The formation of the binary rare earth carbides has been summarized in table 2.
The crystal structure and lattice p a r a m e t e r data listed in this table were quoted from the review "Critical evaluation of binary rare earth phase diagrams" (Gschneidner and Calderwood 1986). The listed lattice parameters were assessed by them and are the mean values when m o r e than one acceptable set of data were presented for an individual compound. In this section, the crystal structures of each binary rare earth carbide will be evaluated in detail.
3.1. Crystal structure of the R C 2 compounds
Rare earth dicarbides are c o m m o n l y formed in the rare-earth (except for e u r o p i u m ) - c a r b o n systems. M a n y investigators, in particular Atoji, have made a great contribution to the determination of the structure of RC2. The neutron diffraction investigations on the structure of the rare earth dicarbide, first by Atoji and Medrud (1959) showed that for the lanthanum dicarbide the atomic coordinates in the
1 1 1
unit cell are: ( 0 0 0 , ~ j _+ (00z) for carbon atoms and z = 0 for lanthanum atoms, and the carbon positional p a r a m e t e r z(A) is 0.403 + 0.002, corresponding to a well- defined m i n i m u m at a C - C distance of 1.28 _+ 0.03 A. LaC2 can p r o b a b l y be described approximately in terms of La 3 + C 2- ions, with the extra electron in a conduction band and thus with a metallic conductivity. In LaCg, the C 2 group appears to be acetylene-like with one nearest lanthanum at 2.65 A from the carbon on a line collinear with the C - C bond. F o u r other l a n t h a n u m a t o m sites are located around the C 2 group as though re-bonded to it. Bond numbers (n), distances and coordination numbers are as follows:
C - C 1.28A, n = 2.73, La 2C 2.65 ]~, n = 0.48, C - L a 2.65A, n = 0.48, L a - 8 C 2.85A, n = 0.22, C - 4 L a 2.85A, n = 0.22, LaM, La 3.93,&, n = 0.12.
B o w m a n et al. (1968) determined the high-temperature structures of the tetragonal LaC2 phase at 900 and 1150°C by means of high-temperature neutron diffraction.
86 G. A D A C H I et al.
The tetragonal-to-cubic transformation was observed at 1060°C with the lattice parameters a o = 4.00, c o = 6.58 ]~ at 900°C and a o = 6.02 ]~ at 1150°C. The structure of the tetragonal phase was found to be Clla type, in agreement with the previous room-temperature results, with a C - C distance of 1.26 4- 0.03 A. The cubic phase was found to be isomorphous with the cubic KCN-type, instead of the CaF2-type, uranium dicarbide (Bowman et al. 1966), space group Fm3m. In this structure, the lanthanum atomic coordinates are (½, ½, ½) and C2 group with centers at (0, 0, 0) randomly oriented along the [-111] directions. The observed C - C distances are in reasonable agreement with the room-temperature value of 1.30 A (Atoji 1961), the actual values may be somewhat larger owing to the effect of thermal motion of the carbon atoms. Both the tetragonal and high-temperature cubic structures of the compounds RC2 are shown in fig. 5 and the difference between both structures is obvious.
In addition to LaC 2, the crystal structures of CeC 2 and TbC 2 (Atoji 1961, 1962, 1967a), PrC2 and N d C 2 (Atoji 1967a), DyC2 (Atoji 1968), HoC2 (Atoji 1967a), ErC 2 (Atoji 1972), TmC 2 (Atoji 1970), YbC 2 (Atoji 1961, 1962, Atoji and Flowers 1970), LuC 2 (Atoji 1961, 1962) and YC2 (Atoji 1961, 1962, Bowman et al. 1967) have also been established by neutron diffraction. The coherent nuclear reflection analysis technique (Atoji 1967a) verified the previous X-ray diffraction results (Spedding et al. 1958) that the chemical unit cell contains two molecules and possesses the body- centered tetragonal symmetry, D]~-I4/mmm, as reported above for LaC 2. Table 5 lists the lattice parameters of the compounds RC2 obtained by the neutron diffraction method at 300 and 5 K. Only one set of data was adopted when more than one set of data was present in different works by the same author. Corresponding to the lattice parameters, the average linear thermal expansion coefficients in the temperature range of 5-300 K are also listed. In the light rare earth dicarbides the expansion along the a axis is about a half of that along the c axis, while the relation is reversed in the heavy rare earth dicarbides. However, the expansion along the c axis is several times larger than that along the a axis in the case of DyC 2 and YbC 2.
Table 5 also summarized other pertinent crystallographic data: the Debye Waller temperature factor coefficients, B in
exp[-2B(sinO/2) 2]
at 3 0 0 K and 5 K; the carbon positional parameters, z in (000, ±±!~222f - - -~ ( 0 0 Z ) , (Z = 0 for the R atoms); the intramolecular C - C distances and the nearest C - R distances.(
io
(a)
C;
l
(b)
Fig. 5. RC 2 with the tetragonal CaC2-type structure at r o o m tem- perature (a) and with cubic K C N - type structure at high temperature
(b).
RARE EARTH CARBIDES 87
The paramagnetic scattering, the interatomic distances, and the C - C energy level indicate that these compounds are composed of R "÷, C 2- , and an (n - 2) conduction electron with n = 3 (except for n = 2.8 in YbC2) and the R ions are in their tripositive Hund ground states (Atoji 1961). Despite the presence of the negative ion C22-, the RC 2 is typically metallic. This aspect has been reasonably interpreted in terms of the 5d-xg2p conduction band that correlates self-consistently with the valency wave- functions (Atoji 1961, 1962, 1967a, b).
The C - C distances in the C2 groups for the rare earth dicarbides are insignificantly different from their weighted average value of 1.286 A. In particular, the C - C distance in YbC2 revealed no substantial effect due to possible anomalous valence of Yb in this compound. The average value in RCz is considerably larger than the 1.20 A in alkaline earth dicarbides (Atoji 1961, 1962, Atoji and Medrud 1959) which usually exhibit nonmetallic characteristics.
Other interatomic distances in the rare earth dicarbides show unusual features.
Pauling's bond number (Pauling 1960) for the C - R and R - R bonds in these dicarbides increases roughly with the atomic number of the rare earth atom: 0.5 (C-La) to 0.9 (C-Lu) (Atoji 1961) for the nearest C - R distance; 0.2 to 0.35 for the next nearest C - 4 R distances; 0.1 to 0.2 for the nearest R - R distances which are equal to the lattice parameters; 3 to 5 and 3.5 to 4.5, respectively, for the total bond numbers of the carbon and rare earth atoms. The bond numbers for YC2 fall between H o and Lu, indicating that Y in YC 2 behaves as a heavy lanthanide (Atoji 1961, 1962).
3.2. Crystal structure of ~he R 2 C 3 compounds
The lanthanide sesquicarbide is body-centered cubic with P u 2 C 3 (D5c)-type struc- ture and I2~3d space group with eight formula units per unit cell. This structure has been confirmed by neutron diffraction studies carried out at 296 K for La2C3 and Pr2C 3 (Atoji and Williams 1961), at 296 to 5 K for Ce2C 3 (Atoji 1967b), Tb2C3 (Atoji 1971), Ho2C 3 (Atoji and Tsunoda 1971), and Pr2C 3, Nd2C 3 and Dy2C 3 (Atoji 1978).
The metal and carbon atoms occupy the sites 16(c) (uuu) and 24(d) (v o¼), respectively.
The least-squares refinement to the neutron diffraction data yielded the position parameters, temperature factor coefficients (B) and interatomic distances. The config- urations of both lanthanide atoms about C2 groups and the C2 groups about lanthanide atoms (point symmetry C3-3) are shown in fig. 6. The point symmetry of the midpoint of the C 2 group is S,-2~ and approximates to D2d-74m2. Referring to fig. 6a,/_ R 1 C a R2 is 79.1 °, while/_ R 3 Ca R4 is 180 °. The angle between R 1 R 2 and R 3 R4 is 84.9 ° (Atoji et al. 1958) and each R atom also has three nearest R neighbors at only 3.630 ~ for R = La (Atoji 1961), compared with 3.75 A for nearest neighbors in 13-La.
All PuzC3-type rare earth sesquicarbides, except Ce2C 3, have a C - C distance of 1.246 A (the average for LazC3, PrzC3, TbzC 3 and Ho2C3). The distance is shorter than the average C - C distance in the rare earth dicarbides, 1.286 A. In C%C 3 the C - C distance, 1.276 _+ 0.005 fk, is significantly different from that in other rare earth sesquicarbides and U2C3 has a much longer value, C - C = 1.42/~ (Novion et al. 1966).
Therefore, these C - C distances seem to indicate that the intramolecular C - C distance in the metal acetylide should become longer as the ionic charge of the metal atom
88 G. A D A C H I et al.
~A
r.2~
~2
e q
e~
©
~2
e4 ~ ~ ~5 e4 ~5 e4 ~
+l +I +1 ÷i
+1 -t-I -H -H
+1 +I -H +1
-H +t --I +t
+1 +1 +1 ÷1
~-I e-q ¢xl
+1 +1 +1
+1 +1 -H
~d~5
÷l
~ c 5 +1
+1 ÷l ÷1
-H +1 --I
~ xzeq "erq . e
z
c4~5
÷1
e.i "
+1
+1
~,D O e ~ C2~
+1
tt3 O +1
~5c5
+1
+1
-H
,-~c5 -t-I
RARE EARTH CARBIDES 89
-FI -FI -FI --FI
+l ÷1 +1 +l
+1 +l +l ÷1
d d d d d d d d
+1 +1 ÷1 +1
-H -H -FI
-H -H -H
c ~ c ~ c 5 -H -Ft 4-1
+1 -H 4-1
-H -FI 4-1 -H ÷ l
+1 -H -H +1 -H -FI 4-1
~.- -H ~ ÷1 -H
-FI 4-1 4-1 H-i
~ ~ +1
-H +1 -H H-I 4-1 -H
~ ~ s ~ ~ ~ s ~ ~
HH ÷1 -FI -H +1 -FI
4-1 -H -H + l -H
-FI -FI 4-1 -FI -H
R
~ E o
90 G. ADACHI et al.
C2 ~
8
C 3 4
( a ) ( b )
Fig. 6. (a) Configuration of the R a t o m s about the C 2 group in R 2C3; (b) Configuration of the C 2 groups about an R a t o m in RzC 3 (Atoji et al. 1958). (Reprinted by permission of the publisher, The American Chemical Society, Inc.)
increases, as in the metal dicarbides, MC 2. In the metal sesquicarbides, M2C3, the C - C bond distances are !.246, 1.276 and 1.42 A when M is a tripositive rare earth, Ce 3"4+ (Atoji 1967b) and U 4+, respectively.
The shortest R - R distances in the rare earth sesquicarbides, Ro-3R 1, are nearly 10% shorter than the shortest R - R distances in the dicarbides, which are equal to their lattice parameters. Other Ro-2R z and Ro-6R 3 distances are also shorter than this value, indicating that there are stronger R - R interactions in the sesquicarbides than in the dicarbides. The interatomic distances in Ce2C3, particularly the Ce-Ce distances are markedly smaller than the expected values for CezC 3 with the pure trivalent Ce atoms. This is in accordance with the result obtained from the para- magnetic scattering analysis (Atoji and Williams 1967).
In the sesquicarbides with the trivalent rare earth metal ions, the number of delocalized electrons is 4 per C 2 group, while the dicarbides with the trivalent lanthanide ions have only one delocalized electron per C 2 group. If the C2 antibond- ing orbital (~g2p) (Atoji and Medrud 1959) participates equally in forming the lowest conduction bands of the sesquicarbides and the dicarbides, the C - C bond distances in the sesquicarbides should be longer than those in the dicarbides, in contradiction to the experimental results. Thus, the rCg2p contribution of the C 2 group to the conduc- tion bands must be smaller in the sesquicarbides than in the dicarbides, i.e. the conduction electrons in the sesquicarbides are associated with the metal orbitals with a higher order than those in the dicarbides. In CeaC 3, more electrons occupy the C2 antibonding orbitals than in other sesquicarbides, and thus a markedly shorter C - C distance was observed.
The neutron diffraction study on the crystal structure of CezC 3 at temperatures between 300 and 4 K (Atoji 1967b) showed an anomalous temperature dependence of the CezC 3 lattice parameter, suggesting a gradual "lattice collapsing" trans- formation, probably due to a 4f-5d transition, ending at about 90 + 5 K and that Ce in CezC 3 below 90 K is essentially tetravalent.
RARE EARTH CARBIDES 91 3.3. Crystal structure o f the R ~ 5 C~ 9 compounds
Since 1958, seven representatives of the intermediate carbides (Spedding et al. 1958), Sc15C19 (Jedlicka et al. 197i), Y15C19 (Bauer and N o w o t n y 1971), ErasCa9 (Bauer 1974), YblsCx9 (Haschke and Eiek 1970a, Bauer and Bienvenu 1980, H/tjek et al.
1984), Lu~sC~9 (Bauer and Bienvenu 1980), Ho15C19 and Tm15C19 (Bauer and Ansel 1985) have been reported. The existence of Gd15C19 has also been noted in the preparation of Gd5Si3Co.95 (A1-Shahery et al. 1983). The crystal structure of SclsC~9 has been determined using a single-crystal X-ray method and a powder method (Jedlicka et al. 1971) to be a pseudocubic tetragonal, a = 7.50 A and c -~ 15.00 ~, with space group P742,
c-Dzd.
In Sc15C19 the scandium atoms are arranged in an orderly way in six almost equidistant layers perpendicular to the c-axis and they form octahedral structural elements [Sc6C] with carbon atoms. In the unit cell with two formulae units of Scl 5C19 the atomic position parameters have also been determined.From fig. 7, it can be seen that the structure in Sc~5C~9 can be accordingly considered as [Sc6C ] and [8c6C2] groups in the c-axis direction:
in z ~ 0 [Sc6C]; in z ~ ~ [Sc6C] and [Sc6C2];
in z ~ ½ [Sc6C ] and [Sc6C2]; in z ~ 21 [-Sc6C];
in z ~ ~ [Sc6C ] and [Sc6C2]; in z ~ ~- [Sc6C ] and [Sc6C2].
The number of carbon atoms in the structure depends on the small metal octahedra surrounding a carbon atom. The size of a Cz pair and the size of the octahedral gap, and the distortions in the metal octahedron are obvious because in the planes perpendicular to the [001] direction the edges deviate from the ideal positions. In this
Fig. 7. Characteristic [Sc2C] and [8c6C2]
groups in Sc1~C19 (Jedlicka et al. 1971). (Re- printed by permission of the publisher, Instit/it f/Jr Anorganische Chemie, Inc.)
92 G. ADACHI et al.
way, a coordination number of seven arises at the center of the prismatic face in accordance with the large deformation of the trigonal prism.
The radius ratio rc/rso of 0.48 is the limiting value for the C2 pair to occupy the octahedron gap. As described above, the occupation of C2 pairs has led to such a large distortion of the structure element that a trigonal prismatic environment occurs.
For a compound with higher carbon content than this compound, no indication that the additional occupation of the C 2 pairs in the metal octahedra occurs was found although the octahedron at z ~ 0 exhibits a relatively large Sc-Sc distance. The shortest interatomic distances, 2.99, 3.11 and 3.18 ,~ for Sc-Sc, as well as 2.24 and 2.26 i for Sc-C, are related to the noticeable ionic portion of the bond. The C - C distance in the C2 pair, 1.25 A, is in the range of that for the dicarbides of Ca, Y and the rare earths. All the interatomic distances have been reported by Jedlicka et al.
(1971), showing that the Sc15C19 compound has relatively large values, 3.30 and 2.55 ,~, for the Sc-Sc and Sc-C distances.
Figure 8 shows the plot of the lattice parameters of the s e v e n R15C19 compounds against the metallic-covalent radii of the lanthanides, which were computed from the lattice parameters of the RC x phases at high carbon concentrations. The values of the radii are intermediate between the covalent and metallic radii of the elements, taking into account the presumed metallo-covalent bond in these carbides. There is a linear relationship between the metal size and the parameters with the exception of yttrium (Bauer and Ansel 1985).
H~ijek et al. (1984a) related the products of the hydrolysis of Sc15C19 to a carbide structure containing isolated carbon atoms and three-atom groups of the type C2-C 1.
The substructure of carbon atoms of the elementary cell of SclsC19 has been calculated from the atom position of the asymmetrical unit (Jedlicka et al. 1971). Of the 38 carbon atoms in the basic carbon substructure of the carbide, 14 are totally isolated with a minimum distance from any carbon neighbor of 3.30/~. The remaining 24 carbon atoms are arranged in groups of three, with internuclear separations of 1.25/~, 2.00 1 and 2.93 A. The following distribution of carbon atom groups along the z axis can be assigned to the elementary cell: z ~ 0, 5C1; z ~ ~, C1 and 2 ( C 2 C1);
1 '~ ~ 2
z ~ ½, C~ and2(C2-C1);z ~ 5,5C~;z ~ ~, Cx and2(C2-C1);z ~ ~, Cl and2(C2-C1).
15£
~5.~
15.z
tS.~
i r • I ' " ' f ' i ' i ' i ' I ' I
• o o
o o
j a
y
i J " i J " , I , , I , ,
.%: Lu YbTmEr HoY
a),
8 . 0
7.8
7 . 6
7."
Fig. 8. Lattice parameters of the R15C19 phases plotted against metallic-covalent radii of the rare earth elements (Bauer and Anse11985). (Reprinted by permission of the publisher, Elsevier Sequoia S.A., Inc.)
RARE EARTH CARBIDES 93 3.4. Crystal structures of the RaC and R2C compounds
The rare earth and carbon systems contain the hypocarbides, RaC (RCx, 0.25 < x < 0.65) for R = Sm through Lu, and Y and R2C for R = Sm through Lu, Sc and Y. The crystal structures of the trigonal R2C and the cubic RCx compounds have been determined. The transformation mechanism between the trigonal and cubic structures was revealed by using a single crystal in which the transient state at the phase transition was arrested (Atoji and Kikuchi 1969).
3.4.1. Crystal structure of the R3C compounds
All of the carbides R3C have the cubic C-deficient NaCl-type structure, c o m m o n l y known as the Fe4N-type. This structure is the high-temperature one and can also exist at r o o m temperature in a metastable state. In this structure, rare earth atoms are arranged in a cubic close-packed structure with C atoms distributed randomly over the octahedral sites. This phase exists over a wide solid solubility range and the reported lattice parameters have been listed in table 2.
The neutron diffraction study of Atoji (1981b) on the crystal and magnetic struc- tures of the cubic ErCo. 6 c o m p o u n d in the temperature range 1.6-296 K confirmed the previously reported results (Spedding et al. 1958, Lallement 1966). Its cubic structure is illustrated in fig. 9, in trigonal coordinates in order to compare it with the trigonal structure of RzC (Atoji and Kikuchi 1969).
Aoki and Williams (1979) pointed out that the NaC1 defect structure is stable in the approximate composition range 0.33 ~< x ~< 0.45. They inferred that in the cubic close- packed lattice built up of atoms of radius r, the octahedral holes will just contain
00 , { 7~U-T-7~Y~I I - - B q 1./.77
[ {~ I j ~ { { ~ r 3.617
T
I I%!o,.I I
i-'-- r - - - I " ~ b,,[ ~ ¢-- r --"~ ~J
Y2C YCx(CUBIO
Fig. 9. Schematic representations of the cubic and trigonal structures of yttrium hypocarbide (Atoji and Kikuchi 1969). (Reprinted by permis- sion of the publisher, The American Institute of Physics.)
94 G. ADACHI et al.
spheres of radius 0.41r, i.e., the smaller atoms will exactly fill the octahedral sites.
Carbides with the interstitial cubic close-packed lattice are actually formed when the radius ratio is between 0.41 and 0.59. By using r(C) = 0.772 ~, which corresponds to the nearest-neighbor atomic distance of diamond, values of r(C)/r(R) of 0.433-0.443 are obtained for the lanthanides, Gd-Tm, respectively; these are within the radius ratio range.
3.4.2. Crystal structure of the
RzC
compoundsAtoji and his co-workers, as well as Lallement and Bacchella and co-workers have studied YzC (Atoji and Kikuchi 1969), Tb2.1C (Atoji 1969), HozC (Atoji 1981a, Lallement 1966, Bacchella et al. 1966), TbzC and Dy2C (Atoji 1981c) by neutron powder diffraction. The anti-CdClz-type trigonal R2C structure can be described by space group D~d -- R3m and the atomic coordinates (0, 0, 0, ~-, ~-, 1 ; " 2 1 ~, ~ 2)_}_ (0 , 2 1 0, Z) for rare earth atoms and _+(0, 0, 0) for carbon atoms and three R2C formula units, as shown in fig. 9. For Y2 C (Atoji and Kikuchi 1969), the intensity analysis gave z = 0.2593(6) for Tb2C (Atoji 1981) and Tb2.1C (Atoji 1969); 0.2575(8) for Dy2C (Atoji 1981); 0.256(1) (Lallement 1966, Bacchella et al. 1966) and 0.2564(8) (Atoji 1981a) for Ho2C; 0.2587(0.2585) for Y2 C (Atoji and Kikuchi 1969). Other crystal data have also been provided by neutron reflections. In RzC , the number of C - C pairs remains negligibly small, while those for the R C pairs are larger than those in the correspond- ing cubic structure. It suggests that the bond number may be neglected for C - C pairs in both the cubic and in the trigonal structures.
3.4.3. The orientation relationship of the cubic-trigonal structural transformation Atoji and Kikuchi (1969) have given the orientation relationship of the cubic-trigonal transformation for the Y3C and YzC compounds by using a single- crystal X-ray analysis. In the cubic structure, the layer sequence along the [111] axis is the repetition of [Ac ~ Ba D Cb D ], where A, B, and C signify the Y layers and a D, b D, and c ~ represent the partly occupied carbon layers. The layer repetition unit of the trigonal structure is given by [AcB D Cb D BaC D ], where a, b and c designate the fully occupied carbon layers and [] denotes vacant layers. Therefore, the cubic-to-trigonal transformation could be accomplished by a short-range transport of the carbon atoms. Upon the ordering of the carbon atoms, the statistical high symmetry in Y3 C breaks down to considerably lower symmetries while no change takes place in the symmetry and the interatomic dimensions within the layers. In the cubic structure, the statistical point symmetry at the Y and C sites is the octahedral m3m group, while in Y2C, that of C becomes the centric 3 m group, representing a distorted octa- hedron (CY6)with C-6Y = 2.483 ___ 0.003/~, /YICIYu = 93°30'± 10' and /YIIC~Ym
= 86°30 ___ 10'; and that of Y is the highly asymmetric 3m group and the Y-C bonding configuration is a trigonal pyramid with Y at its apex. The orientation relationship between the two phases is shown clearly in fig. 9, [111]cubic I[
[-001]trlgonal,
and (111)cubic I[ (001)trigonal" When choosing the (111) plane of Y3C(cubic) and the (001) plane of Y2C(trigonal) as coherent interfaces, the minimum interface energy could be attained (Atoji and Kikuchi 1969).
RARE EARTH CARBIDES 95 The cubic-to-trigonal or disorder-to-order transformation accompanies a small unit cell volume expansion of 1.32%, apparently contrary to a commonly conceived concept. Despite this, the total bond energy in Y2 C appears to be considerably larger than that in Y3C(cubic). Here, the relative bond strength was estimated using Pauling's formula (Pauling 1960), which gave the total bond numbers of C and Y, 3.2 and 4.2 in YaC(cubic), and 4.2 and 5.3 in Y2 C, respectively (Atoji and Kikuchi 1969).
3.4.4. Bondin9 character of the hypocarbides
As has been noted, the trigonal REC structure can be composed of the stacking of the hexagonal layers along the c axis in the sequence AcB D CbA D BaC [] . . . . Thus, this structure may be viewed as the cubic closest packing of the rare earth atoms interleaved alternately by the filled and vacant carbon layers. The perpendicular distance between the adjacent rare earth layers across the carbon layer is much shorter than that across the vacant layer as indicated by the values of 2.68(2) and 3.35(2) ~ in TbzC at 4 K, 2.71(3) and 3.25(3)~ in DyzC at 4 K, 2.73 and 3.16 ,~ in HozC at 4 K, and 2.687 and 3.299/~ in Y2 C at room temperature, respectively, in contrast to the transition-metal carbide, e.g. in ~-TazC the corresponding distances are 2.505 and 2.432 ~ (Bowman et al. 1965).
The metal-metal, metal-carbon and c a r b o n - c a r b o n bond distances (in angstroms) in R2C are given in table 6. The R(I)-R(III) distance across the carbon layer is considerably shorter than the bonding distance R(I)-R(IV) across the vacant layer.
For comparison, the nearest-neighbor distances for Tb, Dy, H o and Y metal are 3.56, 3.55 (Atoji 1968), 3.486 (Atoji 1981a) and 3.556/~ (Gschneidner 1961), respectively.
These distances indicate that the carbon atom strengthens the metallic bond in R2C, also in contrast to the transition-metal carbide (Bowman et al. 1965).
The carbon atom is bonded to the rare earth atoms at a comparable distance to that in the RC 2 compounds, however, the C - C bonding in the R2C compound remains negligibly small. This suggests that the carbon atoms exist in the form of isolated atoms instead of C C pairs and that they provide a considerable number of bonding electrons to the s-d bond orbitals among the rare earth atoms so that the lattice parameter of the hypocarbides, either the cubic R3C compound or the trigonal R2C compound, decreases as the carbon content increases (Atoji 1981c).
Aoki and Williams (1979) have estimated the bonding characters of the cubic R3C and the trigonal RzC compounds from Pauling's equation (Pauling 1960). The bond
TABLE 6
Bond distance TbEC Dy2C HozC Y2C
R(I)-3R(III) across the C layer 3.381(9) 3.41(1) 3.416(15) 3.094(8) R(I)-GR(II) within the layer 3.570(3) 3.578(8) 3.550(8) 3.617(2) R(I)-3R(IV) across the vacant layer 3.94(2) 3.85(3) 3.76(3) 3.402(7)
C~SR 2.458(6) 2.470(9) 2.46(1) 2.483(3)
C-6C " " 3.550(8) 3.617
Not determined.