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Electronegativity and crystal field splittings in rare earth compounds
• Solid State Communications,
Vol. 13, pp. 215—220, 1973.
Pergamon Press.
Printed in Great Britain
ELECTRONEGATIVITY AND CRYSTAL FIELD SPLITTINGS IN RARE EARTh COMPOUNDS E. Bucher and J.P. Malta Bell Laboratories, Murray Hill, New Jersey 07974, U.S.A. (Received 6 April 1973 by J.L. Olsen)
Crystal field studies in a variety of 4f-and some Sfelectron-systems reveal a correlation between crystal field splittings, i.e. sign and charge strength of simple ligands and their electronegativities. Deviations occur in several very dilute f.c.c. noble metals, as well as noble metal compounds presumably due to the d-electron contribution and perhaps ill-defined valence states, in particular in transition metal compounds.
INTRODUCTION THERE is at present considerable confusion about crystal field splittings in rare earth intermetallic compounds, mainly arising from the fact, that ligand charges in various ligands can exhibit both signs and appreciable variation in charge strength. Furthermore, quite contrary to what was expected from the frequent breakdown of the pointcharge model in insulators, this model appeared to work remarkably well in a whole group of metallic Compounds,1’2 and also contrary to expectation, conduction electrons do not seem to matter very much in cases studied thus far.
field splittings were measured by inelastic neutron scattering”2 and by analysis of the Schottky specific heat anomaly.The former method of course is much superior for larger overall splittings (say 100°K)as the conversion of C~to C~and lattice and electronic corrections (usually by subtracting the specific heat of a corresponding La or Lu compound) introduce considerable error bars at higher temperatures (say 30°K), therefore strongly limiting the accuracy by which crystal field potential terms can be determined. Nevertheless, we have been able to reach qualitative conclusions and unambiguous determination at least of the charge sign in a number of cases. In order to simplify our conclusions, we shall restrict ourselves mostly to discussions of a 3H 4 system in cubic point 2F symmetry. [Wediscard here thepoint simpler case of for512 3~)or 6115,2 (Sm3~)in cubic symmetry (Ce various reasons] Preliminary results have been discussed on two recent meetings.4’5
The purpose of the present paper is to unravel empirical rules concerning crystal field (CF) splittings in rare earth compounds, (mostly metallic) in the hope to make at least qualitative (or perhaps quantitative) prediction atomistic of the individual ligands. Thefrom empirical rulesparameters which we will develop on the basis of results of various simple structure groups are intuitively very transparent, but we will not attempt a theoretical analysis.
.~
3 RESULTS 3. 1. PrX (~ NaCI)
2. METHOD OF ANALYSIS The crystal field splitting of a ground state multiplet 28~1L~ (assuming L 4 0) is used to probe the sign and charge strength of the ligands. Crystal
PrX represents the most thoroughly studied group of compounds with respect to crystal field properties. It has been shown that these compounds follow very closely the effective point charge approximation and 215
•2l6
CRYSTAL FIELD SPLITTINGS IN RARE EARTH COMPOUNDS
we will discuss all our results within this model. It will serve to outline ideas which we wifi try to extend further to the whole field of intermetallic compounds. The 4th order crystal field potential for this structure type (due to the 1st neighbors) is given by:
A
4)
=
7 Ze2
j~
~-~-
(r4)
(1)
4 (r Ze is the effective ligand charge,R the hgand distance. (R = a/2 a = lattice constant.) Contributions to A 4 from higher order unscreened neighbors would amount to +7 per cent. This contribution balanced we by 4).6 isTherefore, recently recomputed values only, of (r but use (r4) values will consider first neighbors of Freeman and Watson.7 In Fig. 1 we plotA 4> vs 4 (r 5 for all 8 NaCl phases of Pr. Theoretical curves 1/a integral values ofZ from —ito —4 are also shown for for this structure type. It is interesting to note that S, Se, Te and N carry charges of —2 and —3 according to their position in the periodic table. Surprisingly the
magnitude higher than monopnictides.8 The agreement between point charge and valence state suggests an interpretation from a purely atomistic point of view. Intuitively Z must be related to the ligands power of attracting electron charge. Pauling9 has introduced the fruitful concept of electronegativity as a measure of it. For furthering our discussion we will use values tabulated by Gordy and Thomas.1°In Fig. 2 we replot A 4> as a function of the ligand electronegativity e. 4 (r splits the pnictide group from the chalcogenides This
P~’X(~NOCt)
N /1 0,
30
zo
.
ec
A~
/
PrX(~NoCI)
1A
I
3~
10
eiL-1*
/
40.
/ I’ ~3o. 20
Vol. 13, No. 2
N,”
Z.—3
z.—a
.
0
1
2I ELECIRONEGATIVITY OF X
3I
4) vs FIG. 2.4th order of crystal field (r type electronegativity ligands forpotentialsA4 all PrX rocksalt structures.
p
10
.
hs
a—’xIo4 ~ FIG. 1.4th order crystal field potentialsA 4 vs inverse of 5th power of lattice constants for 4 all
leading to a roughly linear relationship between A 4) and e. In this representation it becomes immediately 4 (r clear why P, As, Sb and Bi behave ‘anomalously’. The electronegativity weakens considerably in going from group VIB elements to neighboring group VB elements and is no longer strong enough to attract all 3 electrons of Pr3” except for N which has a much larger e value. The gradually decreasing electronegativity from N to Bi also explains why Z drops from N to Bi. An interesting implication is that probably all Ln34N are expected to be intrinsic semiconductors whereas all other monopnictides are most likely to be intrinsically metals (or semimetals). The following facts may amplify this point: LaN was found to have zero electronic specific heat~~ and LaN and PrN
Vol. 13, No. 2
CRYSTAL FIELD SPLITTINGS IN RARE EARTH COMPOUNDS
exhibit the same black lustre as divalent rare-earth monosulfides and monoselenides, exhibiting a charge compensated unit cell. All other monpnictides are bright silvery in aspect. Recent measurements in rareearth monopnictides (phosphides—bismuthides) show indeed metallic characteristics with resistivities of 1—50 ~2 cm at 4.2°Kand a small linear specific heat term at low temperatures.’2
217
~ LO,~
‘4~
_____
-‘IO.s ~oa
— ~11
WI
Wi.
Wi—.—
otis
o.~os.
One may raise the question here about the general validity of our relationship between pointcharge and
\~4
z~
~
-Ifr
electronegativity within the totality of rare earth compounds. We have studied4’5 a number of other compounds with the rare earth in cubic point symmetry such as: Cu 3Au, CsCI, MgCu2, BiF3, NaZn13, CaF2, CaB6 phases as well as dilute alloys. A series of new features are encountered which we will discuss in more detail for the case of Cu3Au phases.
(r’)~—I.—
3.2.Cu3Au phases
____
~
LI~-TT~
1.0-
_~,.,,
os _•..~.
Wi. —
o~i~ o~,,s
~m~so ~4
The results of these4PrX3 wheretype X =compounds Pd, Sn, Pb,have 11, In. recently been discussed, The former 3 ligands exhibit a weakly negative charge,
~
‘s
Z~I ‘ZI
OS
~ -0.4~
x 4-o.?s7s--1
whereas In and TI must be assumed to be positive to obtain a singlet ground state I”~.Our conclusions are drawn from diagrams as shown in Fig. 3. As electronegativity of the first neighbors weakens, and consequently the negligible. point charge order neighbors are no longer Wealso, havehigher included contributions from second neighbors Z2 (usually rare earth ions, assuming Z2 >0) and plotted crystal field ground states and the x parameter of the Lea—Leask—Wolf modeP’~as a function of Z1 /Z2, the ratio of first to second neighbor ligand charge. Combining specific heat and susceptibility measurements one can in most cases find approximate numbers of x and therefore determine the sign of Z1. Results and conclusions shown in Table 1 have generally been drawn from diagrams as shown typically for Cu3 Au phases in Fig. 3. Recent studies 4~ onis U~X3 with3~) Cu3 Au also incompounds, a 3H structureessentially (where U the same results4 (in state as Pr revealed spite of a noticeable electronegativity difference between Pr3~ and U4~)X = Si, Ge, Sn, Pb fit the negative ligand charge model, whereas Ga and most likely In and Ti are positive.14 Inelastic neutron scattering on TmA1 15 3 also show that this group IIIB element carries a positive charge as in many other Al compounds, and dilute alloys.’6 It is interesting to relate these findings to
-in’
________________________________________ FIG. 3. Crystal field ground x parameter 3 vs.states pointand charge ratios of of Lea—Leask—Woif model’ first and second neighbors for Cu 3 Au type structure of Pr and Tm. (Z2 > 0 assumed.) (x measures the ratio of 4th to 6th order crystal field potentials.)
Fig. 2. An extrapolation of the chalcogenide and pnictide straight line leads to critical values ~ of 1.3 and 1.5 for a change in ligand charge sign respectively. In spite of structural differences one may extrapolate further a value of ~ 1.7 for groups IB—IVB where electronegativity differences are no longer as pronounced as in group VIB and VB. as a matter of fact, all elements IVB the negative sign and values of of e =group 1.8 (in theexhibit tetravalent state) whereas group IIIB elements have lower values (“—1.5) and in contrast show a positive sign. 33. Other compounds Other structure types involving new ligands (e.g. Be, Mg, Cd, H) essentially confirm our results stated in 3.2. Ligands with low electronegativities in general
218
CRYSTAL FIELD SPLITTINGS IN RARE EARTH COMPOUNDS
Vol. 13, No. 2
Table 1. Crystal field ground states,and point charges and electronegativities of a number ofPr3”’ and U4~compounds alloys in various cubic point symmetries Comp, PrX Pr(met) Th : Pr La:Pr PrPb 3 PrSn3 PrIn3 PrTl3 PrPd3 PrMg3 PrCd3 PrH2 PrB6 PrBe13 PrNi2 PrA12 PrMg2 PrPt2 PrRh2 PrAg(,4) USi3(14) UGe3(4) USn3() tJPb3() UGa3(4) Uln3(,4) UTI3
Struct.
Crystal field ground state
Z,
NaCI f.c.c. f.c.c. f.c.c.
r,
—1.7—3.0 + +
[‘,
+
Cu3Au Cu3Au Cu3Au Cu3Au Cu3Au BiF3 BiF3 CaF2 CaB6 NaZn,3 MgCu2 MgCu2 MgCu2 MgCu2 MgCu2 CsCl Cu3Au Cu3Au Cu3Au Cu3Au Cu3Au Cu3Au Cu3 Au
[‘3
—
[‘5
—
I’~
+ +
~ 0
[‘5
r3
+ + —(20)
[‘3
1’5 l”~ F,
—
+
e 1.8—3.0 1.1 1.0 1.1 l.8(Pb1V)
l.8(SnIV) 1.5 1.5 (Tl’) 2.0 1.2 1.5 2.15 2.0
F~ F~ F~
+ + + + 0
[‘3
—
1.5 1.8 1.5 1.2 2.1 2.1 1.8 1.8
[‘3
—
1.8
[‘3
—
1.8 (SnW)
[‘3 ([‘5?)
—
1.8 (PbIV)
~0
[‘~
F~ [‘5
+
F~(?) l”~(?)
exhibit positive ligand charges, high electronegativities negative ones (see Table 1). Complications do occur in the case of transition metal ligands, related probably to the possibility of a variety of valencies which in turn involve different electronegativities. Deviations also appear to occur in some very dilute f.c.c. noble metal systems (Rh, Ir, 17 Ag,probably Au), as recently related toobserved the not by EPR measurements well understood d.electron contribution to the crystal field. In contrast recent investigations of Pd: ~ follow our empirical rule.18 Our present study and knowledge of rare earth compounds therefore leads to conclusions as summarized in part 4.
4. GENERAL CONCLUSIONS 4.1. Simple ligands with weak electronegativities in general fit the positive ligand charge model, whereas
(+) (+)
1.5 1.5 1.5 (TI’)
ligands with large electronegativities fit the negative ligand charge model. For the proper intermetallic compounds, a sign change occurs at e 1 .7, roughly independent of structural details (see Table I). This rule may be useful in predicting crystal field ground states in simple cases. 4.2. In ligands with weak electronegativities, second (mostly rare earth) neighbors become important, which leads to ambiguous conclusions about the sign of the ligand charge, in particular, if the crystal field ground state only is known. (see Fig. 3 as example, where l’~is possible for Z 1/Z2~<0.) 4.3. In weak crystal field splittings due to weak electronegativities and/or the influence of more distant higher neighbors, exchange forces become increasingly important, leading to strong crystal field .
.
Vol. 13, No.2
CRYSTAL FIELD SPUTTINGS IN RARE EARTH COMPOUNDS
dispersion often inhibiting crystal field analysis. l’his applies in particular to CsC1- and MgCu2-type compounds of Pr and Tm in which attempts failed to determine crystal field levels, 4.4. The effective point charge model in many compounds is often violated by 6th order crystal field potentials exceeding expected values. (see e.g. Fig. 3 where the [‘3 ground state in PrPb 3 is not allowed in the effective point charge approximation). The case of the NaCl phases of Pr must be considered as exceptional. 4.5. The rule stated in 4.1. is often obscured by ligands exhibiting several valence states, and therefore different electronegativities in particular as far as transition metals are concerned. For this reason, our relationship between ligand charge and electronegativity cannot readily be checked for transition
219
metal compounds, which otherwise would be interesting from the point of view of d-electron-contributions to crystal fields. On the other hand, recent in Rh, 17’19 studies (Ag, Au, some very to dilute f.c.c. metalsdue to the not well Ir) appear violate 4.1noble probably understood d-electron contribution,19 leading to opposite signs in the 4th and 6th order crystal field potential terms. 4.6. Experimental and theoretical studies in particular band structure calculations including charge distribution around ligands would be most valuable in providing some theoretical background to our empirical results. Acknowledgements We would like to thank C. Herring and J.C. Phillips for constructive comments on this work, and H.L. Davis and H.A. Mook for making available a number of crystal field results. —
REFERENCES 1.
TURBERFIELD K.C., PASSELL L., BIRGENEAU R.J., and BUCHER E.,J. appl. Phys. 42, 1746 (1971).
2.
DAVIS H.L. and MOOK H.A., Proc. 18th Annual Conf on Magnetism and Magnetic Materials, Denver (1972). 3~,the closeness of the Fermi-and the 4f.level leads in most cases to anomalous behavior. Sm3”’ on the In Ce hand is unfavorable for inelastic neutron scattering due to its high neutron capture cross section (except other ‘47Sm). In addition, a single r’ 7—r8 transition leads to inconclusive results if higher neighbors must be taken into account.
3.
4.
BUCHER E., ANDRES K., GOSSARD A.C. and MAlTA J.P.,Proc. 13th mt. Nati. Low Temp Conf, Boulder, August 2 1—26, to be published (1972).
5.
BUCHER E. and MAlTA J.P., 10th Rare Earth Research Conf., Carefree (Az), April 30—May 3 (1973).
6.
WAKIM F.G., SYNEK M., GROSSGUT P. and DA MOMMIO A.,Phys. Rev. A5, 1121(1972).
7.
FREEMAN A.J. and WATSON R.E., Phys. Rev. 127, 2058 (1962).
8.
BUCHER E., GOSSARD A.C., ANDRES K., MAlTA J.P. and COOPER A.S., Proc. 8th Rare Earth Research Conf 1970, Vol. 1, p. 74, U.S. GPO, Washington, D.C. (1970).
9.
PAULING L.,J. Am. Chem. Soc. 54, 3570 (1932) and PAULING L., The Nature ofthe Chemical Bond, p.64, Cornell University Press, Ithaca, New York (1960).
10.
GORDY W. and THOMAS WJ.O., J. Chem. Phys. 24,439(1956).
11.
STUTIUS W., Phys. Kondens Mat. 10, 152 (1969).
12. 13.
DISALVO F.J., ANDRES K., BUCHER E. and MAlTA J.P., unpublished. LEA K.R., LEASK M.J.M. and WOLF W.P.,J. Phys. Chem. Solids 23, 1381 (1962).
14.
MULAIU. and MISHJK A., BulL Acad. Polon. Sci. 19, 207 (1971); MISIUK A., MULAK J. and CZOPNIK A., ibid. 20,459 and 891 (1972).
15. 16.
DAVIS H.L., MOOK H.A. and BUCHER E., unpublished. RETTORI C., DAVIDOV D., ORBACH R. and CHOCK E.P.,Phys. Rev. 7, 1(1973).
220 17. 18.
CRYSTAL FIELD SPLITTINGS IN RARE EARTH COMPOUNDS
Vol. 13, No. 2
DAVIDOV D., ORBACH R., RETTORI C., TAO L.J. and CHOCK E.P.,Phys. Rev. Lett. 28,490(1972) and Phys. Lett. 34A, 379 (1971); DAVIDOV D., ORBACH R., RETTORI C., SHALTIEL D., TAO L.J. and RICKS B.,Solid State Commun. 10,451 (1972). DEVINE R.A., MORET J.M., ORTELLI J., SHALTIELD., ZINGG W. and PETER M.,Solid State Commun. 10, 575 (1972); PRADDAUDE H.C.,Phys. Lett. 42A, 97 (1972).
19.
WILLIAMS G. and HIRST L.L.,Phys. Rev. 185, 407 (1969).
20.
A similar conclusion was reached by BIEGANSKI Z.,J. Chem. Thermodynamics 5, 1(1973).
Kristallfeldstudien in einer Anzahl von Verbindungen mit 4f.und Sf. Elementen zeigen eine Korrelation zwischen Kristallfeldaufspaltung und Elektronegativitàt einfacher Liganden. Letztere zeigen i.A. positive Ladung für schwache und negative Ladung für starke Elektronegativitat. Im Falle von Edelmetalisystemen zeigen sich Abweichungen vermutlich infolge des d-Elektronenbeitrages und moglicherweise zufolge schlecht definiertem Valenzzustand.
Vol. 13, pp. 215—220, 1973.
Pergamon Press.
Printed in Great Britain
ELECTRONEGATIVITY AND CRYSTAL FIELD SPLITTINGS IN RARE EARTh COMPOUNDS E. Bucher and J.P. Malta Bell Laboratories, Murray Hill, New Jersey 07974, U.S.A. (Received 6 April 1973 by J.L. Olsen)
Crystal field studies in a variety of 4f-and some Sfelectron-systems reveal a correlation between crystal field splittings, i.e. sign and charge strength of simple ligands and their electronegativities. Deviations occur in several very dilute f.c.c. noble metals, as well as noble metal compounds presumably due to the d-electron contribution and perhaps ill-defined valence states, in particular in transition metal compounds.
INTRODUCTION THERE is at present considerable confusion about crystal field splittings in rare earth intermetallic compounds, mainly arising from the fact, that ligand charges in various ligands can exhibit both signs and appreciable variation in charge strength. Furthermore, quite contrary to what was expected from the frequent breakdown of the pointcharge model in insulators, this model appeared to work remarkably well in a whole group of metallic Compounds,1’2 and also contrary to expectation, conduction electrons do not seem to matter very much in cases studied thus far.
field splittings were measured by inelastic neutron scattering”2 and by analysis of the Schottky specific heat anomaly.The former method of course is much superior for larger overall splittings (say 100°K)as the conversion of C~to C~and lattice and electronic corrections (usually by subtracting the specific heat of a corresponding La or Lu compound) introduce considerable error bars at higher temperatures (say 30°K), therefore strongly limiting the accuracy by which crystal field potential terms can be determined. Nevertheless, we have been able to reach qualitative conclusions and unambiguous determination at least of the charge sign in a number of cases. In order to simplify our conclusions, we shall restrict ourselves mostly to discussions of a 3H 4 system in cubic point 2F symmetry. [Wediscard here thepoint simpler case of for512 3~)or 6115,2 (Sm3~)in cubic symmetry (Ce various reasons] Preliminary results have been discussed on two recent meetings.4’5
The purpose of the present paper is to unravel empirical rules concerning crystal field (CF) splittings in rare earth compounds, (mostly metallic) in the hope to make at least qualitative (or perhaps quantitative) prediction atomistic of the individual ligands. Thefrom empirical rulesparameters which we will develop on the basis of results of various simple structure groups are intuitively very transparent, but we will not attempt a theoretical analysis.
.~
3 RESULTS 3. 1. PrX (~ NaCI)
2. METHOD OF ANALYSIS The crystal field splitting of a ground state multiplet 28~1L~ (assuming L 4 0) is used to probe the sign and charge strength of the ligands. Crystal
PrX represents the most thoroughly studied group of compounds with respect to crystal field properties. It has been shown that these compounds follow very closely the effective point charge approximation and 215
•2l6
CRYSTAL FIELD SPLITTINGS IN RARE EARTH COMPOUNDS
we will discuss all our results within this model. It will serve to outline ideas which we wifi try to extend further to the whole field of intermetallic compounds. The 4th order crystal field potential for this structure type (due to the 1st neighbors) is given by:
A
4)
=
7 Ze2
j~
~-~-
(r4)
(1)
4 (r Ze is the effective ligand charge,R the hgand distance. (R = a/2 a = lattice constant.) Contributions to A 4 from higher order unscreened neighbors would amount to +7 per cent. This contribution balanced we by 4).6 isTherefore, recently recomputed values only, of (r but use (r4) values will consider first neighbors of Freeman and Watson.7 In Fig. 1 we plotA 4> vs 4 (r 5 for all 8 NaCl phases of Pr. Theoretical curves 1/a integral values ofZ from —ito —4 are also shown for for this structure type. It is interesting to note that S, Se, Te and N carry charges of —2 and —3 according to their position in the periodic table. Surprisingly the
magnitude higher than monopnictides.8 The agreement between point charge and valence state suggests an interpretation from a purely atomistic point of view. Intuitively Z must be related to the ligands power of attracting electron charge. Pauling9 has introduced the fruitful concept of electronegativity as a measure of it. For furthering our discussion we will use values tabulated by Gordy and Thomas.1°In Fig. 2 we replot A 4> as a function of the ligand electronegativity e. 4 (r splits the pnictide group from the chalcogenides This
P~’X(~NOCt)
N /1 0,
30
zo
.
ec
A~
/
PrX(~NoCI)
1A
I
3~
10
eiL-1*
/
40.
/ I’ ~3o. 20
Vol. 13, No. 2
N,”
Z.—3
z.—a
.
0
1
2I ELECIRONEGATIVITY OF X
3I
4) vs FIG. 2.4th order of crystal field (r type electronegativity ligands forpotentialsA4 all PrX rocksalt structures.
p
10
.
hs
a—’xIo4 ~ FIG. 1.4th order crystal field potentialsA 4 vs inverse of 5th power of lattice constants for 4 all
leading to a roughly linear relationship between A 4) and e. In this representation it becomes immediately 4 (r clear why P, As, Sb and Bi behave ‘anomalously’. The electronegativity weakens considerably in going from group VIB elements to neighboring group VB elements and is no longer strong enough to attract all 3 electrons of Pr3” except for N which has a much larger e value. The gradually decreasing electronegativity from N to Bi also explains why Z drops from N to Bi. An interesting implication is that probably all Ln34N are expected to be intrinsic semiconductors whereas all other monopnictides are most likely to be intrinsically metals (or semimetals). The following facts may amplify this point: LaN was found to have zero electronic specific heat~~ and LaN and PrN
Vol. 13, No. 2
CRYSTAL FIELD SPLITTINGS IN RARE EARTH COMPOUNDS
exhibit the same black lustre as divalent rare-earth monosulfides and monoselenides, exhibiting a charge compensated unit cell. All other monpnictides are bright silvery in aspect. Recent measurements in rareearth monopnictides (phosphides—bismuthides) show indeed metallic characteristics with resistivities of 1—50 ~2 cm at 4.2°Kand a small linear specific heat term at low temperatures.’2
217
~ LO,~
‘4~
_____
-‘IO.s ~oa
— ~11
WI
Wi.
Wi—.—
otis
o.~os.
One may raise the question here about the general validity of our relationship between pointcharge and
\~4
z~
~
-Ifr
electronegativity within the totality of rare earth compounds. We have studied4’5 a number of other compounds with the rare earth in cubic point symmetry such as: Cu 3Au, CsCI, MgCu2, BiF3, NaZn13, CaF2, CaB6 phases as well as dilute alloys. A series of new features are encountered which we will discuss in more detail for the case of Cu3Au phases.
(r’)~—I.—
3.2.Cu3Au phases
____
~
LI~-TT~
1.0-
_~,.,,
os _•..~.
Wi. —
o~i~ o~,,s
~m~so ~4
The results of these4PrX3 wheretype X =compounds Pd, Sn, Pb,have 11, In. recently been discussed, The former 3 ligands exhibit a weakly negative charge,
~
‘s
Z~I ‘ZI
OS
~ -0.4~
x 4-o.?s7s--1
whereas In and TI must be assumed to be positive to obtain a singlet ground state I”~.Our conclusions are drawn from diagrams as shown in Fig. 3. As electronegativity of the first neighbors weakens, and consequently the negligible. point charge order neighbors are no longer Wealso, havehigher included contributions from second neighbors Z2 (usually rare earth ions, assuming Z2 >0) and plotted crystal field ground states and the x parameter of the Lea—Leask—Wolf modeP’~as a function of Z1 /Z2, the ratio of first to second neighbor ligand charge. Combining specific heat and susceptibility measurements one can in most cases find approximate numbers of x and therefore determine the sign of Z1. Results and conclusions shown in Table 1 have generally been drawn from diagrams as shown typically for Cu3 Au phases in Fig. 3. Recent studies 4~ onis U~X3 with3~) Cu3 Au also incompounds, a 3H structureessentially (where U the same results4 (in state as Pr revealed spite of a noticeable electronegativity difference between Pr3~ and U4~)X = Si, Ge, Sn, Pb fit the negative ligand charge model, whereas Ga and most likely In and Ti are positive.14 Inelastic neutron scattering on TmA1 15 3 also show that this group IIIB element carries a positive charge as in many other Al compounds, and dilute alloys.’6 It is interesting to relate these findings to
-in’
________________________________________ FIG. 3. Crystal field ground x parameter 3 vs.states pointand charge ratios of of Lea—Leask—Woif model’ first and second neighbors for Cu 3 Au type structure of Pr and Tm. (Z2 > 0 assumed.) (x measures the ratio of 4th to 6th order crystal field potentials.)
Fig. 2. An extrapolation of the chalcogenide and pnictide straight line leads to critical values ~ of 1.3 and 1.5 for a change in ligand charge sign respectively. In spite of structural differences one may extrapolate further a value of ~ 1.7 for groups IB—IVB where electronegativity differences are no longer as pronounced as in group VIB and VB. as a matter of fact, all elements IVB the negative sign and values of of e =group 1.8 (in theexhibit tetravalent state) whereas group IIIB elements have lower values (“—1.5) and in contrast show a positive sign. 33. Other compounds Other structure types involving new ligands (e.g. Be, Mg, Cd, H) essentially confirm our results stated in 3.2. Ligands with low electronegativities in general
218
CRYSTAL FIELD SPLITTINGS IN RARE EARTH COMPOUNDS
Vol. 13, No. 2
Table 1. Crystal field ground states,and point charges and electronegativities of a number ofPr3”’ and U4~compounds alloys in various cubic point symmetries Comp, PrX Pr(met) Th : Pr La:Pr PrPb 3 PrSn3 PrIn3 PrTl3 PrPd3 PrMg3 PrCd3 PrH2 PrB6 PrBe13 PrNi2 PrA12 PrMg2 PrPt2 PrRh2 PrAg(,4) USi3(14) UGe3(4) USn3() tJPb3() UGa3(4) Uln3(,4) UTI3
Struct.
Crystal field ground state
Z,
NaCI f.c.c. f.c.c. f.c.c.
r,
—1.7—3.0 + +
[‘,
+
Cu3Au Cu3Au Cu3Au Cu3Au Cu3Au BiF3 BiF3 CaF2 CaB6 NaZn,3 MgCu2 MgCu2 MgCu2 MgCu2 MgCu2 CsCl Cu3Au Cu3Au Cu3Au Cu3Au Cu3Au Cu3Au Cu3 Au
[‘3
—
[‘5
—
I’~
+ +
~ 0
[‘5
r3
+ + —(20)
[‘3
1’5 l”~ F,
—
+
e 1.8—3.0 1.1 1.0 1.1 l.8(Pb1V)
l.8(SnIV) 1.5 1.5 (Tl’) 2.0 1.2 1.5 2.15 2.0
F~ F~ F~
+ + + + 0
[‘3
—
1.5 1.8 1.5 1.2 2.1 2.1 1.8 1.8
[‘3
—
1.8
[‘3
—
1.8 (SnW)
[‘3 ([‘5?)
—
1.8 (PbIV)
~0
[‘~
F~ [‘5
+
F~(?) l”~(?)
exhibit positive ligand charges, high electronegativities negative ones (see Table 1). Complications do occur in the case of transition metal ligands, related probably to the possibility of a variety of valencies which in turn involve different electronegativities. Deviations also appear to occur in some very dilute f.c.c. noble metal systems (Rh, Ir, 17 Ag,probably Au), as recently related toobserved the not by EPR measurements well understood d.electron contribution to the crystal field. In contrast recent investigations of Pd: ~ follow our empirical rule.18 Our present study and knowledge of rare earth compounds therefore leads to conclusions as summarized in part 4.
4. GENERAL CONCLUSIONS 4.1. Simple ligands with weak electronegativities in general fit the positive ligand charge model, whereas
(+) (+)
1.5 1.5 1.5 (TI’)
ligands with large electronegativities fit the negative ligand charge model. For the proper intermetallic compounds, a sign change occurs at e 1 .7, roughly independent of structural details (see Table I). This rule may be useful in predicting crystal field ground states in simple cases. 4.2. In ligands with weak electronegativities, second (mostly rare earth) neighbors become important, which leads to ambiguous conclusions about the sign of the ligand charge, in particular, if the crystal field ground state only is known. (see Fig. 3 as example, where l’~is possible for Z 1/Z2~<0.) 4.3. In weak crystal field splittings due to weak electronegativities and/or the influence of more distant higher neighbors, exchange forces become increasingly important, leading to strong crystal field .
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CRYSTAL FIELD SPUTTINGS IN RARE EARTH COMPOUNDS
dispersion often inhibiting crystal field analysis. l’his applies in particular to CsC1- and MgCu2-type compounds of Pr and Tm in which attempts failed to determine crystal field levels, 4.4. The effective point charge model in many compounds is often violated by 6th order crystal field potentials exceeding expected values. (see e.g. Fig. 3 where the [‘3 ground state in PrPb 3 is not allowed in the effective point charge approximation). The case of the NaCl phases of Pr must be considered as exceptional. 4.5. The rule stated in 4.1. is often obscured by ligands exhibiting several valence states, and therefore different electronegativities in particular as far as transition metals are concerned. For this reason, our relationship between ligand charge and electronegativity cannot readily be checked for transition
219
metal compounds, which otherwise would be interesting from the point of view of d-electron-contributions to crystal fields. On the other hand, recent in Rh, 17’19 studies (Ag, Au, some very to dilute f.c.c. metalsdue to the not well Ir) appear violate 4.1noble probably understood d-electron contribution,19 leading to opposite signs in the 4th and 6th order crystal field potential terms. 4.6. Experimental and theoretical studies in particular band structure calculations including charge distribution around ligands would be most valuable in providing some theoretical background to our empirical results. Acknowledgements We would like to thank C. Herring and J.C. Phillips for constructive comments on this work, and H.L. Davis and H.A. Mook for making available a number of crystal field results. —
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TURBERFIELD K.C., PASSELL L., BIRGENEAU R.J., and BUCHER E.,J. appl. Phys. 42, 1746 (1971).
2.
DAVIS H.L. and MOOK H.A., Proc. 18th Annual Conf on Magnetism and Magnetic Materials, Denver (1972). 3~,the closeness of the Fermi-and the 4f.level leads in most cases to anomalous behavior. Sm3”’ on the In Ce hand is unfavorable for inelastic neutron scattering due to its high neutron capture cross section (except other ‘47Sm). In addition, a single r’ 7—r8 transition leads to inconclusive results if higher neighbors must be taken into account.
3.
4.
BUCHER E., ANDRES K., GOSSARD A.C. and MAlTA J.P.,Proc. 13th mt. Nati. Low Temp Conf, Boulder, August 2 1—26, to be published (1972).
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BUCHER E. and MAlTA J.P., 10th Rare Earth Research Conf., Carefree (Az), April 30—May 3 (1973).
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WAKIM F.G., SYNEK M., GROSSGUT P. and DA MOMMIO A.,Phys. Rev. A5, 1121(1972).
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FREEMAN A.J. and WATSON R.E., Phys. Rev. 127, 2058 (1962).
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BUCHER E., GOSSARD A.C., ANDRES K., MAlTA J.P. and COOPER A.S., Proc. 8th Rare Earth Research Conf 1970, Vol. 1, p. 74, U.S. GPO, Washington, D.C. (1970).
9.
PAULING L.,J. Am. Chem. Soc. 54, 3570 (1932) and PAULING L., The Nature ofthe Chemical Bond, p.64, Cornell University Press, Ithaca, New York (1960).
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GORDY W. and THOMAS WJ.O., J. Chem. Phys. 24,439(1956).
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STUTIUS W., Phys. Kondens Mat. 10, 152 (1969).
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DISALVO F.J., ANDRES K., BUCHER E. and MAlTA J.P., unpublished. LEA K.R., LEASK M.J.M. and WOLF W.P.,J. Phys. Chem. Solids 23, 1381 (1962).
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MULAIU. and MISHJK A., BulL Acad. Polon. Sci. 19, 207 (1971); MISIUK A., MULAK J. and CZOPNIK A., ibid. 20,459 and 891 (1972).
15. 16.
DAVIS H.L., MOOK H.A. and BUCHER E., unpublished. RETTORI C., DAVIDOV D., ORBACH R. and CHOCK E.P.,Phys. Rev. 7, 1(1973).
220 17. 18.
CRYSTAL FIELD SPLITTINGS IN RARE EARTH COMPOUNDS
Vol. 13, No. 2
DAVIDOV D., ORBACH R., RETTORI C., TAO L.J. and CHOCK E.P.,Phys. Rev. Lett. 28,490(1972) and Phys. Lett. 34A, 379 (1971); DAVIDOV D., ORBACH R., RETTORI C., SHALTIEL D., TAO L.J. and RICKS B.,Solid State Commun. 10,451 (1972). DEVINE R.A., MORET J.M., ORTELLI J., SHALTIELD., ZINGG W. and PETER M.,Solid State Commun. 10, 575 (1972); PRADDAUDE H.C.,Phys. Lett. 42A, 97 (1972).
19.
WILLIAMS G. and HIRST L.L.,Phys. Rev. 185, 407 (1969).
20.
A similar conclusion was reached by BIEGANSKI Z.,J. Chem. Thermodynamics 5, 1(1973).
Kristallfeldstudien in einer Anzahl von Verbindungen mit 4f.und Sf. Elementen zeigen eine Korrelation zwischen Kristallfeldaufspaltung und Elektronegativitàt einfacher Liganden. Letztere zeigen i.A. positive Ladung für schwache und negative Ladung für starke Elektronegativitat. Im Falle von Edelmetalisystemen zeigen sich Abweichungen vermutlich infolge des d-Elektronenbeitrages und moglicherweise zufolge schlecht definiertem Valenzzustand.