4.1. Mixed rare earth dicarbides (RI-xR'~)Cz with different structures 4.1.1. Formation of R,_xRxC2
In the mixed rare earth dicarbide and the rare-earth-actinide carbide systems, the ternary compounds were found to be present in the form of a solid solution with the same structure as the component carbide. Thus, these carbides have also been called pseudobinary carbides.
Adachi et al. (1970) studied the mixed rare earth dicarbides containing two different rare earth ions with either similar or very different radii, and pointed out (i) that in the former case the solid solutions also have a body-centered tetragonal structure like the pure components and (ii) that the relation between the lattice constants and the mole fraction of the rare earths obeys Vegard's law over the whole region. Such solid solutions include LaC 2 (Ce, Tb)C2, CeC2-(Pr, Ho, Y)C 2 and PrCz-(Nd, Tm)C 2 (Adachi et al. 1973). In the latter case, e.g. in the systems LaC2-(Dy, Tm, Y)Cz, CeCz-(Er, Lu)C~ and P r C z - L u C 2 , the face-centered cubic phases were observed in a 1 : 1 mole ratio of two-component carbides (Adachi et al. 1970, 1973). The cubic-to- tetragonal transformation observed for the one-component dicarbides seems not to occur in these systems. The limit of the ionic radius difference for the formation o f a fcc phase is about 14% in the L a - R - C system or 15% in the C e - R - C system. A mixed dicarbide of lanthanum with lutetium (La: Lu = 1 : 1) appeared to be hexagonal with lattice parameters a = 5.78 ,~, c = 8.32 ,~ (Adachi et al. 1973).
4.1.2. Structure of R l _ x R " C 2
As described above, the mixed rare earth dicarbides were found to form in three different structures, bct, fcc and hexagonal (Adachi et al. 1973). With respect to the
!00 G. ADACHI et al.
tetragonal structure of some mixed rare earth dicarbides, crystal structure line profile refinements have been made for neutron powder diffraction data collected at room temperature from YxHo l_xC 2 and CexNd 1 xC2 (x = 0.25, 0.50, 0.75) (Jones et al.
1984, 1986). The results show that in both YxHOl -xC2 and C % N d l -~C2, the unit cell dimensions a and c progressively decrease with decreasing x. The C - C bond lengths are essentially the same, 1.28 A for the entire composition range in Y x H o l _ x C 2 (although the actual values are slightly higher, 1.281-1.282,~, in the range x = 0.25 0.50), while in CexNdl _xC 2 they pass through a minimum, 1.275(5) A, in the middle of the composition range, presumably indicative of rather stronger bonding at this composition.
4.1.3. Cubic-to-tetragonal transformation in rare earth dicarbide solid solutions The cubic-to-tetragonal phase transformation temperature of various binary dicar- bide solid solutions have been measured (McColm et al. 1973, Adachi et al. 1974, 1976, 1978, Loe et al. 1976). A typical example is shown in fig. 13.
The results showed that the transformation temperatures for pure dicarbides exceed 1000°C but those for the solid solutions fall rapidly as the concentration of the NdC2, GdC2, or H o C 2 increases with respect to that of the LaC 2 or PrC 2 up to nearly 50 mol.% NdC2, G d C 2 o r H o C 2 , respectively.
This type of lowering in the transformation temperature has been explained by McColm et al. (1973) using a strain model. According to this model, a relationship was established between the depression of Tt and the difference in the unit cell volumes A V of the dicarbides, ATt = K ( A V ) 2, for 50 mol.% solid solutions. These authors empha- sized that the solvent should be defined as that dicarbide possessing the smaller unit cell volume, regardless of the relative concentrations. Loe et al. (1976) found that the same relationship holds for other compositions and proposed that a local strain on the C2 z - ions, caused by local variations in ion size and represented by an X-ray unit cell volume difference, is responsible for lowering the nucleation temperature of a
E
8 g
o
F- 1200
1150
1100
105(]
1000
b.c.t.
, i J i i , , , i
20 40 60 80
NdC 2 mole°/, Fig. 13. Transformation temperature of the L a C 2 - N d C 2 solid solu- tion (Adachi et al. 1976).
RARE EARTH CARBIDES 101 tetragonal nucleus in a cubic matrix. They derived the strain energy, Es, from DTA results and found it to be as large as 13.8kJmo1-1 in the H o C 2 - N d C 2 and G d C 2 - L a C 2 systems. They estimated that when the strain exceeds a value of 16 kJ m o l - 1, the cubic phases are stabilized down to ambient temperature.
In McColm's model, the entropy of transformation for the dicarbides AS t . . . . was presumed to be constant for all CaC2-type carbides. However, as was evident from the thermal data of some rare earth dicarbides (Adachi et al. 1974, 1976, 1978), the observed value of AS t .... for the solid solution changes with its composition.
Adachi et al. (1974, 1976, 1978) measured the values of the heat of transformation in the systems L a C 2 - N d C 2, LaC 2 GdC2, LaC2 CeC2, LaC2 TbC2 and LaC 2 DyC2, as well as those of the pure dicarbides, showing that the values for the solid solutions are smaller than those of the pure dicarbides (about 16.72 kJ mol-1). In the case of La0.47Gdo.53C 2 it becomes as small as about 3.34 kJmo1-1, as well as in the case of the L a C 2 - D y C 2 solid solution, where the apparent heat of transformation becomes almost zero at both 26 mol% DyC2 and 69 mol% DyC 2. They suggested that the volume difference between a pure dicarbide and a solid solution, A V, would lead to the strain energy "Ej' of the solid solution and if the amount of the strain energy evolved is equal to the heat of transformation, no thermal effect will be observed at all. Within the range of 26 < x < 69 m o l % DyC2, a face-centered cubic phase appeared even at room temperature since the strain energy in the solid solution was probably much greater than the heat of the transformation.
The strain energy "E~" in the systems L a C z - C e C 2, LaC2-TbC2 (Adachi et al. 1978), LaC2-NdC2, LaC2 GdC2 and LaC2-DyC2 (Adachi et al. 1976, 1974), as well as N d C 2 - H o C 2 (Loe et al. 1976) has been determined by using the following equation:
E~ = A H h y p o - z~Hobs, (1)
where AHhypo is the heat of transformation in a hypothetical strain-free solid solution and Hobs is the observed value. Hhypo can be calculated from eq. (2) by assuming that the solid solution is ideal:
AHhypo = XAHRc 2 + (1 - x)AHR,c2, (2)
where x is the mole fraction of RC 2 in the R C 2 - R ' C 2 solid solution, and AHRc 2 and AHR,c2 are the heats of the transformation of RC 2 and R'C2, respectively.
In order to find the relationship between E~ and volume difference, Adachi et al.
(1978) introduced a new term (a ratio of AV to the volume of a major component dicarbide of the solid solution V, namely A V/V), where A V = [unit cell volume of a given RC2 R'C2 solid solution] - [unit cell volume of pure RC2 ( > 50 tool.% RC2) or R'C 2 ( > 50 mol.% R'C2) ]. Finally, they discovered that in the light-light lanthan- ide diearbide solid solution systems, such as L a C 2 - C e C 2, LaC2 NdC2, A V/V is proportional to E~, and in the heavy-light lanthanide systems, LaC 2 GdC2, L a C 2 - T b C 2 and L a C z - D y C 2 , straight lines are given only in the high-Es region and curves in the low-E s region. The intercepts obtained by an extrapolation of the straight-line portions are different. This difference in the intercepts may reflect the difference in bonding energy between La3+-C22- and the other R3+-C22- com- pounds (R' = Ce, Nd, Gd, Tb, Dy).
102 G. ADACHI et al.
These facts suggest that in light-light lanthanide systems such as L a G 2 C e C 2 and L a C z - N d C 2 the effect of the volume difference ratio A V / V on the strain energy is predominant, while in light-heavy rare earth systems the bonding energy difference between the two rare earth ions to C ~-, as well as the volume difference, is significant (Adachi et al. 1978).
4.2. Mixed rare earth carbide (R l_xRx)15C19
Hfijek et al. (1984b) remelted the carbon-reduced product containing Sc and Dy in a molar ratio of R15C19 at nearly 1800°C and obtained a Sc15C19-type mixed scandium-dysprosium phase, (Sc0.94Dy0.o6)15 C19, in amounts detectable by X-ray diffraction (P7421c, a = 7.53 _+ 0.01 A, c = 1.506 _+ 0.03 A). The presence o f C 3 hydro- carbons in the products of hydrolysis of the mixed phases, in amounts of about 1 2vo1.% provides evidence of the occurrence of 6 12 wt.% Ra5C19 phases. No report with respect to the formation of other Sc~ s C~ 9-type mixed crystals was found.
4.3. Solid solutions of the rare earth carbides and the uranium carbides
The pseudobinary systems U C 2 - C e C 2 and U C z - L a C 2 have been investigated (McColm et al. 1972), as well as the high-carbon portion of the uranium gadolinium-carbon system (Wallace et al. 1964) and the solid solubilities of cerium, lanthanum and neodymium in UC and U2C3 (Lorenzelli and Marcon 1972, Stecher et al. 1964, Haines and Potter 1970). The phase diagrams from these investigations have been presented by Wallace et al. (1964), and McColm et al. (1972).
4.3.1. Formation and the cubic-to-tetragonal transformation of (U 1 - x Rx) C 2
As in the mixed rare earth dicarbide systems, the rare earth dicarbides also form a solid solution with uranium dicarbide and there exists a composition dependence of the cubic-to-tetragonal phase transformation for the UC2 LaC2 or the U C z - C e C 2 solid solutions (McColm et al. 1972), as well as for the U C z - G d C 2 solid solution (Wallace et al. 1964).
For the U - C e - C and the U L a - C systems, the existence of cubic phases down to room temperature has been established for ternary carbides within the composition limits Lao.loUo.9oC 2 Lao.85Uo.15C 2 and Ceo.16Uo.84C 2 Ce0.alUo.19C 2 (McColm et al. 1972). In the U - G d - C system the situation is more complex. UC2 and GdC2 form a continuous series of solid solutions above 1785°C, with the solid solution solidus and carbon eutectic temperatures decreasing in a regular manner from the UC2 boundary to the G d C 2 boundary. In addition, there is a narrow two-phase region [tetragonal-(U, Gd)C 2 + cubic-(U, Gd)C2] lying along a line connecting UC2 at 1785°C and approximately (Uo.sGdo.2)C2 at 1510°C (fig. 14). At 1300°C the solid solution is still stable over the region from (Uo.12Gdo.88)C 2 to GdC2. The lattice parameter of the quenched tetragonal (U, Gd)C 2 solid solution phase varies contin- uously with composition from a o = 3.522 ,~ and c o = 5.982 A at UC2 to a o = 3.717 and c o = 6.264 A at G d C 2. The tetragonal-to-cubic transformation temperature of 1785 _ 20°C for UC2 was found to decrease with the addition of GdC2; likewise, this
RARE EARTH CARBIDES 103
CUBIC UC:
TEq TETRAGONAL TE TRAGONAL (U,G:
CUBIC (U,G(
U2C3+CUBIC UC~- o C U2 C 3 + 18 OO/' T ETRAGONAL UC2~
1700 ,/.
TETRAGONAL (U.Gd)C2~
1600 / (U rad)2C 3 --
1500 / U2C3+C - - 1400 / ( U , ~ ) 2 C 3 + C - - 1300
(Uo.sLGdo.o 9 )
/
J
\i~Coo
~ 1 7 0 0
~ i C+CUBIC (Gd, U) C 2 60O
~.1500
CUBIC (U,Gd)C 2 1400
~ 1 3 0 0 : 3 +(Uo.12Gdo.88)C2 + C
Fig. 14, Perspective drawing of the high-carbon portion of the Gd U C ternary system (Wallace et al.
1964). (Reprinted by permission of the publisher, The Electrochemical Society, Inc.)
transformation temperature of 1275 _+ 20°C for GdC 2 was also found to decrease with the addition of UC2, and thus a minimum occurs at 1155 _+ 20°C and a composition of ( U o . 3 4 G d o . 6 6 ) C 2. However, such a minimum does not occur in the U - C e - C and the U - L a - C systems. McColm et al. found that there are two face-centered cubic phases present in the same melt over a composition range. One based on fcc UC2 with a parameter increasing with increasing lanthanum or cerium content of the solid solution, and the other based on fcc LaC2 or CeC z with a parameter falling with increasing uranium content. Thus, McColm et al. indicate a miscibility gap in the phase diagram, although the shape and the temperature to which it extends have not been fixed to date.
4.3.2. Decomposition of ( U1 - xRx) C2
McColm et al. found that when some samples of the cubic phase (La, U ) C 2 w e r e
annealed at 1720°C for 6 h in vacuum and cooled to below 800°C within about 3 rain, the precipitation of UC occurred, showing that precipitation of UC begins from the cubic [3 phase instead of the tetragonal ~ phase. In addition, the experiments also showed that the ternary fcc solid solutions containing C 2 units do not occur when the overall carbon/total metal ratio falls below 2: 1. In such preparations the phases in the melt are only UC and the lanthanide carbide expected from the melt stoichiometry (McColm et al. 1972).
In contrast to the decomposition products of the U - C e (or La) dicarbide, (U0.95Gdo.os)C z decomposed between 1515 and 1550°C, and (Uo.s9Gdo.11)C 2 be- tween 1515 and 1535°C, to give (U, Gd)2C 3 and C, while the samples with a higher GdC2 content decomposed into three phases: (U, Gd)2 C3, (U, Gd)C2 and C (Wallace
104 G. ADACHI et al.
et al. 1964). These results are in good agreement with the eutectoid decomposition of the pure uranium dicarbide to U2C3 + C at 1500 __ 25°C (Langer 1963). The gadolinium-carbide-rich phase boundary of the (U, Gd)2C3 phase was determined to be (U0,91Gdo.09)2C3, and is essentially constant in the temperature range 1300-1500°C, and the decomposition curve progresses from the UC2 boundary (1525°C) to a composition of (UoAzGdo.88)C2 at 1300°C.
4.3.3. Solid solubility of R in uranium carbides
The limiting solubilities of the rare earth elements in the uranium carbides and of uranium in the rare earth carbides have been determined, those of Ce in UC and of U in CezC 3 are 4.5 and 5.5 at.% total metal, respectively (McColm et al. 1972). However, these results obtained from McColm et al. are significantly smaller than those reported by Stecher et al. (1964) and Haines and Potter (1970) (30 at.% Ce at 1600°C and 9.5 at.% Ce at 1450°C in UC, respectively), but in agreement with those obtained from an accurate determination of solubility limits in various phase fields of the U - C e - C , U - N d C and U - L a - C systems (Lorenzelli and Marcon 1972). The isother- mal sections of the phase diagram at 1250°C and 1600°C have been carefully investigated for the system described above. At 1600°C the limited solubilities of Ce in the solid solution (CexU l_x)C in equilibrium with U2C 3 +
CeC2,
Ce2C 3 + CeC2, and Ce2C3 + Ce are 1%, 7%, and 14%, respectively; those of Ce in U2C3 and U in Ce2 C3 are 4.2% and 2.2%, respectively. However, the value of U in CeC2 is very low.Similar values were obtained for the U - L a - C and the U - N d - C system, e.g. the values o f R (La and Nd) in (RxU 1 _~)C in the presence of U2C3 + RC2 and RC 2 + R2C 3 are 0.5 to 1% and 2 to 8%, and those of La and Nd in U2C 3 are 0.4 to 2.5%.
4.3.4. Mechanism of decrease in transition temperature
The mechanism of the decrease in the tetragonal-to-cubic transformation temper- ature by adding the rare earth atom to UC2 has been discussed in terms of a strain energy model, which was also applied to the mixed rare earth dicarbide system, see sect. 4.1.3 (McColm et al. 1973, Adachi et al. 1974, 1976, 1978). The cubic-to- tetragonal transformation was described by Chang (1961) as a diffusionless trans- formation. McColm et al. (1972) suggested that this is an isothermal martensite-type transformation for (U1-xRx)C2, and in such a case nucleation rather than growth is the rate-determining step. However, nucleation of the tetragonal phase within the cubic dicarbide must involve the coherent alignment of a considerable number of C 2 units over a number of unit cells to provide a viable domain of the tetragonal carbide.
The random ( 111 ) orientation must be replaced by an ordered orientation along the tetragonal ( 0 0 1 ) direction. However, in a dicarbide containing solute ions with a different size from the host, this preferred orientation will be influenced by the presence of a nearest-neighbor metal ion larger or smaller than the others. C2 units will tend to orient "side on" to a larger ion and "end on" to a smaller ion because this minimizes the strain in the lattice. Thus, each different-sized ion gives a preferred orientation. However, as the solute ions are distributed randomly, the preferred orientations would be incoherent and make more difficult any concerted action to align C2 units parallel to each other and thus form a tetragonal nucleus. Only by
RARE EARTH CARBIDES 105 further lowering the temperature to allow the M - C - C M interactions to become important compared to the thermal energy, would the C2 units be able to align in a given orientation.
This model gives a satisfactory explanation for the effect of size difference on the cubic-to-tetragonal transformation (McColm et al. 1972), and has been verified by the neutron diffraction of Ceo.33Uo.67C 2 and Ceo.67Llo.33C2 over 296 to 4 K (Atoji 1980). In the two ternary CaCz-type compounds the cubic NaCl-type structure can be arrested down to 4 K because of the large strain energy of the disordered lattice. A random distribution of Ce and U atoms as well as the orientational disordering of C2 units are also retained down to 4 K. The lattice parameters indicate no valency change over the range 296 4 K, such as Ce 3+ ---> C e 4+.
4.4. Solid solutions (Ca, Y)C2 and (Th, Y)zC3
The solid solutions in the system CaC2-YC2 can be formed over the entire composition range; however, no Vegard's law behavior with respect to the composi- tion dependence of the lattice parameters was found (Hfijek et al. 1971), e.g., the solid solution Cao.33Y0.66C2 has essentially the same lattice parameters (a = 3.62A, c = 6.06 A) as the yttrium dicarbide (a = 3.62 A, c = 6.05 A) (Brozek etoal. 1970). The lattice parameters of the solid solution with 33 mol% YC 2 (a -- 3.64 A, c = 6.16 ~,) are only slightly larger than those of YC2 but markedly lower than those of CaC 2 (a = 3.87 A, c = 6.38 A), indicating that the anomalous valence state of the yttrium ion in these solid solutions leads to an irregular change in lattice parameters.
At high temperatures and under high pressures, Th formed a single-phase solid solution series with Y2C 3 over a wide ternary composition field (Krupka et al. 1969).
The new phase, crystallizing into the body-centered cubic Pu2Ca-type structure, was superconducting over its entire range of homogeneity with a variable transition temperature < 4 ~ 17 K. Annealing at high temperature and ambient pressure destroyed both the bcc structure and the superconductivity.
5. Thermodynamic properties of binary rare earth carbides