIeHElR aTOMOB ymepoaa, ~ ~ B H C H J U ~ H OT Tpex O~HoKoMnoHeHTHbix napaMeTpoB nopHma.

1. Introduction

Most of the transition metal carbides are nonstoichiometric compounds with high- symmetry f.c.c. and h.c.p. structures. These compounds exhibit wide regions of homogeneity within which they contain a considerable number of structural vacancies. The presence of structural vacancies in nonstoichiometric compounds may, under certain conditions, give rise to atomic ordering. As a phase transition, ordering results from the redistribution of atoms in the crystal lattice sites. It is accompanied by a lowering of the space group of the crystal since part of the symmetry transformations that bring the filled and empty nonmetal sublattice sites into coincidence with each other cease to be symmetry elements of the ordered crystal because of the crystallo- graphic nonequivalence of these sites. As a rule, ordering is accompanied by a displacement of the atoms from the ideal positions of the initial high-symmetry lattice.

Within the region of homogeneity (0.72 (= y 5 1.0) the niobium carbide NbC, possesses a B1-type structure in which the carbon atoms are statistically distributed in the nonmetallic sublattice. An electron diffraction study [l] has revealed that annealing of NbC, a t temperatures below 1313 K entails the occurrence of an ordered Nb,C, phase over the composition range between 44.5 and 47.0 atyo C (the existence of an Nb,C,-type superstructure [2] has not been confirmed by the authors of [l]). According to [l], the ordered niobium carbide phase NbC, has a trigonal structure similar t o that proposed for V,C, [3], but no exact structure determination for Nb,C5 has been carried out in [l]. An NMR study of short-range order in an ordered niobium carbide phase Nb,C, [4] has shown the character of short-range order in the region of existence of an ordered phase to be determined by the mutual repulsion of vacancies.

~

I ) Pervomaiskaya 91, 620219 Sverdlovsk, USSR.

72 A. I. GUSEV and A. A. REMPEL

Thus, the available data on ordering in niobium carbide are far from being complete: The structure of the ordered phase has not been determined snd the kind of the order-disorder phase transition in the niobium carbide is not known.

In this context the purpose of the present paper is to fill this gap. Using neutron diffraction structure analysis and radiography techniques we investigate the character of ordering in a nonstoichiometric niobium carbide, determine the channel and kind of the order-disorder transition observed, and, using the static concentration waves method [5 ] , find the distribution function of carbon atoms in the crystal lattice of this compound.

2. Specimen Preparation and Experimental Techniques

Specimens of different composition within the region of homogeneity of the niobium carbide were synthesized by solid-phase sintering of metallic niobium and carbon powders a t a temperature of 2300 K in 0.01 Pa vacuum during 20 h. The composition of the homogeneous and one-phase niobium carbide specimens with B1-type structure that were thus produced was determined by chemical analysis. The results obtained are presented in Table 1 (the impurity content of the specimens did not exceed 0.1 wt%). To produce niobium carbide speciiiiens in states with different degree of ordering, the samples synthesized were heat-treated under varying conditions which differed in temperature, annealing time, and rate of quenching (Fig. 1). To choose appropriate annealing temperatures, the order-disorder transition temper-

Table 1 Conditions of thermal treatment and phase composition of niobium carbide NbC,

analytical thermal conditions of thermal treatment phase composition (%) formula treatment of mc, regime temperature duration of rate of disordered ordered

of annealing annealing cooling phase phase (K) (h) (K/mW

a &

a b

b &

C

a b

b &

C

a b 0

&

b

b

b

a

8

2300 2300 2300 1300 1800 1300 1300 2300 1300 2300 1300 1300 1800 1300 1300 2300 1300 1800 1300 2300 1300

6 6 6

100 5

100 10 6

100 6

100 10 5

100 10 6

100 5

100 6

100

100 100 100

5 300

5 0.5

100 5

100 5 0.5

300 5 0.5

100 5

300 5

100 5

100 100 100 100 100

100 100

30 70

40 60 100

50 50 25 75

100

100

100

100 100 100 100 100 100

Order-Disorder Phase Transition Channel in Niobium Carbide 73

Fig. 1. Heat treatment conditions used to produce niobium carbide NbC, with different degrees of ordering

0 20 40 60 80 7UU 720 f lhl -

atures were determined using the DTA method. To this end, an HT-1500 CETARAM calorimeter was employed. The order-disorder transition temperatures were found to be 1355, 1304, and 1258 for NbC0,68, NbC0.63, and Nb0.81 respectively. These values give a fairly good fit to the Ttrans = 1313 K quoted for NbC0,R3 in [l]. Heat treatment conditions had an appreciable effect on the phase composition of the specimens : Annealing a t temperatures above Ttrsns (> 1300 K) followed by quenching (regime “a”) resulted in the production of disordered specimens ; annealing at a temperature of 1300 K followed by slow cooling (regime “c”) led to the production of ordered specimens; annealing a t a temperature of 1300 K followed by rapid cooling (regime “b”) entailed the production of two-phase specimens containing an ordered and a disordered phase simultaneously.

The initial structural determination of the NbC, specimens investigated was carried out by the method of X-ray photography in the presence of a standard sample, which allowed the parameter of the f.c.c. sublattice of niobium in NbC, to be measured to within +O.OOOOl nm (the standard sample was monocrystalline silicon powder). The niobium sublattice parameter for the ordered phase turned out t o be larger than that for the disordered carbide, thus indicating changes in crystal volume during ordering. The difference of the metal sublattice parameters for the ordered and disordered niobium carbide phases permitted the phase composition of niobium carbide specimens to be determined using the X-ray method from the ratio of the intensities of the lines corresponding to the f.c.c. lattice of niobium atoms in each of these phases. The results of the determination of the phase composition are cited in Table 1.

Neutron diffraction and radiography methods were employed t o determine the structure of the ordered phase. Neutron diffraction measurements (neutron diffraction patterns were photographed by I. F. Berger under the guidance of V. G. Zubkov) were carried out using a beam of neutrons of wavelength 1 = 1.694 x 10-1 nm. Beam monochromatization was effected by reflecting neutrons from the (111) plane of a germanium single crystal. X-ray spectra of the ordered phase were registered on a DRON-UMl diffractometer. Neutron and X-ray diffraction spectra were registered by step scanning with steps of A 28 = 0.1” and an exposure of 5 and 2 min at each point.

3. Analysis of Experimental Results

Neutron diffraction spectra were recorded of both quenched and annealed niobium carbide specimens of all the compositions synthesized. Neutron diffraction patterns were identified for a B1-type lattice using the parameter 4.458 x 10-lnm determined by the X-ray method. Continuous annealing of NbC, specimens with y 5 0.77

A. I. GUSEV and A. A. REMPEL

Fig. 2. Neutron diffraction spectra of niobium carbide NbC, with different degrees of ordering upon heat treatment under conditions a, b, and c

I U J J ' I

20" 40" 50" 80" 28 -

other Nb,C,-type ordered phases similar t o was reported earlier [2]. Meanwhile, 8 conjoint analysis- of the neutron diffraction spectra of annealed NbC, specimens (y (= 0.75) and of the NMR spectra for 9SNb nuclei in annealed NbC0,7j carbide that were obtained earlier [4] indicates the possible presence of &Nb,C, in these specimens [6]. The most elaborate studies have been made of niobium carbide specimens NbCO.RB that correspond to the stoichiometric composition of an ordered Nb,C, phase. Long-exposure scanning has permitted the detection of superstructural reflections not only on neutron diffraction patterns but

and y 2 0.93 entailed no occurrence of superstructural lines on neutron diffraction patterns. Superstructural reflections were observed on the neutron diffraction patterns of annealed

specimens, the intensity of these reflections being much lower than that of structural reflections (Big. 2). Ana- lysis of the position and intensity of superstructural reflections has shown the presence of only one Nb,C,-type ordered phase in the compositlon range NbC0,81 to NbCo.ss. Beyond this composition range, it has not been possible to detect the existence of

V,C, or Nb,C,, the existence of which

NbCo.81, NbC0.83, NbCO.845, and NbC~.titi

Fig. 3. X-ray spectrum of ordered niobium carbide Nb,C5

Order-Disorder Phase Transition Channel in Niobium Carbide 7.5

Fig. 4. Position of the monoclinic unit cell of the ordered Nb,C, phase in a NaC1-type lattice: o carbon .toms, vacancies, niobium atoms

UCl

also on X-ray patterns, despite the small amplitude of X-radiation scattering by carbon atoms in comparison with niobium atoms (Fig. 3).

To determine the symmetry of an ordered Nb,C, phase and the parameters of its unit cell, a calculation in accord with [7] was carried out which involved theuseof experimental data on the position of structural and superstructural reflections. Ac- cording t o the results of the calculation, the unit cell is monoclinic and has the follow- ing parameters: a = c = 5.4605 x 10-1 nm, b = 9.4579 x 10-1 nm, (Y = y = go", and ,!l = 109.47'. The unit cell belongs to the space group C2/m and comprises two formula units of Nb,C,, i.e., twelve niobium atoms, ten carbon atoms, and two vacancies (Fig. 4). The translation vectors of this cell with respect to the initial cubic cell have the form: a = {f, -+, - l } , b = {+,+,O}, and c = {f, -f, l } (thecoordinates of the atoms and vacancies in the structure of Nb,C, are specified in Table 2). In addition, we may take also the triclinic cell which in this structure is primitive with respect t o the vacancy sublattice and has the parameters a = b = c = 5.4605 x x 10-1 nm, LX = ,!l = 99.6", and y = 120" and for which there are six niobium atoms, five carbon atoms, and one vacancy.

A preliminary calculation has shown that the intensity of all superstructural reflections cannot be explained in terms of the ideal structure of an ordered Kb,C, phase. Apparently, along with the ordered distribution of interstitial atoms, static

Table 2 Parameters for the monoclinic structure of Nb&: space group C2/m, a = c = = 0.5460(5) nm, b = 0.9457(9) nm, B = 109.47(1)'

atom equipoint coordinates of atoms coordinates of atoms

static displacements static displacements position without allowance for their with allowance for their

vacancy 2(a) 0 0 0 0 0 0 C(1) 2(d) C(2)

0 0.5 0.5 0 0.5 0.5

(73) 4(h) 0 0.167 0.5 0 0.184 0.5 0.755 Wl) 46) 0.25 0 0.75 0.245 0

N V ) W) 0.25 0.667 0.75 0.264 0.660 0.750

0.333 0 0 0.320 0 4(g) 0


displaceiiients of atoms froin the ideal positions of the initial f.c.c. lattice exist in the niobium carbide. The possible displacement of each atom in the monoclinic cell of the Nb,C, carbide is determined, in the context of this space group, by the number of free parameters of the equipoint position they occupy. Thus, for carbon atoms C (1) in equipoint positions 2 (d) static displacements are forbidden, whereas static displacements along the b axis are possible for carbon atoms C ( 2 ) and C (3) in equipoint positions 4 (g) and 4 (h), respectively. For niobium atoms in equipoint positions 4 (i) static displacements along the a and c axes are allowed, and in equipoint positions8 ( j ) displacements along all the three axes are siniultaneously possible. The coordinates of the atonis in the structure of Nb,C, with allowance for their static displacements are presented in Table 2. The processing of experimental spectra with allowance for

possible static atomic displacements has shown that in addition to static displace nients it is nec- essary to take into account one more possible cause of some discrep- ancy between the observed and calculated intensities, i.e., the degree of long-range order in the relative positions of carbon atoms and vacancies in the specimens investigated is apparently somewhat smal- ler than unity.

The Nb,C, structure determined in the present paper is similar to a V,C,-type trigonal superstructure [3] and the monoclinic superstructure proposed for a low-teni- perature ordered V,C,phase [8]. The relation between these structures is depicted in Fig. 5. If we restrict our attention to the nonmetallic sublattice (the syninietry of the metallic sublattice practically does not alter in the case of ordering we are concerned with), the complete planes, all the sites of which are filled with carbon atoms, and the

Fig. 5. Models of affine structures of Me,C,-type ordered phases: a) monoclinic Nb,C, structure proposed; b) trigonal V,C,-type structure [3]; c) monoclinic V,C,-type structure [8]; d) position of a Me,C,n quasimolecule in it

d NaC1-type lattice; o carbon atoms; 0 vacancies; niobium atoms


Fig. 6. A comparison of experimental (1) and theoretical neutron diffraction spectra of ordering carbide Nb,C, with different possible structures: (2) monoclinic structure established in this paper; (3) trigonal V,C,-type structure [3] ; (4) monoclinic V,C,- type structure [8]

1" za" X J O 4u" 50" w 70" 28 -

partially defective planes that contain both carbon atoms and vacancies will alternate in succession in the [lI1]NaC1 direction (Fig. 4). In defective planes the vacancies occupy one third of all the sites and form regular hexagons in the plane. The relative position of the defective planes, which assures the production of three differing structures, is illustrated in Fig. 5. A successive three-fold relative displacement of the atoms and vacancies of equidistant defective planes in one direction along the vector {f, -f, l } (in the cubic system of coordinates) leads to the structure model proposed in the present paper (Fig. 5a). In the case of successive displacement along the vectors {$, -$, 1}, {+, -1, f} , and (1, -+, $} a trigonal V,C,- type superstructure [3] (Fig. 5 b) arises. When the atoms and vacancies of defective planes are alternately displaced along the vectors {f, -f, 1 ) and {$, -1, f } (Fig. 5c), a monoclinic superstructure is formed which is proposed for the low- temperature ordered V,C, phase [8]. As is seen from Fig. 5 , all the superstructures involved may be represented a s a set of Me,C,O quasimolecules (Fig. 5d ) arranged in a certain order. The afore-mentioned superstructures are identical in the character of short-range order and do not differ from each other up to the third coordination sphere with respect t o the metal atom. The general and distinctive features of these superstructures are considered in detail in [9, 101. A calculation of theoretical neutron diffraction spectra for possible structure models of a Me&,-type ordered phase (Big. 6) has shown that the best fit to the experimental spectrum is given by the monoclinic Nb,C, structure established in this study.

4. Theoretical Treatment and Discussion

The translation of all the superstructural sites of the reciprocal lattice of ordered niobium carbide shows that the first Brillouin zone of a disordered f.c.c. niobium carbide contains five nonequivalent superstructural vectors that belong to three stars { k 9 } , {k4} , and {k , } having four, twelve, and twenty four arms, respectively (the numbering of the stars and the representation of their arms coincide with the notation adopted in [ll]). All of the three observed superstructural modulations are selfinitiated [ 121 and the phase transition channel comprises the superstructural vectors of all the three stars: one arm of the first star k(g3) = $b2, two arms of the second star kv) = +(b, + + b, + 2b,) and k(q2) = -L (b, + b, + 2b,), and two arms of the third star kL4) =

refers to the number of the star, and the superscript t o the number of i tsarm; b1,2,3 stands for the primitive translation vectors of the reciprocal f.c.c. crystal lattice). The simultaneous symmetry distortion with respect to three irreducible representations indicates that the ordering in a nonstoichiometric niobium carbide is a first-order phase transition. The fact that the order-disorder transformation in NbC, follows the

_ - - (-2b1 + 6, + 2b,) and kL3) = f(2b1 - b, - 2 4 ) (the subscript of the vector k


mechanism of the first-order phase transition also is supported by experimental data such as abrupt volume variation during ordering and the existence of a two-phase region.

According to the static concentration waves method [5], the distribution function ?a(r), which in this case determines the probability of the nonmetal sublattice sites being filled with carbon atoms, may be expressed in terms of the concentration c of carbon atoms in the niobium carbide (for NbC,, c = y) and the superposition of static plane waves d k ( r ) , i.e.

where r = {xI, yr, zI} is a vector that determines the coordinates of the Ising lattice sites (in the case of interest the f.c.c. carbon sublattice is an Ising lattice). The summa- tion in (1) is performed over all the nonequivalent superstructural vectors incorporated in the first Brillouin zone of the disordered crystal. The standing static plane wave A k ( r ) with the wave vector k

(2) describes the spatially periodic modulation of the distribution of atonis in crystal lattice sites, i.e., the deviation of the probability n ( r ) from its value in case of a statistical distribution. In (2) exp (ikr) is a static plane wave of amplitude qy(k), where q is the long-range order parameter and y ( k ) a coefficient which is chosen so that the long-range order parameter in a completely ordered state is equal to unity. The order-disorder phase transition in niobium carbide is associated with three wave vector stars and the distribution function in the general cases therefore will involve three long-range order parameters ql, qz, and q3 corresponding to the stars { kg}, {k4}, and { k 3 } . The quantity ql is a one-component parameter since the phase transition channel contains one arm of star {kg}. The quantities qz and q3 also are one-component parameters since =

A calculation has shown that the distribution function of the carbon atoms of niobium carbide for any composition and arbitrary long-range order parameters may be represented as

dk(r) = + q [ y ( k ) exp (ikr) + y*(k) exp ( - - ikr)]

- -k$) and k(34) = -k(3). 3 -

For a fully ordered crystal, the coniposition of an ordered niobium carbide phase cor- responds, according to the calculation, to Nb,C,, i.e., c = 516. When written with allowance for ql = qz = qs = q = 1, the distribution function becomes

If we consider the nonmetallic sublattice only, a feature peculiar to the structure of a completely ordered niobium carbide Nb,C,, as has already been noted, is that the complete and defective planes alternate in succession in the [lIl]gacl direction (Fig. 4). In this context it is of interest to analyze the distribution of carbon atoms and vacancies in the (l i l)Nacl plane as a function of the ratio of long-range order parameters. The distribution function calculated in the (lI1)x,cl plane is a superposition of the concentration waves (or probability density waves) portrayed in Fig. 7.

It follows from an analysis of (3) that the parameter ql is responsible for the mainten- ance of the order in which the carbon planes alternate in the niobium carbide structure: When ql = 1 the complete and the defective carbon planes ( 1 I l ) ~ ~ c l alternate


Fig. 7. Concentration waves in the ( ~ I I ) ~ , c ~ plane of an ordered niobium carbide: a)

= 72 = 3 - 9

A-im.

= q2 = r], = 1; b) 7, s, q2 = 0, r] , = ;-; 0) r ] ,

in succession; when 0 < ql < 1 part of the carbon atonis pass from complete to defective planes, but the character of the alternation of b

V these planes is maintained; when ql = 0 the occupancy of all carbon planes becomes equal and amounts t o y for NbC,. The parameters q2 and q3 are responsible for the relative position of the carbon atoms and vacancies in defective planes: For Nb,C, with q1 = qz = q3 = 1 each vacancy in the defective ( l i l ) ~ , ~ , planes is surrounded by six carbon atoms; with decreasing

q2 and q3 the degree of order in the defective planes lowers and when q2 = q3 = 0 the distribution function on all the sites of the defective (lil)xaCI plane takes on only one value, i.e. describes the completely disordered arrangement of the carbon atoms and vacancies in these planes.

If we assume the long-range order parameters to be equal to each other, ql = qz = = q3 = 17, the analysis of (4) allows us to find the dependence of the maximum degree of long-range order on the composition of NbC,,

6(1 - y) if y z ; , if y < $ .

The changes in the properties of the crystal, which are directly related to the for- mation of long-range order, should apparently be described by dependences similar to (5). For example, the difference of the crystal lattice periods in the ordered and disordered niobium carbide phases depends on the composition of NbC, in this way [lo].

5. Conclusion

Thus, the investigation performed has revealed that an order-disorder phase transformation obeying the mechanism of a first-order phase transition occurs in the region of compositions NbCO.81 to NbCo.ss in the temperature interval 1258 to 1355K. An experimental determination of the structure of the ordered Nb,C, phase has made i t

80 A. I. GUSEV and A. A. REMPEL: Order-Disorder Phase Transition Channel

possible to find the channel of the structural order-disorder phase transition end to compute the distribution function describing the atomic ordering in a nonstoichiometric niobium carbide.

Acknowledgement

The authors wish to thank V. G. Zubkov for permanent assistance in structural re- search and for helpful discussions.

References [l] J. BILLINGHAM, P. S. BELL, and M. H. LEWIS, Acta cryst. A28, 602 (1972). [2] V. G. ZUBKOV, L. B. DUBROVSKAYA, P. V. GELD, V. A. TSKHAI, and Yu. A. DOROFEEV, Dokl.

[3] J. D. VENABLES, D. KAHN, and R. G. LYE, Phil. Mag. 18, 177 (1968). [4] A. A. REMPEL and A. I. GUSEV, Fiz. tverd. Tela 25, 3169 (1983). [5] A. G. KHACHATURIAN, Theory of Structural Transformations in Solids, Wiley, New York 1983. [6] K. YVON and E. PARTHE, Acta cryst. B26, 149 (1970). [7] T. ITO, X-Ray Studies of Polymorphism, Marusen Co., Ltd., Tokyo 1950. [8] J. BILLINGHAM, P. S. BELL, and M. H. LEWIS, Phil. Mag. 26, 661 (1972). [9] A. A. REMPEL, A. I. GUSEV, V. G. ZUBKOV, and G. P. SWEIKIN, Dokl. Akad. Nauk SSSR

[lo] A. A. REMPEL and A. I. GUSEV, Ordering in Nonstoichiometric Niobium Monocarbide, Insti-

[ll] 0. V. KOVALEV, Irreducible Representation of Space GroJps, Izd. Akad. Nauk Ukr. SSR,

[12] A. P. LEVANUK and D. G. SANNIKOV, Uspekhi fiz. Nauk 112, 561 (1974).

Akad. Nauk SSSR 184,874 (1969).

2i5,883 (1984).

tute of Chemistry, Sverdlovsk 1983 (in Russian).

Kiev 1961 (in Russian).

(Received July 16, 1985)

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Order-Disorder Phase Transition Channel in Niobium Carbide