Crystal-field analysis of U3+ ions in K2LaX5 (X=Cl, Br or I) single crystals

Spectrochimica Acta Part A 54 (1998) 2035 – 2044

Crystal-field analysis of U3 + ions in K2LaX5 (X= Cl, Br or I) single crystals M. Karbowiak a, N. Edelstein b, Z. Gajek c, J. Droz; dz; yn´ski a,* a Uni6ersity of Wrocl*aw, Faculty of Chemistry, ul. F. Joliot-Curie 14, 50 -383 Wrocl*aw, Poland Lawrence Berkeley National Laboratory, Chemical Sciences Di6ision, MS 70A-1150, Berkeley, CA 94720, USA c W. Trzebiatowski Institute of Low Temperatures and Structure Researches, Polish Academy of Sciences, P.O. Box 937, 50 -937 Wrocl*aw, ul Oko´lna 2, Poland b

Received 30 November 1997; accepted 13 January 1998

Abstract An analysis of low temperature absorption spectra of U3 + ions doped in K2LaX5 (X =Cl, Br or I) single crystals is reported. The energy levels of the U3 + ion in the single crystals were assigned and fitted to a semiempirical Hamiltonian representing the combined atomic and crystal-field interactions at the Cs symmetry site. An analysis of the nephelauxetic effect and crystal-field splittings in the series of compounds is also reported. © 1998 Elsevier Science B.V. All rights reserved. Keywords: Crystal-field; U3 + ions; Absorbtion spectra

1. Introduction Andres et al. have reported investigations of low temperature absorption and luminescence spectra of U3 + doped K2LaX5:U3 + (X =Cl, Br or I) single crystals [1]. They have shown that the variation of the chemical environment of U3 + without changing the structure provides considerable insight into the electronic structure and the nature of the excited states. The authors deliberately have not attempted to fit the observed band energies with a theoretical model based on an effective Hamiltonian because for such an ion as U3 + the empirical parameters are in, their opin* Corresponding author.

ion, difficult to interpret physically. However, basing on luminescence and inelastic neutron scattering measurements [2] they have determined the values of the crystal-field splittings of the 4I9/2 ground multiplet and by mean-square fits the values of five crystal-field parameters. The crystalfield level scheme of the ground state was analyzed by introducing geometrical dependencies of the crystal-field parameters which has provided a good description of both crystal-field energy levels and transition probabilities. Since the crystal-field parameters determined by Keller et al. [2] enabled the description for the 4 I9/2 ground multiplet only we have performed investigations in order to find a better set of parameters by carrying out least-squares fits with

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Table 1 Calculated and experimental energy levels for U3+: K2LaCl5 2S+1

LaJ

Crystal field levelb

Eigenvectors

4

Z1 Z2 Z3 Z4 Z5 Y1 Y2 Y3 Y4 Y5 Y6 X1 X2 W1 W2 W3 W4 W5 W6 W7 A1

84.1 4I9/2+12.3 2H29/2 83.8 4I9/2+12.7 2H29/2 83.5 4I9/2+13.2 2H29/2 82.1 4I9/2+13.6 2H29/2 81.2 4I9/2+14.4 2H29/2 94.0 4I11/2+3.2 2H211/2 94.1 4I11/2+3.7 2H211/2 93.8 4I11/2+3.5 2H211/2 93.6 4I11/2+3.5 2H211/2 92.3 4I11/2+3.8 2H211/2 93.4 4I11/2+3.9 2H211/2 61.8 4F3/2+20.9 2D13/2 61.6 4F3/2+21.2 2D13/2 91.3 4I13/2+5.5 2K13/2 90.6 4I13/2+4.4 2K13/2 90.4 4I13/2+4.9 2K13/2 90.3 4I13/2+4.8 2K13/2 90.4 4I13/2+5.2 2K13/2 90.5 4I13/2+5.1 2K13/2 91.1 4I13/2+5.1 2K13/2 27.1 2H29/2+16.5 2G19/2+12.7 4I9/2+12.6 2 G29/2+11.5 4F9/2 29.1 2H29/2+17.7 2G19/2+12.1 4I9/2+12.5 2 G29/2+11.7 4F9/2 30.2 2H29/2+17.4 2G19/2+11.1 4I9/2+11.9 2 G29/2+11.1 4F9/2 29.2 2H29/2+15.6 2G19/2+10.2 4I9/2+11.8 2 G29/2+10.2 4F9/2 32.0 2H29/2+17.2 2G19/2+10.2 4I9/2+11.7 2 G29/2+10.6 4F9/2 55.8 4F5/2+20.2 4G5/2 65.6 4F5/2+12.2 4G5/2 64.4 4F5/2+8.9 4G5/2 61.1 4G5/2+9.0 4F5/2+6.2 4S3/2 26.0 4S3/2+15.2 4G5/2+13.4 4I15/2 20.5 4I15/2+19.6 4S3/2+11.6 4G5/2+10.2 4 F7/2 10.2 4F7/2+26.9 4I15/2+19.7 4S3/2+12.1 4 G5/2 49.5 4I15/2+12.1 4F7/2+8.3 2K15/2+7.04 G5/2 23.9 4I15/2+27.6 4G5/2+11.6 4F7/2 20.4 4G5/2+28.7 4I15/2+18.4 4F7/2 37.4 4I15/2+15.8 4G5/2+11.6 4S3/2+7.3 4F7/2 55.5 4I15/2+9.8 2K15/2+6.8 4G5/2 48.9 4I15/2+11.8 4S3/2+8.7 2K15/2 24.2 4I15/2+24.4 4F7/2+3.3 4G5/2 27.5 4F7/2+15.7 4G5/2+17.3 4I15/2+11.2 2 G17/2 37.7 4I15/2+25.8 4F7/2+9.3 2G17/2 51.6 4I15/2+13.5 4F7/2+10.1 2K15/2

I9/2

4

I11/2

4

F3/2

4

I13/2

2

H9/2

A2 A3 A4 A5 4

F5/2

A6 A7 A8 4 G5/2+ B1 4 S3/2+ B2 4 F7/2+ C1 4

I15/2

C2 C3 D1 D2 D3 D4 D5 D6 D7 D8 E1

Calculated energy Experimental (cm−1) energyc (cm−1)

Ecalc.−Eexp.. (cm−1)

0 74 147 311 451 4304 4376 4405 4481 4577 4630 6905 7045 7976 8037 8092 8142 8268 8350 8388 9275

0 78 145 294 475 4298 4368 4410 4475 4568 4614 6897 7032 7985 8059 8115 8151 8279 8323 8356 9254

0 −4 2 17 −24 6 8 −5 6 9 16 8 13 −9 −22 −23 −23 −11 27 32 21

9343

9313

30

9453

9443

10

9546

9585

−39

9603

9618

−15

9804 9901 9954 10 742 (11 020) (11 070)

9782 9884 9618 10 785 (10 824) (11 020)

22 17 −15 −43 (196) (50)

(11 105)

(11 082)

(23)

(11 158) (11 231) (11 295) (11 347) (11 409) (11 469) (11 533) (11 558)

(11 122) (11 188) (11 227) (11 346) (11 446) (11 520) (11 536) (11 597)

(36) (43) (68) (1) (−37) (−51) (−3) (−39)

(11 666) (11 681)

(11 634) (11 701)

(32) (−20)

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Table 1 (Continued) 2S+1

LaJ

4

G7/2

4

F9/2

Crystal field levelb

Eigenvectors

E2 E3 E4 F1 F2 F3 F4 G1 G2 G3 G4 G5

52.4 76.4 67.5 69.6 67.4 67.4 66.4 56.4 57.1 57.3 58.6 58.5

4

I15/2+17.4 4F7/2+9.4 2K15/2 I15/2+14.5 2K15/2 4 I15/2+12.8 2K15/2 4 G7/2+18.6 4F7/2 4 G7/2+20.5 4F7/2 4 G7/2+21.5 4F7/2 4 G7/2+22.8 4F7/2 4 F9/2+21.3 2H29/2 4 F9/2+21.5 2H29/2 4 F9/2+22.0 2H29/2 4 F9/2+23.4 2H29/2 4 F9/2+23.6 2H29/2 4

Calculated energy Experimental (cm−1) energyc (cm−1) (11 767) (11 818) (11 996) 13 106 13 207 13 309 13 411 14 423 14 468 14 532 14 669 14 750

Ecalc.−Eexp.. (cm−1)

(11 758) (11 792) (11 872) 13 109 13 173

(9) (26) (124) −3 34

13 428 14 393 14 440 14 524 14 709 14 793

−17 30 28 8 −40 −43

a

Nominal quantum numbers for the atomic state associated with the group (major component of eigenvector); bThe symbols follows the nomenclature of ref. [1]; c Levels in brackets were not included in the fitting procedure

the inclusion of all well identified crystal-field bands. Unfortunately the U3 + ions in the compounds are at the Cs site of 7-fold coordination which leads to 15 independent crystal field parameters [2]. Due to the large number of parameters provided by theory we have carried out ab initio calculations which have permitted the determination of the ratios of the B qk parameters and in consequence a large reduction of independent parameters. This work reports the assignment of the crystal-field levels and the determination of the, ‘free-ion’ and crystal-field parameters for U3 + ions doped into the K2LaX5 (X= Cl, Br or I) single crystals.

2. Theory and fitting procedure The experimental energies of the crystal-field levels obtained from investigations of low temperature spectra of the K2LaX5 (X = Cl, Br or I) single crystals were taken from reference [1]. For the energy level calculations we have applied the effective operator model currently used to analyze lanthanide and actinide spectra. The theoretical approach is discussed in numerous articles [3–6] and will not be presented here in detail. The eigenvectors and eigenvalues of the crystal-field levels were obtained by simultaneous diagonaliza-

tion of the combined ‘free ion’ and crystal-field energy matrices. The complete Hamiltonian includes the following terms: %

H=H0 +

F k(nf, nf)fk + z5fASO

k = 0, 2, 4, 6

+ aL(L+ 1)+ bG(G2)+ gG(R7) %

%

T iti +

i = 2, 3, 4, 6, 7, 8

P fpf +

f = 2, 4, 6

%

M hmh

h = 0, 2, 4

+ % B kqC kq(i) k, q, i

where, H0 is the spherically symmetric one-electron part of the Hamiltonian, F k (nf, nf ) and z5f represent the radial parts of the electrostatic and spin–orbit interactions while fk and ASO are the angular parts of these interactions, respectively. The following parameters, a, b and g are associated with the two-body corrections terms. G(G2) and G(R7) are Casimir’s operators for the groups G2 and R7. L is the total orbital angular momentum. The three-particle configuration interaction is expressed by T i ti (i= 2,3,4,6,7,8), where T i are parameters and ti are three-particle operators. The electrostatically correlated spin–orbit perturbation is represented by the P f parameters and those of the spin–spin and spin–other–orbit relativistic corrections by the Mh parameters. The operators associated with these parameters are designated mh and pf respectively. The last term of the Hamil-

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Table 2 Calculated and experimental energy levels for U3+: K2LaBr5. 2S+1

LaJ Crystal field levelb

4

I9/2

4

I11/2

4

F3/2

4

I13/2

2

H9/2

Z1 Z2 Z3 Z4 Z5 Y1 Y2 Y3 Y4 Y5 Y6 X1 X2 W1 W2 W3 W4 W5 W6 W7 A1 A2 A3 A4 A5

4

F5/2

4

G5/2

A6 A7 A8 B1

+ S3/2+ B2 4 F7/2+ C1 4 I15/2 C2 C3 D1 D2 D3 D4 D5 D6 D7 D8 E1 E2 E3 E4 4

Eigenvectors

84.1 4I9/2+12.8 2H29/2 83.9 4I9/2+12.9 2H29/2 83.3 4I9/2+13.0 2H29/2 82.5 4I9/2+13.9 2H29/2 81.8 4I9/2+14.4 2H29/2 94.5 4I11/2+3.0 2H211/2 94.6 4I11/2+3.2 2H211/2 94.3 4I11/2+3.3 2H211/2 94.1 4I11/2+3.4 2H211/2 94.1 4I11/2+3.5 2H211/2 93.6 4I11/2+3.8 2H211/2 62.8 4F3/2+21.1 2D13/2 62.5 4F3/2+21.4 2D13/2 91.6 4I13/2+5.3 2K13/2 91.6 4I13/2+5.5 2K13/2 91.2 4I13/2+5.5 2K13/2 91.2 4I13/2+4.7 2K13/2 90.9 4I13/2+5.7 2K13/2 91.2 4I13/2+5.4 2K13/2 91.0 4I13/2+5.4 2K13/2 28.2 2H29/2+17.0 2G19/2+12.5 4I9/2+12.8 2 G29/2+11.8 4F9/2 29.7 2H29/2+17.8 2G19/2+12.2 4I9/2+12.8 2 G29/2+12.0 4F9/2 31.0 2H29/2+17.9 2G19/2+11.4 4I9/2+12.6 2 G29/2+11.4 4F9/2 30.3 2H29/2+15.9 2G19/2+10.4 4I9/2+12.0 2 G29/2+10.5 4F9/2 32.3 2H29/2+17.2 2G19/2+10.7 4I9/2+12.4 2 G29/2+10.8 4F9/2 58.7 4F5/2+20.6 4G5/2 66.7 4F5/2+13.5 4G5/2 67.0 4F5/2+9.9 4G5/2 67.5 4G5/2+10.6 4F5/2+5.4 4S3/2 24.7 19.0 18.1 33.2 64.9 23.4 43.1 49.2 56.8 44.2 32.2 59.5 27.6 67.5 74.4 71.0

4

S3/2+23.5 4G5/2+9.6 4F5/2 G5/2+29.1 4S3/2+8.8 4F7/2 4 S3/2+15.6 4F7/2+9.1 4G5/2+22.9 4I15/2 4 G5/2+14.7 4F7/2+11.64I15/2+7.6 4S3/2 4 I15/2+12.1 2K15/2+7.5 4G5/2 4 G5/2+16.6 4I15/2+21.2 4F7/2 4 I15/2+8.8 4S3/2+14.5 4F7/2 4 I15/2+11.9 4G5/2+6.8 4S3/2 4 I15/2+10.1 2K15/2+7.1 4F7/2 4 I15/2+20.0 4F7/2+7.5 2K15/2 4 F7/2+21.8 4I15/2+13.0 2G17/2 4 I15/2+12.4 4F7/2+11.4 2K15/2 4 I15/2+33.8 4F7/2+12.9 2G17/2 4 I15/2+7.8 4F7/2+12.8 2K15/2 4 I15/2+13.4 2K15/2 4 I15/2+13.4 2K15/2 4

Calculated energy Experimental (cm−1) energy (cm−1)

Ecalc.−Eexp.. (cm−1)

0 51 120 246 352 4306 4361 4384 4446 4517 4572 6871 6991 8003 8042 8092 8138 8222 8296 8337 9292

0 61 114 231 391 4308 4358 4395 4442 4509 4556 6857 6978 8016 8064 8116 8142 8231 8266 8304 9264

0 −10 6 15 −39 −2 3 −11 4 8 16 14 13 −13 −22 −24 −4 −9 30 33 28

9354

9319

35

9443

9439

4

9526

9561

−35

9565

9582

−17

9766 9842 9890 10 771

9748 9825 9891 10 813

18 17 −1 −42

(11 029) (11 068) (11 122) (11 171) (11 228) (11 265) (11 340) (11 391) (11 422) (11 450) (11 493) (11 593) (11 603) (11 710) (11 736) (11 860)

(10 841) (11 014) (11 062) (11 111) (11 144) (11 233) (11 282) (11 321) (11 410) (11 467) (11 497) (11 562) (11 634) (11 682) (11 725) (11 775)

(188) (54) (60) (61) (84) (32) (58) (70) (12) (−17) (−4) (31) (−31) (28) (11) (85)

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Table 2 (Continued) 2S+1

LaJ Crystal field levelb

4

G7/2

4

F9/2

2

H211/2

F1 F2 F3 F4 G1 G2 G3 G4 G5 H1

Eigenvectors

71.2 69.0 69.1 67.8 58.5 58.4 58.9 59.9 60.3 50.7

4

G7/2+19.1 4F7/2 G7/2+20.8 4F7/2 4 G7/2+21.4 4F7/2 4 G7/2+23.2 4F7/2 4 F9/2+24.3 2H29/2 4 F9/2+23.9 2H29/2 4 F9/2+22.8 2H29/2 4 F9/2+23.8 2H29/2 4 F9/2+23.8 2H29/2 2 H211/2+25.1 4G11/2 4

Calculated energy Experimental (cm−1) energy (cm−1) 13 059 13 152 13 235 13 322 14 441 14 474 14 521 14 627 14 691 15 203

Ecalc.−Eexp.. (cm−1)

13 075 13 125

−16 27

13 340 14 405 14 449 14 502 14 652 14 720 15 234

−18 36 25 19 −25 −29 −31

a

Nominal quantum numbers for the atomic state associated with the group (major component of eigenvector). The symbols follows the nomenclature of ref. [1]. c Levels in brakets were not included in the fitting procedure b

tonian represents the crystal-field interactions, where C k2(i ) is a spherical tensor of rank k and B k2 are crystal-field parameters. The experimental energy levels were fitted to the parameters of the phenomenological Hamiltonian described above. For Cs symmetry the crystal-field interaction term contains 15 parameters. In order to reduce the number of free parameters we have performed ab initio calculations which enabled a reasonable determination of reliable ratios of the parameters. In consequence the number of independent parameters has been reduced to the seven B 20 B 40 B 60 B 22 B 42 B 44 B 64 parameters. The ab initio crystal field model has been derived on the basis of the many-body perturbation theory in the non-orthogonal space of free-ion wave functions and the one-electron approximation of the effective oneelectron crystal field Hamiltonian of the bond ion [7,8]. The model affords possibilities for a better understanding of the subtle crystal field properties and gives an insight into the particular physicochemical mechanism involved. Such problems have also been discussed for a number of lanthanide and actinide compounds [9 – 11]. The reader interested in the calculational details should see some of the earlier papers [8 –11]. We believe that in comparison with predictions received from the Newman’s superposition model [11] our results reflect much better the dependence of the ligand interaction on metal – ligand distances which is crucial in the case of nonequiva-

lent ligand systems [12]. In the calculations we have taken into account all non-negligible contributions of further neighbors of the uranium ion which may modify the ratios of the crystal field parameters. Since for low symmetries there exists some freedom in the determination of the coordination system corresponding to a given set of crystal field parameters, we have chosen the z-axis to be in line with the single halide ions above the plane of the remaining four halide atoms (see figure 1 of Keller et al. [2]). This axis is close to the direction of the ordered magnetic moment [2]. The system may be obtained from the crystallographic one by rotation of 52.51° along the yaxis. The energy level calculations were performed in several steps. Initially, by taking into account the centers of gravity of the S%L%J% multiplets we have determined the F 2, F 4,,F 6 and z5f parameters, only. The remaining, ‘free ion’ parameters were fixed at their starting points determined by Carnall et al. [6]. In the next two fitting procedures the seven independent B qk parameters were added successively and the least-squares fits were performed to all well-defined experimental crystalfield energy levels. In the subsequent fit only the remaining eight, so far fixed, B qk parameters were treated as adjustable parameters. The empirical values were then taken for calculations of the new, corrected B k2/B k0 ratios. The values of the new ratios (in parenthesis) do not differ markedly

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Table 3 Calculated and experimental energy levels for U3+: K2LaI5 2S+1

LaJ Crystal field levelb

4

I9/2

4

I11/2

4

F3/2

4

I13/2

2

H9/2

Z1 Z2 Z3 Z4 Z5 Y1 Y2 Y3 Y4 Y5 Y6 X1 X2 W1 W2 W3 W4 W5 W6 W7 A1 A2 A3 A4 A5

4

F5/2

4

G5/2

A6 A7 A8 B1

+ S3/2+ B2 4 F7/2+ C1 4 I15/2 C2 C3 D1 D2 D3 D4 D5 D6 D7 D8 E1 E2 E3 E4 4

Eigenvectors

83.9 4I9/2+13.2 2H29/2 83.8 4I9/2+13.1 2H29/2 83.2 4I9/2+13.6 2H29/2 82.3 4I9/2+13.9 2H29/2 82.2 4I9/2+13.9 2H29/2 94.2 4I11/2+3.9 2H211/2 95.1 4I11/2+4.0 2H211/2 94.5 4I11/2+3.7 2H211/2 94.3 4I11/2+3.6 2H211/2 94.3 4I11/2+3.8 2H211/2 94.3 4I11/2+3.7 2H211/2 63.3 4F3/2+21.7 2D13/2 62.6 4F3/2+21.7 2D13/2 92.3 4I13/2+5.8 2K13/2 91.7 4I13/2+5.8 2K13/2 91.6 4I13/2+5.2 2K13/2 91.2 4I13/2+5.7 2K13/2 91.6 4I13/2+5.8 2K13/2 91.8 4I13/2+5.3 2K13/2 91.9 4I13/2+5.3 2K13/2 30.2 2H29/2+17.8 2G19/2+13.1 2G29/2 +12.0 4F9/2 30.9 2H29/2+18.3 2G19/2+13.2 2G29/2 +12.1 4F9/2 31.7 2H29/2+18.0 2G19/2+12.6 2G29/2 +11.6 4F9/2 34.9 2H29/2+18.2 2G19/2+12.8 2G29/2 +11.4 4F9/2 31.8 2H29/2+17.1 2G19/2+12.2 2G29/2 +10.9 4F9/2 61.9 4F5/2+21.6 4G5/2 65.6 4F5/2+17.1 4G5/2 69.0 4F5/2+12.4 4G5/2 72.5 4G5/2+15.2 4F5/2 52.8 41.8 52.4 50.1 40.8 65.5 39.4 53.9 37.6 60.7 67.5 31.3 73.9 80.4 73.2 77.1

4

G5/2+12.7 4S3/2+16.6 4F5/2 S3/2+17.8 4G5/2+15.8 2P3/2 4 G5/2+20.2 4F5/2+7.1 4F7/2 4 S3/2+17.7 2P3/2+11.3 4F3/2 4 F7/2+14.9 2G17/2+10.0 2G27/2 4 I15/2+12.4 2K15/2+7.6 4F7/2 4 F7/2+19.1 4I15/2+14.6 2G17/2 4 I15/2+17.6 4F7/2+10.0 2K15/2 4 F7/2+22.1 4I15/2+13.9 2G17/2 4 I15/2+11.7 4F7/2+11.9 2K15/2 4 I15/2+12.1 2K15/2+6.6 4F7/2 4 I15/2+31.5 4F7/2+12.4 2G17/2 4 I15/2+14.5 2K15/2 4 I15/2+15.3 2K15/2 4 I15/2+14.2 2K15/2 4 I15/2+15.3 2K15/2 4

Calculated energy Experimental energy (cm−1) (cm−1)

Ecalc.−Eexp.. (cm−1)

0 38 89 193 267 4322 4343 4380 4403 4453 4499 6781 6857 8018 8045 8094 8113 8167 8214 8265 9272

0 39 84 170 293 4317 4349 4374 4399 4437 4484 6770 6860 8043 8063 8106 8126 8168 8200 8234 9228

0 −1 5 23 −26 5 −6 6 4 16 15 11 −3 −25 −18 −12 −13 −1 14 31 44

9313

9282

31

9388

9392

−4

9454

9485

−31

9472

9504

−32

9654 9711 9735 10 765

9653 9699 9756 10 775

1 12 −21 −9

(10 933) (10 984) (11 016) (11 068) (11 148) (11 214) (11 265) (11 286) (11 338) (11 398) (11 421) (11 462) (11 508) (11 573) (11 636) (11 731)

(10 795) (10 935) (10 969) (11 026) (11 087) (11 160) (11 215) (11 242) (11 319) (11 394) (11 418) (11 451) (11 551) (11 585) (11 635) (11 658)

(138) (49) (47) (42) (61) (54) (50) (44) (19) (4) (3) (11) (−43) (−12) (1) (72)

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Table 3 (Continued) 2S+1

LaJ Crystal field levelb

4

G7/2

F1 F2 F3 F4

Eigenvectors

71.5 70.0 70.4 69.5

Calculated energy Experimental energy (cm−1) (cm−1)

4

4

4

4

G7/2+20.3 G7/2+22.0 4 G7/2+21.5 4 G7/2+22.7

F7/2 F7/2 4 F7/2 4 F7/2

12 941 13 011 13 055 13 122

12 942 12 981 13 051 13 144

Ecalc.−Eexp.. (cm−1) −1 30 4 −22

a

Nominal quantum numbers for the atomic state associated with the group (major component of eigenvector). The symbols follows the nomenclature of ref. [1]. c Levels in brakets were not included in the fitting procedure b

from the initial ones, as for example, one may note for the K2LaCl5:U3 + single crystal: B 21/B 20 = 0.80 (0.85),B 22/B 20 = − 0.32 ( −0.49), B 41/B 40 = − 0.34 (− 0.16) B 42B 40/ =0.50 (0.50), B 43/B 40 = 0.27 (0.42), B 44/B 40 = − 0.24 (0.24), B 61/B 60 = − 2.05 (−1.98), B 62/B 60 = −0.21 ( −0.43), B 63/B 60 = − 0.59 (−1.045), B 64/B 60 =2.75 (1.53), B 65/B 60 = − 0.98 (− 1.09) B 66/B 60 =1.40 (1.35). In the final step the four ‘free ion’ and the seven crystal-field parameters were treated as adjustable parameters. The remaining ‘free ion’ parameters as well as the ratios of the crystal-field parameters were kept constant. The inclusion of more than seven CF parameters in the fits has not markedly influenced the empirical values. The experimental and calculated energy level values are listed in Tables 1–3 whereas the best sets of the obtained parameters for all crystals are given in Table 4. 33 to 37 experimental crystal-field levels were included in the final fits.

values of the assigned crystal-field levels does not exceed 43 cm − 1. Fig. 1 shows the experimental and calculated energy levels of the first two S%L%J% multiplets. In 10500–12000 cm − 1 range the crystal-field components of the 4S3/2, 4G5/2, 4I15/2 and 4 F5/2 are highly mixed and could not be unambiguously identified. Except for the first component (B1) of the 4G5/2 multiplet (Tables 1–3) all others have not been included in the least-squares fits in spite of the relatively small energy differences between the observed and computed levels. An exception is the relatively large difference between the calculated and observed energies of the components assigned as B2 and E4. The differences for these two levels are much greater than for the other levels and the origin of these differences is not understood. Because of the results obtained from the fitting procedures a reassignment of the F3 and F4 levels is also proposed (Tables 1–3).

3.2. Nephelauxetic effect 3. Results and discussion

3.1. Free ion interactions The rms errors obtained from the above fitting procedures for U3 + in K2LaCl5, K2LaBr5 and K2LaI5 (Tables 1 – 3) indicate very good agreement between the calculated and the experimental energy levels. Hence, one may assume that the ‘free-ion’ and crystal-field parameters are sufficiently well determined. The arbitrary alphabetic labelling of the multiplets follows the nomenclature used by Andres et al [1]. The largest difference between the calculated and experimental

In the analyzed absorption spectra one observes a red shift (nephelauxetic effect) of the 2S + 1LJ levels with increasing covalency and decreasing values of the repulsion parameters i.e. along the K2LaX5 (X=Cl, Br or I) series of the complex halides. As has been already demonstrated [13] the F 2 parameter is the one most affected by environment and therefore it provides the best measure of covalence. The nephelauxetic effect may be expressed by the ratios b= F 2(crystal)/ F 2(free ion) [14] or r42 = F4/F2 [15]. Fig. 2 shows the variation of the r42 parameter in the series of complexes as a function of the ionic radius of the

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Table 4 Values of the parameters obtained by fitting the experimental energy levels Parameter

U3+: K2LaCl5 (cm−1)a,b

U3+: K2LaBr5 (cm−1)a,b

U3+: K2LaI5 (cm−1)a,b

F2 F4 F6 z B 02 B 04 B 06 B 22 B 24 B 44 B 46 B 12/B 02 B 14/B 04 B 34/B 04 B 16/B 06 B 26/B 06 B 36/B 06 B 56/B 06 B 66/B 06 nc sd Nv

38 952 (160) 32 707 (180) 22 336 (274) 1621 (2) 733 (56) 1553 (140) 402 (39) −362 (78) 727 (153) 379 (156) 614 (99) 0.847 −0.155 0.417 −1.983 −0.428 −1.045 −1.090 1.353 37 26 3069

38 962 (131) 32 779 (168) 22 488 (224) 1626 (2) 603 (47) 1142 (143) 305 (39) −315 (76) 582 (177) 242 (171) 501 (97) 0.954 −0.123 0.415 −2.246 −0.223 −1.200 −0.993 0.757 38 26 2402

38 433 (145) 32 700 (142) 22 352 (246) 1626 (2) 463 (46) 531 (142) 295 (26) −220 (63) 158 (127) 41 (186) 238 (145) 0.836 −0.185 0.247 −2.603 −0.159 −0.708 −0.363 0.695 33 23 1520

a

Numbers in parentheses indicate errors in determination of the parameter value. M0 =0.67, M2/M0 = 0.552, M4/M0 = 0.388; P2 = 1216, P4/P2 =0.5, P6/P2 =0.1; T2 =306, T3 =42, T4 =188, T6 =−242, T7 =447, T8 =300. c Number of levels included in the fitting procedure. d Deviation s= S[Di)/(n−p)]1/2, where Di is the difference between the observed and calculated energies, n is the number of levels fitted and p is the number of parameters freely varied. b

anion. The empirical r42 values are equal to 0.840, 0.841 and 0.851, respectively, which suggest an increase in covalency (or nephelauxetic effect) with heavier halide ion. In Fig. 3 the energy changes of 4I9/2 and 4F3/2 multiplets are presented as an example of the variation of the L%J%S% levels of U3 + in the compounds as a function of anionic radius of the anions. However, one should be aware that due to the relatively small number of crystal-field levels included in least-squares fits the Fk parameters may not be sufficiently well determined for a precise elucidation of the nephelauxetic effect.

3.3. Crystal-field effects The empirical crystal-field parameters decrease smoothly in the series of compounds.

The magnitude of the total crystal-field strength is expressed by the scalar parameter [16]:



Nv = % (B kq)2 k, q

n

4p (2k + 1)

1/2

For the K2LaCl5:U3 + , K2LaBr5:U3 + and K2LaI5:U3 + single crystals these values are equal to 3069, 2402 and 1520 cm − 1, respectively and are in accordance with the observed decrease of the crystal field splitting of the corresponding S%L%J% multiplets. These values correspond also with those determined from previous spectroscopic studies of U3 + :LaCl3 (Nv = 2144 cm − 1, the total crystal field splitting value of the ground multiplet D= 451 cm − 1) [17], U3 + :LiYF4:U3 + (Nv = 7231 cm − 1, D= 1113 cm − 1) [18] and RbY2Cl7:U3 + (Nv = 3613 cm − 1, site A

M. Karbowiak et al. / Spectrochimica Acta Part A 54 (1998) 2035–2044

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Fig. 1. Experimental and calculated energy levels of the first two S%L%J% multiplets.

and 4354 cm − 1, site B; D =567 cm − 1) [19]. In Fig. 3. the crystal-field strength parameter Nv is plotted versus the values of the total crystal-field

splitting of the ground multiplet of the hitherto investigated single crystals of lanthanide chlorides and complex chlorides doped with U3+ ions.

Fig. 2. The variation of the energy of the 4I9/2 and 4F3/2 states as well as the r42 parameter in the series of complexes as a function of the ionic radius of the anion.

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Acknowledgements This work was supported in part by the Polish Committee for Scientific Research within the project 3 TO9A 090 10, which is gratefully acknowledged. References

Fig. 3. The dependence of the crystal-field strength parameter Nv from the values of the total crystal-field splitting of the ground multiplet of the hitherto investigated U3 + doped single crystals of lanthanide chlorides and complex chlorides.

4. Conclusions The optical spectra of the U3 + ion in K2LaX5 (X= Cl, Br or I) series of single crystals have been analyzed. The analysis enabled a reassignment of some of the earlier reported crystal-field levels as well as the determination of the ‘free ion’ and crystal-field parameters. The results are in good agreement with those reported in earlier studies for other U3 + doped single crystals. The values of the B kq and Nv parameters smoothly decreases in the K2LaX5:U3 + (X = Cl, Br or I) series of complexes. .

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