Thermodynamics of binary metallic carbides: A review

Materials Science and Engineering, 76 (1985) 1-50

Review Paper Thermodynamics

of Binary Metallic Carbides:

A Review

R. G. COLTTERS

Department of Materials Science, Universidad SimSn Bolivar, Caracas (Venezuela) (Received February 4, 1985)

ABSTRACT

A general survey is made o f the thermodynamic data available on solid binary metallic carbides. Data for the free energies o f formation o f carbides as a function o f the temperature are presented as Ellingham diagrams. The equations and the estimated accuracy when available are given for each carbide. The free energies are normalized with respect to 1 tool o f carbon.

1. INTRODUCTION

Carbon combines with almost every other element in the periodic table, b u t some elements (e.g. copper) do n o t form carbides or form only highly unstable carbides [ 1-3 ]. Carbides offer a unique collection of properties: they are c o m p o u n d s which exist over a wide composition range [4, 5], they have very high melting points, good elasticity [6] and extreme hardness (transition metal carbides) [7, 8] and they exhibit an unusual mixture of ionic, covalent and metallic behaviour [ 9 - 1 5 ] . Over the last few years, the thermodynamic properties of carbides have been determined by a number of researchers and these results have been published in the literature. This review brings up to date the earlier surveys of Richardson [16], Wicks and Block [17], Schick [18], Storms [19], Kelley [20, 21], Stull ( J A N A F Thermochemical Tables) [22] and Kubaschewski and Alcock [23]. Data for the free energy of formation of carbides as a function of temperature for rapid and approximate calculations are presented as freeenergy diagrams. In this paper the free energy of formation is given for the general reaction 0025-5416/85/$3.30

x 1 - M + C = - MxCy Y Y

(1)

For these reactions the standard states selected for the various compounds are as follows: (a) for solid or liquid metal, a coexistence with its lowest carbide and, for gas metal, a pure phase; (b) for carbon, graphite; (c) for carbides, the solid or liquid carbide in equilibrium with the other condensed phase of the reaction. The standard free-energy change AG°T for each reaction is related to the standard enthalpy change AH°T and the standard entropy change AS°T by the following equation: AV°T

:

AH°T

--

T AS°T

(2)

Many of the free-energy data have been derived from both heat of formation and heat capacity data and from equilibrium measurements, using the following expression: T

298

T

298

Since Cp is normally expressed as Cp = a + b T + c T -2 + d T 2 eqn. (3) can be readily integrated. Also, some values of the free energy of formation were estimated from the heats of formation at 298 K and free-energy functions according to the following relationship: A G°T : &H°298 + A ( G°T ~- -H°298~ \ T /

(4)

The magnitudes of the errors in AG°T resulting from neglecting the thermodynamic © Elsevier Sequoia/Printed in The Netherlands

values for phase transitions have been assessed. Above the transition temperature Tt, each transition contributes t o AGOT an a m o u n t given by ~/-/°t (1 - - T/Tt) where A/-/°t is the enthalpy of the phase transition. The values of AH°t for solid state phase transitions are small [22], b u t neglecting them could lead to a AG°10oo error of a b o u t -- 5 kJ mo1-1 or less. The AH°t contribution to AG°T from melting and vaporization of elements will be included in the calculations, whereas the enthalpy of melting of the c o m p o u n d is ignored because the AG°T calculations generally will n o t be extended above the melting temperatures. Methods for estimating the S ° values for crystalline c o m p o u n d s can be found in the literature [ 1 6 - 2 0 ] . Usually the entropy AS~° of formation is obtained from the entropies o f the elements. This average value of ASt ° is then used to calculate the u n k n o w n S ° value.

1.1. Data sources Values of the 298.15 K enthalpies and entropies for the species considered here were obtained from standard reference tables [17, 18, 2 0 - 2 5 ] unless otherwise stipulated. When values for a given c o m p o u n d appeared in more than one of these tables, the value in the more recent table was used. Phase equilibrium diagrams in binary and ternary systems were obtained from compendia [1-3] and other publications noted below. 2. ALKALI AND ALKALINE EARTH CARBIDES

2.1. Description of an alkali carbide 2.1.1. Sodium carbide Na2C2 There is little information a b o u t Na2C2. Elliot and Gleiser [24] and Richardson [16] gave a value of 35.56 + 4.20 kJ mo1-1 for the standard enthalpy AH°29s of formation of Na2C2. For the standard free energy AG°29s of formation, R i c h a r d s o n [ 16 ] proposed a value of 1.6.74 kJ tool -1 which is based on the measured value of A/-/°29s and on the assumption that AS°29s is negligible. 2.2. Descriptions of alkaline earth carbides 2.2.1. Beryllium carbide Be2C There have been some attempts to measure the thermodynamic properties of Be2C by

calorimetric and gas equilibrium techniques. There is significant disagreement between the reported data on the standard heat of formation of Be2C. The heat of solution measurements of Be2C in aqueous hydrochloric acid made by Blachnik et al. [25] at 383 K lead to a heat of formation of -- 117 + 1 kJ mo1-1 for Be2C. Motzfeldt [26] and Muratov and Novoselova [27, 28] determined the pressure of CO in equilibrium with the solids Be2C, BeO and carbon according to the following reaction: 2BeO(s) + 3C(s) = B e 2 C ( s ) + 2CO(g)

(5)

Rinehart and Behrens [29] recalculated the standard enthalpy of formation for Be2C from experimental AH°298 values for reaction (5) measured in the three earlier works [ 2 6 28]. These values are shown in Table 1. The calculations were made using AH°298 = - - 1 1 0 . 5 + 0.2 kJ mo1-1 for CO [30] and A/-/~29s = -- 608.4 + 3.3 kJ mo1-1 for BeO [22]. Rinehart and Behrens [29] measured the vapour pressure of B e 2 C in the temperature range 1 3 8 8 - 1 7 6 3 K, using Knudsen effusion mass spectrometry. Pollock [31] also measured the vapour pressure of Be2C in the temperature range 1 4 3 0 - 1 6 6 9 K by the Knudsen effusion method. Rinehart and Behrens [29] and Pollock [31] obtained, for the standard enthalpy AH°29s of formation of Be2C, values o f - - 9 2 . 5 + 15.7 kJ mo1-1 and -- 97.7 + 10.1 kJ mo1-1 respectively. Table 1 shows the experimental results of all these investigations. Enthalpies of formation derived from B e O - C - B e 2 C - C O equilibrium measurements are in p o o r agreement with one another. This suggests problems of solid solubility and of establishing equilibrium CO pressures. Also there is a great disagreem e n t between the value reported by Blachnik et al. [25] and that derived from mass spectrometry and Knudsen effusion measurements. The enthalpy of formation reported by Rinehart and Behrens [29] is in excellent agreement with the Knudsen effusion result of Pollock [31]. Thus, the r e c o m m e n d e d hH°29s value is - - 9 5 . 1 + 9.33 kJ mo1-1 for the standard heat of formation of Be2Ccs); this is an average of the values reported by Rinehart and Behrens [29] and by Pollock [31]. Spencer [32] reported a value of 16.3 + 3.3 J mo1-1 K -1 for the standard e n t r o p y of

TABLE 1 Thermodynamic properties of Be2C Study

-- ~ub/° 298

(kJ tool -1) Blachnik et al. [25] Motzfeldt [ 26] Muratov and Novoselova [ 27] Muratov and Novoselova [ 28] Rinehart and Behrens [ 29]

117.0 136.2 227.3 182.6 92.5

SO298 AGf ° (J mo1-1 K-1) (kJ tool -1 K -1)

Solution calorimetry BeO-C-BeC2-CO equilibrium BeO-C-BeC2-CO equilibrium BeO-C-BeC2-CO equilibrium Knudsen effusion mass spectrometry Knudsen effusion mass loss

+ 0.9 + 4.9 a -+ 8.8 a +- 4.7 a +- 15.7

Pollock [31]

97.7 + 10.1

Recommended value

95.1 + 9.3 16.32 -+ 3.35

Spencer [32] This work

-

aRecalculated by Rinehart and Behrens [29] using ~ / 0 2 9 8 --608.4 + 3.3 kJ tool -1 for BeO(s) [22].

f o r m a t i o n o f Be2C. This e s t i m a t e d value is also s h o w n in Table 1. No direct experimental measurements of t h e s t a n d a r d free e n e r g y o f f o r m a t i o n o f Be2C have b e e n made. H o w e v e r , f r o m t h e results o b t a i n e d in t h e K n u d s e n e f f u s i o n t e c h n i q u e s [29, 31] and t h e h e a t c a p a c i t y and S°298 d a t a f o r b e r y l l i u m [ 3 2 ] , c a r b o n [22] and Be2C [ 3 2 ] , it is possible t o estimate t h a t A G ~ ° ( + 1 3 6 5 ) ------ 6 8 3 7 3 - - 5 0 T J mo1-1 K -1

(298-1110 K)

------ -

68373 - 50T (298-1110 K)

Estimated Estimated

110.5 + 0.2 kJ mo1-1 for CO [30]

and

~-/°298

:

f o r m a g n e s i u m [36, 37] and c a r b o n [ 2 2 ] , it is possible t o estimate f o r Mg2C 3 t h a t AG~°(+140) ---- 2 7 7 8 7 - - 9 . 8 T J mo1-1 K -1 ( 2 9 3 - 9 2 3 K)

(8)

for the reaction 2Mg(s) + C(s) = ½Mg2C3(s )

(9)

and t h a t AGf°(±

552) = 1 5 9 1 2 + 3 . 5 6 T J mo1-1 K -1

(6)

for the reaction 2Be(s) + C(s) -- Be2C(s)

Me thod

( 9 2 3 - 1 1 5 0 K)

(10)

for the r e a c t i o n (7)

2.2.2. M a g n e s i u m carbides Mg2Cs and MgC2 Magnesium f o r m s t w o carbides Mg2C 3 and MgC2. T h e heats o f f o r m a t i o n o f Mg2C a and MgC2 were d e t e r m i n e d b y I r m a n n [33] f r o m the heats o f s o l u t i o n o f the carbides in a q u e o u s h y d r o c h l o r i c acid. H e f o u n d A/-/°298 values o f 79.5 ± 33.5 kJ mo1-1 and 87.9 ± 20.9 kJ m o l -~ f o r Mg2C 3 a n d MgCz respectively. The standard entropies of formation of 58.6 + 12.6 J mo1-1 K -1 and 55.4 + 8.4 J m o l -~ K -1 f o r Mg2 Ca and MgC2 r e s p e c t i v e l y are t h o s e given b y F u r u k a w a et al. [34] and K r i k o r i a n [ 3 5 ]. Using these values o f AH°298 and S°298 f o r Mg2C 3 w i t h t h e h e a t c a p a c i t y and S°298 d a t a

2Mg(liq) + C(s) = ~M2Cats 1 , )

(11)

Similarly f o r MgC 2 t h e e s t i m a t e d s t a n d a r d free e n e r g y o f f o r m a t i o n is given b y A G ° ( ± 1 7 0 ) = 4 5 3 1 9 - - 9 . 7 T J mo1-1 K -1 ( 2 9 3 - 9 2 3 K)

(12)

for the reaction ½Mg(s) + C(s) = ½MgC2(s)

(13)

and b y A G ° ( ± 1 9 8 ) = 3 6 0 5 6 + 0 . 5 T J mo1-1 K -1 ( 9 2 3 - 1 1 5 0 K)

(14)

f o r the r e a c t i o n ½Mg(liq) + C(s) -- ½MgC2(s )

(15)

Table 2 shows the e x p e r i m e n t a l results and the e s t i m a t e d values.

4 TABLE 2 Thermodynamic properties of magnesium carbides Carbide

Study

Mg2C3 Mg2C3 Mg2C3 Mg2C3 Mg2C3

Irmann [33] Furukawa et al. [34]

MgC2 MgC2 MgC2 MgC2

Irmann [33] Krikorian [35]

~r'/°29 s

S°298

AGf °

(kJ mol-1)

(J mol-1 K-I)

(J tool-1 K-l)

Method

79.5 ± 33.5 15912 + 3.56T (923-1150 K) 45319-- 9.7T(293-923 K) 36056 + 0.5T(923-1150 K)

Calorimetry Calorimetry Estimated Estimated Estimated

27787 - 9.8T (293-923 K) 15912 + 3.56T(923-1150 K)

Calorimetry Calorimetry Estimated Estimated

58.6 ± 12.6

87.9 ± 20.9 55.4 ± 8.4

TABLE 3 Thermodynamic properties of CaC2(s ) Study

-- ~/°298 (kJ tool-1)

Ruff and Josephy [38] Kameyama and Inoue [39] Faircloth et al. [41]

59.0±8.4 59.4±1.7 59.0±2.9 a

Recommended value

59.1±3.1

Kelley [42] Richardson Richardson Richardson Richardson

2.2.3.

S°298 (J mo1-1 K-I)

AGf° (J tool-1K -1)

Calorimetry Calorimetry Knudsen effusion Calorimetry

70.3 + 2.1 [16] [ 16] [16] [16]

-

-

Calcium carbide CaCe

(16)

Geiseler and Biichner [40] measured t he h e a t o f f o r m a t i o n calorimetrically at 291 K on the same system as t h a t of R u f f and J o s e p h y [38] and t h a t o f K a m e y a m a e t al. [39] and r e p o r t e d a AH°29s value of -- 59.4 + 1.7 kJ mo1-1 f o r CaC2. Faircloth e t al. [41] measured t he pressure o f calcium v ap o u r in equilibrium with CaC2 in the t e m p e r a t u r e range 1 3 0 0 - 1 9 0 0 K according to the following reaction: CaC2(s) ~ Ca(g) + 2C(s)

28451- 12.3T(298-720 K) 24309-- 18.1T(720-1123 K) 28660-- 14.2T(1123-1760 K) -- 104977 + 29.2T(1760-2500 K) -

-

-

R u f f and J o s e p h y [38] and K a m e y a m a and I n o u e [39] measured the heat o f f o r m a t i o n o f CaC2 by means o f calorimetry and r e p o r t e d A H ° : z 9 8 values o f - - 59.0 + 8.4 kJ tool -1 and -- 44.4 kJ mo l -~ respectively f or t he reaction Ca(s) + 2C(graphite) = CaC2(s)

Method

(17)

-

A third-law calculation of AH°298 for reaction (17) gave a mean AH°29s value of 237.2 + 2.5 kJ mo1-1. A second-law calculation o f AH°29s for react i on (17) gave a AH°2ss value of 227.2 + 4.2 kJ tool -1. Usually, the results obtained f r o m the third-law t r e a t m e n t are m o r e reliable; thus, using AH°29s = 237.2 + 2.5 kJ mo1-1 for react i on (17), the calculated value o f the standard enthalpy AH°z9s of f o r m a t i o n for CaC2 is - - 5 9 . 0 + 3.0 kJ mo1-1. A comparison o f the AH°29s values f o u n d for CaC2 is shown in Table 3. These AH°29s values are in excellent agreement and their uncertainties arise largely from the published vaporization enthalpies o f calcium [43]. Thus, the r e c o m m e n d e d AH°29s value for CaC 2 is -- 59.1 + 3.1 kJ tool -1. This value is an average of the values shown in Table 3. Kelley

[42, 44] measured the S°298 value and obtained 70.3 + 2.1 J mo1-1 K -1 for C a C 2 , which is also shown in Table 3. There is little information a b o u t the standard free energy of formation of CaC2. Brunner [45] measured the CO pressures in the equilibrium CaO(s) + 3C(s) = CaC2(s) + CO(g) ( 1 7 6 3 - 2 0 7 3 K)

(18)

R u f f and Foerster [46] measured the pressure of calcium vapour developed by CaC2 in the presence of graphite at temperatures of 2 2 9 8 - 2 7 7 3 K. Kameyama et al. [47] studied the dissociation of C a C 2 in a graphite crucible by measuring the mass loss of C a C 2 in the temperature range 1 8 7 3 - 1 9 7 3 K. From the results of these three high temperature studies, Richardson [ 16 ] r e c o m m e n d e d the following equations for the standard free energy of formation of CaC2 : AG°(+12600)

AG°T

= --

113400 + 35.8T J mo1-1 K -1 ( 1 2 0 0 - 1 5 0 0 K)

(27)

for the reaction -~Sr(g) + C(s) = ½SrC2(s)

{28)

When eqn. (27) is combined with the vapour pressure data for the reaction Sr(~, 7, liq) -~ St(g)

= -- 2 8 4 5 1 - 12.3T J mo1-1 K -1 ( 2 9 8 - 7 2 0 K)

2.2.4. Strontium carbide SrC2 No reports of high temperature calorimetric measurements have been published for SrC2. Flowers and Rauh [48] measured the vapour pressure of S r C 2 in the temperature range 1 1 0 0 - 1 6 0 0 K, using both an effusion and a mass spectrometry technique. They reported values of 84.5 + 12.6 kJ mo1-1 and 71.1 + 8.4 J mo1-1 K -1 for the standard heat and entropy of formation of S r C 2 respectively. No reports of high temperature free-energy measurements have been published. Flowers and Rauh [48] showed that, from effusion measurements,

(19)

for the reaction

given by Hultgren et al. [37] it is possible to estimate that AG°(+31.5) = -- 36726 -- 12.35T J mo1-1K -1

½Ca(a) + C(s) = ½CaC2(s)

(20)

AGO( + 12600)

( 2 9 8 - 1 0 4 1 K)

(29)

for the reaction

= -- 24309 -- 18.1T J mo1-1 K -1 ( 7 2 0 - 1 1 2 3 K)

½St(s) + C(s) = SrC2(s) (21)

for the reaction

(30)

and that AG°(+85.5)

½Ca(H) + C(s) ----~CaC2(.¢~ 1

(22)

= -- 41505.7 -- 7.73T J mo1-1 K -1

AGO( + 12600) {1041-1600 K) =

- -

28660 -- 14.2T J mo1-1 K -1 ( 1 1 2 3 - 1 7 6 0 K)

for the reaction (23)

for the reaction ~Ca(liq) + C(s) = ½CaC2(s)

(31)

(24)

½Sr(liq) + C(s)

= SrC2(s )

(32)

Table 4 shows the experimental results and the estimated values.

and AG°( + 12600) = - - 1 0 4 9 7 7 + 29.2T J tool -~ K -~ ( 1 7 6 0 - 2 5 0 0 K)

(25)

for the reaction 1Ca(g) + C(s) = 1CaC2(s)

(26)

These equations are also shown in Table 3.

2.2.5. Barium carbide BaC2 Heats of formation of BaC 2 have been measured by several techniques. Atki~s et al. [49], using impure BazC, measured the heat of solution in water at 298 K and obtained from the experimental results a AH°29s value of -- 20.9 kJ mo1-1 for the standard enthalpy of formation of BaC2(s). H o c h [ 50] used a Knudsen effusion m e t h o d to measure the par-

6 TABLE 4 T h e r m o d y n a m i c p r o p e r t i e s o f SrC 2 a n d BaC 2

Carbide

Study

- ZkH°298 ( k J tool -1

S°298 (J tool -1 K -1 )

SrC 2

F l o w e r s a n d R a u h [48]

84.5 -+ 12.6

71.1 +- 8.4

SrC 2

F l o w e r s a n d R a u h [48]

-- 1 1 3 4 0 0 + 3 5 . 8 T ( 1 2 0 0 - 1 5 0 0 K) - 36726- 12.35T ( 2 9 8 - 1 0 4 1 K) - 41505.7 - 7.73T ( 1 0 4 1 - 1 6 0 0 K)

SrC2 SrC2 BaC 2 BaC 2 BaC 2

A t k i n s et al. [49] H o c h [50] Flowers and Rauh [48]

BaC 2

Flowers and Rauh [48]

Method

AGf ° ( k J tool -1 K -1)

20.9 50.6 + 16.7 74.1 + 12.6

- 234700 + 60.3T ( 1 3 0 0 - 1 6 5 0 K) -- 2 8 7 9 4 - - 1 7 . 8 T ( 2 9 8 - 1 0 0 2 K) -- 3 9 6 3 4 . 5 - - 6 . 6 5 T ( 1 0 0 2 - 1 6 0 0 K)

tial pressure of Ba(g) in equilibrium with BaC2 in the temperature range 1 3 5 5 - 1 6 7 1 K. He obtained a AH°2ss value of -- 50.6 + 16.7 kJ mo1-1 for the standard enthalpy of formation of BaC2(s). Flowers and Rauh [48], using b o t h effusion and mass spectrometry techniques, measured the partial pressure of Ba(g) above pure BaC2 in the temperature range 1 3 0 0 - 1 6 5 0 K. They reported a AH°298 value of --74.1 + 12.6 kJ mo1-1. The disagreement between these values of AH°298 is possibly due to the difficulties encountered in obtaining pure samples of BaC2. The work of Flowers and Rauh showed good agreement between effusion and mass spectrometry experiments; thus the r e c o m m e n d e d value for the standard enthalpy AH°298 of formation of B a C 2 is - - 74.1 + 12.6 kJ mo1-1. Also, they obtained a value of 87.9 + 8.4 J m o 1 - 1 K -1 for the standard e n t r o p y S°298 oi formation for BaC2(s). These values are shown in Table 4. No high temperature free-energy measurements have been published. Flowers and Rauh [48] reported that, from effusion measurements, AG ° : -- 234700 + 60.3T J mo1-1 ( 1 3 0 0 - 1 6 5 0 K)

8 7 . 9 -+ 8.4

(33)

E f f u s i o n a n d mass spectrometry E f f u s i o n a n d mass spectrometry Estimated Estimated Heat of solution Knudsen effusion E f f u s i o n a n d mass spectrometry E f f u s i o n a n d mass spectrometry Estimated Estimated

for the reaction Ba(g) + 2C(s) = B a C 2 ( s )

(34)

When eqn. (34) is combined with the vapour pressure data for the reaction Ba(s, liq) --> Ba(g) given by Hultgren et al. [37] it is possible to estimate that AGO( + 435) = -- 28794.4 -- 17.8T J mo1-1 K -1 ( 2 9 8 - 1 0 0 2 K)

(35)

for the reaction ½Sa(s) + C(s) = ½BaC2(s)

(36)

and that AG°(+173) = -- 39634.5 -- 6.65T J mo1-1 K -1 ( 1 0 0 2 - 1 6 0 0 K)

(37)

for the reaction ½Sa(liq) + C(s) = 1 BaC2(s)

(38)

2. 3. Free-energy diagram for the alkali and alkaline earth carbides Figure 1 is the free-energy diagram for the alkali and alkaline earth carbides.

104 102 10

16151o'61d2:o 2' 0

L)00

1

lO4

10"1

lO5

800

Corbor oct tity

10-2

lO 6

1200

1600

-3' 10 10

2000

6 10

[]

Mg2C3 -4, 10 5 10

I

[ ] SrC 2

[]

-5 10 ,

-1

106

-2 10

lO

CH 4

!

lo3

[~]Trensition point rMIMelting point r'BI Boiling point 0

400

800 , , ,

P

Pc°2

(above400oc) PCH4

c'c)

1200

lO-151 1o .......

2 1() 151613

1(~6 10%

1600

102

2000

1(~2 10-1

10-11 10-10

-7 tO

-3 10

-8 I0

'1

10"9

-4 10

{obove400'C}

Fig. 1. Ellingham diagram for the alkali and alkaline earth carbides. (It should be noted that the temperatures in this diagram are in degrees Celsius and not in kelvins as in the text.)

3. G R O U P II CARBIDES AND A G R O U P IV CARBIDE, SILICON CARBIDE

by oxygen, fluorine bomb and solution calorimetry. Domalski and Armstrong [ 51], using fluorine combustion calorimetry, obtained a value of -- 71.55 + 11.30 kJ mo1-1 for the standard enthalpy of formation of B4C. Gal'chenko et al. [ 52] reported the standard enthalpy of formation of B4.2aaC to be -- 57.32 + 14.64 kJ mo1-1, based on chlorination calorimetry. More recently, Hong and Kleppa [ 53 ], using high temperature solution calorimetry at 1 3 2 0 K, obtained a AH°298 value of - - 6 9 . 8 7 + 6.28 kJ mo1-1. This result, the value obtained by Domalski and Armstrong [51] and that of Gal'chenko et al. [52] all fall well within the sum of the stated uncertainties of the respective investigations. According to Kubaschewski and Alcock [23], the value of Domalski and Armstrong [ 51] is believed to be the most reliable of the published values. Thus, the recommended value for the standard enthalpy AH°298 of formation of B4C is -- 71.55 + 11.30 kJ mol -z. Kelley [54] measured the specific heat of B4C; from his results he obtained an S°298 value of 27.13 + 0.13 J mo1-1K -~. No direct experimental determinations of the standard free energy of formation of B4C(s) have been made. Turkdogan [ 55] reported the following equation for the standard free energy of formation of B4C(s): AGO( + 4200) = - - 56819 + 7.1T J mo1-1 K -1

3.1. Descriptions of group 1H carbides 3.1.1. Boron carbide B4C

( 2 9 8 - 1 1 7 3 K)

There is a very considerable lack of reliable thermodynamic data on B4C. This is particularly true of the enthalpies of formation, which generally have been obtained indirectly

(39)

for the reaction 4B(s) + C(s) = B4C(s)

(40)

Table 5 shows the experimental values.

TABLE 5 Thermodynamic properties of B4C(s ) Study

- ~-/°298 (kJ tool -1)

Domalski and Armstrong [51] Gal'chenko et al. [52] Hong and Kleppa [53 ]

71.55 + 11.30 57.32 -+ 14.64 69.87 -+ 6.28

Recommended value

71.55 + 11.30

Kelley [54] Turkdogan [ 55]

S°298 (J tool-1 K - l )

AGf ° (J tool-1 K - l )

Method

Combustion Calorimetry Calorimetry

27.13 -+ 0.13

Calorimetry 56819 + 9 . 1 T ( 2 9 8 - 1 1 7 3 K)

3.1.2. Aluminium carbide Al4C3 There is considerable disagreement between the thermodynamic data reported on A14Cs. This is particularly true of the enthalpies of formation, which have been obtained b y several experimental techniques. Meschi and Searcy [56], using both a Knudsen effusion and a torsion technique measured the vapour pressure of A14C3 in the temperature range 1 5 0 0 - 1 8 0 0 K. They obtained a AH°29s value of -- 260.4 + 60.2 kJ mo1-1 for the standard enthalpy of formation of A14C3(s). Plante and Schreyer [ 57] studied the vaporization of A14Cs(s) by the Knudsen effusion mass loss m e t h o d in the temperature range 1 6 5 1 - 1 9 2 4 K. They obtained a AH°29s value of -- 228.4 + 35.1 kJ mo1-1 for the standard enthalpy of formation of A14Cs(s). Potter et al. [ 58] also measured the vapour pressure of A14Cs(s) by the torsion effusion method. Details of their investigation are not readily available in the literature. Rinehart and Behrens [ 59] quote the standard enthalpy

AH°29s of formation of A14C3 obtained by Potter et al. as -- 259.4 + 34.0 kJ mo1-1. Thoburn [60] measured the vapour pressure of A14Cs(s) in the temperature range 2 1 5 0 - 2 2 2 4 K using a differential thermal analysis technique. He obtained a AH°29s value o f - - 1 3 8 . 4 + 33.7 kJ mo1-1. Rinehart and Behrens [59] recently measured the vapour pressure of A14Cs(s) over the temperature range 1 3 2 1 - 1 6 0 7 K using both Knudsen effusion and mass spectrometry techniques. F r o m their results a AH°2ss value of - - 1 8 7 + 34 kJ mo1-1 was obtained. The enthalpies of formation of A14Cs(s) obtained by other experimental techniques [61-66] are summarized in Table 6. The values of the enthalpy of formation derived from effusion techniques are also given in Table 6. The values of the enthalpy of formation of A14C3(s) obtained by Knudsen effusion measurements do n o t agree very well with each other, and the enthalpies of formation of A14Cs(s) derived from these measurements do not agree well with the calorimetric and

TABLE 6 T h e r m o d y n a m i c properties of AI4C3(s ) Study

- - L~-/° 29 S

S°298

AGf °

(kJ mo1-1)

(J mo1-1 K -1)

(J mo1-1 K -1)

Meshi and Searcy [ 5 6 ]

260.4 +- 60.2

104.6 a

Plante and Schreyer [ 57] P o t t e r e t al. [58] R i n e h a r t and Behrens [59]

228.4 +- 35.1 259.4 +- 34.0 187.4 -+ 33.6

T h o b u r n [60]

138.4 -+ 33.7

G r j o t h e i m e t al. [61] Campbell [62]

244.8 214.2

C h o u d a r y and Belton [63]

221.8 -+ 11.2

Mah [64] Blachnik e t al. [65] King and A r m s t r o n g [66] JA N A F T h e r m o c h e m i c a l Tables [67] Kubaschewski and Alcock [23]

223.4 + 8.4 207.3 + 2.4 207.9 -+ 5.0

Kubaschewski and Alcock [ 23 ]

Mass loss effusion and torsion effusion Mass loss effusion Torsion effusion Knudsen effusion mass spectrometry Differential thermal analysis MgO-AI4C3 equilibrium Activity m e a s u r e m e n t s of Al in A14C 3 Activit'y of Al in C-saturated F e - A 1 alloys Combustion calorimetry S o l u t i o n calorimetry Combustion calorimetry Estimated

88.70 +- 0.42 b -- 71965 + 1 3 . 9 5 T ( 2 9 8 - 9 3 3 K) -- 8 8 8 4 0 + 3 2 . 1 T

(933-2000 K) a E s t i m a t e d value. b R e c o m m e n d e d value.

Method

Estimated Estimated

equilibrium values. The reasons for these disagreements are not clear at this time. It appears that further work must be done to resolve these problems and to enable a reliable comparison to be made of the enthalpies of formation obtained from different techniques. T h e S°298 values for AltC3 have been estimated as follows: Meschi and Searcy [56] gave an S°298 value of 104.6 J mo1-1 K -1 and J A N A F Tables [67] an S°29s value of 88.7 -+ 0.42 J mo1-1 K -1. The r e c o m m e n d e d S°298 value is 88.7 -+ 0.42 J tool -1 K -1. No direct experimental measurements of the standard free energy of formation of A14C3 have been made. However, Kubaschewski and Alcock [23] give the following equations:

AGO( + 420) = -- 4 8 8 0 9 - - 9.9T J mo1-1 K -1 ( 2 9 8 - 1 6 0 3 K) for the reaction (46)

½Y(s) + C(s) = ½yc2((~) that

71965 + 13.95T J mo1-1 K -1 ( 2 9 8 - 9 3 3 K)

( 1 6 0 3 - 1 7 9 9 K) (411

for the reaction (42)

and

(47)

for the reaction 1y(s) + C(s) = ½YC(~)

}AI(s) + C(s) = ½A14C3(s)

(481

and that AG°(-+ 340) = -- 5 4 5 2 2 - - 6 . 9 8 T J mo1-1 K -~

AG°(-+ 2800) --

(45)

AGO( + 700) = -- 4 5 8 6 0 - - 1 1 . 9 T J mo1-1 K -1

AG°(_+ 2800) -

The value of 63.26 + 0.42 J mol-~K -1 reported for the standard entropy S°29s of formation of YC2 was obtained by combining the results of mass spectrometry work [60, 70, 71] with the S°29s data for yttrium [72] and carbon [22]. From the free-energy functions reported by De Maria et al. [69], it is possible to estimate that

( 1 7 9 9 - 2 1 0 0 K)

88840 + 32.1T J mo1-1 K -1 ( 9 3 3 - 2 0 0 0 K)

for the reaction (43)

for the reaction -~Al(liq) + C(s) = ½A14C3(s)

(49)

(44)

3.1.3. Y t t r i u m dicarbide Y C 2 Yttrium forms four carbides [68] : Y3C, YC, Y2C3 and YC2. The most important of these is YC2. De Maria et al. [69] made a mass spectrometry study of the Y - C system in the temperature range 2 0 7 5 - 2 3 4 0 K. They obtained a AH°298 value of -- 112.97 -+ 25.1 kJ mo1-1 for the standard enthalpy of formation of YC2(s). Kohl and Stearns [ 70, 71] also measured the vapour pressure of YC2(s ) by mass spectrometry in the temperature range 2 2 7 0 - 2 5 5 0 K. They obtained a ~kH°29S value of -- 92.1 -+ 17.0 kJ mol -I. There is good agreement between these t w o values. Thus, the recommended ~JL/°298 value is - - 1 0 2 . 5 1 + 15.10 kJ mo1-1 for the standard heat of formation of YC2(s); this is an average of the values reported by de Maria et al. [69] and Kohl and Stearns [70, 71].

½Y(liq) + C(s) = ½YC2(~)

(50)

The experimental results and the estimated values are shown in Table 7. 2.1.4. L a n t h a n u m dicarbide LaC2

Lanthanum forms two carbides [ 7 4 - 7 6 ] : La2C3 and LaC2. The most important is LaC2. Faircloth et al. [73] made a mass spectrometry study of LaCe in the temperature range 1 3 0 0 - 2 4 0 0 K; they obtained a AH°29s value of -- 90.0 + 10.5 kJ mo1-1 for the standard enthalpy of formation of LaC2(s ). The value of 71.21 + 0.08 J mo1-1 K -1 reported for the entropy S°29s of formation of LaC2(s) was obtained by combining the experimental results [ 73] with the S°29s data for lanthanum [37] and carbon [22]. From the free-energy functions reported by Faircloth et al. [ 73], it is possible to estimate that AGO(-+ 330) = - - 4 1 3 7 2 - - 10.71T J tool -1 ( 2 9 8 - 1 1 9 3 K)

(51)

10 TABLE 7 Thermodynamic properties of YC 2 and LaC 2 Carbide

Study

- ~/°298 (kJ mol-1)

YC2 YC 2

De Maria et al. [69] 112.97 + 25.1 Kohl and Stearns 92.1 + 17.0 [70, 71]

Re c o m m en d ed vMue YC 2

S°298 (J tool-1 K-l)

102.51-+15.10 Thorbun [60], Kohl and Stearns [70, 71]

63.26 + 0.42

Mass spectrometry

-- 48809-- 9.9T ( 2 9 8 - 1 6 0 3 K) - - 4 5 8 6 0 - - 11.9T ( 1 6 0 3 - 1 7 9 9 K) -- 5 4 5 2 2 - - 6 . 9 8 T ( 1 7 9 9 - 2 1 0 0 K)

YC 2 YC 2

Faircloth et al. [73] Faircloth et al. [ 73]

90.0 + 10.5 71.21+0.08

LaC 2 LaC 2

for the reaction ½La(s) + C(s) = ~LaC2(a)

(52)

that AGO( + 630) = -- 39646 -- 12.5T J mo1-1 {1193-1333 K)

(53)

for the reaction ½La(liq) + C(s) = ½aaC2(a )

{54)

and that AGO( + 200) = -- 41595 -- 12.8T J mol -~ (55)

for the reaction ~La(liq) + C(s) = ½LaC2(~)

(56)

The experimental results and the estimated values are also shown in Table 7.

-

o f a group I V carbide carbide SiC phases of SiC [77]: ~-SiC has and a-SiC which has a hex-

Estimated Estimated Estimated

Mass spectrometry Mass spectrometry - 4 1 3 7 2 - 10.71T Estimated ( 2 9 8 - 1 1 9 3 K) - 3 9 6 4 6 - 12.5T Estimated (1193-1333 K) - 4 1 5 9 5 - 12.8T Estimated ( 1 3 3 3 - 2 0 0 0 K)

agonal structure. For the ~ -~ a transition, there are still no accurate data [ 7 7 - 8 3 ] . There have been a great number of determinations of the heat of formation of SiC{s) and these originally reported values have needed corrections corresponding to newer data [84]. For example, the early result of H u m p h r e y et al. [85], which was obtained by measuring the heat of formation of SiC(s) by means of calorimetry, was corrected because of a more recent redetermination of the heat of formation of SiO2 [86]. Thus, the corrected values are, for hexagonal SiC, AH°298 = 82.63 + 3.85 kJ mo1-1 and, for cubic SiC, AH°298 = -- 87.20 + 3.85 kJ mo1-1. Vaporization studies were made by Grieveson and Alcock [87], Davis et al. [88] and Drowart and De Maria [89]. Greenberg et al. [ 90], using fluorine calorimetry, obtained AH°29s = -- 70.09 + 1.93 kJ mo1-1 for a-SiC and AH°2s8 = 73.18 + 1.80 kJ mo1-1 for ~-SiC. Other studies include those involving SiO2C-SiC-CO equilibria [91-93] and those related to solubility determinations of SiC(s) in various metallic solvents [93, 94]. -

{1333-2000 K)

3.2. Description 3.2.1. Silicon There are two a cubic structure

Me thod

Mass spectrometry Mass spectrometry

YC 2

LaC 2 LaC 2 LaC 2

A Gf° (J m o l - l K - 1 )

-

-

11 A summary of the experimental results is shown in Table 8. When a comparison is made of the data in Table 8 and if the work of H u m p h r e y et al. [85] and of Grieveson and Alcock [87] is n o t taken into account, it can be seen that the data based on the SO2-CSiC-CO equilibria are in good agreement with the data of solubility determinations [93, 94] and with the data of Davis et al. [88], Drowart and De Maria [89] and Greenberg et al. [90]. The averages of these determinations are - - 6 9 . 3 6 kJ mo1-1 and - - 6 9 . 4 2 kJ mol -~ for s-SiC and fl-SiC respectively. Kelley and King [95] reported an S°298 value of 16.49 + 0.08 J mol -z K -~ for hexagonal SiC and an S°298 value of 16.61 + 0.08 J mo1-1 K -1 for cubic SiC; these are also shown in Table 8. From their measurements of the heat of combustion of both the cubic and hexagonal forms, H u m p h r e y et al. [85] reported the following equations for the free energy of formation of SiC(s): AG°(+12600) = - - 53430 + 6.95T J mo1-1 K -1 (298-1683 K)

(62)

Thus, the recommended equations are eqns. (59) and (61), which are shown in Table 8. 3.3. Free-energy diagram for the group III carbides and SiC Figure 2 is the free-energy diagram for carbides of group III and SiC.

4. THE LANTHANIDE CARBIDES The t h e r m o d y n a m i c properties of the lanthanide (rare earth) carbides have been determined or estimated by a number of researchers and have been published in the literature. However, m a n y of the known t h e r m o d y n a m i c data are for gaseous species which do n o t exist in the liquid or solid state. Because of the lack of t h e r m o d y n a m i c data as a function of temperature for sesquicarbides, these data have n o t been included in this review. 4.1. Descriptions of the lanthanide carbides 4.1.1. Cerium carbides CeC2 and CeC According to Spedding et al. [96], too m a n y carbides have been suggested; the most important are CeC2 and CeC [97].

(58)

4.1.1.1. CeCe. Baker et al. [98] measured the heat of combustion by means of oxygen bomb calorimetry and reported that AH°29s = -- 97.07 + 5.44 kJ mo1-1 for the standard enthalpy of formation of CeC2(s). Kubaschewski and Alcock [23] reported an S°2ss value of 89.96 + 8.34 J mo1-1 K -1 for the enthalpy of formation of CeC2(s ). From the free-energy functions of CeC2 [76] and the reported data [23, 98], it is possible to estimate that

AG°(+12600) --- 100456 + 34.85T J mo1-1 K -1

for/3-SIC. However, Kubaschewski and Alcock [ 23] from the work of Richardson [16] and Davis et al. [88], reported the following equations: AG°(+10500) -- -- 58576 -- 5.44T log T + + 23.77T J mo1-1 K -1 (298-1686 K)

Si(liq) + C(s) = SiC(s)

(57)

for s-SiC and

(1683-2000 K)

for the reaction

(59)

AGO(+ 300) = -- 4 3 9 0 5 - - 1 1 . 9 3 T J mo1-1K -1

for the reaction

(60)

Si(s) + C(s) = SiC(s)

(298-1071 K)

and

for the reaction

AG°(+ 8400)

½Ce(s) + C(s) -- ½CeC2(s)

= - -

(64)

and that

113386-- 11.42Tlog T +

+ 75.73T J mo1-1 K -1 ( 1 6 8 6 - 2 0 0 0 K)

(63)

AGO( + 200) = -- 4 2 2 1 8 - - 13.9T J mo1-1K -1 (61)

(1071-2000 K)

(65)

12

~.~o

o

o

~,~

~.o.o~ ~ ~ ~ ~,~. .~

~1 . ~

~1 ° ~ " ~

12.-

+ + ,--q

o

,-oo ~0 LoOO o00'~ t.O

I oO 0 +1

¢o °~

¢.0 ¢.0

oo 0 +1

ro °~ r~

oO

oO

+1

+1

c ~ oO

~2"- t",-

t",, ~O

oO

CO 0'~

+1

+1

,.4

I

oO

t",-

~,.0 t".- ~0

oO

oO

0

o °~

E..,

t~-

o

13 104 102 10 q !

q

i~)15166 162 102 0

400

1

l

10"1

•

Carbon

activity

i

105

104

800

10-2

l

106

1200

1600

-3 " 10 I0

2000 6 I0

i~4 - I

C; 5 10 ,

B~ :_~

,

c>

1o5 .

10-'

AGO( + 500) = -- 4 2 5 0 0 - - 1 2 . 9 9 T J mo1-1K -1

,o4 I

I

'~J

They reported a AH°298 value of -- 94.14 + 20.92 kJ mo1-1. The value of 85.55 + 0.30 J mo1-1 K -1 estimated for the e n t r o p y S°298 of formation of PrC2 was obtained by combining the results of Anderson and Bagshaw [ 101] with the S°298 data for praseodymium [37] and carbon [22]. From the free-energy functions of PrC2 [76] and the reported data [23, 101], it is possible to estimate that

¥C2

( 2 9 8 - 1 2 0 4 K)

CH~,

-6 10

-2 10

103

(69)

for the reaction ½Pr(s) + C(s) -- ½PrC2(c~)

(70)

that -7 lO2"*I0

Element :ar bide .

.[ransitJon point Melting point

0

PC20/Pr

400

800

-z

1200

(1204-1408 K) 1600

2000

(above400oc) 1(~15 1(~10 1(~6 1(~4 1(~2 10-1 1 .

.

.

1613

AGo(-+ 60) = -- 3 9 4 3 8 - - 16.2T J mo1-1 K -1

[]

T('C)

PCH4 2 1615

-3 IO

T

.

I()11

.

.

10-10

10

tlo' -4

.

lO

for the reaction ½Pr(liq) + C(s) = ½PrC2(~)

(72)

I139

and that

(above 400°C)

Fig. 2. Ellingham diagram for group III carbides and SiC. (It should be noted that the temperatures in this diagram are in degrees Celsius and not in kelvins as in the text).

AG°(-+ 900) = -- 42009 -- 13.94T J mo1-1K -1 (1408-2500 K)

for the reaction ½Ce + C(s) - ½CeC2(s)

(66)

4.1.1.2. CeC. For CeS(s), no thermodynamic information is available [23, 37]. However, Dancy et al. [99] studied the equilibrium of CeC in CHa-H 2 mixtures. They reported the following equation for the standard free energy of formation of CeC(s): AG ° = - - 116734 + 34.31T J mo1-1 K -1 (815-940 K)

(67)

for the reaction (68)

4.1.2. Praseodymium dicarbide PrC2 Two carbides, Pr2C 3 and PrC2, have been identified [ 100]. Anderson and Bagshaw [101], using a solid state e.m.f, technique, determined the enthalpy of formation of PrC2(s).

(73)

for the reaction ½Pr(liq) + C(s) = ½PrC2(~)

Ce(s) + C(s) -- CeC

(71)

(74)

4.1.3. Neodymium dicarbide NdC2 In the Nd-C system there are two carbides: NdC2 and Nd~C2 [102]. For NdC2(s) the t h e r m o d y n a m i c information available is scarce. Anderson and Bagshaw [101 ], using the solid state e.m.f, technique, de~ermined the enthalpy of formation of NdC2(s). They reported a AH°298 value of -- 97.86 + 10.50 kJ mo1-1. The value of 82.75 + 4.20 J mo1-1 K -1 estimated for the entropy S°298 of formation of NdC 2 was obtained by combining the results of Anderson and Bagshaw [101] with the S°298 data for n e o d y m i u m [37] and carbon [22]. From the free-energy functions of NdC2 [76] and the reported data [23, 101], it is possible to estimate that AGO( + 500) ------ 4 3 4 5 5 - - 1 3 . 8 5 T J mo1-1 K -1 (500-1128 K)

(75)

for the reaction ½Nd(~) + C(s)'--1idC2(~)

(76)

14 that

that

AG°(+- 200)

AG°(+100) = -- 3 8 0 0 8 - 6.7T J mol -t K - '

= -- 41571.4 -- 15.9T J mo1-1 K -1 (1128-1289 K)

(1345-1443 K) (77)

for the reaction

for the reaction ½Sm(liq) + C(s) = ½SmC2(~)

½Nd(~) + C(s) = ½NdC2(~ )

(78)

(87)

(88)

and that AG°{ + 100) = -- 37370.3-- 7.1T J mo1-1K -1

that

(1443-2500 K)

AG°(+100) ------ 3 9 4 6 4 - - 17.6T J mo1-1 K -1 (1289-1423 K)

(79)

for the reaction ½Sm(liq) + C(s) = ½SmC2(~)

for the reaction

½Nd(liq) + C(s) = ½NdC2(o~)

(80)

and that AGO( + 200) = -- 47623.5 -- 11.8T J tool -1 K -1 (1423-2500 K)

(81)

for the reaction ½Nd(liq) + C(s) = ½NdC2(~)

(82)

4.1.4. Samarium dicarbide SmC2 The heats of formation of S m C 2 have been measured by vaporization techniques [103105]. Recently, Kubaschewski and Alcock [23] have reported a AH°29s value of -- 97.9 + 8.4 kJ mo1-1 and an S°298 value of 77.82 + 8.4 J mo1-1 K -t for the standard enthalpy and e n t r o p y of formation respectively of SmCu(s). F r o m the free-energy functions of SmCu [103] and the reported data [ 1 0 4 , 1 0 5 ] , it is possible to estimate t h a t

(89)

(90)

4.1.5. Gadolinium dicarbide GdCe Three gadolinium carbides, GdsC, Gd2Ca and GdC2, have been identified [1, 3 , 1 0 6 ] ; no t h e r m o d y n a m i c information is available for Gd3C and Gd2Ca [18, 23]. The heat of formation of GdC2(s) was measured by Hoening et al. [107] using the Knudsen effusion technique. They reported a H°2~s value o f - - 1 2 5 . 5 2 + 37.70 kJ mo1-1. The value of 86.87 + 0.82 J tool -1 K -1 reported for the entropy S°298 of formation of GdC2 was obtained by combining the results of Hoening et al. [107] with S°zgs data for gadolinium [37] and carbon [22]. From the reported heat of formation and free-energy functions of GdC2 [107], it is possible to estimate that AGO( + 900) = -- 57418-- 8.22T J tool -1 K -1 ( 2 9 8 - 1 5 8 5 K)

(91)

for the reaction

½Gd(~) ÷ C(s) -- ½GdC2(o~)

(92)

and that

AGO( + - 200)

AG°(+100)

= -- 36392.9 -- 7.45T J mo1-1 K -1

(298-1190 K)

(83)

= -- 53944.5 -- 10.94T J mo1-1 K -1 (1585-2500 K)

for the reaction ½Sm(a) + C(s) = SmC2((x)

(84)

for the reaction ½Gd(liq) + C(s) = ½GdC2(/])

that AG°(+100) = -- 34882 -- 9.0T J mo1-1 K -1 (1190-1345 K)

(85)

for the reaction ½Sm(fl) + C(s) = ½SmC2(~)

(86)

(93)

(94)

4.2. Free-energy diagram for lanthanide carbides Figure 3 is the free-energy diagram for lanthanide carbides and Fig. 4 shows an expanded version of Fig. 3.

15 104 102 10 • t i

16151661d2 lO 2

0

i

lO~

400

800

1

10"1

i

lO s

Car ban activity

10-2

i

/

lO6

1200

1600

40l

163 ' 10

2000

~-50 'i-

6 lO

E -. -60

5 10 ~

n

C

2

-70

[] I

id 5. d 1

o

400

GdC2

I0 6 3 10

Element Carbide - 0

Transitionpoint

[]

Melting point

[]

T

t

t

Pc%/P42 lo"1510"13 10-11 10-1°

-2 10

lo.9

-8

0

TiC

-4 IO

ZrC

(above 400°C)

Fig. 3. Ellingham diagram for the lanthanide carbides. (It should be n o t e d that the t e m p e r a t u r e s in this diagram are in degrees Celsius and n o t in kelvins as in the text.)

5. T R A N S I T I O N M E T A L C A R B I D E S

The transition metal carbides discussed in this article are those of the first to third transition series o f the periodic table. Figure 5 shows the carbides of these elements. In the first transition series, every el em e nt forms at least one carbide; in the second and third series, carbide f o r m a t i o n is restricted to elements o f groups I V - V I I . T he carbides of groups I V - V I have high melting points and these materials are f r e q u e n t l y referred to as " r e f r a c t o r y carbides". Carbides of manganese, iron, cobalt and nickel are i m p o r t a n t in steel making.

Descriptions o f carbides o f the first transition series 5.1.1. Titanium carbide TiC Only one carbide o f titanium is k n o w n to exist [ 1 - 3 ] : TiC. T he heat of f o r m a t i o n o f TiC has been d eter m i ne d by a n u m b e r o f researchers. 5.1.

I

I

~6oo

2000

Fig. 4. An e x p a n d e d version of Fig. 3 showing those carbides whose standard free energies of f o r m a t i o n in the t e m p e r a t u r e range 2 7 3 - 2 2 7 3 K lie b e t w e e n - 4 0 and - 8 0 kJ real -1 K -1. (It should be n o t e d that the temperatures in this diagram are in degrees Celsius and n o t in kelvins as in the text.)

IVB

400

I (°C)

-7 2 I0 -3 10 10

800 1200 1600 2000 Tc'c~ t t |t t i t • i 02 1615 1610 10"6 10.4 1(~2 10-1 1 lO (above400'C) __. ,,, , , , ,

~o/~c

] 12oo

Temperoture

4 10 CH 4

I 800

HfC

VB VC V2C

VIB

VIIB

Cr3C2 Un3C Cr/C 3 MnTC 3Mn5C2 Cr23C6 Mnl~C6

NbC MoCl-x Nb2C M02C TcC Mo3C2 Ta C Ta2C

WC W2C W3C2

ReC

[

Fe3C

Vlll

I

Co2C C03C Ni3C

IB

lIB

Cu2C

ZnC2

Ru

Rh

Pd

(Ag2C2) Cd

OsC

I_r

PJ

Au2C ~

H_Q

Fig. 5. Transition metal carbides: - - , highly explosive; (), highly unstable; , no carbide formation.

Humphrey [108] measured the heat of combustion of TiC and reported a heat AH°29s of formation of - - 1 8 3 . 4 7 + 1.63 kJ mo1-1. This value was corrected to - - 1 8 4 . 5 1 + 1.63 kJ mo1-1 when a more recent value for the heat of formation of TiO2 [109] was used. Morozova e t al. [110], using a calorimetric technique, obtained a value o f - - 1 9 2 . 5 kJ mo1-1 for the standard enthalpy AH°298 of formation. Lowell and Williams [111] measured the heat of reaction of titanium with carbon. They found that A H ° 2 9 8 ---- - - 190.4 + 19.3 kJ mo1-1. Chupka e t al. [112], using mass spectrometry, obtained a AH°298 value o f - - 1 9 0 . 4 kJ mo1-1. Coffman e t al. [113] reported studies which utilized both the Lagmuir mass loss method and atomic absorption spectroscopy. F r o m one of these studies, t h e y obtained a ~ ° 2 9 8 value o f - - 1 7 9 . 1 + 5.0 kJ mo1-1 and, from the other, a AH°29s value o f - - 1 7 8 . 8 + 2.1 kJ mo1-1. From the available heat of formation data, it is seen that a range of values has been re-

16

ported. However, in view of the generally good accuracy of calorimetric data, Humphrey's corrected value of --184.51 + 1.63 kJ mo1-1 is recommended. The experimental values are shown in Table 9. Kelley and King [95] reported an S°298 value of 24.23 + 0.21 J mo1-1 K -i for the standard entropy o f formation of TiC. The same value is also reported by Kubaschewski and Alcock [23] ; these values are also shown in Table 9. Richardson [16] reported two free-energy equations, derived from the results of Humphrey [108], which apply to a-Ti and ~-Ti:

[ 17 ]. They report the following equations: AG ° -- -- 188698.4 -- 10.38T In T ÷ + 5.73X 10-aT 2 + 3.096× 105T -1 + + 81.17T J mol -i K -i for reaction (96) in the temperature range 2 9 8 - 1 1 5 0 K and AG ° = -- 189116.8 -- 0.96T In T + ÷ 0.46 X 10-aT 2 + 3.096 X 10-ST -1 + + 20.75T J mol -i K -i

AG°(+12600) = -- 183050 + 10.08T J mol -i K -i (298-1150 K)

(95)

for the reaction Wi(a) + C(s) = TiC(s)

(99)

(96)

(100)

for reaction (98) in the temperature range 1150-1800 K. Fujishiro and Gokcen [114], using a Knudsen cell, f o u n d the following equation for the standard free energy of formation of TiC: AGO( + 8400) = -- 590211.8 + 146.4T J mo1-1 K -1

and

(2383-2593 K) (101)

AG°(+12600) for the reaction

= -- 186606 + 13.22T J mol -i K -i (1150-2000 K)

(97)

for the reaction Ti(fl) + C(s) = TiC(s)

(98)

These early measurements are in good agreement with the data of Wicks and Block

Ti(liq) + C(s) = TiC(s)

(102)

Equations (99) and (100) are more complicated and both give results which agree with those given by eqns. (95) and (97). Thus the recommended equations are eqns. (95), (97) and (101) which are shown in Table 9.

TABLE 9 Thermodynamic properties of TiC Study

- ~/°298 (kJ tool -1 )

Humphrey [108] Morozova e t al. [110] Lowell and Williams [ 111] Chupka e t al. [112] Coffman e t al. [113]

184.51 -+1.63 192.5 190.4+19.3 190.4 179.1 +- 5.O

Recommended value

184.51 + 1.63

Kelley and King [95] Richardson [16] Richardson [16] Fujishiro and Gokcen [114]

S°29S (J tool -1 K -i)

AGf ° (J mo1-1 K -1 )

Method

Calorimetry Calorimetry Heat of reaction Mass spectrometry Lagmuir

24.23 + 0.21 -- 183050 + 10.08T ( 2 9 8 - 1 1 5 0 K) -- 186606 + 13.22T ( 1 1 5 0 - 2 0 0 0 K) -- 590211.8 + 146T (2383-2593 K)

Calorimetry [ 108] Calorimetry [108] Knudsen

17 5.1.2. Vanadium carbides Vanadium forms t w o carbides [1-3]: V2C and VC. V2C has a narrow homogeneity range and VC exhibits a large degree of non-stoichio m e t r y [3]. Storms [19] and Storms and McNeal [115] reported that ~-V2C is found between VC0.47 and VC0.5 and that VC exists between VCo.73 and VCo.ss in the temperature ranges 7 7 3 - 2 9 7 3 K and 7 7 3 - 2 4 3 8 K respectively. There are few published thermodynamic data on the vanadium carbides and they are usually measured by calorimetric and gas equilibrium techniques.

AS°298 . When this value is combined with the 8°298 data for vanadium [23] and carbon [ 22 ], the standard entropy S°~s of formation is estimated to be 36.23 + 0.42 J mo1-1 K -1. Thus, the r e c o m m e n d e d values of 5/4°298 and S°298 are those reported by Worrell and Chipman [119]. Alekseev and Shwartsman [117] investigated the equilibrium V2C(s) + 2H2(g) ~ 2V(s) + CH4(g) in the temperature range 9 7 3 - 1 2 7 3 K and obtained the free energy of formation of V2C as AG ° = -- 48116 -- 2.05T J mo1-1 K -1

5.1.2.1. V2C. Volkova and Gel'd [116] measured the heat of formation of V2C by b o m b calorimetry. They investigated several compositions V2CI-x and obtained the following equation: AH°298 = -

at V)+

/ ~42.26 + 5 3 . 6 at.% + 2.51 kJ mo1-1

where at.% C/at.% V is the ratio of the atomic percentage of carbon to the atomic percentage of vanadium in V2C. Their data give a AH°298 value of -- 69.04 kJ mo1-1. Alekseev and Shwartsman [117] investigated the V VuC-Hu-CH4 equilibrium in the temperature range 9 2 7 - 1 2 7 3 K and obtained a AH°2ss value o f - - 4 8 . 1 2 + 2.09 kJ mol -~. Worrell [ 118] observed that the ratio HM2c/HMcof the calorimetric value of a group V carbide to that of a group VI carbide is equal to 1.375 -+ 0.01. On the basis of this empirical formula, Worrell and Chipman [119] estimated a AH°usa value of -- 147.23 + 20.92 kJ mo1-1. The m e t h o d of Kireev and Karapetyantus [ 120] gave a AH°2ss value o f - - 167.4 kJ mo1-1. Pillai and Sundaresan [121], using a galvanic cell technique, obtained a AH°zss value of - - 1 7 5 . 4 kJ mol -~. A comparison of the AH°29s values for V2C is shown in Table 10. It can be seen from this table that the first t w o experimental values reported agree very poorly with the estimated values, whereas the value obtained b y Pillai and Sundaresan [121] is much nearer to the theoretical value. The e n t r o p y of formation of V2C was estimated by Worrell [118]; he obtained a value of 4.2 J mo1-1 K -1 for

( 9 7 3 - 1 2 7 3 K)

(103)

Worrell and Chipman [119] estimated the following equation for the free energy of formation of V2C: AGO( + 8400) = -- 147273 + 4.2T J tool -x K -z ( 1 1 8 0 - 1 3 7 0 K)

(104)

for the reaction 2V(s) + C(s) = V2C(s)

(105)

Pillai and Sundaresan [121] measured AGf ° for V2C using a galvanic cell with solid electrolyte in the temi~erature range 7 7 0 - 8 5 0 K. They obtained AG ° = -- 175602.5 (+ 11.3) + + 88.96 ( + 4 . 6 0 ) T J mo1-1 K -1

(106)

Since this cell study was made in a narrow range of only 80 K, its results yield impossibly high entropy changes (88.96 J mo1-1 K -1) for the condensed state reaction {105). It can be seen that the experimental results disagree greatly with one another. It appears that further experimental work is needed to enable a reliable comparison to be made of the standard free energies of formation obtained from different experimental techniques. Thus, the recommended equation is that given by Worrell and Chipman [119]. 5.1.2.2. VC. There are few published thermodynamic data on VC. The heat of formation AH°298 of VC was studied as a function of composition by Volkova and Gel'd [ 116 ]. They obtained the following equation:

18 TABLE 10 Thermodynamic properties of V2C -- ~r-~ 298 (kJmol-1)

Study

Volkova and Gel'd [116] Alekseev and Shwartsman [117]

69.04 48.12+2.09

Worrell and Chipman [119] Kireev and Karapetyantus [ 120] Pillai and Sundaresan [ 121] Worrell and Chipman [119]

147.23 + 20.92 167.4 175.4

AH°29s = -- ( 4 8 . 1 2 + 6 6 . 1 1 at.% + 6.69 kJ mol -~ Their data agree with the value of - - 1 0 1 . 8 8 + 1.67 kJ mo1-1 obtained by Mah [122] from heat of combustion experiments using samples of questionable purity and stoichiometry. Worrell and Chipman [119] measured the pressure of CO in equilibrium with the solids VC0.s8, V205 and carbon in the temperature range 1 1 8 0 - 1 3 7 0 K. They obtained 100.83 + 2.93 kJ mo1-1 as the heat of formation of VC0.ss. Also, they estimated a AH°29s value of -- 92.88 + 8.37 kJ mol -z for the heat of formation of VCo.73. Fujishiro and Gokcen [123], using the data of Fujishiro [124], calculated a A H ° ~ s value of 94.98 + 20.98 kJ mo1-1 for VC0.ss. Kubaschewski and Alcock [23] give a AH°29s value o f - - 1 0 0 . 8 3 + 0.33 kJ tool -1 for the vanadium carbide of variable composition. They do n o t state the phase composition of the carbide and the applied experimental technique. A comparison of the AH°29s values for VC is shown in Table 11. It can be seen from this table that there is excellent agreement between the calorimetric values [ 1 1 6 , 1 2 2 ] and the values obtained by Worrell and Chipman [119]. Thus, the r e c o m m e n d e d AH°29s value is - - 1 0 1 . 8 8 + 1.67 kJ mo1-1. Storms [19], using the data of Shomate and Kelley [125], reported an S°~s value of 27.66 + 0.13 J tool -1 K -1 for VC0.B8. Mah [122] obtained an S°~s value of 27.66 + 0.33 J tool -1 K -1 for VCo.88. The entropy AS°298 of formation of VCo.s8 reported by Worrell and Chipman [119] i s - - 6 . 2 8 J mol -z K -z. -

-

-

S°298 (J mol-1 K - l )

AGf °

Method

(J m o l - l K - 1 )

36.23+0.42

-- 147273 + 4.2T ( 1 1 8 0 - 1 3 7 0 K)

Calorimetry V-V2C-H2-CH 4 equilibria Estimated Estimated E.m.f. (CaF2) Estimated

When this value is combined with S°29s data for vanadium [23] and carbon [22], the standard entropy S°298 of formation is 27.72 + 0.42 J mo1-1 K -1. Also, Worrell and Chipman estimated AS°29s to be - - 6 . 2 8 J mo1-1 K -1 for VCo.73. Combining this value with S°~8 data for vanadium [23] and carbon [22] leads to an S°298 value of 26.86 + 0.42 J mo1-1 K -1 for VCo.Ta. A comparison of the S°~8 values obtained for VC0.ss is also shown in Table 11. As illustrated in Table 11, there is excellent agreem e n t between the reported values. Thus, the r e c o m m e n d e d S°~8 value is 27.66 + 0.33 J mol -I K-I. Worrell and Chipman [119] reported that AG°(+ 3600) = -- 100834 + 6.28T J tool-I K-I

-

( 1 1 8 0 - 1 3 7 0 K)

(107)

for the reaction V(s) + C(s) = VC(s)

(lO8)

Equation (103) gives values more negative than those reported by Richardson [16]. Fujishiro [124] measured the equilibrium pressure of vanadium over VC and graphite in a graphite Knudsen effusion cell between 2350 and 2550 K and obtained for the free energy of formation that AG°(+ 21000) = -- 97487 + 8.34T kJ tool -1 K -1

(109)

The experimental uncertainty in this equation is large and, in the absence of more experimental work, eqn. (107) is recommended.

19

5.1.3. Chromium carbides Chromium forms three stable carbides: Cr23C6, CrTCa and Cr3C2 [1]. Below 1273 K, no significant homogeneity range has been detected for Cr23C6, C7C3 or CraC2 [ 1 ]. There have been m a n y investigations of the thermodynamic properties of chromium carbides; many of these earlier studies are unreliable, and there are large uncertainties in the results. •- .~ ~. ~ ~

.

>>N>

g?

d +1

d

~

+1

+1

t'.-

~

tZ

+1

I

+I +1 +1 +I

>

~

5.1.3.1. Cre3Cs. Mah [126] measured the enthalpy of formation of the three chromium carbides by combustion calorimetry. The corrected A/-/°298 value of Mah [127] is -- 27.1 + 23.2 kJ mo] -1 for the standard enthalpy of formation of Cr23C6. Kulkarni and Worrell [127] used a torsion effusion cell to measure the equilibrium pressure of CO over a Cr23C6Cr2Oa-Cr mixture in the temperature range 1100-1300 K. They obtained a AH°298 value of -- 342.7 + 10.9 kJ mo1-1 for Cr23C6. Kelley et al. [128] measured the CO pressure above the same mixtures using a manometric technique in the temperature range 1569-1770 K. However, Kelley and coworkers [ 129] have expressed misgivings about these data. Alekseev and Shwartsman [130] studied the equilibrium between CH4-H 2 and Cr-Cr23C 6 mixtures using a circulating gas technique. They obtained a AH°298 value of -- 258.8 kJ mol -I for Cr23C6. Dawson and Sale [131] used adiabatic oxygen combustion calorimetry to determine the enthalpy of formation of C r 2 3 C 6. They obtained a value of -- 295.0 + 27.6 kJ mol -I. Table 12 shows a comparison of the experimental results for the enthalpies of formation of C r 2 3 C 6. The two calorimetric measurements [126,131] are in good agreement. Thus, the recommended ~/°298 value is -- 295.0 + 27.6 kJ mo1-1 for C23C6. A value of 105.9 + 1.3 J mol -I K -I has been given for the standard entropy S°298 of formation of C r 2 3 C 6 by Kubaschewski and Alcock [23]. From torsion effusion measurements, Kulkarni and Worrell [127] obtained the following equation for the AG~° value of C r 2 3 C 6 :

~u

AGO(-+ 833) r52~

= -- 53666.7 -- 12.77T J mo1-1 K -1 (1150-1300 K)

(110)

for the reaction 236 C r ~- C -~- I C r 2 3 C 6

(111)

20 TABLE 12 Thermodynamic properties of Cr23C 6 Study

-

z~kH°298 (kJ mo1-1) -

Kulkarni and Worrell [ 127]

342.7 -+10.9

Alekseev and Shwartsman [ 130]

258.0

Mah [126] Dawson and Sale [131] Kubaschewski and Alcock [ 23 ]

271.1-+23.2 295.0 + 27.6

S°29S

(J tool-1 K-l)

AGf°(-+ 833) (J tool-1 K-l)

Method

-- 53666.7-- 12.77T (1150-1300 K)

c o equilibrium pressure CH4-H2 equilibrium pressure Calorimetry Calorimetry

105.9-+1.3

Equation (110) does n o t agree with the previous data reported by Wicks and Block [17] and Richardson [16]. The torsion effusion experiments performed by Kulkarni and Worrell [127] are believed to be more reliable; thus, eqn. (110) is recommended. The standard e n t r o p y S°29s of formation and eqn. (110) are also shown in Table 12. 5.1.3.2. CrTC3. The standard heat of formation o f Cr7C 3 has also been determined using a variety of techniques: gas equilibrium [ 1 2 7 , 1 2 8 , 1 3 2 - 1 3 4 ] , calorimetric [ 1 2 6 , 1 3 1 ] and galvanic cell techniques [135, 136]. Kulkarni and Worrell [127] measured the equilibrium pressure of CO in the temperature range 1 1 0 0 - 1 3 0 0 K; t h e y obtained a AH°29s value of - - 1 5 3 . 6 + 4.2 kJ mol -z. Kelley et al. [128] measured the equilibrium pressure of CO in the temperature range 1 5 0 0 - 1 7 0 0 K; they obtained a AH°29s value o f - - 1 5 5 . 6 + 6.3 kJ mol-1; Alekseev and Shwartsman [132] investigated the equilibrium between CH4-H 2 and Cr7C3-Cr2sCe mixtures; they obtained a AH°29s value of - - 1 3 1 . 4 kJ tool -z. Hancock and Pidgeon [133] investigated the Cr2Oa-Cr7Cs-Cr2sC6-CO equilibrium using a circulating inert gas technique, b u t they did n o t analyse their data. Bolgar et al. [134] measured the chromium dissociation pressure over CruC3- Cr3C 2 and over CraC2-C mixtures; they obtained a AH°29s value of --196.8 + 84.0 kJ mol -I for the heat of formation of Cr7Cs. This value is considered to be unreliable because of its large uncertainty. Oxygen b o m b calorimetric measurements by Mah [126] and Dawson and Sale [131] give AH°29s = -- 143.1 + 8.5 kJ mol -I and

AH°29s = -- 149.2 + 8.5 kJ mol -z respectively for the heat of formation of Cr7C3. E.m.f. measurements by Kleykamp [ 13 5 ] and Coltters and Belton [136] using CaF 2 and BaC2-BaF 2 solid solution electrolytes give z~/°298 ---- - - 112.1 + 4.2 kJ mo1-1 and AH°298 ----- - 142.2 + 8.5 kJ tool -I respectively for the standard enthalpy of formation of Cr7C3. Table 13 shows a comparison of the experimental results. As illustrated in Table 13, Kleykamp [135] gives a value for the standard enthalpy of formation of Cr7Cs which is significantly less negative than the rest of the experimental determinations. Kulkarni and Worrell [127] suggested that the results of Kleykamp [135] may be caused by some electronic conduction in the sintered CaF 2 electrolyte. The values obtained by Mah [126] and Coltters and Belton [136] using t w o different experimental techniques are in excellent agreement, and both are in good agreement with the results of Dawson and Sale [131]. Thus, the r e c o m m e n d e d value is that given by Mah a s ~ k l L / ° 2 9 s ---- - - 143.1 + 8.5 kJ mol -z for Cr7C3. A value of 200.8 + 1.3 J mo1-1 K -z has been given by Kubaschewski and Alcock [ 23 ] for the standard e n t r o p y $ 0 2 9 8 of formation of Cr7C3. The free energy of formation of CrTC3 has been determined by several investigators. In Table 13 the results (AG~°) of these studies are compared. Kleykamp [135] reported results which are 54.4-58.6 kJ mol -z less negative than the results of any other investigation. This could be due to the electronic conduction in the CaF2 polycrystaUine electrolyte used in his studies. As illustrated in Table 13,

21 TABLE 13 Thermodynamic properties of CrTC3 Study

- - z~r-/° 29 S

S°298

(kJ tool-l)

(J tool-1 K-l)

Kulkarni and Worrell [127]

153.6 -+ 4.2

Kelley et al. [ 128]

155.6 -+6.3

Alekseev and Shwartsman [ 132]

131.4

Mah [126] Dawson and Sale [ 131] Coltters and Belton [136]

143.1 -+8.5 149.2 +-8.5 142.2 + - 8.5

Kleykamp [ 135]

112.1-+4.2

AGf ° (J tool-1 K-I)

Method

-- 47976.7 -- 12.7T (1100-1250 K) (-+2.0) - 50487 -- 11.43T (1500-1720 K)

CO equilibrium pressure

--51803.3(+57.7) _ 11.9(+0.1)T (920-1250 K) - - 3 3 1 2 3 . 3 - - 11.87T

CO equilibrium pressure CH4-H 2 equilibrium pressure Calorimetry Calorimetry E.m.f. (BaC2-BaF2)

E.m.f. (CaF2)

(920-I080 K) Kubaschewski and Alcock [ 23]

200.8 + 1.3

there is good agreement between the results of Kelley et al. [ 128], Kulkarni and Worrell [127] and Coltters and Belton [136]. Thus, the r e c o m m e n d e d equation for the AGf ° value of CrTC 3 is AGO( + 800) = -- 51803.3(+ 57.7) -- 11.9(+

--

0 . 1 ) T J m o 1 - 1 K -1

( 9 2 0 - 1 2 5 0 K)

(112)

for the reaction ~Cr(s) ÷ C(s) = ½CrTCs(s )

(113)

5.1.3.3. Cr3C2. There have been m a n y investigations of the thermodynamic properties of Cr3C2 [ 1 2 6 , 1 2 8 , 1 3 1 - 1 3 9 ] . Significant disagreement occurs between the various published data for Cr3C 2. Kelley et al. [128] and Gleiser [137] independently measured the CO pressure over a C r 2 0 3- C r 3 C 2 - C mixture; their results disagree. Gleiser's [137] results yield a A H ° ~ s value for Cr3C2 which is more negative than all the others. Vitaikin [138] determined AH°zgs by measuring the ratio of the dissociation pressure o v e r Cr3C 2 to that over pure chromium metal in a modified Knudsen cell. He obtained a AH°ms value of --56.9 kJ mo1-1 which is t o o low and does n o t seem to have taken the influence of scattering loss into account. Kleykamp's e.m.f, data [135] for CrsC 2 yield

a value which is less negative than those from other studies. This could be due to electronic conduction in the C a F 2 electrolyte. Mabushi et al. [139] determined the thermodynamic properties of Cr3C2 at temperatures between 1073 and 1303 K using a galvanic cell with a ThO2 (Y2Oa) electrolyte. They obtained a'AH°29s value of -- 70.1 + 4.2 kJ mo1-1 for Cr3C 2. Coltters and Belton [136], using a galvanic cell with a BaC2-BaF2 electrolyte, obtained a A/-/°29s value of -- 85.9 + 4.1 kJ mo1-1 for Cr3C 2. Table 14 shows a comparison of the experimental results for the enthalpies of formation of CrsC2. As shown in Table 14, the AH°~s value obtained by Coltters and Belton [136] is in excellent agreement with that measured by Dawson and Sale [131]. Thus, the recommended AH°29s value is -- 81.1 + 2.9 kJ mo1-1. A value of 85.4 + 0.8 J mo1-1 K -1 has been given by Kubaschewski and Alcock [23] for the standard entropy S°29s of formation of Cr3C2.

The free energy of formati6n of Cr3C 2 has been determined by several investigators. In Table 14 the results (AG~°) of these studies are compared. As illustrated in Table 14, the standard free energy of formation of Cr3C2 obtained by Coltters and Belton [136] is in good agreement with the results obtained by Kelley et al. [128] and by Gleiser [137].

22 TABLE 14 Thermodynamic properties of Cr3C 2 - ~J-]°29 S (kJ tool -1)

Study

Kelley e t al. [128]

S°298 (J tool -1 K -1)

77 + 4.2

Gleiser [ 137]

69

Mah [126] Dawson and Sale [131] Kleykamp [135]

77.8 +-3.7 81.1 + 2.9 56.5 -+ 2.1

Coltters and Belton [136]

85.9 +-4.1

Mabushi e t al. [ 139]

70.1+-4.2

Method

-- 43472-- 9.4T (1200-1400 K) -- 5 4 1 8 3 - 8.15T ( 1 3 0 0 - 1 4 0 0 K)

144.6

Alekseev and Shwartsman [132]

A G I°

(J mol-1 K-l)

-- 1 5 0 6 2 . 5 -- 1 6 . 8 T

CO equilibrium pressure CO equilibrium pressure CH4-H 2 equilibrium pressure Calorimetry Calorimetry E.m.f. (CaF2)

( 8 0 0 - I I 0 0 K)

--46430(+-105)-9.7(+0.1)T (973-1173 K) -- 21757-- 15.4T (1073-1303 K) -- 39750-- 0.63T (973-1233 K)

Alekseev e t al. [ 140] Kubaschewski and Alcock [ 23]

AGO( + 600) = -- 46430(+ 1.05)

--

J m o 1 - 1 K -1

( 9 7 3 - 1 1 7 3 K)

(114)

for the reaction 3Cr( s)2

+ C(s) = 1Cr3C2(s)

(115)

5.1.4. Manganese carbides The c o m p o u n d s that exist in the M n - C system are still n o t fully defined [ 3 7 , 1 4 1 ] , although the existence of MnTC3 [ 3 7 , 1 4 2 144] and Mn23C6 [ 3 7 , 1 4 4 ] is well established. However, the carbides lying between these two, such as Mn5C 2 [37], MnsC 3 [144] and M n 3 C [37], have n o t been well supported by experimental evidence. There have been few studies on the thermodynamics of the M n - C system. This lack of thermodynamic information is caused b y the considerable experimental difficulties due to the high vapour pressure of manganese and the very slow rate of formation of these carbides. This makes it very difficult to prepare and handle homogeneous samples. 5.1.4.1.

M n 7 C 3.

E.m.f. (ThO2-Y203) E.m.f. (NaC1-KC1-

Cl-)

85.4+-0.8

Thus, the r e c o m m e n d e d equation for the G~° value of Cr3C 2 is

-- 9.7(+ 0.1)T

E.m.f. (BaC2-BaF2)

The heat of formation of

M n 7 C 3 was determined by Gokcen and Fuji-

shiro [145] who measured the manganese pressure in equilibrium with Mn7C a and graphite, using the Knudsen effusion technique in the temperature range 1 2 9 8 - 1 4 1 8 K. They obtained a AH°298 value of -- 110.88 + 10.46 kJ mo1-1. Galvanic cell measurements by Moattar and Anderson [146] using a CaF2 electrolyte in the temperature range 9 0 0 1100 K gave a AH°29s value o f - - 132.4 + 2.1 kJ mo1-1. Thus, the AH°298 value recommended as the standard enthalpy of formation of Mn7C 3 is -- 110.88 + 10.46 kJ tool -1. A value of 238.9 + 4.2 J mol -~ K -1 has been determined by Gokcen and Fujishiro [145] for the standard entropy S°29s of formation of Mn7C3. The free energy of formation of MnTCa has been measured b y several investigators [ 1 4 6 148]. Moattar and Anderson [146] obtained the following equation for the AG~° value of Mn7C3 : AG°(+I800) = - - 42397.9 + 12.6T J mol - I K - I

( 9 0 0 - 1 1 0 0 K)

(116)

for the reaction ]Mn(~) + C(s) = ½Mn7C3(s)

(117)

McCabe and Hudson [147], using a Knudsen cell, determined the free energy of formation

23

of M n T C 3 in the temperature range 9 0 0 - 1 3 6 0 K. They obtained AG ° = 2147.9 -- 48.8T J mo1-1 K -1 for reaction (117). Tanaka et al. [148], using a galvanic cell with CaF2 as the electrolyte in the temperature range of 8931073 K, obtained the following equations: AG ° --- -- 11910.5 -- 23.0T J mo1-1 K -1 ( 8 9 3 - 9 9 0 K)

(118)

for the reaction 7Mn(~) + C(s) -- 1 M n 7 C 3 ( s )

(119)

and AG ° = - - 1 6 7 9 2 - - 17.96T J mo1-1 K -1 (990-1073 K)

{120)

of any other investigators [147, 148]. This could be due to side reactions at the electrodeCaF 2 interface. Thus, the recommended AGf ° values for MnTC3 are eqns. (118) and (120).

5.1.4.2. Mn5C2. There are no calorimetric data for the standard enthalpy AH°298of formation for Mn~C2 in the literature. Kleppa and Hong [151], using liquid alloy solution calorimetry, measured the enthalpy of formation of MnsC2 at 1320 K. They f o u n d AHO132o to be --69.91 + 3.81 kJ mo1-1. Moattar and Anderson [146] also determined the free energy of formation of MnsC2 and obtained AG°(+ 1200)

for the reaction {121)

= -- 45145.4 + 13.4T J mo1-1 K -~

Table 15 shows a comparison of the experimental results (AG~°) for MnTC3. Moattar and Anderson [ 146] reported results which are 510 kJ mo1-1 K -~ less negative than the results

(900-1100 K)

~Mn{/]) + C(s) = 1 M n T C 3 ( s )

(122)

for the reaction ~Mn(~3) + C = ½Mn~C2(s)

(123)

T A B L E 15 T h e r m o d y n a m i c properties of manganese carbides Carbide

Study

- ~r-/° 298 (kJ mo1-1)

S°298

110.9 +- 10.5 132.4-+ 2.1

238.9 -+ 4.2

(J tool -1 K - ! )

AGf ° (J mo1-1 K -1)

Method

MnTC 3 Mn7C 3

G o k c e n and Fujishiro [ 145] M o a t t a r and A n d e r s o n [ 146 ]

Mn7C 3

McCabe and H u d s o n [147]

Mn7C 3

Tanakaetal.

[148]

Mn7C 3

Tanakaetal.

[148]

Mn5C 2

Moattar and A n d e r s o n [146]

-- 45145.4 + 1 3 . 4 T ( 9 0 0 - 1 1 0 0 K)

E.m.f. (CaF2)

MnBC 3

Tanaka e t al. [ 149]

E.m.f. (CaF2)

MnsC 3

Tanaka e t al. [ 149]

-- 16289.7 - 2 2 . 5 T (893-991K) -- 21882.3 -- 16.5T ( 9 9 1 - 1 0 7 3 K)

Mn3C

C h o u d a r y and Chang [ 150]

-- 1 6 9 0 0 - - 15T ( 1 2 4 3 - 1 3 2 3 K)

Estimated

Mn23C 6

M o a t t a r and A n d e r s o n [146]

E.m.f. (CaF2)

Mn23C 6

C h o u d a r y and Chang [150]

Mn23C 6

C h o u d a r y and Chang [150]

-- 64155 + 23T ( 9 0 0 - 1 1 0 0 K) -- 2 4 6 8 6 - - 2 3 . 3 T (893-991K) - 3 2 7 6 8 - - 15.0T ( 9 9 1 - 1 0 7 3 K)

387.4 + 2.1

-- 42397.9 + 1 2 . 6 T (900-1100 K) + 21447.9-48.8T ( 9 9 0 - 1 3 6 0 K) --16792-- 17.96T ( 9 9 0 - 1 0 7 3 K) --11910.5--23.0T ( 8 9 3 - 9 9 0 K)

K n u d s e n effusion E.m.f. (CaF2) Knudsen effusion E.m.f. (CaF2) E.m.f. (CaF2)

E.m.f. (CaF2)

E.m.f. (CaF2) E.m.f. (CaF2)

24 5.1.4.3. MnsC3. F o r the c o m p o u n d MnsC s there are no reported thermodynamic data. Tanaka et al. [149], using a galvanic cell with CaF 2 as the electrolyte in the temperature range 8 9 3 - 1 0 7 3 K, measured the free energy of formation of MnsCa. They obtained

Tanaka et al. [153] reported t w o freeenergy equations, derived from their e.m.f. measurements:

AG ° = -- 16289.7 -- 22.5T J mo1-1 K -1

for the reaction

( 8 9 3 - 9 9 1 K)

{124)

for the reaction

AG° ------ 24686 -- 23.3T J mol-I K-I (843-991 K)

~Mn((~) + C(s) -- ~Mn23Cs(s)

(132)

(133)

and

~Mn(~) + C(s) = ½MnsCs(s)

(125)

AG° = - - 32768-- 15.0TJ tool-I K-I

and

(991-1073 K)

AG ° = -- 21882.3 -- 16.5T J m o l - ' K -1 ( 9 9 1 - 1 0 7 3 K)

for the reaction (126)

for the reaction ~Mn(/3) + C(s) -- ½MnsCs(s)

(127)

5.1.4.4. Mn3C. The heat of formation o f MnsC was determined by Ulich and Siemonsen [ 152] who measured the combustion enthalpy of MnsC. At the time of their investigation, it was assumed that Mn3C was stable at all temperatures, contrary to the present phase diagram [37] in which the Mn3C stability range is 1 2 4 3 - 1 3 2 3 K. The free energy of formation was estimated by Choudary and Chang [150] using a thermodynamic m e t h o d [153]; they found that AG ° = -- 16900 -- 15T J mo1-1 K -1 ( 1 2 4 3 - 1 3 2 3 K)

(128)

for the reaction 3Mn(/3) + C(s) -- Mn3C(s)

(129)

5.1.4.5. MnesCs. F o r the c o m p o u n d Mnz3C6 there are no reported calorimetry measurements for the determination of the standard enthalpy of formation. Moattar and Anderson [146] obtained a AH°~gs value of -- 387.4 + 4.2 kJ mo1-1 for the heat of formation of Mn2sCs(s), and the following equation for G~°: AGO( + 5000) = -- 6 4 1 5 5 + 2 3 T J mo1-1 K -1 ( 9 0 0 - 1 1 0 0 K)

(130)

for the reaction ~Mn(~) ÷ C(s) --~Mn2aCs(s)

(134)

(131)

~Mn(~) + C(s) = ~Mn23C6(s)

(135)

Table 15 shows a comparison of the experimental results (AGf°) for Mn23C6. Moattar and Anderson [ 146] reported results which are 710 kJ mol-I K-I less negative than the results of Tanaka et al. [149]. This could be due to side reactions at the electrode-CaF 2 interface. Thus, the recommended AG~° values for Mn2aC6 are eqns. (132) and (134). 5.1.5. Iron carbides Several iron carbides have been reported, ranging in composition from Fe4C to Fe2C [37]. The composition of the metastable carbides are uncertain; even Fe3C, which has long been considered as stoichiometric, may exist over a range of compositions. The following phases are known to exist [37]: the phase, "Fe4C", with a cubic structure; the 0 phase, " F e s C " or cementite, with an orthorhombic structure (it has been found that the lattice parameter of Fe3C varies with quenching temperature [ 1 5 4 - 1 5 7 ], which suggests a departure from stoichiometry); the × phase, "Fe2.zC", which is the H~igg carbide [158] with a monoclinic structure [159, 160] ; the e phase, "e-Fe2-sC", with a hexagonal structure [161] and variable composition, c o m m o n l y a b o u t Fe2.4C; the ~/phase, "FeTCs", which is the Ekstrom and Adcock [162] carbide, with a hexagonal structure. Thermodynamic data for some iron carbides have been reported in the literature; reviews of these data by Hultgren et al. [37], Darken and Gurry [ 1 6 3 , 1 6 4 ] , Richardson and Dennis [165], Poirier [166] and Chipman [ 1 6 7 - 1 6 9 ] should be mentioned.

25 5.1.5.1. Cementite (0 phase) "Fe3C". The t h e r m o d y n a m i c properties of cementite have been measured by several investigators. Darken and Gurry [163,164] recalculated the data from Naeser [170] and Umino [171] and obtained AH°298 25.0 + 7.3 kJ mo1-1 for the 0 phase, cementite. Similarly, Kelley [172] used the same data plus the data of Schwarz and Ulich [173] to arrive at the same results. Low temperature measurements (68- 298 K) were made by Seltz et al. [174]. From these plus the data of Schwarz and Ulich [173] and Naeser [170], Kelley and King [95] proposed an average S°298 value of 101.3 + 4.2 J mo1-1 K -1. High temperature data on free-energy calculations gave an S°298 value of 104.6 + 4.2 J mol -z K -1. This value has been adopted for calculations and it is recommended. Experimental measurements were made by Watase [ 175], who studied the equilibrium =

Fe3C + 2H 2 = 3Fe(~) + CH4 in the temperature range 9 9 8 - 1 1 4 8 K. This equilibrium was also studied by Browning et al. [176] in the temperature range 568721 K. None of these measurements was accurate because the samples were n o t single phase. In order to improve this, with the aid of solubility data for cementite in austenite obtained by Ban-ya et al. [177] and Smith [ 178 ] and the CO- CO2 equilibria measurements of Scheil et al. [179], Chipman [169]

estimated the standard free-energy change for the reaction 3Fe(7) + C(graphite) = Fe3C Chipman's results [169] are shown in Fig. 6. The curvature of this is greater than is usually expected in this type of plot. The reasons for this behaviour remain u n k n o w n [169]. In Fig. 6 a point is shown at 1000 K which is calculated from the solubility of cementite in (~-Fe and the known free-energy difference between a-Fe and 7-Fe. Chipman [169] obtained the following equation: AGO( + 250) = 11234 -- 10.983T J mo1-1 K -1 (1115-1500 K)

(136)

for the reaction 3Fe(7) + C(graphite) = Fe3C(0)

(137)

An estimate of the free energy of formation of cementite in the a-Fe range up to 1048 K is made from Chipman's data [169]. In the ~-Fe temperature range 2 9 8 - 1 0 4 8 K, the free energy is approximately AG°( + 260) = 28714 -- 27.66T J mo1-1 K -1 (298-1048 K)

(138)

for the reaction 3Fe(a) + C(graphite) = FeaC(0)

(139)

From the measurements of Browning et al. [176], Richardson [16] recommended the following equation:

200

AG°( + 4200) -200

= 10355 -- 10.17T J mo1-1 K -1

? -400

(1500-1811 K)

E -600

'~

(140)

for the reaction

-800

3Fe(5) + C(s) = Fe3C(liq)

(141)

-1000

-120C 1000

'

' 1100

] | , 12 O 0 Temperature (K)

• 1300

,

I 14.00

Fig. 6. Standard free energy of the reaction 3Fe('),) + C(graphite)= Fe3C(0 ) (the formula assumed is Fe3C): o, data of Scheil et al. [179]; A, data of Smith [178] (interpolated); D, eutectic data of Chipman [ 169] ; X, data of Chipman [169] from solubility in a-Fe. (After Chipman [169].)

5.1.5.2. The H6gg carbide (× phase) "Fe2.2C". Browning et al. [176] measured the equilibrium Fe2C + 2H 2 = 2Fe(~) + CH4 in the temperature range 568-632 K, after forming the X phase by carburizing ~-Fe with butane at 548 K. They f o u n d that this carbide

26

was converted to Fe3C by heating to 773 K. F o r the purposes of this discussion, Chipman [169] represented this phase as Fe2.2C; he plotted the average equilibrium values of Browning et al. [176] as a function of the temperature, obtaining the plot in Fig. 7. The slope is n o t well defined b u t the data are represented approximately by the equation

are unknown. It was recognized by Jack [180] as a result of the tempering of martensite and by Tsou et al. [181] in the quenchaging of iron. Chipman [ 169] estimated the free energy of formation of the carbide precipitates from its apparent solubility and that of graphite in ~-Fe and obtained

AG ° = 20292.4 -- 10.5T J mo1-1 K -1

AG ° = 80751.2 -- 25.65T J mo1-1 K -1

( 4 5 0 - 6 5 0 K)

( 2 7 3 - 5 0 3 K)

(142)

for the reaction

(144)

for the reaction

2.2Fe(~) + C(graphite) = Fe2.2C(x )

(143)

2.4Fe(~) + C(graphite) = F e 2 . 4 C ( e p r e c i p i t a t e ) (145)

5.1.5.3. The e carbide Fe2-3C. This car-

bide occurs as a transition phase in the tempering and aging of steel. It has n o t been isolated and its thermodynamic properties

A summary of the thermodynamic properties of iron carbides is shown in Table 16. 5.1.6. Cobalt carbides

I

~ I

I

2 *2 " " ' ~ " ' " " ' "

]

I

[

I

I

I

O

o ~.1 tD <3

i 600

i

I

i

800

I

l

1000

Temperclture

i 1200

1400

Two rather unstable carbides of cobalt have been reported: Co3C and Co2C(s) (range of stability, 7 7 3 - 1 0 7 3 K). There are no reported calorimetric measurements for the determination of the standard enthalpy of formation of Co2C(s). Kubaschewski and Alcock [23] reported values of 16.74 + 1.67 kJ mo1-1 and 74.5 + 10.5 J mo1-1 K -~ for the standard enthalpy AH°29s and entropy S°298 of formation of Co2C(s) respectively. Richardson [16] reported that

(K)

AGO( + 2100)

Fig. 7. Standard free energy of formation of Fe3C(0) and Fe2.2C(X ) from e-Fe and graphite: •, Fe3C data of Watase [175] ; A, Fe3C data of Browning et al. [ 1 7 6 ] ; - - - , Fe3C solubility data of Schwartz and Ulich [173]; Fe3C data from ~'-Fe data of Chipman [169]; v, x-Fe2C data of Browning et al. [176]; +, Fe3C data of Chipman [169] from solubility in e-Fe. ( After Chipman [ 169 ]. )

---- 1 6 5 2 7 - - 8.7T J mo1-1 K -1 ( 2 9 8 - 1 2 0 0 K)

(146)

for the reaction 2Co(s) + C(s) = Co2C(s)

(147)

TABLE 16 Thermodynamic properties of iron carbides Carbide

Study

~/°298

S°298

25.0 -+ 7.3

104.6 +-4.2

(kJ mol-1)

Fe3C(0 )

Chipman [169] Chipman [169]

(J mol-1 K-l)

AGf ° (J mol-1 K-l)

Method

28714 -- 27.66T(298-1048 K) 11234 -- 10.983T(1048-1500 K)

Estimated

Fe3C(liq)

Richardson [16]

1 0 3 3 5 - 10.17T(1500-1811K)

Fe2.2C(x )

Chipman [169]

20292.4-- 10.5T(450-650 K)

Estimated

80751.2 -- 25.65T (273-503 K)

Estimated

Fe2.4C (eprecipitate) Chipman [ 169]

27 IO41o 21o

5.1.7. Nickel carbide Ni3C O n e c a r b i d e o f nickel has b e e n r e p o r t e d [1, 3] : NiaC. I t is n o t k n o w n w h e t h e r t h e r e is a t e m p e r a t u r e r a n g e w i t h i n w h i c h Ni3C is t h e stable p h a s e or w h e t h e r t h e c a r b i d e is a m e t a stable p h a s e at a n y t e m p e r a t u r e [1, 3 ] . According to Richardson [16], the heat of f o r m a t i o n o f Ni~C at r o o m t e m p e r a t u r e was measured by Roth [182], who reported a AH°298 value o f 34.5 + 6.3 k J m o t -1. R i c h a r d son [ 1 6 ] r e p o r t e d t h a t

0

400

C

Car bon activity

io-2 106

1200

1600

ld3" 10

2000

104 "

TI ~"'6 -'-'C~Fe3c

05 I() 5 . i(~ I 2

I 0~_C(23% ..~,

/

vc

-6

10

i

(148)

for the reaction ~V2C

3Ni(s)

4- C(s) = Ni3C(s)

(149) 0

5.1.8. Copper and zinc carbides

~ C r ( s ) + C(s) = ~ Cr23C6(s )

400

800

1200

+

O n l y t h e e x p l o s i v e c a r b i d e Cu2C 2 a n d t h e c o m p o u n d ZnC2 h a v e b e e n r e p o r t e d [1, 3], b u t n o f u r t h e r w o r k has b e e n r e p o r t e d [ 1 8 3 ] .

Figure 8 is a f r e e - e n e r g y d i a g r a m f o r t h e first-transition-series carbides. F o r c h r o m i u m , t h e f o l l o w i n g equilibria are c o n s i d e r e d : t h e reaction

-2 10

-7 10

-3 t0

10 C

5.1.9. Free-energy diagram for the firsttransition-series carbides

1

~A4tl~C~"~---" Mn5C2 Mn-C

= 3 3 9 3 2 - - 7 . 1 1 T J m o l -~ K -~ ( 2 9 8 - 1 0 0 0 K)

1o-I

105

~00

I

ca 4

A G O (+- 1 2 6 0 0 )

I

1()15106 1(32 102" '104~

(obove400oc) 1515 i{~10 10-610-4 .

.

.

.

PCH4 2 1615 16 13 (above 400"C)

1600

2000

-8 10

cl

10-11

.

.

10

10-2 161 1 .

10-10

-4 10

10-9

Fig. 8. Ellingham diagram for the first-transitionseries carbides. (It should be noted that the temperatures in this diagram are in degrees Celsius and not in kelvins as in the text.)

/

!

I

[]Troo+i...... ,or

(111)

with "7

AG ° = - - 5 3 6 6 6 . 7 - - 1 2 . 7 7 T J m o l - t K -1 ( 1 1 5 0 - 1 3 0 0 K)

~J~----~,/~C'---=-~.

-~

- - - - ~

o - 4 0 : ....

(110)

~

~Cr2aC6(s) + C(s) = ~CrTCa(s)

(150)

with

( 9 2 0 - 1 3 0 0 K)

(151)

and the reaction

+ C(s) __ g7 Cr3C2(s)

m

400

3z

-

I

i

~

800 1200 Ternperoture {°C)

4

1600

version of Fig. 8 showing

2000 those

carbides whose standard free energies of formation in the temperature range 273-2273 K lie between --20 and 60 kJ mo1-1 K -1. (It should be noted that the temperatures in this diagram are in degrees Celsius and not in kelvins as in the text.)

(152)

with AG ° = - - 3 3 9 2 0 - - 6 . 4 4 T J mo1-1 K -1 ( 9 2 0 - 1 2 5 0 K)

73Mn23C 6

F i g . 9. A n e x p a n d e d

AG ° = - - 3 0 2 1 5 . 1 - - 6 . 8 3 T J mo1-1 K -1

'

,4"a~_LCr7C3-Cr23C 6 - -

-50 ....

the reaction

3Cr7C3(s)

-

(153)

Figure 9 is an e x p a n d e d version o f Fig. 8; it s h o w s t h o s e c a r b i d e s w h o s e s t a n d a r d free energies o f f o r m a t i o n in t h e t e m p e r a t u r e r a n g e 2 7 3 - 2 2 7 3 K lie b e t w e e n - - 20 a n d --90 k J mo1-1 K - 1 .

28 5.2. Descriptions o f carbides o f the second transition series 5.2.1. Zirconium carbide ZrC Only one carbide of zirconium has been reported: 7-ZrC [2]. A value of --196.6 + 2.5 kJ tool -1 was obtained by Mah [184] for the heat AH°29s of formation of ZrC from combustion experiments. Vaporization experiments were reported by Pollock [185], Coffman et al. [186], Fujishiro and Gokcen [187] and Bolgar et al. [188]. Pollock [185] used both the Knudsen and the Lagmuir technique in the temperature range 26202747 K and obtained AH°29s values o f - 199.6 kJ mol -x and --200.4 kJ mo1-1 for the two techniques respectively. The vaporization data of Coffman et al. [186] were obtained by the Lagmuir technique (2246-2898 K). They obtained a AH°29s value of --200.8 kJ tool -1. The agreement between this value and those of Pollock is extremely good. The vaporization experiments of Bolgar et al. [188] and Fujishiro and Gokcen [187] gave results which disagreed seriously with the previously reported data. Equilibrium techniques have also been used [189-193] to determine the heat of formation of ZrC by study of the ZrO2-C-ZrC-CO equilibrium. Usually the phases in the Zr-O-C system are not well defined at high temperatures [191,192]; this leads to results which are not accurate and hence they are not considered further here. Kubaschewski and Alcock [23] reported that AH°29s = --201.96 + 2.51 kJ tool -1 for ZrCo.9e. Thus, the recommended value of the heat AH°z9s of formation is --201.05 + 2.51 kJ mo1-1 which is an average of the values reported by Pollock [185], Coffman et al. [186] and Kubaschewski and Alcock [23]. The entrooy of formation was determined by Mah and Boyle [194] from low temperature heat capacity measurements. Their data yield S°29s = 33.17 + 2.1 J mol -x K -1. Kubaschewski and Alcock [23] reported the following equation for AG ° :

AGO(+ 12600) = -- 184514 + 9.2T J mol -x K -1 (298-2220 K) (154) for the reaction Zr(s) + C(s) = ZrC(s)

(155)

5.2.2. N i o b i u m carbides The Nb-C system has two phases: NbC and Nb2C. These carbides exhibit a homogeneity range [1-3]. 5.2.2.1. NbC. The heat of formation of NbC at 298 K has been determined by means of combustion calorimetry [194-198]. Mah and Boyle [194] found a AH°29s value of --132.84 + 3.35 kJ mo1-1 for NbCo.9445. They extrapolated to the stoichiometric composition to obtain a AH°zgs value of --140.58 + 3.35 kJ mo1-1 for NbC. Huberetal. [195] studied a range of compositions from NbCoAs9 to NbCo.984, giving AH°298 = -- 140.58 + 2.51 kJ mo1-1. Kornilov et al. [196] obtained a AH°29s value of -- 129.7 + 2.5 kJ mo1-1 for NbCo.91s and they extrapolated their data to the stoichiometric composition, giving ~ / ° 2 9 s : - - 142.06 + 2.74 kJ mo1-1. A comparison of the AH0298 values for NbC is shown in Table 17. These values are in good agreement. Thus, the recommended AH°29s value is 140.58 + 3.35 kJ mo1-1 for the hypothetical NbC1.0 composition. The heats of formation of refractory carbides vary significantly with stoichiometry, and the variations are difficult to estimate. Worrell and Chipman [119] measured the CO pressure over a mixture of NbC, carbon and NbO2 between 1170 and 1260 K. The resulting heat AH°29s of formation was --133.1 + 3.8 kJ mo1-1 for NbCo.99. The standard entropy S°ugs of formation for NbC has been estimated from the Cp measurements (51-297 K) of Pankratz et al. [199] and Sandenaw and Storms [200]. The reported values were 35.40 J mol ~1 K -x and 35.54 J mol -x K -x respectively. WorreU and Chipman [119] measured the CO pressure in equilibrium with NbO2(s), NbC(s) and carbon in the temperature range 1180-1370 K according to the equilibrium NbO2(s ) + 3C(s) = NbC(s) + 2CO(g) They obtained a ~S°29s value of -- 6.69 J mol-x K-x for NbC. When this result is combined with S°29s data for niobium [202] and carbon [22], it is possible to obtain an S°29s value of 34.89 J mol-x K-x for NbC. A comparison of S°298 values for NbC is also shown in Table 17. These values are in excellent agreement. Thus, the recommended S°298 value is 35.28 J mol-x K-X;this is an

29

'7. '~ "V. 0

0

0

0 I

0 oO

¢q

-4 +

+ ¢q I

o

-~

cq

+1

I

O',~O

oO

Ot~

4~

Q +1 oO o3

0 +1 +1 +1

+1

+~

¢q

0

"0

<

. o0

.9=

_= >

o~ e~

t'-.-

=

"0

ZZZ

¢~ Z Z Z

ZZ

¢~

ZZ

30 average of the values reported by Pankratz et al. [199], Sandenaw and Storms [200] and Worrell and Chipman [119]. The free energy of formation of NbC was also determined from the measurements of Worrell and Chipman [119]. They obtained

low temperatures (this is called the ~ form) and hexagonal at high temperatures (this is called the ~ form). There are no thermodynamic data available for the MoCl_x phase.

AGO(+ 2500)

5.2.3.1. Mo3 C2. The enthalpy o f formation of Mo3C 2 was measured by Johnson et al. [204] by means of fluorine bomb calorimetry. They reported that AH°sgs = -- 20.84 + 3.18 kJ mo1-1 for MoCo.651; on the assumption that the enthalpy of formation of this compound is a linear function of the carbon content, this gives a AH°~s value of -- 64.0 + 9.6 kJ mo1-1 for Mo3C 2. Neither low temperature heat capacity nor free-energy measurements have been made on Mo3C2.

= -- 130122 + 1.67T J mo1-1 K -1 (1180-1370 K)

(156)

for the reaction Nb(s) + C(s) = NbC(s)

(157)

This result is in excellent agreement with the data obtained by Pankratz et al. [199].

5.2.2.2. Nb2C. Huber et al. [195] also measured the heat of formation of Nb2C and obtained a AH°298 value of -- 195.0 + 5.0 kJ mo1-1. Kusenko and Gel'd [201] also measured the heat of formation and obtained a AH°~s value of --190.0 kJ mo1-1. According to Schick [86], the data of Huber et al. [195] are recommended; the choice of their data is also preferred to maintain consistency with the earlier choice of their data for NbC. The standard entropy of formation has been estimated. Schick [86] used empirically estimated Debye temperatures to calculate that S°29s : 63.50 J mo1-1 K -1 for NbsC. Kubaschewski and Alcock [23] reported that S°29s = 6 4 . 0 1 + 0 . 4 2 J mo1-1 K -1. Worrell and Chipman [119], using the thermodynamic data obtained for NbC, reported the following equation for the AGf° value of NbzC:

AG°(+ 3800) = -- 192464 + 4.2T J mo1-1 K -1 (1180-1370 K)

(158)

for the reaction 2Nb(s) + C(s) = Nb2C(s)

(159)

The experimental results and the equations are shown in Table 17.

5.2.3. Molybdenum carbides There are three molybdenum carbides [203] : hexagonal MosCs, Mo2C which has two crystal forms, and cubic M O C l - x . All three of these c o m p o u n d s exist over a range of compositions. M o ~ C is orthorhombic at

5.2.3.2. Mo2C. The heat of formation of Mo2C was determined by Mah [205] by means of oxygen bomb calorimetry and she obtained a value of --46.02 + 2.93 kJ tool -1. Johnson et al. [204], using fluorine bomb calorimetry, measured the heat of formation of Mo2C and they obtained a AH°29s value of - - 5 3 . 1 4 + 6.28 kJ mo1-1. Coltters and Belton [206], using a galvanic cell technique, studied the galvanic cell reaction 1 ~d~Cr(s) + Mo2C(s ) = ~ Cr23Ce(s ) + 2Mo(s) (160) Using the third-law method, the standard enthalpy change for reaction (160) is --6.7 + 0.I kJ. From this, they obtained that ~-/°~s -- -- 42.5 + 4.6 kJ mo1-1 for the standard heat of formation of Mo2C. A comparison of AH~29svalues for Mo2C is shown in Table 18. These ~t/°29s values are in agreement within the combined uncertainties. Mah's result for Mo2C was obtained with a sample which did not have a well~characterized composition.Johnson et al. [204] measured the energies of combustion in fluorine of samples with well-characterized compositions. Thus, the recommended ~{°29s value is -- 53.14 + 6.28 kJ mol-I for the heat of formation of Mo2C(s). Low temperature heat capacity measurements were made by Pankratz et al. [207]; from their data it was reported that S°29s -65.7 + 0.8 J tool-1 K-I for the standard entropy of formation of Mo2C.

31

,.~'~ ~

Free-energy determinations of Mo2C have been made by several researchers. Gleiser and Chipman [208] measured the pressure of CO and CO 2 in equilibrium with Mo2C-MoO2-Mo mixtures in the temperature range 1 1 9 9 - 1 3 4 1 K. From the equilibrium measurements they obtained the following equation for the standard free energy of formation of Mo2C: AG ° = -- 4 8 9 5 3 -- 7.7T J mo1-1 K -1

u~ O

c~

(161)

In addition to the older work of Schenck e t al. [209] who used a static system, there

O 00 v

,-~ v

00

o0 O O

c~ u~

c)

<1

have been t w o more recent studies [210, 211] of the CH4-H2 equilibrium with M o Mo2C mixtures using dynamic methods which, in principle, should reduce the thermal segregation problems. These studies by Browning e t al. [176] and by Alekseev and Shwartsman [210] yield impossibly high entropy changes (about 68 J mol-1 K - l ) for the condensed state reaction 2Mo(s) ÷ C(s) = Mo2C(s )

oO O +[

Coltters and Belton [206] carried o u t a study of the stability of Mo2C using a galvanic cell technique. From the e.m.f, data they obtained the following equation for the standard free energy of formation of Mo2C:

00 ¢xl

c-i

AGO( + 900)

+l +1 o

= -- 4 7 9 0 0 -- 8.8T J mo1-1 K -1 ( 8 9 0 - 1 1 0 5 K)

(162)

for the reaction O

O ¢q

C

0

~-~.~ e~

g

r~

2Mo(s) ÷ C(s) = Mo2C(s )

(163)

Equations (162) and (161) demonstrate the excellent agreement between the results of Coltters and Belton [ 2 0 6 ] and those of Gleiser and Chipman [208]. The values of the free energy of formation of Mo2C obtained in all the investigations are compared in Fig. 10. When the values obtained by Coltters and Belton [206] and those obtained by Gleiser and Chipman [208] are compared with the values obtained in all the other investigations (Fig. 10), it can be seen that there are substantial differences. Storms [19] suggested that the main reason for the discrepancy between the measurements is due to the presence of oxygen in the systems. Thus, eqn. (158) is recommended for the standard free energy of formation of Mo2C.

32 280

I

I

I

I

I

103 10 1

I

I 240

roll, ~'~

"Da°r'a~

C:

400

T('C) 1200

--

V

;"°4 i1

-------~I

V

05

i

W2C

V

-5.11(~1 ~10

o4

i

Mo2C

.x

~ 120

1600

J iM'lMelting point

V

._.200 "7 "6 E160

f

lO, 0

Carbon activity

16 3

162

161

o

0

80

_,~6162

CH4:

0 0

I

03

0

40

I

TaC I.ISrzrC,

0

.1() 7 i02 103

I I

700 800

I

I

I

I

Ta2c

I

900 1000 1100 1200 1300 1400 T(K)

Fig. 10. Free energy of formation of Mo2C: e, data of Schenck e t al. [209]; o, data of Browning e t al. [176]; v, data of Alekseev and Shwartsman [210]; D, data of Gleiser and Chipman [ 208]; A, data of Coltters and Belton [206 ].

5.2.4. Ruthenium, rhodium, palladium, silver and cadmium carbides Ruthenium, rhodium and palladium form eutectic phase diagrams with carbon [1]. No compound formation has been reported. However, RuC [211] has been identified as a gaseous compound. Sneed and Brasted [212] reported the existence of the highly unstable AgzC2. Also, there has been no reported compound formation in the Cd-C system. 5.2.5. Free-energy diagram for the secondtransition-series carbides The free-energy diagram for the secondtransition-series carbides (and the thirdtransition~series carbides) is given in Fig. 11. 5.3. Descnp~lons o f carbides o f the third transition series 5.3.1. Hafnium carbide HfC There is only one hafnium carbide: HfC. It has a range of stoichiometry [2, 19]. Calorimetric determinations of the enthalpy of formation of HfC have been published [184, 2 1 3 - 2 1 5 ] . The enthalpies of formation of non-stoichiometric carbides HfCx (0.67 ~ x 1.00) were determined by Zhelankin and

I0

400

800 T(oc) 1200 1600 L

t

t

t

[i

i

%

1

4oo.c),1 1 , 1 1o 1y16 ,,0" PCH4/PH2 1(3161614 1012 10"11 (above 400% )

i

•

i04

2000

lO-1

1(~10

•

i05

Fig. 11. Ellingham diagram for the second- and thirdtransition-series carbides. (It should be noted that the temperatures in this diagram are in degrees Celsius and not in kelvins as in the text.)

Kutsev' [213]. The data from the work of Zhelankin and Kutsev [213] was recalculated by Storms [19] and, in this case, AH~°(HfCx) appears to be independent of x; the change in AHf°(HfCx ) is about 10.04 kJ mo1-1 within the homogeneity region, with an average value o f - - 2 1 7 . 6 kJ tool -1. Certain doubts about the correctness of the data [213] arise from this small variation in AH~° (HfC~) with composition, in contrast with the variation in the heat of formation of other refractory carbides. For example, the change in AH~° for niobium and tantalum carbides [19] is about 62.8 kJ mol -z within the homogeneity region. For zirconium carbides [216] this change is about 58.6 kJ tool -1. Mah [184] obtained a value of - - 2 0 9 . 5 kJ tool -1 for the heat of formation of HfC0.gss; on the assumption that the enthalpy of formation of this compound is a linear function of the carbon content, this gives a ~J/°29 s value of --209.5 + 1.5 kJ mo1-1 for HfC. Since the sample used by Mah was demonstrated to be pure [19], her AH°29s

33 value of - - 2 0 9 . 5 + 1.5 kJ mo1-1 for HfC is recommended. Kubaschewski and Alcock [23] reported an S°z9s value of 39.54 + 0.42 J mo1-1 K -1 as the standard e n t r o p y of formation for HfC. F r o m the free-energy data reported by Huitgren et al. [37] it is possible to estimate that AG°( + 200) ------ 218402 + 8.1T J tool -1 K -1 ( 2 9 8 - 2 0 1 3 K)

(164)

for the reaction Hf(~) + C(s) -- HfC(s)

(165)

and that AG°( +

100)

= -- 2 2 9 1 0 6 + 13.64T J mol -~ K -z ( 2 0 1 3 - 2 3 0 0 K)

(166)

for the reaction Hf(~) + C(s) = HfC(s)

(167)

5.3.2. T a n t a l u m carbides

There are t w o carbides, TaC and Ta2C , in the T a - C system [19]. These carbides exhibit a h o m o g e n e i t y range [19].

WorreU and Chipman [119] measured the CO pressure over a T a C - C - T a 2 0 ~ mixture. From their results, Worrell and Chipman [119] calculated a value of 150.5 + 3.0 kJ mo1-1 for TaC containing a small b u t unk n o w n a m o u n t of dissolved oxygen. A comparison of the AH°ugs values for TaC is shown in Table 19. There is good agreement between the reported data with the exception of Humphrey's work. In view of the above data, it appears that Mah's [220] data, which are in good agreement with the results of Huber et al. [217], Kornilov et al. [218] and Worrell and Chipman [119], are to be recommended. L o w temperature heat capacity data for TaC were obtained by Kelley [221]. He obtained an S°~s value of 42.3 -+ 0.42 J mo1-1 K -1 for TaC. By measuring the pressure of CO in equilibrium with a C - T a C - T a 2 0 5 mixture using the torsion effusion technique, Kulkarni and Worrell [224] obtained the following expression for the free energy of formation of TaC between 1250 and 1400 K: AGO( + 2500) = -- 146022 + 2.1T J mo1-1 K -1

(168)

for the reaction Ta(s) + C(s) = TaC(s)

(169)

5.3.2.1. TaC. There have been several heat

o f formation measurements using calorimetric techniques; these reported values show poor agreement. Storms [19] reported that, if these values are recalculated using - - 2 . 0 4 4 + 2 kJ mo1-1 as the heat o f formation of Ta205 [ 217 ], the agreement improves considerably. H u b e r e t al. [217 ] studied ten compositions in the TaCx phase region. For 0.724 ~< x ~< 0.998, the heat of formation varied from - - 1 1 3 . 4 + 5.4 to - - 1 4 4 . 8 + 5.0 kJ mol -t. A linear extrapolation then yielded AH°29s = - - 1 4 5 . 1 -+ 5 kJ mo1-1 for TaC1.00. In these calculations they used a AH°29s value of - - 2 0 4 4 -+ 2 for Ta205. The ~ H ° ~ s value recalculated on the basis of the work of Kornilov e t al. [218] becomes -- 142.3 kJ mo1-1 for the heat of formation of TaC. The new zSJ-/°~s value based on H u m p h r e y ' s [219] work becomes - - 1 6 1 . 1 kJ tool -1 for the heat of formation of TaC. The new AH°29s value based on Mah's [220] w o r k becomes - - 1 4 8 . 1 + 4.2 kJ mo1-1 for TaC.

5.3.2.2. TazC. The standard enthalpy of formation of Ta2C was measured using combustion calorimetry b y Smirnova and Ormont [222], H u b e r et al. [217] and Kornilov et al. [223]. Kulkarni and Worrell [224] measured the pressure of CO in equilibrium with a Ta-Ta2C-Ta205 mixture at temperatures between 1740 and 1900 K using the torsion effusion technique. From the equilibrium data they were able to calculate AH°29s for Ta2C. Their results for AH°29s are shown in Table 19. As Storms [19] has indicated, the data of Smirnova and Ormont [222] are difficult to evaluate because of the uncertainty a b o u t the composition of their samples, and their results are n o t considered. There is a close agreement between Kulkarni and Worrell's value [224] and that of Huber e t al. [217]; thus, the AH°29a value of -- 197.5 + 14.2 kJ tool -1 for Ta2C is recommended. Krikorian [225] has estimated that S°298 -87.0 + 4.2 J mo1-1 K -1. Smirnova and Ormont

84

.~.~.~.~ OO~

~

O

O

c~

c~

0 0

O O

J

I O t',,v

N

÷

÷

? o

"8

? ,5 -H ¢O

e~

C~

~4

4~

&J+l

+l+l

-H

-H

"4-1

~NM~d ~

t'-. O

~l

Q

cq~cI

O

~,~ . ~ ~.~ ~ "~

~

~

~ ~

O

"~ o

o

O~

e~

cl

e~

35 [222] estimated that S°~98 = 83.1 J mo1-1 K -1. Kubaschewski and Alcock [23] reported that S°29s = 83.7 + 5.0 J mol -z K -~. These values are shown in Table 19. From these estimates, an S°29s value of 84.6 + 2.2 J mol -~ K -~ is recommended; this is an average of the values shown in Table 19. Using the torsion effusion technique, Kulkarni and Worrell [224] obtained the following expression for the free energy of formation of Ta2C between 1740 and 1900 K:

~

¢q 03

AGO( + 1260)

{ 00 [.. 00

= -- 1 9 6 6 4 8 + 8.8T J mo1-1 K -1 ( 1 7 4 0 - 1 9 0 0 K)

(170)

u¢3

~D ¢D

o ¢O

c4

O

O O

O o¢ 03

O 03

{

<1

5.3.3. Tungsten carbides There are two tungsten carbides, WC and W2C, which are stable below 2000 K, although only WC is stable at room temperature.

% 5.3.3.1. WC. The heat of formation of WC was determined by Mah [205] and McGraw et al. [226], w h o independently conducted combustion studies of WC, obtaining ~ 4 ° ~ 8 values o f - 1196.4 kJ mo1-1 and - - 1 1 9 5 . 8 kJ mol -z respectively. This gives ~kH°~8 = -- 40.5 + 1.7 kJ mol -~ as the standard enthalpy of formation of WC. Coltters and Belton [227] studied the galvanic cell reaction

i

I

u~

oc

¢4 -t-{ +} +{

+{

+l

{

¢q ¢J O

Cq

¢q

o

}

+1 00 r-4

z ~ C r + WC = ~ Cr23C6 -~- W using a galvanic cell technique. From these measurements they obtained a AH°29s value of - - 4 0 . 9 -+ 4.6 kJ mo1-1. A comparison of the AH°~s values for WC is shown in Table 20. There is excellent agreement between the values; thus, the recommended AH°2~s value is - - 4 0 . 6 -+ 1.7 kJ tool -~, which is an average of the values shown in Table 20. No data for low temperature heat contents have been reported. Kubaschewski and Alcock [23] reported that S°~ss = 41.8 +- 4.2 J mol -z K -1 for the standard entropy of formation of WC. The standard free energy of formation of WC was obtained from e.m.f, measurements by Coltters and Belton [227]. They obtained

{

t~ uo r~

o0

I

(171)

¢D

CO

tf~

for the reaction 2Ta(s) + C(s) -- TauC(s)

O O ¢q r-~ { O

O

oJ

_=

@J

O

L) L)

36 the following expression for the free energy of formation of WC: AGO( + 1000)

using data from Storms [19] and Schick [18] obtained the following equation for the standard free energy of WC: AG ° = -- 38000 -- 8.4T J mo1-1 K -1

= -- 37866 -- 6.5T J tool -1 K -1 (878-1132 K) for the reaction W(s) + C(s) = WC(s)

(500-1200 K)

(172)

(173)

The free energy of formation of WC has also been investigated by measurements of the equilibrium occurring in the W-WC-CH~-H 2 and W-WC-CO-CO2 systems. There is significant disagreement between the values reported in the literature. Alekseev and Shwartsman [210] studied the equilibrium described by the following reaction: WC + 2H9. = 2W + CH4 Orton [230] studied the equilibrium WC + 2H2 = W ÷ CH4 and obtained values for the free energy of formation of WC which are lower, by a factor of 4, than the values reported by Gleiser and Chipman [231] who studied the equilibrium

Their derived equation is in close agreement with the experimental equation, eqn. (172). This equation is also shown in Fig. 11. Thus, eqn. (172) is recommended for the standard free energy of formation as a function of the temperature for WC.

5.3.3.2. W2C. The heat of formation of W2C was measured by Mah [205] by means of combustion calorimetry. She obtained a AH°29s value of --26.4 + 2.5 kJ mo1-1. No low temperature heat capacity data are available for W2C. The standard free energy of formation of W2C was measured by Gupta and Seigle [229] by means of an equilibrium technique. They obtained the following equation for the standard free energy of formation of W2C: AGO(+ 400) = -- 30500 -- 2.34T J mo1-1 K -1

WC + CO~ = W ÷ 2CO in the temperature range 1 2 1 5 - 1 2 6 6 K. These results were recalculated by Storms [19] and are shown in Fig. 11. Tanaka et al. [228]

(1575-1660 K)

I

I

vVV I

I

V

V

I

I

40 E

3O o o

(.9 l

(176)

5.3.4. Rhenium, iridium, platinum and mercury carbides No carbide compounds have been reported [1] for rhenium, iridium, platinum and mercury.

V

o

-~

(175)

for the reaction 2W(s) + C(s) = W2C(s)

50

(174)

o O

20

10 i

I

I

I

I

',00 900 1000 1100 1200 1300 1400 T(K) Fig. 12. Free energy o f tormation of WC: o, data of Gleiser and C h i p m a n [231]; $, data o f Orton [230]; D, m, data o f Alekseev and Shwartsman [ 210] ; V, data o f Coltters and Belton [ 2 2 7 ] ; , data o f Tanaka e t al. [ 2 2 8 ] .

5.3.5. Osmium and gold carbides A eutectic system with the compound OsC(s) has been reported [1] for osmium. Sneed and Brasted [212] reported the existence of the highly explosive AuzC 2 compound. 5.3.6. Free-energy diagram for the thirdtransition-series carbides The free-energy diagram for the thirdtransition-series carbides (and the secondtransition-series carbides) is given in Fig. 11.

37 6. T H E A C T I N I D E C A R B I D E S

Because of the potential use of the actinide carbides [232] as nuclear fuels, there has been considerable interest in the t h e r m o d y n a m i c behaviour of these materials. However, the k n o w n t h e r m o d y n a m i c properties of these carbides are limited because of the lack of high temperature measurements.

6.1. Description of the actinide carbides 6.1.1. Thorium carbides There are t w o carbides in the Th~C system [19] : ThC which is a cubic phase and ThC2 which is monoclinic at low temperatures. 6.1.1.1. ThC. Huber and Holley [ 2 3 3 , 2 3 4 ] measured the heat of thorium carbides by combustion calorimetry and they obtained the following values: -- 70.7 + 6.7 kJ mo1-1, - - 9 9 . 2 -+ 3.8 kJ m o l - 1 , - - 119.2 + 7.9 kJ mol -z, --123.8 + 4.6 kJ mol -~ and - - 1 2 4 . 3 + 7.5 kJ

104 102 10

1015 106 16 2 10~ ' 0

400

1

161

101. 105 800

1200

Carbon

16 2

activity

106 1600

153 ,o

2000

i06 1~4 ioS

1°s" 1o'

~ThC2

1o4

U2C3

CH~

.

[]

166

UC

"

103

I(3 2

i~ 7 [TITra nsit ion point

102

i~3

[ ] Melting point 0 R 2 /~

400

800 1200 T('C)

1600

1611 10"10

6.1.1.2. ThCe. The heat of formation of ThC~ was measured indirectly b y Prescott and Hincke [239] w h o studied the reaction of ThO 2 with carbon. Using the new value for the heat of formation of ThO2, Lofgren and Krikorian [237] calculated from the results of Prescott and Hincke [239] that AH°29a = - - 1 3 2 . 2 + 5.0 kJ mol -z for ThC2. Kubaschewski and Alcock [23] reported a AH°29s value o f - - 1 1 7 . 2 + 10.5 kJ mo1-1 for ThCz.9a; linear extrapolation then yielded AH°29s = - - 1 2 0 . 8 + 10.8 kJ mo1-1 for ThC2. Thus, the r e c o m m e n d e d value is -- 120.8 + 10.8 kJ mo1-1 for the heat AH°29a of formation of ThC2, which is also shown in Table 21. The free energy of formation of ThC2 was measured by Egan [238] by means of a galvanic cell technique. He obtained the following expression: AGO( + 700) = -- 77613 + 15.1T J mo1-1 K -1

2000

. L . . . . 4 (above400OC)lO 15 1010 10610 10 2 1(~1 "~ 1 PCH4/PI-~2 i0"15 id13 (above 400"C)

mo1-1 for ThC0.75, ThC0.sl, ThCo.91, ThC1.0o and ThCx.9x respectively. No experimental low temperature data have been reported. Kubaschewski and Alcock [ 23 ] reported that S°29s = 58.99 + 0.84 J mo1-1 K -1 for ThCo.97. A linear extrapolation then yielded S°29s = 60.81 + 0.92 J mo1-1 K -1 for ThC1.0o. There do n o t appear to be any direct experimental measurements of the free energy of formation of ThC. Aronson and Sadofsky [235] and Satow [236] made e.m.f, measurements using a Th, ThF~l CaF21ThF4, ThCl-x galvanic cell from which they obtained the partial molar functions A ~ , A/~ and ~ of thorium in ThCl-x as functions of composition at 1173 K. By performing a G i b b s - D u h e m integration and combining the result with A ~ of thorium, Aronson and Sadofsky [235] calculated a value of - - 9 9 . 1 6 kJ mo1-1 K -1 for the free energy of formation of ThCo.96 at 1173 K. The values of the heat of formation and entropy for ThC are listed in Table 21.

-8 10 10

( 9 7 3 - 1 2 7 3 K) 14~4

(177)

for the reaction

10"9

Fig. 13. E l l i n g h a m d i a g r a m f o r t h e a c t i n i d e c a r b i d e s . (It s h o u l d b e n o t e d t h a t t h e t e m p e r a t u r e s in t h i s d i a g r a m a r e in d e g r e e s C e l s i u s a n d n o t in k e l v i n s as in the text.)

~2 Th(s) + C(s) = x ThC2(s)

(178)

6.1.2. Uranium carbides There are three compounds, UC, U2C 3 and UC2, in the U - C system [19]. 6-UC is

38

0

stable from room temperature to 2 7 9 8 K, e-V2C 3 decomposes at about 1993 K without melting, and ~-UC2 is stable from about 1773 K to its melting point.

•

oq I

+

+1 +1 u~

¢q

~aO

+I+I+I+I

+1 +1 +1

°~

0

0

0000~

~ N ~ N M

o~

~

g~

gq

gq

6.1.2.1. UC. There have been several experimental determinations of the heat of formation of UC [ 2 4 0 - 2 4 6 ] . Farr e t al. [240], Droege e t al. [241] and Huber e t al. [242] determined the heat o f formation of UC by means of combustion calorimetry. They obtained values of - - 8 7 . 9 + 4.2 kJ mo1-1, - - 8 2 . 4 + 20.9 kJ mo1-1 and - - 8 8 . 3 + 4.2 kJ mo1-1 respectively. The last value [242] was obtained for UCo.96. A linear extrapolation then yielded AH°29s = - - 9 2 . 0 + 4.4 kJ mo1-1 for UC1.0o. Storms and Huber [243] also made combustion measurement and obtained - - 9 6 . 2 + 4.2 kJ m o l -I for ~ H °298. Vapour pressure measurements by Storms [244] and Vozella e t al. [ 2 4 5 ] gave - - 9 7 . 5 -+ 3.8 kJ m o l -I and - - 9 3 . 7 kJ mol -I respectively for O AH 298- Robinson and Chiotti [246] studied several compositions of UCxOI_x by a galvanic cell technique and obtained a value of - - 6 8 . 2 kJ mol -I for the heat of formation of UC. A comparison o f the AH°298 values for UC is shown in Table 22. The result of Robinson and Chiotti [246] is t o o low; this suggests that they were actually measuring the partial molar free energy of uranium in UCI-x. There is excellent agreement between the combustion measurements made by Storms and Huber [243] and the vapour pressure measurements made by Storms [ 2 4 4 ] . Thus, the recommended value of ~/°298 is --96.9 -+ 2.8 kJ tool -I for UC. This value is an average of the values obtained by Storms and Huber [243] and Storms [244]. Two low temperature heat capacity experiments have been carried o u t [ 2 4 7 , 2 4 8 ] . Westrum e t al. [ 2 4 7 ] obtained an S°2ss value of 59.75 J tool -1 K -1 and A n d o n e t al. [248] obtained an S°298 value of 58.70 J mol -x K -1. The values are in excellent agreement. Thus, the recommended value is 59.23 J mo1-1 K -1, which is an average of the value reported by Westrum e t al. [247] and that of Andon e t al. [248]. Kubaschewski and Alcock [23] reported the following expressions for the free energy of formation of UC:

39

0 ~a •

~0 O~

~ D ~ ~ OOOO

o o o ~ O 0 00~

0

~a~ ~oooo ~. ~.

.

M

"~m

t--

~d

OO OtO I 0

000

CO0

I+

I

I I

I

I I

4~

t'-Cq 0c~I ~0

I

<1

o,1

0,1

+l

-H •~ o , 1 0.,1 0,1 ¢O

-I-I tra o,1

4

od~o~

o~

~4 L'~t'~-

o00 ~t ~

0-1

'~ L'~

t-:~Z tZ

+l+l+l+l+l

+1

+1

+I

+1 ~

~ g g d d d g d d d

I ¢,,1 c'l

g

-a-

gg

tO'gO O,lt-O

tO~ O,1 e.~

~, t'-.-

t"~'

' ~ ~'~

~ i~ ~ ~'--~ 0 . ~ ~

kOtO ¢~ ¢',1 ~1

.-~

.O,1

~ ~

O o

_

e~

aa

o o

0

.<

0

e o ~

g g g g g g g g g g ~.~ D

d ,...i d ,-i d ,.d d ,d ,-i d r,0 r-,o r,.) r..o ~ ~ r,.0 ~ ¢0 ~ D D D D D a D D D D

,.4,.4,4

o

4O AGO( + 6 3 0 0 )

and AGO( + 6 3 0 0 )

= - - 9 0 3 7 . 4 - - 6 . 3 T J mo1-1 K -1 (298-1400

= - - 1 0 2 9 2 6 . 4 + 5 . 0 T J mo1-1 K -1

K)

(1400-2500

(179) for the reaction U(s) + C(s) =

K) ( 1 8 1 )

for the reaction

(180)

VC(s)

V ( l i q ) + C(s) = V C ( s )

(182)

TABLE 23 Standard free energies of formation of carbides Reaction

P a r a m e t e r s (J mo1-1 K -I) in AG ° = A + BT

A 2Be(s) + C(s) = Be2C(s)

Error

Temperature range (K)

Reference

B

(-68373) (27787) (15912) (45319) (36056)

}Mg(s) + C(s) =½Mg2C3(s ) }Mg(liq) + C(s) =~Mg2C3(s ) }Mg(s) + C(s) =}MgC2(s) ~Mg(liq) + C(s) =-~ MgC2(s)

(-50) (-9.8) (3.56) (--9.7) (0.5)

298-1110

+0.14 -+0.5 -+0.17 -+0.2

293-923 923-1150 298-720 720-1123

-+12.6 -+12.6 +12.6 •+12.6

1123-1760 1760-2500 1123-1760 1760-2500

-~Ca(o0 + C(s)=ICaC2(s) -~Ca(~) + C(s)=~CaC2(s ) -~Ca(liq) + C(s) =~ CaC2(s) }Ca(g) + C(s) =-~ CaC2(s)

-- 28451 24309 -28660 -104977

}Sr(s) + C(s) =-~ SrC2(s ) } Sr(liq) + C(s)=-~SrC2(s)

(--36726) (--41505.7)

(--12.35) ( - 7.73)

• +0.03 +0.09

298-1041 1041-1200

}Ba(s) + C(s)=}BaC2(s ) Ba(liq) + C(s) =4 BaC2(s)

(-- 28794.4) ( - 39634.5)

(-- 17.8) (-- 6.65)

-+0.5 •+0.1

298-1002 1002-1600

-

-

-- 12.3 -- 18.1 --14.2 29.2

-+1.4

[16] [16] [41]

4B(s) + C(s) = B4C(s )

--56819

7.1

•+4.2

298-1173

[55]

~Al(s) + C(s) =-~ A14C3(s ) ~ Al(liq) + C(s)=½AI4C3(s)

--71965 -88840

13.95 32.1

-+2.8 -+2.8

298-932 932-2000

[23] [23]

-~Y(s) + C(s) =-~ YC2(00 }Y(s) + C(s) =-~YC2(~) ~ Y(liq) + C(s)=½YC2(~)

(-- 48809) (--45860) (--54522)

( - 9.9) (-- 11.9) (--6.98)

+0.4 • +0.7 •+0.3

298-1603 1603-1799 1799-7100

-~La(s) + C(s) = ~ LaC2(00 -~La(liq) + C(s) =4LaC2(00 -~La(liq) + C(s) =-~ LaC2(~)

(--41372) (-- 39646) (--41595)

(--10.71) (-- 12.5) (--12.8)

-+0.3 •+0.6 -+0.2

298-1193 1193-1333 1333-2500

Si(s) + C(s) = SiC(s)

A G ° = - - 58576-- 5.44Tlog T +

•+10.5

Si(liq)+ C(s) = SiC(s)

+ 23.77T A G ° = - - 113386-- 11.42T log T + + 75.73T

298-1686

[16, 23]

-+8.4

1686-2500

[16, 23]

298-1071 1071-2000 915- 940

[94]

-~Ce(s) + C(s) ---~CeC2(s ) -~Ce(liq) + C(s)=-~ CeC2(s ) Ce(s) + C(s) = CeC

(-- 43905) (42218) -- 116734

(-- 11.93) (--13.9) 34.31

+0.3 +0.2

~Pr(s) + C(s) =~PrC(a) -~Pr(liq) + C(s) =~PrC(~) -~Pr(liq) + C(s) =-~PrC03)

(--42500) (-- 39438) (-- 42009)

(-- 12.99) (-- 16.2) (-- 13.94)

+0.5 +0.06 +0.9

298-1204 1204-1408 1408-2500

-~Nd(c0 + C(s)=-~ NdC2(00 }Nd(~) + C(s) =~NdC2(00 }Nd(liq) + C(s) =}NdC2(00 -~Nd(liq) + C(s) =-~ NdC2(/~)

(-- 43455) (--41571.4) (-- 39464) (-- 47623.5)

(-- 13.85) (--15.9) (-- 17.6) (-- 11.8)

-+0.5 • +0.2 -+0.1 •+0.2

500-1128 1128-1289 1289-1423 1423-2500

41 TABLE 23 ( c o n t i n u e d ) Reaction

Parameters (J tool - 1 K -1) in AG ° = A + BT A

(--36392.9) (-- 34882)

(--7.45)

(-38008)

-~Gd(a) + C(s)---~ GdC2(o~ ) -~Gd(liq) + C(s) =-~ GdC2(~)

2V(s) + C(s) = V2C(s) V(s) + C(s) = VC(s)

Temperature range ( K )

Reference

B

-~Sm(a) + C(s)=~ SmC2(a) -~Sm(/~) + C(s)---~SmC2(a ) -~Sm(liq) + C(s) = ~ S m C 2 ( a ) ½Sm(liq) + C(s) =-~ SmC2(/] )

Ti(o~) + C(s) = TiC(s) Ti(/3) + C(s) = TiC(s) Ti(liq) + C(s) = TiC(s)

Error

(--6.71) (--7.1)

+0.2 +0.1 -+0.1 -+0.1

298-1190 1190-1345 1345-1443 1443-2500

(--57418) (--53945)

(--8.22) (-- 10:94)

-+0.9 -+0.1

298-1585 1585-2500

-- 183050 -186606 -590211.8

10.08 13.22 146.4

-+12.60 -+12.60 -+8.4

298-1150 1150-2000 2383-2593

[16, 231 [16, 231 [1141

-+8.4 +3.6

1180-1370 1180-1370

[119] [1191

-+0.8 -+0.8

1150-1300 920-1250 973-1173

[127] [1361 [1361

893-990 990-1073 900-1100 1243-1323 893-991 991-1073 893-991 991-1073

[1481 [148] [146] [1501 [149] [149] [149] [149]

+0.26 -+0.25 -+0.26

298-1048 1048-1500 1500-1811 450-650 273-503

[169] [161 [169] [169]

-+2.1

298-1200

[161

(--37370)

(-- 147273) -- 100834

Cr(s) + C(s) =4 Cr23C6(s) ~Cr(s) + C(s)=½Cr7C3(s ) ~Cr(s) + C(s) =-~ Cr3C2(s )

-- 53666.7 51803.3

--

- - 4 6 4 3 0

~ M n ( a ) + C(s)=-~Mn7C3(s ) ~Mn(~) + C(s) ---~Mn7C3(s ) ~Mn(~) + C(s) ---½Mn5C2(s) 3Mn(~) + C(s) = Mn3C(s) ~Mn(ol) + C(s)--½MnsC3(s) }Mn(~]) + C(s) --~Mn8C3(s) Mn(a) + C(s) = ~Mn23C6(s) Mn(~) + C(s) = ~Mn23C6(s)

- - 1 1 9 1 0 . 5

--16792 --45145.4 -16900 -16289.7 - - 2 1 8 8 2 . 3

24686 --32768 --

(-9.0)

(4.2) 6.28 --12.77 --11.9 --9.7 --2.3 -- 17.96 13.4 -15.0 --22.5 --16.5 --23.3 --15.0

-+0.6

-+1.2

3Fe(a) + C(s) -- Fe3C(a ) 3Fe('),) + C(s) -- Fe3C(e ) 3Fe(~/) + C(s) = Fe3C(liq) 2.2Fe(a) + C(s) = Fe2.2C(x ) 2.4Fe(o~) + C(s) = Fe2.4C(e )

28714 11234 10335 20292.4 80751.2

2Co(s) + C(s) = Co2C(s )

16527

--8.7

3Ni(s) + C(s) = Ni3C(s )

33932

--7.11

-+12.6

298-1000

[16]

9.2

-+12.6

298-2200

[23]

1.67 (4.2)

+-2.5 +3.8

1180-7370 1180-1370

[119] [119]

890-1105

[206]

Zr(s) + C(s) = ZrC(s)

-- 184514

Nb(s) + C(s) = NbC(s) 2Nb(s) + C(s) -- Nb2C(s )

(--194138)

2Mo(s) + C(s) -- Mo2C(s )

-- 47900

- - 1 3 0 1 2 2

--27.66 --10.983 --10.17 --10.5 --2565

--8.8

i0.9

Hf(a) + C(s) = HfC(s) Hf(~) + C(s) = HfC(s)

-- 218402 -- 229106

8.1 13.64

!0.2 -+0.i

298-2013 2013-2300

Ta(s) + C(s) = TaC(s) 2Ta(s) + C(s) = Ta2C(s)

--146022 --196648

2.1 8.8

-+2.5 -+1.3

1250-1400 1740-1900

-- 30500

--6.5 -- 2.34

-+1 -+0.4

878-1132 1575-1600

--76613

15.1

+-0.7

973-1273

[1191 [2241 [227] [229] [238]

--6.3 5.0 -- 11.44 --17.15 --10.9

+-6.3 +6.3

298-1400 1400-2500 973-1173 298-1044 1044-1173

[23] [23] [250] [2501 [2501

W(s) + C(s) = WC(s) 2W(s) + C(s) = W2C(s )

--

½Wh(s) + C(s)=½ThC2(s ) U(s) + C(s) = UC(s) U(liq) + C(s) = UC(s)

~v(~) + C(s)-- ~' v 2Ca(s) -~u(~) + C(s) = ~ u c 2 ( s ) ~ u ( 7 ) + C(s) =-~ UC2(s)

--

37866

-- 90374.4 102926.4 --61170.1 --33095.4

--39706.2

Estimated values are given in parentheses.

42

e,i I

+I

O

+1

+I

N

~ ,-.-t

F_

+I

e4

"4"I

"H

+I

q-1

+I

+I

+I

+I

+I

+I

•

~

+I

~. ,,..-t

~E

+I +I

I

+b

+I ~

+I +I

d

c~

c~

c~

+I ~

+I

+I

-H ~

q'l

~4

T

÷1 ~

+1 +1 ~

+~ ~

~

~

÷1 ~

+1 +1

÷1 ÷1

÷1 ÷1

~I

÷I +I +I

+~

+I +I

+I +I

+I ÷I

÷I +I

+I +I

+I +I +I

+I ~ ~ 0 +1 +1 +1

+1 +1

÷1

+1

+1

~ +1

÷1

+1

÷1 +t

~ ~ ~ +1 ÷1 +1

I

I

II

t"-

+1

--

m

+1 ÷1

+1

+1

+1

+1 ~

+1

I

II

43

o~

+,

+,

+,

+,

+~

+,

~

~

+'

~

+I

+'

o

¢Xl ~Xl c~

0 0 "m" tO

c.D

+1 0

+1

~ d d d

d

d

g

+I

~

+I

+1 +1 0"~

o~

~

+I

c6

+I

+I ao +I

+I

+I

M

+I ~

,.~ +[ +~

~

+I

c~d

,--4

c~'~

~

+I +I

,-4

~

~

~ o

~o~

~

~,~

~

~00

~.~o.

~

+I

+i

+I +~

+I +I

+I

+I +I

+L +I

+I +I

+I +I +I

'~+

~+

~I

~l I

~

~I

~'~I .I . .l ,. .'~'~i .l

+i +1

o

,~rm

I

I

+

l i ~l

r~

44 6.1.2.2. U2Cs. The heat of formation of U2C 8 was measured by Huber and Holley [233] from the heat of combustion; t h e y obtained a AH°29s value of --205.0 + 16.7 kJ mol -~. Two low temperature heat capacity measurements have been made [ 2 4 8 , 2 4 9 ] . Andon et al. [248] obtained an S°29s value of 137.78 J tool -1 K -1 and F a r r e t al. [249] obtained an S°298 value of 137.70 J mol -I K -1. These values are also shown in Table 22. As can be seen, the data are in excellent agreement. Thus, the r e c o m m e n d e d value is 137.74 which is an average o f the values listed in Table 22. The free energy of formation was measured by Bell and Egan [250] by means of the galvanic cell U, UFsl CaF21UFa, U2Ca, C. They obtained the following expression:

the case with this compound, the data shown in Table 22 are in good agreement. In view of such good agreement between these diverse measurements, a value of --96.2 + 2.0 kJ mo1-1 is recommended. This is an average of the values listed in Table 22 with the exception of the result of Besmann and Lindemer [255]. Low temperature heat capacity measurements by Westrum et al. [247], Farr et al. [249] and Andon et al. [248] gave S°~s values of 68.2 J mo1-1 K -i, 68.32 J mo1-1 K -1 and 68.24 + 0.42 J mo1-1 K -1 respectively. The free energy of formation of UC2 was determined by Bell and Egan [250] using a galvanic cell technique. They obtained the following expressions:

AG ° = -- 61170.1 -- 11.44T J mo1-1 K -1

for the reaction

(973-1173 K)

(183)

(298-1044 K)

1 V(~) -}- C(s) : i UC2(s)

(185)

(186)

and

for the reaction 2 U(~) + C(s) = ~ U2Ca(s)

AG ° : -- 33095.4 -- 17.15T J mo1-1 K -1

(184)

AG ° = -- 39706.2 -- 10.9T J mo1-1 K -1 (1044-1173 K)

6.1.2.3. UC2. The heat of formation of UC2 was measured by Huber et al. [242] by combustion calorimetry; t h e y obtained a value of --88.3 + 8.4 kJ tool -1 for 2d/°29s. A n u m b e r of vapour pressure measurements have been made. Storms [244] and Laitnaker and Godfrey [251] obtained a value o f - - 9 4 . 1 4 kJ mo1-1, Eich et al. [252] f o u n d a value o f - - 9 5 . 4 kJ mo1-1, and Norman and Winchell [253] reported a value of - - 1 0 1 . 7 kJ mo1-1. Measurements o f CO(g) pressure in equilibrium with a mixture of UO2, UC2 and C(s) have been made by a number of investigators [254-257]. Piazza and Sinnott [254] obtained a ~-/°298 value of -- 92.88 -+ 2.9 kJ mo1-1 at 1 7 1 4 - 1 9 2 2 K and 4 9 9 - 8 3 7 0 Pa. Besmann and Lindemer [255] obtained ~ / 0 2 9 s values of - - 8 7 . 1 -+ 3 . 9 kJ mo1-1 and --81.1 -+ 2.2 kJ tool -1 from second- and thirdlaw treatments respectively for U C l m at 1 2 0 1 - 1 7 7 4 K and 4.5 × 10-8-103 Pa. Bell and Egan [250], using a galvanic cell technique, obtained a AH~29s value of --90.4 +- 2.1 kJ tool -1 for UC1.9x. A comparison of the zkH°29s values for UC1.91 is shown in Table 22. As is generally

(187)

for the reaction 1 u(7) +

C(s) = 1 UC2(s)

(188)

6.1.3. Plutonium carbides There are three compounds, PuC, Pu2C 3 and PuC2, in the P u - C system [19]. 6.1.3.1. PuC. Kubaschewski and Alcock [23 ] reported a AH°~s value of - - 4 6 . 4 4 + 3.35 kJ tool -1 for the heat of formation of PuC0.ss. High temperature enthalpies of PuC0.s2 were determined by Oetting [258] by means of calorimetry. He obtained the following expressions for the enthalpy and heat capacity as a f u n c t i o n of the temperature for PuC0.82.

~ T --/'I°298 : -- 20737 + 65.938T -- 2.423 X 10-2T 2 + + 1 . 5 2 2 X 10-ST a + 8.433 × 105T -1 J mo1-1

(298-1500 K)

(189)

The heat capacity equation is given by C~ = 65.938 -- 4.846× 10-2T + 4.566X 10-5T 2 -- - 8 . 4 3 3 X 105T-2 J

mo1-1 K - I

(298-1500 K)

(190)

45 T h e s t a n d a r d e n t r o p y S°298 o f f o r m a t i o n was d e t e r m i n e d b y Hall e t al. [ 2 5 9 ] . T h e i r r e p o r t e d S°29s value is 6 9 . 3 3 J mo1-1 K -1. Sandenaw and Gibney [260] obtained an S°298 value o f 7 0 . 4 6 J tool -1 K -1 f o r PuC0.sl. T h u s , t h e r e c o m m e n d e d value is 6 9 . 9 0 J mo1-1 K -1 f o r t h e s t a n d a r d e n t h a l p y S°29s o f f o r m a t i o n ; this is a n average o f t h e r e p o r t e d values.

A summary of the thermodynamic properties o f c a r b i d e s are s h o w n in T a b l e s 2 3 a n d 24.

6.1.3.2. P u e C 3. T h e h e a t o f f o r m a t i o n o f PuC1. 5 has b e e n d e t e r m i n e d b y m e a n s o f Knudsen effusion, e.m.f, and calorimetric t e c h n i q u e s . T h e r e p o r t e d values r a n g e f r o m - - 5 1 . 5 t o - - 1 0 2 k J mo1-1 [ 2 6 1 - 2 6 6 ] . Besmann and Lindemer [267] measured the p r e s s u r e o f CO o v e r a PuC1.5-PuO1.5-C m i x t u r e b e t w e e n 1 3 4 8 a n d 1 9 2 3 K. T h e y o b t a i n e d a AH°29s value o f - - 9 3 . 3 + 3.3 k J mo1-1. T h e high t e m p e r a t u r e e n t h a l p i e s o f Pu2C2.98 were determined by Oetting [258] by means of calorimetry. He obtained the following e x p r e s s i o n f o r t h e e n t h a l p y as a f u n c t i o n o f t h e t e m p e r a t u r e f o r Pu2C2.98 :

REFERENCES

H°T --/-/°298 = -- 50885.1 + 156.0T -- 3.989 X 10-2T 2 + + 2.348 × 10-5T -3 + + 2.176 × I06T-x J mol -I (298-1500 K)

(191)

He also obtained a heat capacity equation which is given by Cp -- 156.0 -- 7.978 × 10-2T + + 7.044 X10-5T2 --- 2.176 × 106T-2 J tool -1 K -1 (198-1500 K)

(192)

The standard entropy S°29s of formation was d e t e r m i n e d b y O e t t i n g [ 2 5 8 ] w h o o b t a i n e d a value o f 1 5 0 J mo1-1 K -1 f o r Pu2C2.98. H e i n e s e t al. [ 2 6 8 ] o b t a i n e d a value o f 1 5 0 J mo1-1 K -~ f o r Pu2C s. T h u s , t h e r e c o m m e n d e d S°29s value is 1 5 0 J mo1-1 K -1. I t can be seen t h a t t h e e x p e r i m e n t a l results disagree g r e a t l y w i t h o n e a n o t h e r . I t a p p e a r s t h a t f u r t h e r e x p e r i m e n t a l w o r k is n e e d e d t o e n a b l e a reliable c o m p a r i s o n t o be m a d e o f t h e results o b t a i n e d f r o m t h e d i f f e r e n t e x p e r i mental techniques.

ACKNOWLEDGMENTS T h e a u t h o r is i n d e b t e d t o Miss H. Pereira f o r h e r valuable assistance w i t h t h e drawings a n d f o r p e r f o r m i n g s o m e calculations.

1 F. A. Shunk, Constitution of Binary Alloys, Second Supplement, McGraw-Hill, New York, 1969. 2 E. Rudy, Compendium of phase diagram data, Tech. Rep. AFML-TR-65-2, Part V, 1969 (Air Force Materials Laboratory, U.S. Air Force Systems Command). 3 R. P. Elliot, Constitution of Binary Alloys, First Supplement, McGraw-Hill, New York, 1965. 4 G.L. Depoorter and T. C. Wallace, in H. H. Hausner and M. G. Bowman (eds.), Fundamentals of Refractory Compounds, Plenum, New York, 1968, p. 1. 5 G. V. Samsonov, I. I. Timofeeva and L. A. Klochkov, Sov. Powder Metall. Met. Ceram., 83 (1969) 918. 6 Y. A. Chang, L. E. Toth and Y. S. Tyan, Metall. Trans., 2 (1971) 315. 7 L. Ramqvlst, Jernkontorets Ann., 152 (1968) 465. 8 S.P. Denker, J. Less-Common Met., 14 (1968) 1. 9 G. V. Samsonov, High temperature inorganic compounds, Tech. Rep. AEC-TR-6873, 1971 (U.S. Atomic Energy Commission). 10 A. F. Wells, Structural Inorganic Chemistry, Clarendon, Oxford, 3rd edn., 1962. 11 V. Ern and A. G. Switendick, Phys. Rev., 137 (1965) 1927. 12 H. Nowotny, H. Boller and G. Zwilling, Solid state chemistry, Proc. 5th Materials Research Syrup., July 1972, in NBS Spec. Publ. 364, 1972 (National Bureau of Standards, U.S. Department of Commerce). 13 J. B. Conklin, Jr., and D. J. Silversmith, Bull. Am. Phys. Soc., 12 (1967) 416. 14 R. G. Lye and E. M. Logothetis, Phys. Rev., 147 (1966) 622. 15 H. Goretzki, H. E. Exner and W. Scheuermann, in H. Hausner (ed.), Modern Developments in Powder Metallurgy Processes, Plenum, New York, 1971. 16 F. D. Richardson, J. Iron Steel Inst., London, 175 (1953) 33. 17 C. E. Wicks and F. E. Block, U.S. Bur. Mines, Bull., 605 (1973). 18 H. L. Schick (ed.), Thermodynamics of Certain Refractory Compounds, Vols. 1, 2, Academic Press, New York, 1966. 19 E.K. Storms,'The Refractory Carbides, Academic Press, New York, 1967.

46 20 K. K. Kelley, Entropies o f the Elements and Inorganic Compounds, U.S. Printing Office, Washington, DC, 1961. 21 K. K. Kelley, High Temperature Heat Capacity and Entropy Data for the Elements and Inorganic Compounds, U.S. Printing Office, Washington, DC, 1960. 22 D. R. Stull, J A N A F Thermochemical Tables, Dow Chemical Co., Midland, MI, 1965. 23 O. Kubaschewski and C. B. Alcock, Metallurgical Thermochemistry, Pergamon, Oxford, 5th edn., 1979. 24 J. F. Elliott and M. Gleiser, Thermochemistry for Steelmaking, Addison-Wesley, Reading, MA, 1960. 25 R. O. G. Blachnik, P. Gross and C. Haymann, NTIS Rep. AD-673897, 1968, p. 28 (National Technical Information Service, U.S. Department of Commerce). 26 K. Motzfeldt, Aeta Chem. Scand., 18 (1964) 495. 27 F. Sh. Muratov and A. V. Novoselova, Proc. Acad. Sci. USSR, Chem. Sect., 129 (1959) 979. 28 F. Sh. Muratov and A. V. Novoselova, Proc. Acad. Sci. USSR, Chem. Sect., 143 (1962) 218. 29 G.H. Rinehart and R. G. Behrens, J. Chem. Thermodyn., 12 (1980) 835. 30 M.W. Chase, J. L. Curnutt, A. T. Hu, H. Prophet, A. N. Syverud and L. C. Walker, JANAF Thermochemical Tables, 1974 Supplement, in J. Phys. Chem. Ref. Data, 3 (1974) 381. 31 B. D. Pollock, J. Phys. Chem., 63 (1959) 587. 32 P.J. Spencer, Beryllium, At. Energy Rev., (4) (1973). 33 F. Irmann, Helv. Chem. Acta, 31 (1948) 1584, 2263. 34 G. T. Furukawa, M. L. ReiUy and J. H. Piccirelli, NBS Rep. 6645, 1960, pp. 10-18 (National Bureau of Standards, U.S. Department of Commerce). 35 O.K. Krikorian, Thermodynamic properties of the carbides, Rep. UCRL 2888, 1955 (Radiation Laboratory, University of California). 36 T.B. Douglas and A. C. Victor, High temperature heat contents, NBS Rep. 6645, 1960, pp. 19-31 (National Bureau of Standards, U.S. Department of Commerce). 37 R. Hultgren, P. Desai, D. Hawkings, M. Gleiser and K. K. Kelley, Selected Values o f the Thermodynamic Properties of Elements and Binary Alloys, American Society for Metals, Metals Park, OH, 1973. 38 O. Ruff and B. Josephy, Z. Anorg. Allg. Chem., 153 (1926) 17. 39 N. Kameyama and Y. Inoue, J. Soc. Chem. Ind. Jpn., 45 (1942) 656. 40 V. G. Geiseler and W. Bfiehner, Z. Anorg. Allg. Chem., 343 (1966) 286. 41 R . L . Faircloth, R. H. Flowers and F. C. W. Pummery, J. Inorg. Nucl. Chem.. 29 (1967) 311. 42 D. R. Stull and G. C. Sinke, Thermodynamic properties of the elements, Adv. Chem. Set., 18(1956). 43 K. K. Kelley, Ind. Eng, Chem., 33 (1941) 1314. 44 K. K. Kelley, U.S. Bur. Mines, Bull., 476 (1949).

45 R. Brunner, Z. Elektrochem., 38 (1932) 55. 46 O. Ruff and E. Foerster, Z. Anorg. Allg. Chem., 65 (1923) 321. 47 N. Kameyama, Y. Ota and Y. Inoue, J. Soe. Chem. Ind. Jpn., 44 (1941) 412B. 48 R.H. Flowers and E. G. Rauh, J. Inorg. Nucl. Chem., 28 (1966) 1355. 49 B. R. Atkins, W. J. Kramers, M. Pirani and H. G. Weil, Coal Res., 68 (1946). 50 M. Hoch, J. Appl. Phys., 29 (1958) 1588. 51 E. S. Domalski and G. T. Armstrong, J. Res. Natl. Bur. Stand., Sect. A, 72 (1968) 133. 52 G. L. Gal'chenko, B. J. Timofeev, G. N. Makarenko and G. V. Samsonov, Russ. J. Phys. Chem., 44 (1970) 1400. 53 K. C. Hong and O. J. Kleppa, J. Chem. Thermodyn., 10 (1978) 797. 54 K.K. Kelley, J. Am. Chem. Soc., 63 (1941) 1137. 55 E.T. Turkdogan, Physical Chemistry o f Oxygen Steelmaking: Thermochemistry and Thermodynamics, United States Steel Co., Monroeville, PA, December 1970, p. 67. 56 D. J. Meschi and A. W. Searcy, J. Phys. Chem., 63 (1959) 1175. 57 E. R. Plante and C. H. Schreyer, J. Res. Natl. Bur. Stand., Sect. A, 70 (1966) 253. 58 N. D. Potter, E. Murand, D. L. Hildenbrand, Y. H. Inani and W. F. Hall, Publ. [7-3748, 1966 (Aeronutronic). 59 G.H. Rinehart and R. G. Behrens, J. Chem. Thermodyn., 12 (1980) 205. 60 W.J. Thorbun, Doctoral Dissertation, University of Toronto, 1964 (University Microfilms Acc. 65-12,190, Ann Arbor, MI, 1964). 61 K. Grjotheim, O. Herstad and K. Stahl-Johanneso sen, Z. Anorg. Allg. Chem., B27 (1964) 267. 62 C. S. Campbell, Metall. Soc. Conf., London, 7 (1962) 412. 63 U. V, Choudary and G. R. Belton, Metall. Trans. B, 8 (1977) 531. 64 A. D. Mah, Rep. Invest. 6415, 1964 (U.S. Bureau of Mines). 65 R. O. Blachnik, P. Gross and C. Hayman, Trans. Faraday Soc., 66 (1970) 1058. 66 R. C. King and G. T. Armstrong, J. Res. Natl. Bur. Stand., Sect. A, 68 (1964) 661. 67 J A N A F Thermochemical Tables, U.S. Department of Commerce-National Bureau of Standards-Institute for Applied Technology, Washington, DC, 1965-1968, June 1971 ; J A N A F Thermoehemical Tables, 1974 Supplement, 1975 Supplement. 68 D. N. Carlson and W. M. Paulson, Trans. Metall. Soc. AIME, 242 (1968) 846. 69 G. De Maria, M. Guido, L. Malaspina and B. Pesce, J. Chem. Phys., 43 (1965) 4449. 70 F. J: Kohl and C. A. Stearns, Tech. Note NASATN-D5646, February 1970 (National Aeronautics and Space Administration). 71 F . J . Kohl and C. A. Stearns, J. Chem. Phys., 52 (1970) 6310. 72 L. D. Jennings, R. E. Miller and F. H. Spedding, J. Chem. Phys., 33 (1960) 1849. 73 R. L. Faircloth, R. H. Flowers and F. C. W. Pummery, J. Inorg. Nucl. Chem., 30 (1968) 499.

47 74 F. H. Spedding, J. Gschneider, Jr., and A. H. Daane, J. A m . Chem. Soc., 80 (1958) 4499. 75 A. L. Bowman, N. H. Krikorian, G. P. Arnold, T. C. Wallace and N. G. Nerenson, Acta Crystallogr., Sect. B, 24 (1968) 459. 76 T. Y. Kosolopova and G. N. Makarenko, Ukr. Khim. Zh., 30 (1964) 784. 77 A. Taylor and D. S. Laidler, Br. J. Appl. Phys., 1 (1950) 174. 78 R. S. Mitchell, J. Chem. Phys., 22 (1954) 1977. 79 E. D. Whitney, Nature (London), 199 (1963) 278. 80 H. N. Baumann, J. Electrochem. Soc., 99 (1952) 109. 81 R . I . Scace and G. A. Slack, J. Chem. Phys., 30 (1959) 1551. 82 R. I. Scace and G. A. Slack, in J. O'Connor and J. Smiltens (eds.), Silicon Carbide, Pergamon, Oxford, 1960. 83 S. Yasuda, Denki Kagaku, 30 (1962) 587. 84 J. Smiltens, J. Phys. Chem., 64 (1960) 368. 85 G. Humphrey, S. Todd, J. Coughlin and E. King, Rep. Invest. 4888, 1952 (U.S. Bureau of Mines); Chem. Absir., 46 (1952) 8949. 86 H. Schick, Thermodynamics o f Refractory Compounds, Vol. 1, Academic Press, New York, 1966. 87 P. Grieveson and C. B. Alcock, in Special Ceramics, Heywood, London, 1961. 88 S. G. Davis, D. F. Anthrop and A. W. Searcy, J. Chem. Phys., 34 (1961) 659. 89 J. Drowart and G. De Maria, in J. O'Connor and J. Smiltens (eds.), Silicon Carbide, Pergamon, Oxford, 1960. 90 E. Greenberg, C. A. Natke and W. N. Hubbard, Rep. A N C 71 75, 1960, p. 138 (Argonne National Laboratory); Rep. A N L 7020, 1965, p. 169 (Argonne National Laboratory). 91 J. D. Baird and J. Taylor, Trans. Faraday Soc., 54 (1958) 526. 92 D. Kay and J. Taylor, Trans. Faraday Soc., 56 (1960) 1372. 93 R. Rein and J. Chipman, J. Phys. Chem., 67 (1963)839. 94 J. C. D ' E n t r e m o n t and J. Chipman, J. Phys. Chem., 67 (1963) 449. 95 K. K. Kelley and E. G. King, U.S. Bur. Mines, Bull., 592 (1961). 96 F. H. Spedding, K. Gschneider, Jr., and A. H. Daane, J. A m . Chem. Soc., 80 (1958) 4499. 97 P. Winchell and N. L. Baldwin, J. Phys. Chem., 71 (1967) 4476. 98 F. B. Baker, E. J. Huber, C. E. Holley and N. H. Krikorian, J. Chem. Thermodyn., 3 (1971) 77. 99 E. A. Dancy, J. H. Everett and C. L. McCabe, Trans. Metall. Soc. AIME, 224 (1962) 1095. 100 N. H. Krikorian, T. C. Wallace, M. G. Bowman, Rep. LA-DC-6819, 1964 (Los Alamos Scientific Laboratory); Int. Colloq. on Semi-metallic Derivatives, Paris, October, 1965. 101 J. S. Anderson and A. N. Bagshaw, in Les Elements des Terres Rares, Vol. I, Centre National de la Recherche Scientifique, Paris, 1970.

102 P. E. Potter, H. R. Haines and J. K. Estall, Rep. AERE-R-6003, 1969 (Atomic Energy Research Establishment). 103 N. D. Staut, C. L. Hoening and P. C. Nordine, J. A m . Ceram. Soc., 52 (1969) 145. 104 R. L. Seiver and H. A. Eick, 8th Rare Earth Research Conf., 1970 Reno, NV, April 19-22, Preprint, pp. 4 3 6 - 4 4 5 . 105 J. Cuthbert, R. L. Faircloth, R. H. Flowers and F. C. Pummery, Proc. Br. Ceram. Soc., 8 (1966) 155. 106 T. C. Wallace, N. H. Krikorian and P. L. Stone, J. Electrochem. Soc., 111 (1964) 1404. 107 C. L. Hoening, N. D. Sout and P. C. Nordine, J. A m . Ceram. Soc., 50 (1967) 385. 108 G. L. Humphrey, J. Am. Ceram. Soc., 34 (1951) 2261. 109 A. D. Mah, K. K. Kelley, N. L. Gellert, E. G. King and C. J. O'Brien, Rep. BM-RI-5316, 1957 (U.S. Bureau of Mines). 110 M. Morozova, M. Khripun and S. Ariya, Zh. Obshch. Khim., 32 (1962) 2072. 111 C . E . Lowell and W. S. Williams, Rev. Sci. Instrum., 32 (1961) 1120. 112 W. A. Chupka, J. Berkowitz, C. Giese and M. Inghram, J. Phys. Chem., 62 (1958) 611. 113 d. Coffman, G. Kibler, T. Lyon and B. Acchione, Carbonization of plastics and refractory materials research, Tech. Rep. WADD TR 60-646, Part II, January 1963 (Research and Technology Division, Air Force Materials Laboratory, U.S. Air Force Systems Command). 114 S. Fujishiro and N. A. Gokcen, J. Phys. Chem., 65 (1961) 161. 115 E. K. Storms and R. J. McNeal, J. Phys. Chem., 66 (1962) 1401. 116 N. M. Volkova and P. V. Gel'd, Izv. Vyssh. Uchebn. Zaved., Tsvetn. Metall., 3 (1965) 77. 117 V . I . Alekseev and L. A. Schwartsman, Dokl. Akad. Nauk SSSR, 133 (1960) 1327. 118 W. Worrell, J. Phys. Chem., 68 (1964) 954. 119 W. Worrell and J. Chipman, J. Phys. Chem., 68 (1964) 860. 120 T. Kireev and R. Karapetyantus, J. Phys. Chem., 70 (1966) 68. 121 P. V. S. Pillai and M. Sundaresan, Trans. Indian Inst. Met., 28 (1975) 319. 122 A. D. Mah, Rep. BM-RI-6177, 1963 (U.S. Bureau of Mines). 123 S. Fujishiro and N. A. Gokcen, J. Electrochem. Soc., 109 (1962) 835. 124 S. Fujishiro, Trans. Jpn. Inst. Met., 1 (1960) 125. 125 C. H. Shomate and K. K. Kelley, J. A m . Chem. Soc., 71 ( 1 9 4 9 ) 3 1 4 . 126 A. D. Mah, Rep. Invest., 721 7, 1969 (U.S. Bureau of Mines). 127 A. D. Kulkarni and W. Worrell, Metall. Trans., 3 (1972) 2363. 128 K. K. Kelley, F. S. Boericke, G. E. Moore, E. H. Huffman and W. M. Bangert, Tech. Paper 662, 1949 (U.S. Bureau of Mines). 129 R. Hultgren, R. L. Orr and K. K. Kelley, Selected Values o f Thermodynamic Properties o f Metals

48 and Alloys, Supplements, University of California, Berkeley, CA, May 1965, October 1966. 130 V. I. Alekseev and L. A. Shwartsman, Fiz. Met. Metalloved., 2 (1961) 545. 131 W.M. Dawson and F. R. Sale, Metall. Trans. A, 8 (1977) 15. 132 V. I. Alekseev and L. A. Shwartsman, Fiz.-Khim. Osn. Met. Protsessov, Komis, Fiz. Khim. Osmovan Proizvod. Stali. Sb. Statei, (1964) 441. 133 H. A. Hancock and L. M. Pidgeon, Trans. Metall. Soc. AIME, 227 (1963) 608. 134 A. S. Bolgar, V. V. Fesenko and G. Gordinko, Poroshk. Metall., 38 (1966) 100. 135 H. Kleykamp, Bet. Bunsenges. Phys. Chem., 73 (1969) 354. 136 R. G. Coltters and G. R. Belton, Metall. Trans. B, 15 (1984) 517. 137 M. Gleiser, J. Phys. Chem., 69 (1965) 1771. 138 F. Z. Vitaikin, Fiz. Met. Metalloved., 16 (1963) 144. 139 H. Mabushi, N. Sano and Y. Matsushita, Metall. Trans., 2 (1971) 1503. 140 H. I. Alekseev, V. I. Malkin and V. V. Pokidyshev, Russ. J. Phys. Chem., 42 (1968) 341. 141 W.A. Frad, Adv. Inorg. Chem. Radiochem., 11 (1968) 188. 142 K. Kuo and L. E. Persson, J. Iron Steel Inst., London, 1 75 (1953) 33; 178 (1954) 39. 143 J. P. Bochard and R. Fruchart, C.R. Acad. Sei., 258 (1954) 3495. 144 M. Picon and J. Flahat, C.R. Acad. Sci., 245 (1957) 534. 145 N. A. Gokcen and S. Fujishiro, Trans. Metall. Soe. AIME, 227 (1963) 542. 146 F. Moattar and J. S. Anderson, Trans. Faraday Soc., 67 (1971) 2303. 147 C. L. McCabe and R. G. Hudson, J. Met., 9 (1957) 17. 148 H. Tanaka, Y. Kishida, A. Yamaguchi and I. Moriyama, Trans. Jpn. Inst. Met., 35 (1971) 997. 149 H. Tanaka, Y. Kishida, T. Kotani and I. Moriyama, Trans. Jpn. Inst. Met., 37 (1973) 568. 150 U. V. Choudary and Y. A. Chang, Calphad, 2 (1978) 169. 151 O.J. Kleppa and K. C. Hong, J. Chem. Thermodyn., 10 (1978) 243. 152 H. Ulich and H. Siemonsen, Arch. Eisenh~ttenwes., 14 (1940) 27. 153 U. V. Choudary and Y. A. Chang, Metall. Trans. B, 7 (1976) 655. 154 N.J. Petch, J. Iron Steel Inst., London, 149 (1944) 143. 155 W. Glud, K. V. Otto and H. Ritter, Ber. Ges. Kohlantech., 3 (1929) 40. 156 V. Hoffmann and E. Groll, Z. Anorg. Allg. Chem., 191 (1930)414. 157 W. Stuckens and A. Michel, C.R. Acad. Sci., 253 (1961} 2358. 158 P. Lasage, Ann. Chim., 6 (1961) 623. 159 G. H~gg, Z. Kristallogr., 89 (1934) 92. 160 K. H. Jack, Proc. R. Soc. London, Ser. A, 195 (1948) 56. 161 J. P. Senateur, R. Fruchart and A. Michel, C.R. Acad. Sci., 255 (1962) 1615.

162 M.C. Eckstrom and W. A. Adcock, J. A m . Chem. Soc., 72 (1950) 1042; Colloq. Int. CNRS, 157 (1967)95. 163 L. S. Darken and R. W. Gurry, J. Met., 3 (1951) 1015. 164 L. S. Darken and R. W. Gurry, Physical Chemistry o f Metals, McGraw-Hill, New York, 1953. 165 F. D. Richardson and W. E. Dennis, Trans. Faraday Soc., 49 (1953) 171. 166 D. R. Poirier, Trans. Metall. Soc. AIME, 240 (1968) 685. 167 J. Chipman, Trans. Metall. Soc. AIME, 239 (1967). 168 J. Chipman,Metall. Trans., 1 (1970) 2163. 169 J. Chipman,Metall. Trans., 3 (1972) 55. 170 G. Naeser, Mitt. Kaiser Wilhelm Inst. Eisenforsch. DUsseldorf, 16 (1934) 207. 171 S. Umino, Sci. Rep. Tohoku Univ., Ser. 1, 23 (1935) 665. 172 K. K. Kelley, U.S. Bur. Mines, Bull., 584 (1960). 173 C. Schwarz and H. Ulich, Arch. Eisenhi~ttenwes., 10 (1936) 11. 174 H. Seltz, J. McDonald and C. Well, Trans. AIME, 140 (1940) 263. 175 T. Watase, J. Chem. Soc. Jpn., 54 (1933) 110. 176 L.C. Browning, T. W. Dewitt and P. H. Emmett, J. A m . Chem. Soc., 72 (1950) 4211. 177 S. Ban-ya, J. F. Elliott and J. Chipman, Metall. Trans., 1 (1970) 1313. 178 R.P. Smith, Trans. Metall. Soc. AIME, 215 (1959) 954. 179 E. Scheil, T. Schmid and J. Wiinning, Arch. Eisenh~ttenwes., 32 (1961) 251. 180 K. H. Jack, J. Iron Steel Inst., London, 169 (1951) 26. 181 A. L. Tsou, J. Nutting and J. W. Menter, J. Iron Steel lnst., London, 172 (1952} 163. 182 W. A. Roth, Z. Elektrochem., 48 (1929) 981. 183 S. R. Shatynski, Oxid. Met., 13 (1979) 105. 184 A. D. Mah, Rep. USBM-6518, 1964 (U.S. Bureau of Mines). 185 B. D. Pollock, J. Phys. Chem., 65 (1961) 731. 186 J. A. Coffman, G. M. Kibler, T. F. Lyon and B. D. Acchione, Tech. Rep. WADD-TR-60-646, Part II, 1963 (Research and Technology Division, Air Force Materials Laboratory, U.S. Air Force Systems Command). 187 S. Fujishiro and N. A. Gokcen, Thermodynamic properties of zirconium carbide at high temperatures, Int. Syrup. on Physical and Chemical Processes in Metals, Pittsburgh, PA, 27 April1 May, 1959. 188 A. S. Bolgar, T. S. Verkhoglyadova and G. R. Samsonov, Izv. Akad. Nauk S.S.S.R., Otd. Tekh. Nauk, Met. Topl., 1 (1961) 142. 189 C. H. Prescott, J. A m . Chem. Soc., 48 (1926) 2534. 190 V.S. Kutsev, B. F. Ormont and V. A. Epel'baum, Dokl. Akad. Nauk S.S.S.R., 104 (1955) 576; Rep. AEC TR-2671, 1960 (U.S. Atomic Energy Commission). 191 V.S. Kutsev, B. F. Ormont and V. A. Epel'baum, Zh. Fiz. Khim., 29 (1955) 629; Rep. AEC TR2861, (U.S. Atomic Energy Commission).

49 192 V . I . Zhelankin, V. S. Kutsev and B. F. Ormont, Zh. Neorg. Khim., 3 (1958) 1237. 193 K. Lorenz and J. Woolcock, Z. Anorg. Allg. Chem., 176 (1928) 289. 194 A. D. Mah and B. J. Boyle, J. A m . Chem. Soc., 77 (1955) 6512. 195 E . J . Huber, Jr., E. L. Head, C. E. Holley, Jr., E. K. Storms and N. H. Krikorian, J. Phys. Chem., 65 (1961) 1846. 196 A. N. Kornilov, V. Ya Leonidov and S. M. Skuratov, Vestn. Mosk. Univ., Khim., 17 (6) (1962) 48. 197 F. G. Kusenko and P. V. Gel'd, Izv. Sib. Otd. Akad. Nauk S.S.S.R., (2) (1960) 46. 198 A. N. Kornilov, I. D. Zaikin, S. M. Skuratov and G. P. Shveikim, Zh. Fiz. Khim., 40 (1966) 1070. 199 L. B. Pankratz, W. W. Weller and K. K. Kelley, Rep. USBM-6446, 1964 (U.S. Bureau of Mines). 200 T. A. Sandenaw and E. K. Storms, Rep. LA-3331, 1965 (Los Alamos Scientific Laboratory); J. Phys. Chem. Solids, 27 (1966) 217. 201 F . G . Kusenko and P. V. Gel'd, Izv. Vyssh. Uchebn. Zaved., Tsvetn. Metall., 2 (1961) 43. 202 K. Clusius, P. Franzosini and V. Piesbergen, Z. Naturforsch., 15 (1960) 728. 203 E. K. Storms, in L. E. Roberts (ed.) MTP International Review o f Science, 1972, pp. 10, 37. 204 G . K . Johnson, W. N. Hubbard and E. K. Storms, J. Chem. Thermodyn., 9 (1977) 1021. 205 A. D. Mah, Heats of combustion and formation of carbides of tungsten and molybdenum, Rep. Invest. 633 7, 1963 {U.S. Bureau of Mines). 206 R. G. Coltters and G. R. Belton, Metall. Trans. B, 11 (1980) 525. 207 L. B. Pankratz, W. W. Weller and E. G. King, Rep. Invest. 6861, 1966 (U.S. Bureau of Mines). 208 M. Gleiser and J. Chipman, J. Phys. Chem., 66 (1962) 1539. 209 R. Schenck, F. Kurzen and H. Wesselcock, Z. Anorg. Allg. Chem., 203 (1932) 159. 210 V. I. Alekseev and L. A. Shwartsman, Izv. Akad. Nauk S.S.S.R., Otd. Tekh. Nauk, Met. Topl., 1 (1963) 91. 211 C. Kempter and M. R. Nadler, J. Chem. Phys., 33 (1960) 1580. 212 M. C. Sneed and R. C. Brasted, Comprehensive Inorganic Chemistry, Vol. II, Van Nostrand, Princeton NJ, 1954, p. 111. 213 V. I. Zhelankin and V. S. Kutsev, Zh. Fiz. Khim., 38 (1964) 562. 214 V. V. Fesenko, A. S. Bolgar, Isparenie tugoplavkikh Soyedineii (Evaporation o f Refractory Compounds), Metallurgiya, Moscow, 1966. 215 V . I . Zhelankin, V. S. Kutsev and B. F. Ormont, Zh. Fiz. Khim., 35 (1961) 2608. 216 F. B. Baker, E. Storms and C. E. Holley, J. Chem. Eng. Data, 14 (1969) 244. 217 E . J . Huber, E. L. Head, C. E. Holley, Jr., and L. A. Bowman, J. Phys. Chem., 67 (1963) 793. 218 A. N. Kornilov, V. Ya. Leonidov and S. M. Skuratov, Vestn. Mosk. Univ., (6) (1962) 48. 219 G. L. Humphrey, J. A m . Chem. Soc., 76 (1954) 978. 220 A. D. Mah, Rep. USBM-6663, 1965 (U.S. Bureau of Mines).

221 K. K. Kelley, J. A m . Chem. Soc., 62 (1940) 818. 222 V. I. Smirnova and B. F. Ormont, Dokl. Akad. Nauk S.S.S.R., 100 (1955) 127. 223 A . N . Kornilov, I. D. Zikin, S. M. Shuratov, L. B. Dubrovskaya and G. P. Shveikin, Zh. Fiz. Khim., 38 (1964) 702. 224 A. D. Kulkarni and W. L. Worrell, Metall. Trans., 4 (1973) 93]. 225 O . H . Krikorian, Estimation of high-temperature heat capacities of carbides, Rep. UCRL-6785, February 6, 1962 (Radiation Laboratory, University of California). 226 L. D. McGraw, H. Seltz and P. E. Snyder, J. A m . Chem. Soc., 69 (1947) 329. 227 R . G . Coltters and G. R. Belton, Metall. Trans. A, 14 (1983) 1915. 228 H. Tanaka, Y. Kishida and J. Moriyama, Trans. Jpn. Inst. Met., 37 (1973) 564. 229 D . K . Gupta and L. L. Seigle, MetaU. Trans. A, 6 (1975) 1939. 230 G. W. Orton, Trans. Metall. Soc. AIME, 230 (1964) 600. 231 M. Gleiser and J. Chipman, Trans. Metall. Soc. AIME, 224 (1962) 1278. 232 P. E. Potter, J. Nucl. Mater., 42 (1972) 1. 233 E.J. Huber, Jr., and C. E. Holley, Jr., in Thermodynamics o f Nuclear Materials, International Atomic Energy Agency, Vienna, 1962, p. 581. 234 E. J. Huber, Jr., and C. E. Holley, Jr., American Chemical Society Meet., Albuquerque, NM, December 1966. 235 S. Aronson and J. Sadofsky, J. Inorg. Nucl. Chem., 27 (1965) 1769. 236 T. Satow, J. Nucl. Mater., 21 (1967) 2 4 9 , 2 5 5 . 237 N. L. Lofgren and O. H. Krikorian, in L. E. Russell (ed.), Carbides in Nuclear Energy, Vol. 1, Physical and Chemical Properties/Phase Diagrams, Macmillan, New York, 1964, p. 315. 238 J. J. Egan, J. Phys. Chem., 68 (1964) 978. 239 C. Prescott and W. Hincke, J. A m . Chem. Soc., 49 (1927) 2744. 240 J. D. Farr, E. J. Huber, E. L. Head and C. E. Holley, Jr., J. Phys. Chem., 63 (1969) 1455. 241 J. W. Droege, A. W. Lemmon, Jr., and R. B, Filbert, Jr., Rep. BMIo1313, 38-A-5, 1959 (Battelle Memorial Institute). 242 E . J . Huber, E. L. Head and C. E. Holley, Jr., J. Phys. Chem., 67 (1963) 1730; Rep. 14, 1963 (International Atomic Energy Agency, Vienna). 243 E . K . Storms and E. J. Huber, Jr., J. Nucl. Mater., 23 (1967) 19. 244 E. K. Storms, Rep. LA-DC-6953, 1965 (Los Alamos Scientific Laboratory). 245 P.A. Vozella, A. D. Miller and M. A. DeCrescente, Rep. CNLM-5619, 1964 (Pratt and Whitney Aircraft Corporation). 246 W. C. Robinson, Jr., and P. Chiotti, ~Rep., 1964 (Ames Laboratory, Iowa State University of Science and Technology, Contract W-7405-erg. 82). 247 E. F. Westrum, Jr., E. Suits and H. K. Lonsdale, Proc. 3rd Symp. on Thermophysical Properties, Lafayette, IN, 1965, American Society for Mechanical Engineers, New York, 1965, p. 156. 248 R . J . L . Andon, J. F. Counsell, J. F. Martin and

50

249

250 251 252

253 254 255 256 257 258 259

H. J. Hedger, Trans. Faraday Soc., 60 (1964) 1030. J. D. Farr, W. G. Witteman, P. L. Stone and E. F. Westrum, Proc. 3rd Syrup. on Thermophysical Properties, Lafayette, IN, 1965, American Society for Mechanical Engineers, New York, 1965, p. 162. W. K. Bell and J. J. Egan, J. Electrochem. Soc., 113 (1966) 376. J . M . Laitnaker and T. G. Godfrey, J. Nucl. Mater., 21 (1967) 175. H. Eich, E. J. Rauh and R. J. Thorn, in Thermodynamics o f Nuclear Materials, International Atomic Energy Agency, Vienna, 1962, p. 549. J. H. Norman and P. Winchell, J. Phys. Chem., 68 (1964) 3802. J. R. Piazza and M. J. Sinnott, J. Chem. Eng. Data, 7 (1962) 451. T . M . Besmann and T. B. Lindemer, J. Chem. Thermodyn., 14 (1982) 419. J. F. A. Henneke and H. L. Scherff, J. Nucl. Matter., 38 (1971) 285. A . J . Heiss, J. Nucl. Mater., 55 (1975) 205. F. L. Oetting, J. Nucl. Mater., 88 (1980) 265. R. O. A. Hall, H. R. Haines, J. A. Lee, M. J. Mortimer and D. McElroy, Rep. A E R E - R 9381, 1979 (Atomic Energy Research Establishment).

260 T. A. Sandenaw and R. B. Gibney, in W. N. Miner (ed.), Plutonium 19 70, Proc. 4th Int. Conf. on Plutonium and Other Actinides, in Nucl. Metali., 17 (1970) 104. 261 J. P. Marcon, J. Poitreau and G. Roullet, in W. N. Miner (ed.), Plutonium 1970, Proc. 4th Int. Conf. on Plutonium and Other Actinides, in Nucl. Metall., 17 (1970) 799. 262 W.M. Olson and R. N. Mulford, in Thermodynamics o f Nuclear Materials 1967, International Atomic Energy Agency, Vienna, 1968, p. 871. 263 R. A. Kent, in K. Ogata and T. Hagakawa (eds.), Recent Developments in Mass Spectroscopy, University Park Press, Baltimore, MD, (1969), p. 1124. 264 J. Battles, W. A. Shinn, P. E. Blackburn and R. W. Edwards, High Temp. Sci., 2 (1970) 80. 265 G . M . Campbell, R. A. Kent and J. A. Leary, in W. N. Miner (ed.), Plutonium 1970, Proc. 4th Int. Conf. on Plutonium and Other Actinides, in Nucl. MetaU., 17 (1970) 1781. 266 R. LorenzeUe, I. De Dieuleveult and J. Melamud, J. Inorg. Nucl. Chem., 33 (1971) 3297. 267 T. Besman and T. B. Lindemer, J. A m . Ceram. Soc., 66 (1983) 782. 268 H. R. Heines, R. O. Hall, J. A. Lee, M. J. Mortimer and D. McElroy, J. Nucl. Mater., 88 (1950) 261.