The tetragonal ThMnl2-type of structure corresponds to the space group I4/mmm. This structure is presented in fig. 3. The 2(a) position is oceupied by the f-electron element whereas in the 8(f), 8(i) and 8(j) positions other atoms are distfibuted. This distribution strongly depends on stoichiometry but also on the elements eonstituting the system. As far as magnetic properties are eoneerned special attention is due to the 8(i) position. The importance ofthis position was reeognized for the first time by Melamud et al. (1987) who elaimed that the 8(i) site is responsible for a "substantial" magnetie moment if oecupied by the Fe atoms, whereas iron in the 8(f) and 8(j) sites does not carry a large moment.
The cause of this behavior is that the Fe atom located in this position has the largest
!
~ 02{o)(~ 8(f)Q 80 )0 8(j 10
Fig. 3. The ThMnl2-type structure. See text for the distribution of the various kinds of atoms on the different sites.152 W. SUSKI Table 2
x-coordinates at 8(i) and 8(j) at room temperature
Compound R atom x(i) x(j) Remarks Ref.
UCr4A18 0.3444(4) 0.2816(4) identified by ND 1
UMn4AI8 0.3439(4) 0.2828(5) identified by ND 1
UFe4A18 0.34399(46) 0.28054(46) identified by XRD 2
UCu4.25A17.75 0.351(2) 0.282(3) identified by ND at 1.6 K 3 RFe10V 2 Nd 0.3634(4) 0.2722(2) identified by ND at RT 4 RFeIoV 2 Tb 0.3613(6) 0.2755(4) identified by ND at RT 4 RFeIoV 2 Dy 0.3612(8) 0.2781(4) identified by ND at RT 4 RFeIoV 2 Ho 0.3627(6) 0.2765(4) identified by ND at RT 4 RFe~0V 2 Er 0.3607(9) 0.2831(5) identified by ND at 4.2 K 4 RFe~0V 2 Y 0.3574(4) 0.2783(2) identified by ND at 4.2 K 4 References
(1) Bourée-Vigneron et al. (1990) (2) Stgpiefi-Damm et al. (1984)
(3) Krimmel et al. (1992) (4) Haije et al. 1990
number o f nearest-neighbor (nn) Fe atoms and the largest average Fe-Fe separation. This last statement concerns compounds with high Fe concentration. In the aluminides the transition elements occupy primarily the 8(f) position, whereas for compounds with larger concentration o f the transition element the latter enters primarily the 8(j) and then the 8(i) positions.
Pearson (1984) noticed that the ThMnl2 structure contains two interpenetrating kagomé nets o f M n atoms that lie in the (100) and (010) planes. The nets are not planar since atoms located in the 8(i) and 8(j) positions have x-parameters o f 0.275-0.284 (see table 2 for the uranium aluminides and the RFel0V2 compounds) instead o f 0.250 for the ideal planar case.
Such arrangement results in interatomic distances that are generally shorter, or not much longer, than the appropriate atomic-radius sums. A compression o f the atoms in the ThMnl2 structure compared with their elemental sizes is a condition that is c o m m o n in the structures o f most intermetallic phases.
Figure 4 presents the change o f the crystallographic unit cell volume for the (R, An)T4A18-type compounds for different T elements (Buschow et al. 1976, Baran et al.
1987). This change is a monotonically decreasing function o f increasing atomic number for actinides (only light ones); but for lanthanides the known lanthanide contraction has some exceptions, which is most pronouneed for cerium compounds, and is probably due to the valence o f cerium being different from 3+, as has been documented by X-ray spectroscopy experiments (Shcherba et al. 1992); table 3 lists the valence values.
The data presented in fig. 4 and table 3 are surprisingly in nice agreement. For cerium compounds the largest deviation from the 3+ valence is observed for the Fe compound which corresponds to the strongest deviation from a smooth curve for the unit cell volume,
ThMn-TYPE COMPOUNDS OF RARE EARTHS AND ACTINIDES
u ~p
153
~~0
~2o
0 >
u
ù'= /,OC Œ
3BC
(An,R)T~ Ats
I , I - I I I I r I I i H i i i i
Lo Pr Pm Eu Tb o Tm Lu
Ce Nd Sm Gd Dv Er Yb
Fig. 4. Unit cell volume for (R, An)T4AI 8 ternaries (solid line, R, Buschow et al.
1976; dashed line, An, Baran et al.
1987).
Table 3
Valence of the (Ce, Yb)T4A18 compounds a
Compound Valence
CeMn4A18 3.18(5)
CeFe4A18 3.28(5)
CeCu4Alg 3.00(5)
YbCr4A18 mixed valence(?)
YbFe4A18 3.00(5)
YbCu4AI 8 2.47(5)
" Data from Shcherba et al. (1992).
but for the Cu compound the valence is 3 and there is no anomaly in fig. 4. For the Yb compounds a similar agreement is observed. Only the Fe compound does not exhibit such a nice correspondenee because the small increase o f the unit eell volume is not related to any valence deviation. Some spaee is devoted to the valence problem here because as far as we know this review is the only report dealing with that problem in the ThMnl2-type compounds. Buschow et al. (1976) have claimed that it does not make much differenee whether one uses for R one o f the (mostly trivalent) lanthanides or (tetravalent) thorium. However, at 1.8 Ä the atomic radius o f Th is close to those o f the lanthanides and evidently, for creation o f the ThMn12-type o f structure, size eonsiderations are more important than the conduction-electron concentration or the relative difference in electronegativity between the components.
154 w. SUSKI
In the actinide aluminides a broad existence range has been reported for UFe4+xAl8_x (Baron et al. 1985, Andreev et al. 1992a), UCu4÷xA18_x (Geibel et al. 1990) and UMn4+xAls-x (Suski et al. 1995). However, information concerning the site occupation is available for eopper eompounds from neutron seattering (Krimmel et al. 1992) and for iron eompounds from 57Fe Mössbauer effeet (ME) (Vagizov et al. 1995), and in these eases the excess Cu and Fe is substituted at the 8(j) sites. AnFe4÷xA18_x eompounds additionally exhibit a defieieney in the AI sublattiee, whieh seems to be the eause of additional eomplieations in the magnetie properties of these materials; this will be diseussed below (Gal et al. 1990).
As eoncerns the rare-earth compounds, aceording to Gladyshevsky et al. (1990), the broad range of existenee was detected for the following aluminide systems: L a - Mn-A1, Ce-Cr-A1, Pr-Cu-A1, Nd-Fe-AI, Sm-Fe-A1, Eu-Mn-A1, Dy-Fe-AI, Ho--Fe- A1 and Er-Fe-A1. Recently, some other systems were reported to exhibit an existenee range: Ho-Cu-A1 (Stelmakhovich 1991), Yb-Cu-A1 (Stelmakhovich et al. 1993) and Lu-Cu-AI (Kuz'ma et al. 1992). Neutron diffraction experiment showed that in the RFesA17 compounds with R = Tb, Ho, Er and Tm the excess Fe atoms enter the 8(j) positions (Kockelmann et al. 1994). The 57Fe ME examinations show that for the RFe6AI6 compounds the 8(f) sites are oceupied by the 8 Fe atoms, the 8(j) sites by the the 8 AI atoms and the remaining Fe and A1 atoms enter the 8(i) sites statistically (Nowik and Feiner 1983).
For the gallides, according to Gladyshevsky et al. (1990) existence ranges have been observed for the Y-Fe-Ga, Pr-Fe-Ga, Pr-Cu-Ga, Nd-Fe-Ga, Sm-Fe-Ga, Sm~Cu - Ga, Tb-Fe-Ga, Dy-Fe-Ga, Dy-Co--Ga, Ho-Fe-Ga, Ho-Cu-Ga, Er-Mn-Ga, Er-Fe- Ga, Tm-Fe-Ga and Yb-Fe-Ga systems. In some systems there exist compounds with a stoiehiometry whieh is different from superstructttre CeMn4AIs, but with a limited composition elose to RTs.sGa6.5 where R = Sm, Dy, Yb and Lu. Additionally, one should notice that gallides are formed also with Co, partieularly, that with the special stoichiometry.
Figures 5-7 present the lattice parameters of the RFel0M2 compounds versus atomic number of the lanthanides or the ionic radius (fig. 5, Si: Buschow 1988a; fig. 6, Mo:
Ermolenko et al. 1990; fig. 7, Re: Gueramian et al. 1991). For comparison, the lattice parameters of the respective uranium compounds are included (Suski et al.
1989, Gueramian et al. 1991). We do not know whether the U ion eorresponds to Pr(U 4+) or to Nd(U3+), so for the sake of the argument, following the preeedent set in fig. 4, its eompounds are loeated at the position of Nd. One can see that as a rule the lattiee parameters of the uranium compounds are smaller than those of respective Nd or Pr compounds and this difference is more pronounced for a- parameters. The differenee probably results mainly from the smaller atomic radius of the uranium (1.38 Ä). The observation is general, but one cannot discuss the absolute values because they strongly depend on the details of the preparation proeess and the small differenees in stoiehiometry. The lattiee parameters presented in figs. 5-7 decrease monotonously with inereasing of the atomic number in accord with the lanthanide contraetion.
ThMn-TYPE COMPOUNDS OF RARE EARTHS AND ACTINIDES 155
0.860
o(nm
0.850
0.840
C
o RFeloSi 2
.:a %....
I I I i I I I I I
Sm
Gd
Dy Er YbNd Pm Tb Ho Tm Lu
0.480 c(nrn)
0.470
O.Z~60
Fig. 5. Lattice parameters a (lower curve, left-hand scale) and c (upper ctLrve, right-hand scale) for RFel0Si2 (Buschow 1988a). The parameters for UFe10Si 2 are indicated by crosses (Suski et al. 1989).
c [nm]~
0.485~,~~ ; : 04751 •UFeloMo2
o [nmlf
0 " 8 6 0 ~ / ~ ~ ~ . ~ . ~ ~ ~ ~ 0850~ • UFeloMo2
I | I f I I I I I I I I ! I J;r
Ce Ncl Sm Gd Dy Er Yb Y Pr Prn Eu Tb Ho Tm Lu
Fig. 6. Lattice parameters a (lower panel) and c (upper panel) for RFeloMo 2 com- pounds (Ermolenko et al. 1990). The results for UFe~0Mo 2 were obtained by Suski et al. (1989).
The decrease of the a-parameters is stronger than that of the c-parameters, except for the Ce compounds, most probably resulting from the valence state of this element being different from 3. However, this is not generally true beeause J. Hu et al. (1988) reported for the RFel0.9Til. 1 series a pronouneed minimum for the compound of Ho and strong increase for the Er compound. The authors do not propose any explanation of this anomaly.
The stoichiometry of the eompounds with a high concentration of the 3d transition element does not necessary correspond to the RM10M~ formula and a deviation is
156 W. SUSKI
[nm]
0.860
085 c.
0.850
«845
0.476~
o.~%t
i
B __ .. . . _C_.~..._._.
I'Oc/epr' I pml E'u i -'rbly' Er '~L'-u Nd Sm Gd DyHoTm Lu ---ionic rodius (r ~3)
Fig. 7. Lattice parameters a (upper curve) and c (lower curve) for RFeloRe2 com- pounds; the diamonds indicate the pa- rameters for UFe]oRe2 (Gueramian et al.
1991).
observed when M --- Fe and M' = Ti (J. Hu et al. 1988), Mo and W (Busehow 1988a,b), V (Verhoef et al. 1988) and Re (Jurezyk 1990a); and for M = Co and M' = Ti (Solzi et al. 1988). It eould be that the stoiehiometry of these materials results from the broad existenee range whieh was reported for many Y systems: Y-Fe-Ti (B.-E Hu et al. 1989a), Y-Fe-V (Verhoef et al. 1988), Y-Fe--Cr (Busehow 1988a), Y-Fe-Mo and Y-Co--Mo (Gladyshevsky et al. 1990), and by Gladyshevsky et al. (1990) for numerous lanthanide systems: Ce-Fe-Mn, Ce-Co-Mn, Ce-Fe--Re, Ce-Mn-Ni, Pr-Co-Mn, Pr-Mn-Ni, N d - Co-Mn, Nd-Mn-Ni, Sm-Co-Mn, Sm-Mn-Ni, Dy--Co-Re and R-Fe-Mo systems where R = Gd-Lu but not Yb alloys. Also the extended existenee range has been reported by Andreev et al. (1991) for UFelz-xSix where 1.3 ~< x ~< 3.
As mentioned above for the (R, An)Mx2_xM~-type eompounds, the R atom enters in prineiple into the 2(a) sites, and the other three sites are available for the M and M' atoms.
The Fe, Co and Ni atoms, beeause of their large number in unit eell, oceupy all types of sites, but there are strong preferenees for the oeeupation of the remaining free sites.
Aeeording to many authors the Mo, Ti, V and Cr atoms demonstrate the preferenee to enter the 8(i) sites, suggesting that the size effeet does not substantially eontribute in the formation of these eompounds (de Mooij and Busehow 1988, Helmholdt et al. 1988a).
The real meehanism for the distribution of the individual atoms is diffieult to understand in terms of the formation enthalpies of R(Fe, M)12 alone. An estimate of the relative enthalpies assoeiated with the formation of a bond between the pairs of atoms involved ean be obtained from the solution enthalpies. It follows from these data that, exeept for Si, the formation of the R - M bond is not advantageously energetie and therefore, the
ThMn-TYPE COMPOUNDS OF RARE EARTHS AND ACT1NIDES 157 M atoms enter the sites which have a minimal contact with the R-sublattice 2(a) sites (Zarechnyuk and Kripyakevieh 1963). This is confirmed by the occupation of the 8(f) and 8(j) and not 8(i) positions by the Si atoms in GdFel0Si2 (Dirken et al. 1989), in SmFel0Si2 (Buschow 1988a) and in UFel0Si2 (Berlureau et al. 1991); Si enters the 8(f) sites in UCol0Si2 (Berlureau et al. 1991) and the 8(j) sites in UNia0Si2 (Suski et al. 1993a).
Finally, in YNil0Si2 (Moze et al. 1991) the Si atoms preferentially oceupy the 8(f) sites, with some small occupancy also for both the 8(i) and 8(j) positions. However, in SmFellTi the Ti atoms enter both the 8(i) and 8(j) sites (Ohashi et al. 1988b).
The statement about the rare-earth atoms exclusively occupying the 2(a) position is not true exactly: Bodak and coworkers reported some admixture of the lanthanide atom in other positions in the following systems: Ce-Co-Mn (Bodak et al. 1981), alloys of Fe and W with Ce, Pr, Nd and Sm (Bodak and Berezyuk 1983), alloys of Fe and Mo with the same lanthanides (Bodak and Berezyuk 1985), and the Dy-Fe-Re system (Sokolovskaya et al. 1985). Moreover, the Ce-Fe-Mo phase exists over a broad composition range of Fe and Mo, and the fraction of Ce entering other than 2(a) positions amounts to 0.025 (Bodak and Berezyuk 1985). This fraction is typical for other lanthanides and does not reach a value higher than 0.05. Unfortunately, the location of these excess lanthanide atoms has not been determined.
From the above discussion one ean see that the ThMn12-type strueture is complex, and it is impossible to formulare any clear-cut general rules of formation for the respective compounds. For the sake of simplieity pseudoternaries are omitted in the above considerations; some attention to their structure will be devoted in the description of their magnetic properties, for which the location of the individual components is of paramount importance.