Crystal-field analysis of Ho3+LaF3 and Er3+LaF3 in C2v site symmetry

Journal

of the Less-Common

Metals,

CRYSTAL-FIELD ANALYSIS Czv SITE SYMMETRY* W. T. CARNALL Chemistry

17

17 - 29

116 (1986)

OF Ho3+-LaF,

AND Er3+-LaF3

IN

and G. L. GOODMAN

Division,

Argonne

National

Laboratory,

Argonne,

IL (U.S.A.)

R. S. RANA Physics

Department,

P. VANDEVELDE, Chemistry

College

of the Holy

Cross,

Worcester,

MA (U.S.A.)

L. FLUYT and C. GORLLER-WALRAND

Department,

University

of Leuven,

Heverlee

(Belgium)

(Received December 2,1985)

Summary

The crystal field level structure in Ho 3+-LaFs has been analyzed assuming an approximate C&-site symmetry. Both free-ion and crystal field parameters of an effective operator Hamiltonian were fit to the data, and close correlation between experimental and computed level energies was obtained. Starting point for the interpretation was a model which included the crystal field parameters for Er3+- LaF3. The results of a partial re-analysis of the energy level structure in Er3+-LaF, are also reported.

1. Introduction We have recently shown that a useful predictive calculation of the crystal field structure in Pr3+-LaF, and Tm3+-LaF, can be carried out assuming a CZV replacement site symmetry in LaF, [l, 21 instead of the actual C2 site [3]. The purpose of the higher approximate symmetry is to reduce somewhat the formidable computational problems in this type of analysis (i.e. 14 variable crystal field parameters in CZ symmetry, of which five are imaginary, compared with nine real parameters in CZVsymmetry). Such an approximate symmetry must be able both satisfactorily to reproduce analyzed experimental data and provide the basis for extending the analysis to unresolved isostructural cases. We examine here the first interaction between predictive analysis of experimental data for a 4fN electron system doped into LaF,, Ho3+-LaF3, where N is an even integer, and refinement of that analysis. The previously reported energy level calculations for Pr3+ and Tm3+, f*(f’*), could not be refined because of the limited sizes of the data sets in comparison with the number of model free-ion and crystal field parameters. *Dedicated to Professor J. D. Corbett on the occasion of his 60th birthday. 0022-5088/86/$3.50

@ Elsevier Sequoia/Printed in The Netherlands

18

A summary of earlier attempts to analyze spectroscopic data for lanthanides doped into single-crystal LaF,, Ln3+-LaF,, was included in ref. 1 and will not be repeated here. However, it is important to emphasize that the present investigation complements work published earlier [4, 51 since we are now able to interpret in detail extensive experimental data obtained in this and other laboratories by exploring the predictions of model energy level calculations. Practically all the experimental spectroscopic data on Ln3+LaF, in the literature predate any relevant crystal field calculations. For example, the more intense transitions in each crystal field group in Er3+-LaF, were reported in ref. 6 and references therein, and classified in terms of parent free-ion states. However, in the absence of an interactive crystal field calculation, the number of component levels and their relative intensities were the criteria for identification. The energies of very weak or zero intensity bands could not be estimated. Such analyses were thus limited to freeion calculations assuming approximate centers of gravity based on the levels observed in relatively isolated groups. In ref. 1 we used a model crystal field, established by fitting the reported crystal field levels in Er 3+-LaF3 [6], to interpret the experimental data for Tm3+- LaF3. The basic assumption was that since crystal field parameters in systems like Ln 3+-LaC1s exhibit only moderate variation over the series, the parameters for one ion should serve as a good first approximation for the nearest neighbor ions. Thus Er3+-LaF, should also be a good model for neighboring Ho 3+-LaF3. In ref. 4 we called attention to the discovery of a mistaken use of standards in calibrating the energies of several groups in a previous paper [6]. While the errors were small, we reproduce here a corrected set of experimental levels of Er3”-LaF, and show the comparison with the computed levels. We then use the new crystal field parameters for Er3+:LaF3 in the interpretation of data for Ho3+-LaF3, and finally report the first optimized set of levels and parameters for Ho3+-LaF,.

2. Experimental details Spectra of both Ho 3+-LaF3 and Er3+-LaF, were obtained at about 4, 77 and 298 K using both a 75 cm crystal-grating recording spectrophotometer and a 1 m HilgerEngis spectrograph equipped with an EM1 95586 photomultiplier. Additional spectra were photographed on a Jarrell-Ash 3.4 m spectrograph to provide a basis for recalibration of the original Er3+LaF3 spectra. Crystals of Ho 3+-LaF3 and Er3+-LaF3 containing 0.1 to about 1% Ln3+ were obtained from Optovac, Inc.

3. Parametric model The effective has been described

operator model used here to interpret f-element spectra in detail in a recent review [7] and is consequently only

19

briefly written H = i

summarized as

here.

The principal

Fk(nf, nf)fk + t,,f electrons

k=O

+I&+&

+

terms

of the hamiltonian

can be

(s-0 + H,*(2) + H,,(3)

c Bqk(Cqk)i k> q, i

The Fk and ci represent the electrostatic and spin-orbit integrals, their coefficients being the angular parts of those respective interactions. H,,(2) and H,,(3) represent two- and three-body operators respectively, introduced to account for the effects of configuration interaction. The twobody operators are parameterized by 01, 0, and y, while the three-body parameters are Tk (h= 2, 3, 4, 6, 7, 8). HP and HM represent second-order magnetically correlated correction terms parameterized by Pk (h= 2, 4, 6) and Mk (h= 0, 2, 4) respectively. The last term represents the crystal field interaction in which the parameters Bqk are those appropriate to a given site symmetry. Preliminary values for all the free-ion interactions could be adopted from the results of previous systematic studies [4, 6, 71. The trial crystal field parameters for Er3+-LaF, were those given by Morrison and Leavitt [ 51 based on lattice sum calculations. A least squares adjustment of the initial parameter fitting to the experimental data converged rapidly to a unique solution. The same ordering of levels in Er3+-LaF, was found for calculations in CZ, CZVand D3h [4] point symmetries.

4 . Er3+-LaF

3

The results of fitting the experimentally observed transition energies are given in Table 1 and the corresponding parameter values are shown in Table 2. We did not obtain fluorescence spectra; thus the values adopted for the crystal field components of the ground term 4I1s,2 are those reported by Krupke and Gruber [8]. Comparison of the remaining levels with those published earlier [5] shows small systematic shifts in energy of certain groups as a result of the correction for an earlier mistaken calibration. In general the results shown in Table 1 are also in good agreement with the somewhat less extensive data reported by others [8, 91. Several incomplete groups were not assigned in the first data fits. For example the 2K15,2 state near 27 800 cm-’ was included later because of the excellent agreement between the calculated splitting pattern and the observed very weak absorption features in this energy range. In the case of the 4G,,, group near 28 250 cm-’ an isolated band at 28 338.1 cm-’ was earlier assigned as one of the crystal field components [ 81, and we could identify a very weak absorption feature near this energy in

20 TABLE1 Energy levels of Er3+-LaF3 SLJa

state

Observedb CalculatedCA (cm-') (cm-') 0

51.2 121.2 199.7 219.4 313.8 400.3 442.9

-14 34 105 182 204 297 383 430

SLJa

state 14 17 15 18 15 17 17 13

6604 630 670 700 723 754 823

6618 645 695 703 737 777 836

-14 -15 -25 -3 -14 -23 -13

10301 311 330 344 358 395

10301 316 336 352 366 406

0 -5 -6 -8 -8 -11

12419 518 615 701 730

12389 506 596 678 715

30 12 19 23 15

15391 432 443 474 527

15405 442 461 486 536

-14 -10 -18 -12 -9

18557 588

18558 591

-1 -3

19266 307 314 363 367 419

19298 323 344 370 380 429

-32 -16 -30 -7 -13 -10

20656 703 734 786

20651 691 729 786

22370 374 407

22374 383 408

5 12 5 0 -4 -9 -1

Observedb CalculatedCA (cm-') (cm-')

2F312 22684 751

22685 740

-1 11

24602 680 754 840 862

24585 694 755 829 861

17 -14 -1 11 1

26526 554 582 (621)d 647 707

26532 557 584 633 639 697

-6 -3 -2 -

27602 616 628 641 668

27606 612 623 635 658

-4 4 5 6 10

27822 835 876 895 932 975 28010 128

-5 -8 -4 3 1 -

28239 255 264

28239 252 260 264

0 -3 -

31695 752

31713 776

-18 -24

2K13,2 33107 116 141 163 186 -

33081 100 148 154 191 220

26 16 -7 9 -5 -

2PW2

33330

2HWz

“%/2

4GWz

2K 15/z

2781’i’

827 872 898 933 (28064)d 28125

‘%IZ

2p312

33346 397

2J&3t2

4Gm

_ -

395 33527 546 651

8 10

-3

0

21 TABLE

1 (continued) Observedb (cm-‘)

Calculated’

34159 197 222 280

34156 183 218 272

35026 052 085

35041 052 089

-15

36520 556 623 720 804

36531 553 638 734 799

-11

4%2

38807 837 844

38810 853 857

-3 -16 -13

4D~iz

39454 537 603 634

39460 542 604 630

-6 -5 -1

41237 294 313 380 395 493

41238 396 331 377 400 492

-1 -2 -18

41680

41690 771 796 806 833 893 928 42012 024

-10 -

SLJa state 4G7/2

2%2

2I-I9/2

*Ill/2

2L,V2

783 802

934 42002 -

A

(cm-‘) 3 14 4 8 0 -4

SLJa state

Observedb

Calculated

(cm-‘)

(cm-‘)

4&/z

42499 529

42476 508

23 21

43090 127

43081 111

9 16

43686 742 759 770 833 914 965

43684 733 758 779 822 906 965

2 9 1

2p3/2

21 13/z

3 -15 -14 5

_47891

951 -

4

48071 -

-

1

2Hwz -

-13 -4 -

2D5/2

49223

6

included

272 357

20

967 987 48052 069 152 176

-16 -

48381 420 452 501 539

-

49213 283 354

10 -11

-

2

3

-10 -

Vhe principal SLJ component of the state is indicated. bAll energies are corrected to vacuum (cm-‘). The energies taken from ref. 8. CEnergy level parameters are given in Table 2. dNot

-9 11 8 0

47871 912

3 -5

A

47312

4D~,2 2Ll5l2

c

in the energy level parameter

of the ground

4I1s,2 state are

fitting.

our spectra. In contrast, the crystal field calculations grouped all components of this level within a very narrow energy range (about 25 cm-‘) consistent with a single observed stronger absorption feature and thus suggested that the weak feature arises from some other mechanism. The character of the spectroscopic features observed in different groups is varied. In many instances the features are sharp and intense, but in some cases a relatively

22

TABLE 2 Parameter values for Er3+-LaFs and Ho3+-LaFsa Parameter

Er3’-LaFsb value (cm-‘)

Ho3’-LaF

f: F6 ;

97401 (147) 68452 (382) 57920 (408) -571.84 17.688 (8.7) (0.17)

94385 66270 (67) (212) 51067 (277) -607.59 17.134 (6) (0.18)

Y ;: T4 T6 f: C z” Bo2 Bo4 Bo6 Bz2 Bz4 B44 Bz6 B46 B66

Levels fit u

1258.1 (107) 623 45 (31) (3) 66 (4) -318 (10) 484 (22) 373 (28) 2376.6 (2) 5944.0 (0.2) (51) -239 (13) 426 (67) 355 (60) -87.0 (10) 327 (43) 407 (42) -491 (38) -256 (38) -535 (39) 128 14

c

value (cm -: )

1909.9 (42) 331 38 (25) (2) 116 (8) -284 (18) 310 (32) 339 (20) 2147.8 (1) 582 [2.633] (15) -145 (21) 548 (31) 403 (33) -128 (12) 214 (22) 508 (20) -570 (20) -235 (22) -551 (24) 189 10

aErrors in individual parameters shown in parentheses. Brackets indicate parameter values that were not varied. bMo was allowed to vary freely but M4 and M6 were constrained by the ratios M4 = 0.5M” and M6 = 0.25M”. Similarly P2 was free but P4 and P6 were constrained by the ratios P4 = 0.75P2 and P6 = 0.50P2. ‘MO was not allowed to vary and the same parameter ratios quoted in b above were assigned.

broad band corresponds to a single isolated crystal field component. The broadening is ascribed to vibronic coupling. One of the interesting aspects of the Er3+-LaF, spectrum is the continuing string of isolated free-ion states extending from 0 to about 28 000 cm-l with major absorption features corresponding to each expected crystal field component. The extent of the experimental data leaves little room for more than one interpretation within the systematic framework adopted here, and suggested a modification of the earlier assignments to some of the higher energy groups where few bands are prominent. Examination of the fit to the data in Table 1 reveals an important aspect of the energy level calculation itself. It is apparent that the CzVcrystal

23

field approximation provides an excellent basis for comparison with experiment. Indeed, what is revealed is some inadequacy of the free-ion part of the model to reproduce fully centers of gravity of certain groups. This includes the ground term multiplet where it is obvious that a small constant adjustment for each free-ion group would considerably improve the overall agreement with experiment. The need for such corrections is not apparent at higher energies suggesting that the intrinsic purity of the lower lying states may limit their adjustment by the model.

5 . Ho3+-LaF

3

Several important conclusions were apparent following the preliminary free-ion energy level calculation for the Ho 3+-LaF3 system with approximate parameters [4] and the crystal field parameters for Er3+-LaF3. On the basis of the overall crystal field splitting calculated for the various levels, the need for adjustment in the trial free-ion parameters was apparent; however, there was obvious excellent correlation between the predicted pattern of crystal field components in isolated groups and the measured spectra. In addition, there were numerous levels computed to be essentially degenerate in energy, thus indicating that the spectrum should be somewhat less complex than might have been thought. Interpretation of our measured spectra was complicated in this case by an extremely low-lying ground state crystal field component at 4.5 cm-i. This level appeared as a satellite on most of the bands we observed at 4 K. However there is an excellent tabulation by Caspers et ~2. (CRF) [lo] of spectra of Ho3+- LaF, observed in both absorption and fluorescence at about 1.5 K. We therefore adopted the procedure of comparing our spectra with the levels reported by CRF. Most of the energies correlated exactly when we introduced small, rt0.6 A, systematic corrections to our data. However in Table 3 we only report levels from the tabulation of CRF which corresponded to spectroscopic features in our spectra, or where there was some evidence that our observations might have been limited by resolution. The actual values cited are therefore those from CRF (ref. 10, Table I). While the 4.5 cm-’ satellite in our spectra limited our solution of structure in some cases, it also provided a check on the identification of electronic transitions. We did not use the fluorescence-supplemented results of CRF given in their Table III except for the ground state. An example of the problem inherent in identifying crystal field levels in earlier free-ion correlations such as our own cited in ref. 1 and that of CRF, is illustrated by comparing the results in Table 1 with those tabulated by CRF in their Table III for the 2, state. The comparison of the spectrum shown in Fig. 1 with the energies given in Table 3 suggests that not all the predicted bands are observed, but in large measure this is ascribed to a number of nearly degenerate energy levels. There is, however, agreement between the observed and computed

24 TABLE3 Energy levels

SLJa state %

of Ho3+-LaF3 SLJa 0 bservedb CalculatedCA state (cm-') (cm-")

0 bservedb CaIcuZatedCA (cm-') (cm-') 0

4.5 42 50 69 122 146 201 215 227 (261)d 307 322 349 387 39% 409 sI7 5193

250 264 273 280 296 309 5hi 8730 735 747 753 761 773 786 814 834

-2 2 29 60 5% 124 155 224 223 234 299 310 320 340 386 397 412 5186 186 240 241 249 250 257 259 277 279 280 289 291 29% 305 8723 725 733 735 740 755 759 772 775 789 805 822 838

2 2 13 -10 11 -2 -10 -23 -8 -7

11304 30% 311 321 332 363 386

-3 2 9 1 1 -3

13286 362 380

7

0 5 -4 0

15576 593 60% 625 659

5 4

70% 730

5

18590 600

0 7 -2 2 1 -3 9 -4

603 620 18677 68% 709 720 737 753

11299 302 302 310 312 31% 326 329 350 36% 389 13245 291 370 394 395 407 447 472 603 15589 609 612 62% 634 659 685 714 715 71% 735

5 6 1 3 6 13 -3

-5 -8 -14

-13 -16 -4 -3 0

-10 -5

18596 597 601 602 620

-6 3

18679 679 713 732 745 757 763

-2 9 -4 -12 -8 -4

1 0

(continued)

25

TABLE 3 (continued) SLJa state

Observedb (cm-‘)

CalculatedC (cm-‘)

A

18776 814

18790 809

-14

20744 754 796 799 826 832 866

20723 753 791 792 820 822 863

21238 265 275 286

21222 228 253 279 284

SLJa state

5 21 1 5 7 6 10 3

10 12 -4 2 6 -5 -3 4 -12 -6 3

579 22220 235 263 276 328 346 361 374 389 407 424 438 454

22237 247 262 300 336 343 348 362 381 387 424 436 482

-17 -12

481 495 514 527 532 550 566

Calculatedc (cm-‘)

22508

22503 508 527

Q-1

%

24112 116 125 146

182

21405 424 426 428 452 457 458 469 479 481 507 517 550 551 566 574 575

21411 419 423 432 440 451 461

Observedb (cm-l)

2 14 7 10 -18 -1 0

196 247 5G4

25985 26008 037 054 084 096 161

3b

26266 277

293

4 298

1 -24 -8 3 13 12 8 20 0 2 -28

312 320 328 328 5GS, 3H6 27749 758 804 815

A

0

24123 126 135 162 166 173 176 179 192 218 218

-11 -10 -10 -16

25979 978 26048 051 056 058 097 152 168

6 30 -11 3

26262 264 268 269 283 287 288 299 302 303 313 317 326 332 334

4

27750 757 790 815 819 827 828

6 4 29

26 -1 -7

9

5

-5 -1 3 -4 -6 -1 1 14 0

(continued)

26 TABLE

3 (continued)

SLP state SGS, 3H6

Observedb (cm-‘)

CalculatedC (cm-‘)

21825 839 854 869

21829 831 843 850 859 879 914 922 932 944 980 986 987 997 28021 077 078

819

932 945

997

28092 SFz

(28346)d*e (380)dqe (426)d,e

A

state -4 2 11 19

‘Fa, 3Ke. 30058 078 094

0 116 0 1

157 186 197 213 234

0

14

28434 450 475 498 504

292

330

sG2

‘G3,% 28981 29020 032 035 039

068 102

122

161 187 230 292

28966 29005 010 010 016 023 032 038 039 043 084 102 104 106 123 132 133 152 156 162 173 182 211 212 294 294

Observedb (cm-‘)

SLJa

-24

31002 020

10 16 12 7

062

CalculatedC (cm-‘) 30022 033 064 072 099 105 121 124 142 158 184 198 198 216 234 237 213 288 308 325 325 337 31007 009 012 035 078

A

-6 6 -5

-8 -1 2 -1 -3 0

-16

-7 -5 8 -16

33289 312 324 337 358 390 417

3D3

25 0

33545 550 555

-1 3Mlo, ‘Ls

34022 061

-1 5 116 18 -2

34038 043 058 068 083 104 130 157 173 198

-16 3

-14

(continued)

27 TABLE 3 (continued) SLJa state

Observedb {cm-l)

‘Mu,, 3Ls 34205

-4 34994 35003 023 049 3c3

35335 369 424 489

-4

36058 070 086 100 111

244

3Po

CalculatedC (cm-’ ) 34209 224 (3424434538)’ 34975 985 985 989 35006 008 023 030 034 35329 340 371 417 437 494 532 36043 071 -82 097 129 213 236 249 265 36308

A

SLJa state

-4

jF* ‘LS 3&

19

15 -3

Observedb (cm-‘)

[36585] 36852 869 894

034

15 6 -2 7

A

[36552 ]

37001

0

CalculatedC (cm-‘)

36874 884 914 945 968 994 37032 038 039 050 075

3pz

[38052]

3L7

[38128]

317

-5 38510 15 -1 4 3 -18

-5 62Bg

38549 550 555 572 578 580 584 599 604 607 609 609 634 637 641

-22 -15 -20

7 -4

-2

-8

-13

aThe principal SLJ-component of the state is given. bThe energies quoted as observed are primarily from ref. 10. In a few instances band energies reported are those found in the present work where no corresponding observations were quoted in ref. 10. CEnergy level parameters are given in Table 2. In some groups where no band structure was observed, only the center of gravity of the computed crystal-field components is given, in brackets, to conserve space. Complete calculations are available from the authors. dNot included in the energy level parameter fitting. eStructure in this energy range was not reported in ref. 10, but was observed in the present work consistent with the expected crystal-field splitting but not consistent with the free-ion parameters. fThere are 24 crystal-field components belonging principally to the 3M10 and 3Ls states computed in the energy range between 34244 and 34538 cm-‘. No structure was observed in this range. sNo structure attributable to f -+ f transitions was observed at energies greater than 38628 cm-l.

WAVELENGTH

lnml

Fig. 1. The absorption spectrum 5320 cm-‘) at about 4 K.

of Ho3+ -LaF3

in the range

1880

- 1930

nm

(5180

-

structure that the total splitting of the state is about 5308 - 5192 = 116 cm-‘. Thus, the extra levels (Y i0 - Y is in ref. 10, Table III of CRF) observed only in fluorescence are assumed to be incorrectly assigned to the 517state. As indicated earlier, extra bands in the tabulation of CRF that could not be accommodated consistently with our observed spectra were excluded from the data fitting. The pattern of absorption shown in Fig. 1 was clearly predicted by the preliminary model calculation although the full W + 1 degeneracy of the state might normally have been expected to yield a much more complex structure. In contrast, for the ‘F, state, CRF detected a number of levels, probably vibronic in origin, near 15 610 cm-’ where the model calculation placed a single level. However, in most cases the predicted levels did correlate with relatively well resolved absorption features in the observed spectra. The power of the predictive calculation was perhaps best expressed in the case of the 3Ks state near 21400 cm-’ where all but one of the possible seventeen W + 1 components could be correlated with an observed absorption feature. One of the features of the Ho 3+-LaF3 data that lends itself to the type of analysis attempted here is the relative isolation of so many states throughout the spectrum up to a limit of about 39 200 cm-’ where stronger general absorption was observed. The latter was probably due to Ce3+ impurity in the LaF,. It is useful to compare the results of the present effort with an earlier effort to classify the levels of Ho 3+-LaC13 [ll]. The same Hamiltonian was used in both cases, but both the electrostatic and crystal field interactions are much larger in Ho 3+-LaF3. The overall structure was found to be similar. Indeed one of the focal points of the spectra in LaF, is that it provides as close an approximation to the gaseous free-ion energy level structure as can be obtained in the solid state. Some of the apparent inadequacies in the Ho3+--LaCl, case do not appear to have arisen in Ho3+-LaF,. For example the 3Ks term proved difficult to fit in LaCl, whereas both the preliminary

29

calculation and the fit shown in Table 3 reproduced the observed structure in LaF, very well. The group is remarkably narrow both in LaCls and in LaF,, spanning a range of only about 160 cm-’ in the latter. In the end, 168 levels were identified in LaCI,, but only 128 served to define the energy level parameters compared with 189 in the present case. There are clear differences in the values for y and in some of the TK in the two cases, but these parameters interact with and are part of the larger FK for Ho3+-LaF,. In the analysis of the Ho 3+-LaC13, some residual problems in the fit were attributed to the crystalfield part of the hamiltonian. In Ho3+LaF, the preliminary and final crystal field parameters were similar and the model appears to be adequate. The latter parameters resembled closely in magnitude the values obtained via the lattice sum calculation [5]. We found some evidence of an inadequate atomic part of the hamiltonian, as was the case for Er3+. While the parameter values for Ho 3+-LaF3 are not as well established as those for Er3+-LaF,, and indeed T2 and T8 are not determined, these are not large effects and they can probably best be treated by fixing these parameters at some systematically relevant value. However, the latter must await completion of analyses of Sm3+, Tb3+ and Dy3+, all in LaF,, which are in progress. This first interactive interpretation of the crystal field for an even 4fN system was successful and provides further evidence of the usefulness of the predictive model approach we have adopted. Acknowledgment This work was performed under the auspices of the Office of Basic Energy Sciences, Division of Chemical Sciences, U.S. Department of Energy under contract number W-31-109-ENG-38. References 1 W. T. Carnal1 and 2 W. T. Carnall, J. (ed.), Systematics p. 389. 3 A. Zalkin, D. H. Cheetham, B. E. 4 5 6 7 8 9 10 11

H. Crosswhite, J. Less-Common Met., 93 (1983) 127. V. Beitz, H. Crosswhite, K. Rajnak and J. B. Mann, in S. P. Sinha and the Properties of the Lanthanides, Reidel, Dordrecht, 1983, Templeton F. Fender,

and T. E. Hopkins, Znorg. Chem., 5 (1966) H. Fuess and A. F. Wright, Acta Crystallogr.,

1466; Sect.

A. K. B, 32

(1976) 94. W. T. Carnall, H. M. Crosswhite and H. Crosswhite, Spec. Rep., 1977 (Chemistry Division, Argonne National Laboratory, Argonne, IL). C. A. Morrison and R. P. Leavitt, J. Chem. Phys., 71 (1979) 2366. W. T. Carnall, P. R. Fields and R. Sarup, J. Chem. Phys., 51 (1969) 2537. H. M. Crosswhite and H. Crosswhite, J. Opt. Sot. Am. B, I (1984) 246. W. F. Krupke and J. B. Gruber, J. Chem. Phys., 41 (1964) 1225; 42 (1965) 1134. M. J. Weber, Phys. Rev., 157 (1967) 262. H. H. Caspers, H. E. Rast and J. L. Fry, J. Chem. Phys., 53 (1970) 3208. H. M. Crosswhite, H. Crosswhite, N. Edelstein and K. Rajnak, J. Chem. Phys., 67 (1977) 3002.