The cubic-tetragonal tranformation in metal decarbides-II Lanthanide dicarbides and some mixed lanthanide dicarbide solid solutions

J. inorg,nucl.Chem., 1973,Vol. 35, pp. 1931-1940. PergamonPress. PrintedinGreat Britain

THE

CUBIC-TETRAGONAL TRANSFORMATION METAL DECARBIDESII

IN

L A N T H A N I D E D I C A R B I D E S A N D SOME M I X E D L A N T H A N I D E DICARBIDE SOLID SOLUTIONS I. J. McCOLM and T. A. Q U I G L E Y School of Materials Science, University of Bradford and N. J. C L A R K School of Physical Sciences, Flinders University of South Australia (Received 17July 1972) A b s t r a c t - T h e c u b i c - ~ tetragonal phase transition temperatures of arc-melted beads of all the lanthanide dicarbides except SmC2, TbC2 and TmC2 have been determined. The effect of intersolution of the dicarbides on the transformation temperature Tt has been studied for twenty-six pairs and a relationship established between depression of Tt and the difference in unit cell volumes AV of the dicarbides. For dissolution of larger cell volume dicarbides into dicarbides of smaller cell volume, ATt = K(AV) 2. No such simple relationship exists for the reverse process, which suggests that lattice strain energy is the dominant effect in determining Tt for mixed dicarbides. Why ATt can be used to indicate lattice strain is shown and the nature of this type of transformation is discussed. INTRODUCTION

THE T~MPERATURE at which the CaC2-type dicarbides are transformed from the low-temperature body-centered tetragonal to the high-temperature cubic form varies from 100 ° for BaC2 to 1760 ° for UC2. The melting points show no parallel large differences and all melt between 2200 ° and 2500 °. These large differences in the transformation temperatures may reflect varying degrees of metal-carbon bonding. We have shown[l] that the addition of LaC2 or CeC2 to UC2 progressively lowered the transformation temperature until for solid solutions between 20 and 80 mole % UC2 the cubic high-temperature phase could be quenched in and studied at room temperature. A model for the nucleation process was suggest which was based on the misfit between dicarbides with different-sized metal ions. The effect of metal ion size on the transition temperature is further examined in this paper for some lanthanide dicarbides and their binary solid solutions. A recent publication[2] shows that cubic lanthanide carbide solid solutions can be prepared by reduction of mixed oxides with carbon in the systems LaC2-YC2, LaCE-DyC~, PrC~-LuC2 at the 50 mole % composition. These could be analogous to the cubic phases in U - L n - C 2 systems in that nucleation of the tetragonal structure has been prevented on cooling from 1750 °, or else they could be oxide-carbides which are not yet well under1. 1. J. McColm, 1. Colquhoun and N. J. Clark, J. inorg, nucl. Chem. 34, 3809 (1972). 2. G. Adachi, H. Kotani, N. Yoshida andJ. Shiokawa, J. less-common Metals 22, 517 (1970). 1931

1932

I . J . McCOLM, T. A. Q U I G L E Y and N. J. C L A R K

stood [3]. The identification of cubic phases in this work suggests that the first

explanation is most likely. EXPERIMENTAL The dicarbides were prepared from the metal (> 99.9% purity, Rare Earth Products Ltd) and excess carbon ( - 10% excess of the calculated weight) from a spectrographically pure carbon rod (Johnson and Matthey), outgassed and cooled under argon, arc melted until metal evaporation no longer fogged the arc furnace window and a cooling curve characteristic of the dicarbide was obtained. Lattice parameters were determined by X-ray powder diffraction using a Philips 11.45 cm camera and CoKa or CrKa radiation. The cooling curves were determined by the method described previously [ 1]. RESULTS

The transformation temperatures of lanthanide dicarbides are shown in Table 1 for this work, together with the published data of Bowman et al. [4]. With the exception of the two end members LaC~ and LuC2, the agreement is good, particularly as Bowman was able to measure the transformation temperature when approached from above and below and averaged the results, which showed hysteresis effects leading to lower values for the cooling experiments. Table I. Cubic to tetragonal transformation temperatures Compound This Work LaC2 CeC2 PrC2 NdC2 SmC2 GdC2 TbC2 DyC2 HoC2 ErC~ TmC2 LuC2 UC2

995 1090 1100 1150

Temperature (°C) Winchel [5] Bowman et al. [4]

1100

1060 1090 1130 1150

1218

1265

1250 1280 1275

1290 1300 1320

1390 1690

1500 1765

The transformation temperatures for various binary dicarbide solid solutions are given in Table 2. The apparatus was insensitive to transformations below 750 ° but X-rays showed that in some systems, for example, 40.4 mole % LAC259.6 mole % ErC2 and 57.5 mole % LaCz-42.5 mole % HoCz, the cubic phase exists down to room temperature. The composition dependence of Tt is shown in Table 3 and Fig. 1 for PrC2-HoC~ solid solutions. 3. N.J. Clark and I. J. McColm J. inorg, nucl. Chem 34, 117 (1972). 4. A. L. Bowman, N. H. Kirkorian, G. P. Arnold, T. C. Wallace and N. G. Nereson, U. S. At. Energy Comm. LA-DC-8451 CESTI, 7 (1967). 5. P. Winchell and N. L. Baldwin, J. phys. Chem. 71, 4476 (1967).

C u b i c - t e t r a g o n a l transformation in metal dicarbides

1933

Table 2. Transition temperatures for solid solutions with compositions around 50 mole %

Sample LnC2 + LnC~

Composition (mole %)

Tt (°C)

A Tt (*C)

AV (/~3)

A V2 (A3)

947 990 965 < 750

-- 143 -- 110 -- 185 -- 500 > 1260

4"14 6"09 8"10 14.9 20"24

17"14 37"10 65"60 222"0 409.6

LnC~-LnC~ (a) (b) (c) (d) (e)

LaC2-CeC2 LaC~-PrC2 LaCs-NdC~ LaC2-GdC2 LaC2-HoC2

50.2 47.1 50.0 50-0 57.5

49.8 52.9 50.0 50-0 42.5

cubic a = 5.72A

(f) LaC2-ErC2

40.4

59.6

cubic

> 1260

21.85

477.3

a = 5.67,~ 1050 1080 975 < 750

- 60 -- 70 - 243 > 500

1.95 3.87 10.84 14.53

3"80 14.98 117.5 211 "2

> 530

15-85

251.2

> 1275

17-71

313.6

-45 - 168 -470 > 530

2.01 8.89 14.15 15.34

4.0 79.2 200-2 235.3

- 103 -- 242 --315 --435 --65 -- 75 -- 150 -- 20 --45 --+0

6.8 10.47 12.14 13"75 3"59 5"26 6"87 1"30 3"02 1"61

57.3 122"0 147.4 189.1 12-9 27"7 47-2 1 "68 9.14 2"59

(g) C e C 2 - P r C z (h) C e C 2 - N d C 2 (i) C e C ~ - G d C 2 (j) C e C ~ - D y C ~

53.8 43.3 48.9 50.0

46.2 56.7 51.1 50.0

(k) C e C 2 - H o C 2

58.4

41.6

(1) C e C z - E r C 2

53.0

47.0

tet < 750 a = 3.77 c = 6.32 <750

cubic a = 5-64+ weak

cubic phase (m) PrC2-NdC~ (n) PrC2-GdC~ (o) P r C 2 - H o C 2 (p) PrC~-ErC2

54.5 54.3 49.7 50.1

45.5 45.7 50.3 49.9

a = 10.7 1105 1050 810 < 750

(q) N d C 2 - G d C 2 (r) N d C 2 - D y C 2 (s) N d C 2 - H o C ~ (t) NdC2-ErC2 (u) G d C ~ - D y C 2 (v) G d C 2 - H o C 2 (w) G d C 2 - E r C z (x) D y C 2 - H o C 2 (y) DyC~-ErC2 (z) HoC~-ErC2

48"1 50.0 45.5 53.2 44.8 46.5 50.0 50.0 50.0 50.4

51-9 50.0 54.5 46.8 55.2 53.5 50.0 50.0 50.0 49.6

1105 1008 965 840 1185 1205 1125 1260 1230 1275

tet

DISCUSSION

The cubic to tetragonal transformation is diffusionless and has been frequently described as martensitic. As the kinetics for propagation of a martensitic transformation approach the velocity of sound in the solid it would seem impossible to quench the transformation. For this reason, to obtain cubic dicarbides at room temperature indicates that the transformation is isothermal martensite type, in which nucleation rather than growth is the rate-controlling step. A mechanism

1934

I . J . McCOLM, T. A. Q U I G L E Y and N. J. C L A R K Table 3. Dependence of transition temperature on composition for the PrCzHoCz system

Tt

Composition (mole %) PrCz HoC=

(°C)

0 9'7 18.4 22"3 24-6 30"0 31"8 39.0 45"0 49.7 55.0 60.9 62.3 69.8 74.9 85.0 87.6 96.2 100

1280 1135 1055 1015 925 830 810 810 815 805 830 860 835 885 985 990 1030 1035 1100

100 90"3 81 '6 77"7 75 "4 70.0 68"2 61"0 55"0 50-3 45.0 39.1 37.7 30.2 24.1 15.0 12.4 3-8 0

1200

IlOO

cubi~

2

//~

I000

g _Tefrogonal

900

800

0

20

\

onol

40

60

80

I O0

Pr C2, mole %

Fig. 1. Transformation temperature of Pr.C2-HoC2 solid solutions.

Cubic-tetragonal transformation in metal dicarbides

1935

for hindering nucleation in solid solutions of dicarbides with different-sized metal ions was proposed in part I [1]. This assumed that nucleation of the tetragonal structure within the cubic matrix required the concerted action of C22- units over a number of unit cell volumes to align parallel and create a viable tetragonal nucleus of minimum size. The presence of solute metal ions smaller or larger than the solvent metal ions would delay this parallel alignment, because the size difference of the solute metal ion creates for the surrounding C22- units orientations which are preferred to the solute ion but random relative to a parallel alignment required for nucleation. The larger the size difference, the more difficult nucleation of the tetragonal phase would become. Strain energy is an important parameter in martensite transformations [5-8], and the strain energy of a solid solution increases with the size difference between the components. The relationship for alloys is represented by [7, 9] E~¢c~ = Al.c(f~s)2 f ( c ) . . .

(1)

where A is a constant,/z is the shear modulus, 1-/$sis a size factor expressed in terms of volume andf(c) is a function of concentration. Thus nucleation should be suppressed if the size difference is large enough, and the strain energy will also increase. As the strain energy is one degree of freedom in the expanded form of the phase rule describing martensitic transformations, the large strain energy existing when the size difference is large may stabilise the cubic form. This is probably the reason why cubic phases exist at room temperature with 50 mole % CeCz-HoC2, LaC2-HoCz, LaC2-ErC2 solid solutions in this work. The limit of ionic radius difference for the formation of a f.c.c, phase (RLn3 + - RLn3+)/RL~3+ has been suggested[2] as being 14%, but this is only one aspect of the phenomenon, which as shown in Fig. 1 and in Eqn (1) is composition dependent. So far the cubic phases obtained in this work do exceed the 14% difference, and the shape of the Tt vs composition curve (Fig. 1) shows that the composition dependence can be neglected at 50 +__10% in these binary solutions, and that Eqn (1) if it applies in this case can be reduced to E(,) = A~(~-~sf)2 . . . .

(2)

If the solid solutions are considered as pseudobinary solutions of two dicarbides, the cell volumes of the pure dicarbides can be compared in calculating size differences. This approach is justified to some extent, for where the lanthanide elements in a solid solution have similar ionic radii it has been shown that the tetragonal cell parameters obey Vegard's Law over the whole composition range[2]. For more widely spaced pairs of dicarbides this has yet to be fully tested. Figure 2 plots the change in transformation temperature ATt for 50___10 mole % solid solutions of various dicarbides against the difference in body6. J. Friexl¢l,Adv. Phys. 3, 446 (1954). 7. J. Frie~lel, Phil. Mag. 46, 514 (1955). 8. L. S. Darken and R. W. Gurry, Physical Chemistry of Metals. McGraw-Hill, New York (1955). 9. J. D. Esh¢lby, SolidSt. Phys. 3, 79 (1956).

1936

1. J. McCOLM, T. A. QU1GLEY and N. J. C L A R K I lk P Tefrogonal of room fernp

-600-

4 -0 0

J~d

/

J*° <~

_!

-2oo

• _.-L i3

~ 2

hj 4

r

I

I

I

I

I

I

r

I

I

I

6

8

I0

12

14

16

18

20

22

24

AV,

~3

Fig. 2. Depression of transformation temperature ATt of ianthanide dicarbides with smaller cell volumes to which larger cell volume dicarbides have been added, vs change in unit cell volume. The legends correspond to samples in Table 2.

centred tetragonal cell volumes AV, and shows a clear dependence of ATt upon AV. If one dicarbide is taken as the solvent and the change in transformation temperature determined for other dicarbides as solutes, a distinction must be made depending on whether the cell volume of the solute is larger or smaller than that of the solvent. Strain should exist in the solvent and become the dominant factor only when the solute cell is larger than the host. Figure 3 plots ATt v's (AV)~, the square of the cell volume difference, for GdCs-LnC2 solid solutions, when LnC2 has a larger cell volume than GdC2; in this case there is a linear relationship. This square relationship exists for all dicarbide pairs where the dicarbide with the smaller cell volume is the "solvent" (Fig. 4). This behaviour is expected from Eqn (2) and suggests a direct relationship between lattice strain -300

-200 F

i

//

-I00

J

I

I

50

JO0

~50

(Av) ~, ~ Fig. 3. Plot of ATt vs (AV) 2 for dissolution of LnC2 in GdC~.

Cubic-tetragonal transformation in metal dicarbides

1937

-500 --

-500

<3

-I00

J

I

,

I

40

,

I

80

,

t

120

,

160

I 200

(Av)2, ~3 Fig. 4. Plot of ATt vs (AV)2 for all pairs of dicarbides examined, taking AT as Tt (small volume dicarbide) - - T t (large volume dicarbide). A = Pr, O = Nd, × = Dy, [] = Ho, O = Er. energy and transformation temperature. When the " s o l u t e " dicarbide has a smaller cell volume, no simple relationship exists (Figs. 5 and 6). T h e s e plots indicate that the transformation t e m p e r a t u r e is only slightly affected until (AV) 2 > ~ 80 A 3, w h e n a sharp drop in T t occurs. Following Ubbelohde[10], when crystal p o l y m o r p h s exist one usually has the larger lattice energy at 0°K; as the t e m p e r a t u r e increases the enthalpy difference b e t w e e n the two does not change much, and the main factor leading to transformation is the increasing divergence of crystal entropies. T h u s AHt,a,~ (cubic --> tetragonal) is approximately constant with respect to t e m p e r a t u r e and determined by, say, the difference in lattice energies only. T h e situation for a firstorder transformation f r o m cubic to tetragonal dicarbide is shown schematically ~,Cubic JTefragonal -600

I

-400

P

<3 -200

0

2

4

6

8

I0

,

I

I

I

I

12

14

16

18

20

AV, ~3 Fig. 5. Depression of transformation temperature against change in cell volume when ATt = Tt (larger volume dicarbide) - Tt (smaller volume dicarbide). 10. A. R. Ubbelohde, Q. Rev. chem Soc. 11, 251 (1957).

1938

I. J. McCOLM, T. A. Q U I G L E Y and N. J. C L A R K

<3

-

4 0 0

--

-

200

i

o

50

I O0

150

200

z~v,~ #

Fig.

6. ATt vs ( A V ) 2 w h e n ATt = Tt

(larger volume dicarbide) dicarbide).

-Tt

(smaller volume

in Fig. 7, where at the crossover point on the free energy curves Tt =

-

AHtrans AS t,ans

(3)

" ""

AHtrans will change with the carbide system under consideration but AStrans, considering only configurational entropy, is determined by structure type and will be constant for all CaC2-type compounds. When ions larger than Ln 3+ are introduced into the matrix a strain energy term Es is introduced which raises Htet to Hcubic in Fig. 7 and the entropy favouring the more disordered cubic phase with C22- ions in [111] stabilizes it. If Es is in sufficient to raise Hte t to Cubic /

'tel //Gtet

/

~ t

~ GCUbic

H

/// Temp

rS

Fig. 7. Free energy relationship between tetragonal and cubic dicarbides.

Cubic-tetragonal transformation in metal dicarbides

19 3 9

Hcubl¢ then transformation will occur at some temperature below Tt (strain free). Then Tt
AS ( Ttobs - - Ttpure)

i.e.

E ~ = A S . ATt...

(4)

where ATt is the lowering of transformation temperature of the pure "solvent" dicarbide due to strain. The use of ATt as an indication of strain energy in Figs. 3 and 4 for mixed lanthanide dicarbides is therefore sensible. Equations (2) and (4) indicate that the slope of the A T vs (AV) 2 line is proportional to the shear modulus of the solvent dicarbide. Data on the mechanical properties of the ianthanide carbides do not appear to exist, but Bowman e t al. [4] have reported low values of the Knoop microhardness for the series from LaC2 to GdCz, about one third of those for the series TbC2 to LuC2. Thus a family of straight lines could exist with minimum slope for LuCz (hardness = 721___29 kg/mm 2) and maximum slope for results involving PrCz (hardness= 166-+-12 kg/mm). This may partly explain the appearance of Fig. 4. This will be studied in future work. For this type of compound the factors leading to a particular value of transformation temperature Tt c a n be related by equating Tt to bond energy, strain energy, concentration and nucleation energy. In the case of pure dicarbides, bond energy and nucleation energy are important while concentration has no meaning, and the strain energy term only has relevance for a domain model involving microdomains of cubic and tetragonal symmetry where strain energy arises from domain boundary alignment. A consequence of this model would be that particle size and cooling rates would affect Tt, but this has so far not been found. In Group II dicarbides, where a purely ionic model involving M 2÷ and C22ion applies, progress might most easily be made in separating the variables leading to a particular Tt when reliable data are available. As the cation size increases from Ca 2+ to Ba 2÷, the ionic bond energy must decrease; T t does decrease but the change T t (within the limits of the available data) is not directly proportional to the decrease in cation radius, and the shape of the curve for T t vs 1Irma+ might reflect the role of the nucleation energy term. This term is the activation energy of the process which produces a viable nucleus with all the Cz 2- ions aligned along [001], and probably decreases as the size of M n÷ increases, which would lead to further lowering to Tt. Conversely, an increase in C - C bond length in C2"- would have the opposite effect, making nucleation more difficult and depressing Tt. In the absence of more detailed X-ray and transformation temperature data for Group II dicarbides the effects of these variables cannot be resolved. The situation with respect to lanthanide dicarbides is more complex. The increase in cation charge to 3+ and the presence of one

1940

I . J . McCOLM, T. A. QU1GLEY and N. J. C L A R K

electron per Ln 3+ in a metal (s-d)-carbon (ptr*pTr*) band will raise the bond energy and so increase Tt relative to CaC2. On the other hand, a decrease in M n+ radius for some of the lanthanides, together with a general increase in C - C bond distance (C-C = 1.191 A in CaC2 and 1.303 in LaC2) make nucleation more difficult and will depress Tt relatively. The large increases observed e.g. DyC2 (Dy 3+ = 0.99 A, C - C = 1.291 A) has Tt = 1250° and CaC2 (Ca 2+ = 0.99, C - C = 1.191 A) has Tt = 450 ° shows that the bond energy increase is much greater than the nucleation effect arising from C - C bond length increase. This situation is again present with UC~, where the cation charge increases to 4+ and there are two electrons per U 4+ present in the metal-carbon bond, but T t does not reach the expected level from such a bond energy increase. Here the lowering caused by the nucleation energy increasing due to small cation size (U 4+ = 0.89 A) acts together with the effect of the increased size of the C22- ion (C-C = 1.340 ,~). The general increase in Tt from LaC2 to LuC2 is somewhat erratic if only the increase in ionic bond energy arising from a decrease in rLn3+ is considered. Since the smaller cations also raise the nucleation energy, the rise in Tt will not be as sharp as expected, and the situation is still more complex because the C - C bond distance falls from 1.303 .~ at LaC2 to 1.276 A at LuC2, which should act in a way to raise Tt. Thus the non-linear variations from member to member of this series might be interpreted. Results from this work show that for the binary solid solutions of the dicarbides the strain energy contribution to Tt is of greatest importance. The lack of a simple relationship when the change in Tt of large cell volume dicarbides, to which smaller cell volume solute is added, is to some extent rationalised on the above model. Where the dicarbide containing the smaller cation is added to the larger the bond energy will increase, since the mean cation size decreases and SO Tt will rise from this term. The strain energy term will have only a small effect, at least up to moderate concentrations of the small cation. The nucleation energy will be the largest effect, for as previously argued[l] the effect of the small cation will be to provide specific local site symmetry, making coherent [001] alignment more difficult and depressing Tt. Since Tt always falls on solid solution, this last effect is the most important, but the plot of ATt vs. concentration is shallow. In the reverse situation the larger cation increases fLn3+ and so depresses Tt. The disruptive effect of local C22- symmetry will be comparable to the first case and will lead to a reduction in Tt. Inclusion of a larger cation in the matrix will lead to strain, another depressing influence on Tt. Now all the terms lead to a drop in Tt and so a sharper curve results (Fig. 1). The linear dependence of ATt on (AV)2 at 50 mole % concentration indicates that the strain energy term is the most important. This work will be extended to determine Tt below 750°C and to study a wider range of materials, and also to study the effects of strain energy present in the cubic room-temperature phases on chemical reactivity.

Acknowledgements-The w o r k

w a s supported by an S.R.C. equipment grant to I.J.M c. and by a grant from the A.R.G.C. and A.I.N.S.E. to N.J.C.