III. – INTERSTITIAL COMPOUNDS.ORDER AND DISORDER IN CARBIDES AND NITRIDES

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III. – INTERSTITIAL COMPOUNDS.ORDER AND

DISORDER IN CARBIDES AND NITRIDES

Ch. de Novion, V. Maurice

To cite this version:

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COMPOUNDS.

ORDER AND DISORDER IN CARBIDES AND NITRIDES

Ch. H. D E NOVION and V. MAURICE

SESI, C.E.N., BP 6,92260 Fontenay aux Roses, France

RhsumC. - Nous prksentons une revue experimentale des proprietes de mise en ordre ri courte et longue distance des dkfauts ponctuels dans les carbures et nitrures mCtalliques de mktaux de transition, de terres rares et d'actinides. Nous insisterons sur le cas des lacunes de carbone dans les mono- carbures de structure NaCI, oh I'ordre semble pouvoir dtre decrit par des modkles gttomktriques trts simples, en termes de couches de coordinence pour les atomes de mCtal, et Etre dQ a des effets chimiques A courte distance plut8t qu'd des interactions elastiques A longue distance. Nous considererons plus brikvement les mononitrures MN, de structure NaCI, les hemicarbures hexagonaux M,C, les phases dzeta M4C3 -,, les solutions solides de haute temperature MC-MC, et I'orientation ordonntte de

paires de carbones dans les dicarbures MC,.

Abstract. - We present a review of the general experimental evidence for short and long-range ordering of point defects in metallic transition metal, rare earth and actinide carbides and nitrides. Emphasis will be put o n the case of carbon vacancies in the rocksalt structure monocarbides, where the ordering seems t o be describable in very simple geometrical terms, with preferred coordination shells for the metal atoms, and due to short-range chemical effects rather than to long-range elastic interac- tions. We shall consider more briefly the rocksalt mononitrides MN,, the hexagonal hemicarbides M,C, the dzeta phases M4C3-,, the MC-MC, high temperature solid solutions and the orientational ordering of carbon pairs in the MC, dicarbides.

1. Introduction. - Many transition metals, rare earths and actinides react with carbon and nitrogen to form metallic carbides and nitrides, with fascinating physical properties, from the point of view of theo- retical solid state physics as well as regarding possible applications : high melting temperatures, great hardness, superconductivity. The best known of these compounds, the cubic rocksalt monocarbides and mononitrides, as well as the hexagonal hemicarbides M,C, are Hagg phases : the small metalloid atoms occupy the octahedral interstices of a close- packed metal sublattice. Another way of presenting these crystal structures emphasizes the real chemical bonding of the.compounds, i.e. the strong hybridi- zation between the metal d and carbon or nitrogen 2p atomic electron states : they may be described by a stacking of units consisting of a central metal atom and of the octahedron formed by its six metalloid first neighbours (the role of metal and metalloid may, besides, be interchanged).

One of the most important properties of these carbides and nitrides is their large composition range, for example Tico.,, to Tic,.,, for titanium monocarbide. In the rocksalt monocarbides, precise density measurements [I] have shown that the departure from

stoichiometry is due to carbon point defects, generally vacancies ; at high temperatures, rare earth and actinide monocarbides can accommodate a large propor- tion of carbon interstitials up to chemical formulae

such as MC,. On the contrary, rocksalt mononitrides may also contain several percent metal vacancies, as for example TiN, which extends from TiN,.,, to TiN,.

, ,

[2]. In the case of rare earth mononitrides, it is now recognized that the range of existence is fairly narrow, occurs near the stoichiometric composition, and is mainly controlled by impurities [3]. At last, the

hexagonal hemicarbides exist in a certain composition range below MC,,,,, where only half of the octahedral sites are occupied. Obviously, many properties of these carbides and nitrides, essentially the transport properties, are controlled by the point defects res- ponsible for non-stoichiometry.

The possibility of ordering these defects has been considered only since 1965. It is now clearly established that, in many cases, carbon or nitrogen vacancies are not random, but order at short or long range.

We shall review here the main experimental evidence for ordering in nonstoichiometric rocksalt monocarbides and mononitrides. As practically no theore- tical work has been performed on the electronic structure of defects in these compounds, our paper will be greatly descriptive.

2. Ordering of carbon vacancies in the rocksalt monocarbides. - These monocarbides, mostly found for transition metals of groups 111, 1V and V, for rare earths (starting at samarium) and actinides (thorium to plutonium), are never obtained stoichiometric at

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C7-212 Ch. H. DE NOVION A N D V. lMAURICE

room temperature, as is evident for example from residual resistivities : typically the highest carbon concentration in titanium monocarbide is Tic,,,,. TaC goes very near stoichiometry (TaC,,,,,), but vanadium monocarbide cannot be obtained above the composition VC,.,, corresponding to the V8C7 superlattice. Rare earth monocarbides are stable in the range MC,

.,.,,,.

Let us first review some general properties of single carbon vacancies in the monocarbides :

- The formation energies are generally not known. In the case of uranium carbide UC, it is estimated to 1.5 eV from diffusion data [4], quenching data [5] and thermodynamic data 161.

- The migration energies are large, of the order of 4 eV [4].

- The incremental residual resistivities per percent vacancies near the stoichiometric composition are between 10 and 20 @cm at room temperature [7], i.e. an order of magnitude larger than in noble metals.

- The effect on lattice parameter a is in general a decrease of about 10-

A

per percent carbon vacancies. But in group IV carbides (Tic, ZrC, HfC), near the stoichiometric composition, carbon vacancies increase the lattice parameter which is maximum around

['l.

-

The main local displacements induced by a vacancy concern its six metal first neighbours, which are axially pushed away by distances of typically 0.1

A

(a: 0.02 a). This was found as well from super-

structures such as V8C7 [8], lattice statics calculations

in UC [9] and Debye-Waller factor measurements [10].

- The description of the electronic structure of a carbon vacancy is probably intermediate between two extremes : an ionic picture where its 2p states are subtracted to the nearly full 2p band, allowing a filling-up of the d band ; and a covalent picture where the d orbitals pointing towards a carbon vacancy are no more split into bonding and antibonding states by interaction with the 2p orbitals, but build-up a new peak of density of states. These two pictures can qualitatively explain the large increase in density of states at the Fermi level with increasing vacancy content in group IV carbides.

We may now present a general picture of the interaction between carbon vacancies :

- In group V carbides, vacancies tend to put themselves as third neighbours on the carbon fcc sublattice, and to avoid first and second neighbour positions. Each metal atom tends to be preferentially surrounded by five carbons and one vacancy. This effect decreases from VC, to TaC, via NbC,, and for each compound is maximum at the composition

-- Near the low carbon boundaries of these penta- valent carbides, one observes an accumulation of large ( l l 1) stacking faults. The grouping and extension

of these faults give rise to the hexagonal f: and M,C phases occurring at lower carbon content (see

5

5).

- In group IV monocarbides, which have been less studied, the vacancies tend probably to avoid the second neighbour position (distant of a and separated by a metal atom). This effect is maximum near the low carbon. boundary.

- In rare earth and group 111 monocarbides, an ordered structure M,C is found, but there is ambiguity

between two space symmetry groups [l l].

- Carbon vacancies tend to cluster in actinide monocarbides, except thorium.

2.1 LONG-RANGE ORDERED PHASES IN GROUP V

MONXARBIDE~ (VC,, NbC,, TaC,).

-

2 . 1 . 1 Crys- tallography. - Vanadium monocarbide has been certainly the most studied system. The two long-range structures V,C, and V6C5 are very easy to form below their order-disorder transitions, which occur respec- tively at 1 120 and 1 2600C [12, 131. Two-phase

samples have been obtained, such as V,C,

+

V,C,, V8C7

+

graphite, V,C5

+

disordered matrix, allowing to draw the phase diagram shown on figure 1. The structure of V8C7 (see figure 2) is cubic, with a lattice parameter doubled from that of the disordered

B1 structure, and may be described by two enantio- morphic space groups P4,32(06) and P4,32(07) [14]. The real crystals consist of mixtures of antiphase domains of the two groups. In this structure, 114 of the vanadium have no vacancy first neighbour, and the 314 others have one vacancy first neighbour. Vacancies are third neighbours on the carbon fcc sublattice. The deformation of the vanadium octahedron surrounding a vacancy is shown on figure 3.

The crystal structure of V6C5 is more complicated as two forms have been observed by electron diffraction : a trigonal form corresponding to the two enan- tiomorphic space groups P,, and P,, [15], and a monoclinic form, which is probably the most stable

C/V RATIO

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ORDER A N D DISORDER IN CARBIDES A N D NITRIDES C7-2 13

Both Vac, and V6C5 can accommodate point defects : carbon vacancies or interstitials. In the case of V6C5, if the samples are annealed slightly below the order-disorder temperature, these defects agglo- merate in non-conservative antiphase boundaries, periodically distributed and parallel to the (110) plane of the B1 structure. These boundaries do not modify the vanadium lattice. Their period can go as far as 40

A

[17, 191.

The Nb6C5 structure is isomorphous to the trigonal V6Ci [20]. Although V a c 7 and V6C5 are obtained completely ordered by natural cooling of a furnace, the ordering of Nb6C5 needs a slow cooling rate in the region of the order-disorder transition, 1 030 OC [20, 211.

Ta6C5 exists probably, but with a very low order- disorder temperature, as Venables and Meyerhoff 1201 observed only short-range order in their specimens.

FIG. 2. - The crystal structure of V&,. Only the carbon vacancies _{2.1 . 2 Thermodynamics.}- Emmons [22] esta-

are shown. (The lattice parameter is b = 8.334 A.) _{blished a very simple Bragg-Williams model to}

describe the V6C5 -, VC,,,,, transformation. He ascribed the difference between the ordered and

4 disordered states only to the different numbers of first

A neighbour carbon-carbon, carbon-vacancy, and

vacancy-vacancy interactions (although second and third neighbour interactions seem to be large, see

9

2.2). The transition was found first order and the predicted enthalpy increase was in good agreement with the results of DTA experiments [13,22] :

AH, = 6.6 T 2.9 cal/g for V6C5 -, VC,

.,,,

,

AHT = 7.0 T 3.1 cal/g for Vac, -+ VC,,,,,

(0.02 eV per sublattice site). The two terms in the measured AHT were separated by several techniques, giving convergent values of the latent heat :

I = 3.3

+

1.0 cal/g for V6C5 -, VC0,833

.

2.1 . 3 ' Physical properties. - Shacklette and Wil- liams '[l 2, 131 measured the electrical resistivities of V,C, and V6C5 from 4 K to 1 400 OC, and found discontinuous changes a t the transition temperatures : FIG. 3. - Deformation of a vanadium octahedron surrounding 14.7 ( f 0. l )

%

for V a c 7 at 1 120 OC and 3.6 (f 0.2)

%

a carbon vacancy in V&,. _{for V6C5 a t 1 260 oC. This, along with the DTA}

curves [13, 221, proves the first order character of the at low temperatures [l 6, 171. The difference in energy transition. No anisotropy could be detected in the between the two structures is certainly very small, one electrical resistivity of V6C5 [l319 although superzone of them being described from the other one by a boundaries normal to ( l11 ) are introduced in the periodical distribution of conservating stacking faults, structure.

of fault vector in the (1 1 1) fcc plane. In both structures [231 and plastic properties f2l1 the stacking of carbon planes in a ( 11 1 ) direction is are greatly modified by the long-range ordering of an alternance of planes with no vacancies and planes carbon vacancies : the order-disorder transitions in containing 113 vacancies. The metal cell is slightly and V6Cs correspond to the brittle-to-ductile distorted along ( 11 1 ) [18]. In the V6C, structures,

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C7-214 Ch. H. DE NOVION A N D V. MAURICE

domains separated by irregular boundaries of vector

a/4 ( 110

).

But the case of V6C5 is more complicated : four types of axial domains are found to coexist, corresponding to the four possible( 11 1 ) directions of the rhombohedral distortion. These domains have been studied by transmission electron microscopy and polarized light reflexion [15]. On cooling, the formation of axial domains is made by nucleation and growth from the short-range ordered phase.

At a given temperature, very different time constants ranging from a fraction of second to several minutes, have been found during the ordering of V&,, depending on the sample form and on the experiment [12,2 l]. Thiq is probably because different time constants s h o u k b e attributed to the nucleation, growth and

"..

coalescence -of axi_al domains.

2.2 SHORT-RANGE ORDER OF VACANCIES IN GROUP V

MONOCARBIDES..

-

The disordered structure VC, can be quenched only for carbon compositions lower than VC,.,,. For these, NMR studies as well as neutron and electron diffuse scattering have shown the existence of short-range order between vacancies, having the same physical origin than the long-range ordered V,C, and V&;.

In a VS1 NMR study of vanadium carbides, eroidevaux and ~ o s s i e r [24] have shown that well defined local electrical field gradients and Knight- shifts can be attributed to each vanadium site, and in first approximation depend only of the composition of the first carbon neighbour shell. This is a conse- quence of the screening of any perturbation potential in a metal. From the intensity analysis of the different NMR lines these authors showed that the vanadium sites with no vacancy or with three or more vacancies first neighbours are much fewer than in the random distribution ; this is consistent with the ordered Vac, and V6C5 structures.

' The electron diffraction pattern of a single crystal VC,.,, shows, beside the fcc diffraction spots, a diffuse scattered intensity distributed in first approximation on a surface (A) of cubic symmetry, periodical in the reciprocal space [25] (see figure 4). Similar surfaces have been observed in NbC, at all compositions (except in slowly cooled Nb6C5, where it is replac- ed by the superlattice spots) and in TaCo.78.0.a5 [20, 21, 25, 261 ; they are typical of short-range ordering..

Sauvage and ParthC [27, 281 have shown that the

analytical form of these surfaces can be justified in terms of stacking of carbon octahedra with one or two compositions' only, but randomly oriented. This connects the NMR results to the diffuse scattering data. These authors have calculated the short-range order parameters a in the carbon fcc lattice of VC,.,, from the electron scattering data of Billingham

et al. 1251, assuming that the scattered intensity is

constant within the surface (A) and vanishes elsewhere. Subsequently a VC,.,, single crystal was studied by

FIG. 4. - Diffuse scattering surface observed by electron dif-

fraction in the reciprocal lattice of VC,,,,.

diffuse neutron scattering in the first Brillouin zone [29], where it was observed that the surface (A) has a certain width, and from which slightly different a Galues were obtained :

for the three first shells of neighbours. The other ai were found small. Unfortunately this study did not take into account the static displacements due to vacancies, which could alter the precise a values, and should be determined by comparing precisely the scattering in several Brillouin zones.

Nevertheless the convergence of the NMR, neutron and electron scattering results shows that this is not a very large effect. The a values found in short-range ordered VC,.,, are qualitatively consistent with the ordered V,C, and Vac, structures : vacancies tend to put themselves as third neighbours on the carbon fcc lattice (a,

>

0) and to avoid first and second neighbour positions (a, and a,

<

0).

Similar short-range order coefficients a, < 0, a, < 0 and a,

>

0 have been deduced by Henfrey and Fender from diffuse neutron scattering on NbC, powders [30].

2 . 3 ORDERING IN GROUP IV MONOCARBIDES (Tic,, ZrC,, HfC,, ThC,). - It has been much less studied than in group V monocarbides.

Billingham et al. 1251 have observed the same electron diffuse scattering surfaces in Tic,.,-,., as in VC,.,, and NbC,-,, but d:d not try to analyse quantitatively these data.

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ORDER AND DISORDER IN CARBIDES AND NITRIDES C7-2 1 5

FIG. 5. -Coordination of the metal atom in various non-stoichiometric transition metal carbides. Black circles : carbon atoms. Squares : carbon vacancies. Empty circles : metal atoms. The arrow indicates the displacement of the metal atom from the

fcc positions.

may be due to the low order-disorder temperature (900 OC) causing slow carbon diffusion, and to a pro- bable departure from the stoichiometric composition Ti,C causing a small APB energy.

More recently, Em et al. [33] showed by neutron diffraction that with convenient heat treatments such as long anneals at 600 OC, this ordered structure could be obtained up to Tic,.,

,,

although complete ordering was not attained.

In the case of zirconium carbide, the situation is rather confusing. Goretzki [31] observed a Zr,C sutxrlattice, isomorphous to Ti,C, at the lower caibon boundary o f i r ~ . Obata and Nakazawa [34] claimed their disagreement with this result, as they found in ZrC,.,,.

,,,,,

but not in ZrC,.,

,,

very small additional X-ray lines inconsistent with the above structure. These reflexions, which weakened after rapid cooling, corresponded to a cubic unit cell of parameter 2 a = b, but the crystal structure could not be determined. A similar structure Th,C3 had been suggested previously by Lorenzelli and de Dieuleveult [35]. The existence of an order-disorder transition in ZrC,,,, around 10600C was also suggested by DTA and resistivity anomalies [34]. Recently, Maurice et al. [36] found by neutron diffraction the Fd3m Zr,C structure on a sample

FIG. 6. - Diffraction neutron pattern of ZrC,

,,

(powder sample) :

a) annealed 100 hours at 800 OC ; 6 ) rapidly cooled from 1 600 OC (incident wavelength : 2.40 A).

0.40 T 0.05 if the ordering is assumed homogeneous in the sample. The zirconium atoms, which occupy the 32(a) positions, are repelled from the vacancies by 0.04

W.

The superstructure could be checked by electron diffraction [37] (see figure 7). It is interesting to note that the superlattice lines were not detected by X-ray diffraction, contrary for example to V,C, ;

this is probably due to the small domain size, about loo to 200

W

[37].

ZrC,.,, annealed 100 hours at 800 OC. The analysis

FIG. 7. - Electron diffraction pattern in the (170) reciprocal of the _{(see figure}_6,_{shows that the ordering} _{lattice plane of ZrC,,,, annealed 100 hours at 800}

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C7-216 Ch. H. DE NOVION AND V. MAURICE

A similar sample, rapidly cooled from 1 600 OC, showed only broad diffuse maxima in the neutron spectrum (instead of the superlattice reflexions, see figure 6). But the two samples, which show so different neutron diffraction patterns, were indistinguishable by electrical resistivity measurements between 4 and 300 K.

Maurice et al. [36] measured also the elastic diffuse neutron scattering 'cross-sections on two polycrys- talline ZrC,.,, samples (rapidly cooled or annealed at 800 OC) at the D7 spectrometer of ILL (Grenoble). These spectra show a broad maximum at the 112 1/2 112 position, which corresponds to the first superlattice line in ZrC,.,,.

This is quite similar to a previous ThC,.,, diffuse scattering -pattern (see figire 8) which--has been analysed in terms of short-range ordering between a vacancy and its three first shells of neighbours [38] ;

according to this analysis, vacancies avoid completely second neighbour positions (as in Ti2C), slightly the first neighbours, and prefer the third neighbour positions. The fitting of the data should be improved by taking into account the size effect of the vacancies. In conclusion, the experimental situation is still not clear in group IV monocarbides. One should in particular look at the influence of impurities, especially H, N and 0; on the appearance of the ordered phases, and on the kinetics of domain growth. Such effects might perhaps explain the observed discrepancy between different experimental works.

2.4 ORDERING IN GROUP I11 AND RARE EARTH

MONOCARBIDES. - A superlattice M2C has been

observed in scandium, yttrium, gadolinium, holmium, dysprosium and erbium monocarbides [39, 40, 411. One observes a rhombohedral distortion of the metal

FIG. 8. - Elastic diffuse neutron scattering cross-section of ThC,.,,. A : Experimental points ; B : Calculated curve neglecting displacements, - and with short-range order coefficients :

a ₁- - _- 0.05 ; or, = - 0.20 ; U, =

+

0.075.

C : Calculated curve with random vacancies and displacements given by the lattice statics calculation of Lesueur [9] using Weber's

[45] interatomic force constants.

cubic cell, except in the case of Sc2C. ParthC and Yvon [l l ] have pointed out that on a powder diffraction pattern it is practically impossible to distinguish between the two following structures :

- Fd3m as in Ti2C with an eventual rhombohedral distortion.

- ~ 3 m with suppression of a carbon sheet over two, perpendicularly to the ( 11 1 ) fcc axis. This was the structure originally suggested for 'Ho2C [40, 411. Nevertheless, it is interesting to remark that the coordination of the metal atom is the same in both structures (see figure 5), and that in both cases, carbon atoms avoid second neighbour positions on the carbon fcc sublattice.

2.5 ORDERING IN ACTINIDE MONOCARBIDES. - In neptunium monocarbide NpC,,,~,',,, the 237N P Mlissbauer spectrum [42] shows the presence of two types of sites, one corresponding certainly to Np atoms with six carbon neighbours as in stoichiometric NpC. But the other one is in much smaller concentration than if it corresponded to Np with one vacancy first neighbour, assuming either a random distribution of vacancies, or a repulsion between vacancies as in VC,. Therefore, we think that in this carbide, carbon vacancies cluster in complex defects, or microdomains with smaller local carbon content [38].

Very remarkable is the case of uranium monocarbide UC, because exceptionally it has a very narrow composition range : UC,.,,.~,,. At smaller. carbon content, uranium metal precipitates. An interesting lattice statics caIculation has been made by, Lesueur [9], using the static Green function inethod, in order to estimate displacements of atoms around vacancies, lattice relaxation energy and elastic interaction energy between two vacancies. Lesueur used two fittings of the phonon spectrum of UC, one by Smith and Gliiser [44] and the other by Weber [45]. Although the two fittings are not very different, Lesueur finds rather different interaction energies (see figure 9). This is due to the fact that the atomic displacements depend mostly on the small and not well known tangential force constants. The model using the Weber fitting of the UC phonon spectrum gives an attractive interaction between first neighbour carbon vacancies, and this might explain the observed precipitation of uranium metal if the vacancy content is larger than 1 to 2

%.

But the value of this calculated interaction energy, - 0.02 eV, is much smaller than the one deduced by Jeanne from thermodynamic data,

- 0.2 eV [6].

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ORDER AND DISORDER IN CARBIDES AND NITRIDES

FIG. 9. - Calculated elastic interaction energies E between two carbon vacancies distant of R in UC (Lesueur, 1976, unpublished). Black triangles : force constants taken from the fitting of Weber [45]. Stars : force constants taken from the fitting of Smith and Glber [44].

metal vacancies. The occurrence of metal vacancies for X 1 may depend on the preparation technique,

as Nagakura et al. [47] found in TiNo.6,.o.g9 a vacancy-free metal sublattice, in contradiction with previous results [2]. An indication of the possible ordering of metal vacancies is the existence of Nb4N, which may be related to the NaCl structure with metal vacancies forming a body-centered quadratic lattice [48]. We recall that NbN, exists up to NbN I . 06

Apart from the two quadratic compoinds M0,N [43] and Nb4N, [59] which may be considered as distorted rocksalt structures with ordering of nitrogen vacancies, the only system studied in detail is the TiN, system. Here, a quadratic superlattice Ti,N was found by Lobier and Marcon [49] and is shown on figure 10. In this structure, which belongs to the space group I4,/amd, the quadratic cell is made of two NaCl primitive cells, and the environments of titanium atoms are all identical,,as shown on figure 5. The metal atoms are displaced of 0.132

A

towards their first nitrogen neighbours. The nitrogen occupa- tions of the neighbouring shells of a vacancy are 213 for the first shell, 113 for the second. One cannot speak as for carbides in simple terms of repulsion between vacancies. This structure was found again at the composition TiN,.,, by Nagakura and Kusunoki [50], who studied its domain configuration.

At higher nitrogen composition, diffuse scattering was found in electron diffraction patterns for all compositions TiN,.,

,

-

,.,,

and 'is comparable in form with those from the compounds NbC, and VC,,,, (see Q 2.2) [25, 501.

FIG. 10. - The crystal structure of Ti,N (from [49]). Black circles :

nitrogen atoms. Squares : nitrogen vacancies; Empty circles :

titanium atoms. Arrows : displacements of the Ti atoms from the fcc positions.

4. The high temperature MC-MC, solid solutions. -

Trivalent transition metals, rare earths and actinides form MC, type carbides where carbon atoms are associated by pairs, and which show several crystallo- graphic forms depending on temperature.

At high temperature, the MC, carbides are cubic and show complete solubility with the rocksalt MC carbides (and even with the fcc Th metal in the thorium- carbon system). The cubic dicarbide UC, has been studied by high temperature neutron diffraction, and the carbon pairs were found to be either rotating freely around their center, or randomly oriented along the four ( l l l ) directions [5 l].

In the high temperature solid solutions such as UC-UC,, single carbon atoms and bound carbon pairs are thought to be randomly distributed in the octahedral sites of the metal fcc sublattice. The carbon diffusion is extremely rapid [4], one of the two carbons forming a pair jumping in a neighbouring site occupied by a single carbon.

The formation energy of a carbon pair in UC has been estimated as 0.64 eV from a statistical model [6] consistent with thermodynamic data and the form of the miscibility gap. Similar calculations of Makino

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C7-218 Ch. H. DE NOVION AND V. MAURICE

chiometric UC the concentration of carbon vacancies and interstitials are of the order of 1

%

[6].

Coming back to the MC, phases, when cooling from the cubic state, one observes a phase transformation (Tc

-

1 500 to 2 000 OC) to a quadratic form corresponding to the orientational ordering of carbon pairs parallel to the

<

001 ) cubic axis.

The body-centered quadratic metal sublattice can be considered as a distortion of the high temperature fcc form with :

The cubic to quadratic transformation is non diffusive and the cubic form cannot be retained from high temperatures in the pure MC, compounds. But in alloys of the type (M,M;-,) C,, the strain energy due to the size difference between M and M' reduces the enthalpy at the transformation and hinders the cubic to quadratic transformation : Tc decreases rapidly with the adjunction of M' in MC, and in some solid solutions such as Lac,-UC,, the cubic form is stabilized at room temperature [53].

It may be remarked that in the Th-C system, the low temperature stable form is monoclinic, and that in the quadratic form (1 430 to 1 480 OC) the carbon pairs rotate freely in the plane perpendicular to the c-axis [54].

5. Ordering of metalloid vacancies in carbides and nitrides with complete or partial hexagonal metal atom stacking. - 5 1 HEMICARBIDES A k D NITRIDES M2X. - In a certain number of transition metal-carbon or nitrogen systems (groups V and V1 essentially), M,X hexagonal carbides and nitrides are found, where the metal sublattice is hcp and the metalloid occupy half of the octahedral sites at the stoichiometric composition. They show some range of existence M,X,-,, but much less than the rocksalt compounds. We shall only recall briefly some properties of these M2X compounds, which are treated in another paper of this conference [S].'

Most of them are found ordered at low temperatures, either in the hexagonal E-Fe,N structure, or in distorted orthorhombic structures. The disordered hexagonal structure may be considered as a stacking of close- packed planes : AyByAyByA

. .

.,

with on the average one atom on two missing in the metalloid y planes. The ordered phases have all the following 'common property that carbon atoms and vacancies occupy alternate octahedral sites on interstitial rows parallel to the c-axis ; alternate y planes are either 112-112, or 113-213 or 1-0 occupied by carbon atoms. A short- range ordering based on this negative correlation occurs in the high temperature disordered hexagonal phases.

5.2 STACKING FAULTS IN THE ROCKSALT CARBIDES AND NITRIDES. - In many rocksalt carbides and

nitrides, especially VC,, NbC,, TaC,, VN, and TiN,, high densities of randomly arranged planar faults are formed near the low carbon or nitrogen boundaries. They can quite generally be described as (1 11) intrinsic shear faults, bounded by Shockley partial dislocations of Burgers vector b = a/6

<

112 ) [22,26, 561.

The stoichiometric rocksalt structure may be considered as a stacking of (111) close-packed planes :

AyBaCPAyBaCP

.

. .

Stacking faults or dissociated dislocations have never been observed in stoichiometric rocksalt carbides ; this is because they produce tetrahedral coordination of carbon, or A upon A stacking of the metal, or if both these are avoided an

extended core normal to the slip plane [57]. In any case the stacking fault energy will be large. However, the removal of a carbon plane allows the fault to be pro- duced by a simple shear, similarly to fcc metals :

AyBaCPAyB, AyBa

...

[57]. Effectively, in TaC, the occurrence of stacking faults increases with vacancy concentration and their energy decreases [56]. In some cases, they are observed altogether with the diffuse scattering patterns described in

5

2.2, but clearly they

replace this diffuse scattering in tantalum monocarbide

below TaC,.,, [26]. In this case,, the cores of the observed (1 1 1) stacking faults are probably carbon deficient [26] and accommodate carbon vacancies. Therefore, at low metalloid content, the occurrence of these stacking faults may compete with the repulsion between carbon vacancies on an unmodified fcc sublattice,

In TaC,:,,, ordering of these stacking faults has been locally observed, and might explain the nucleation of the dzeta phase Ta4C3-, [26].

5.3 THE DZETA PHASES M4C3-,. -These structures, which may be considered as a stacking of ele- mentary MC and M,C blocks, or as a 12 layer periodic metal atom stacking (hhcc),, have been identified for the three systems V-C, Nb-C and Ta-C [22, 581. The exact distribution of carbon atoms is not known. One description of the phases, starting from the rocksalt structure, consists' in the regular removal of one over four (111) carbon planes, followed by shearing ; this leads to the stacking :

which can be considered as a periodic distribution of the (1 11) stacking faults described above [26]. But this complete absence of carbon 'in the planes indicated by an arrow is hypothetic, and, in the case of VC,-, and NbC, W,, difficult to reconcile with the observation of weak bands of diffuse scattering, suggesting short- range order within the close-packed octahedral carbon planes [22].

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ORDER AND DISORDER IN CARBIDES AND NITRIDES C7-2 19

sical properties with the degree of order has yet been attempted.

Nevertheless, a general picture of the atomic distribution of carbon vacancies in carbides is now emerging :

- First, it is interesting to remark that in the short- range orderld state (of vanadium carbide crystals, at least), no microdomains were visible in high resolution dark-field images using regions of diffuse electron intensity maxima [25] ; this confirms the validity of the description of the short-range ordering in terms of non-random pair probabilities.

- Second, this short and long-range ordering seems to be describable in very simple geometrical terms, with preferred coordination shells for the metal atoms (see figure 5); systematic behaviours of the vacancy arrangements are found, such as the tendency of vacancies to be third neighbours in group V monocarbides, to avoid second neighbour positions in group I11 and IV monocarbides, or to occupy alternate octahedral sites on interstitial rows parallel to the c axis in hemicarbides.

These behaviours suggest that the origin of ordering in carbides and nitrides is due to short-range chemical

effects, associated to the metallo-covalent bonding, rather than to long-range elastic or electrical interactions. Effectively, the elastic interaction energies between carbon vacancy pairs in uranium monocarbide [9] are an order of magnitude lower than the interaction energies deduced from thermodynamic data on the same system [6], or from Bragg-Williams models for ordering in the V-C system. On the other hand, as the compounds are metallic, long-range electrical forces are screened by the conduction electron gas.

Unfortunately, the calculation of the interaction energies between defects in such compounds, starting from the electronic structure, has been barely attempted up to now. The (< Xa-scattering )) calculation of

Schwarz and RBsch [60] for a carbon vacancy in NbC and the calculation of Kauffer [61] for a nitrogen vacancy in NbN (treating the defect as a localised potential in a LCAO band structure) give both a resonant level at 1 eV below the Fermi level (see the discussion at the beginning of

4

2). But the calculation of Kauffer [61] gave no satisfying result for the interaction energies between vacancies, because these were found very sensitive to the LCAO parameters used to describe the band structure.

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