Spectroscopic properties of K5Li2UF10

Article abstract of DOI:10.1016/j.chemphys.2004.10.040

A new uranium (III) fluoro-complex of the formula K₅Li ₂UF₁₀ has been synthesised and characterised by X-ray powder diffraction and electronic absorption spectra measurements. The compound crystallises in the orthorhombic system, space group Pnma, with a = 20.723, b = 7.809, c = 6.932 ?, V = 1121.89 ?³, Z = 4 and is isostructural with its K₅Li₂NdF₁₀ and K ₅Li₂LaF₁₀ analogous. The absorption spectrum of a polycrystalline sample of K₅Li₂UF₁₀ was recorded at 4.2 K in the 3500-45,000 cm^-1 range and is discussed. The observed crystal-field levels were assigned and fitted to parameters of the simplified angular overlap model (AOM) and next to those of a semi-empirical Hamiltonian, which was representing the combined atomic and one-electron crystal-field interactions. The starting values of the AOM parameters were obtained from ab initio calculations. The analysis of the spectra enabled the assignment of 71 crystal-field levels of U³⁺ with a relatively small r.m.s. deviation of 37 cm^-1. The total splitting of 714 cm ^-1 was calculated for the ⁴I_9/2 ground multiplet.

Full text of DOI:10.1016/j.chemphys.2004.10.040

Chemical Physics 310 (2005) 239–248
www.elsevier.com/locate/chemphys
Spectroscopic properties of K Li UF
5
2
10
a,
b
a
*
M. Karbowiak , Z. Gajek , J. Dro z_ d z_ y n´ ski
a
Faculty of Chemistry, University of Wrocław, ul. F. Joliot-Curie 14, 50-383 Wrocław, Poland
W. Trzebiatowski Institute of Low Temperature and Structure Research, Polish Academy of Sciences, P.O. Box 1410, 50-950 Wrocław, Poland
b
Received 30 June 2004; accepted 26 October 2004
Abstract
A new uranium (III) fluoro-complex of the formula K
5 2
Li UF10 has been synthesised and characterised by X-ray powder diffrac-
tion and electronic absorption spectra measurements. The compound crystallises in the orthorhombic system, space group Pnma,
˚
˚
3
with a = 20.723, b = 7.809, c = 6.932 A, V = 1121.89 A , Z = 4 and is isostructural with its K
gous. The absorption spectrum of a polycrystalline sample of K Li UF10 was recorded at 4.2 K in the 3500–45,000 cm range
and is discussed. The observed crystal-field levels were assigned and fitted to parameters of the simplified angular overlap model
AOM) and next to those of a semi-empirical Hamiltonian, which was representing the combined atomic and one-electron crys-
tal-field interactions. The starting values of the AOM parameters were obtained from ab initio calculations. The analysis of the spec-
5 2 5 2
Li NdF10 and K Li LaF10 analo-
ꢀ
1
5
2
(
3
+
ꢀ1
tra enabled the assignment of 71 crystal-field levels of U with a relatively small r.m.s. deviation of 37 cm . The total splitting of
ꢀ
1
4
7
ꢀ
14 cm was calculated for the I9/2 ground multiplet.
2004 Elsevier B.V. All rights reserved.
3
+
1
. Introduction
have been for the most part performed for U doped
chloride single crystals [6–10]. Optical analyses of the
ion in a fluorine surroundings were restricted to the
MF (M = Ca, Sr and Ba) and LiYF host single crys-
Although in the scientific literature the identification
of more than 150 uranium (III) compounds were re-
ported [1], only a few fluoro-compounds of the ion could
be so far prepared and characterized. Among them, the
most thoroughly studied was uranium trifluoride, due
to its stability in atmospheric conditions and a relatively
2
4
tals. From absorption and fluorescence measurements
3
+
of the U :MF single crystals a number of energy levels
2
3
+
could be derived [11] but so far, only for U :LiYF a
4
complete crystal-field analysis has been performed [12].
This paper presents the preparation as well as a charac-
terisation by X-ray powder diffraction, magnetic and
spectroscopic methods of a new uranium (III) fluoro-
complex of the formula K Li UF . The crystal-field en-
easy synthesis by reduction of UF with metallic uranium
4
[
1]. Hitherto, magnetic susceptibility data are available
for UF [2,3], UZrF and UZr F [4] and absorption
spectra for UF only, by means of the teflon disk tech-
3
7
2 11
3
5
2
10
nique [5]. Besides, the identification of a number of fluor-
ergy levels were determined from a low temperature
absorption spectrum and have been analysed in terms
of the AOM and parametric Hamiltonian models.
ouranates (III) in the MF–UF (M = Na, K, Rb, Cs)
3
systems have been reported, but physico-chemical char-
acterisations of the phases were limited to analyses of
powder diffraction data [1]. Crystal-field investigations
2. Experimental
*
Corresponding author. Tel.: +48 71 3757304; fax: +48 71
For the preparation of K Li UF a well ground sto-
3282348.
5
2
10
E-mail address: karb@wchuwr.chem.uni.wroc.pl (M. Karbowiak).
ichiometric mixture of KF, LiF and UF was put in a
3
0
301-0104/$ - see front matter ꢀ 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.chemphys.2004.10.040

240
M. Karbowiak et al. / Chemical Physics 310 (2005) 239–248
graphite crucible, which was next placed in a quartz tube
and sealed under vacuum. The mixture was heated at
parameters are associated with the two-body correction
ˆ
ˆ
terms. G(G ) and G(R ) are Casimir operators for the G
2
2
7
ˆ
4
50 ꢁC for 2 days. UF was obtained by reduction of
and R groups and L is the total orbital angular momen-
3
7
UF4 with metallic U powder, obtained by thermal
decomposition of UH . UF was precipitated in anhy-
tum. The three-particle configuration interactions are
i
i
expressed by Tt ði ¼ 2; 3; 4; 6; 7; 8Þ, where T are param-
3
4
i
drous methanol by dropping an excess of a NH F solu-
eters and tˆ are three-particle operators. The electrostat-
4
i
tion to that of uranium tetrachloride. KF, LiF and UF4
were dried by heating under high dynamic vacuum at
ically correlated spin–orbit perturbation is represented
k
by the P parameters and those of the spin–spin and
j
4
00 ꢁC.
X-ray powder diffraction measurements of the com-
spin-other-orbit relativistic corrections by the M
parameters. The operators associated with these param-
pound were carried out on a ‘‘Stoe Fast Powder Diffrac-
tometer’’, using Cu Ka radiation. The unit cell
parameters were obtained by least-squares refinement
of all observed reflections in the 10–60 2h range. For this
purpose, the Crysfire Powder Indexing System and
Chekcell Graphical Powder Indexing Cell and Spacegroup
Assignment software were applied [13].
eters are designated by mˆ and pˆ , respectively.
The HCF term of the Hamiltonian represents the one
electron crystal-field interactions and is for the C site
j
k
s
symmetry defined as [14,16],
ꢀ
ꢁ
X
X
k
q
ðkÞ
q
ðkÞ
ꢀq
k
ðkÞ
^
H
¼
B
C
þ ðꢀ1Þ C
þ
B C ;
ð3Þ
CF
q
0
0
k;q>0
ðkÞ
k
Absorption spectra of thin film of the compound
were recorded on a Cary-50 UV–Vis–NIR spectropho-
where C ðiÞ is the spherical tensor operator of rank k,
q
which acts on all the i electrons in the open shell,
ꢀ
1
X
tometer in the 3500–50,000 cm range. A well ground
mixture of the compound with some chlorinated naph-
thalene oil (Halowax, index of refraction 1.635) was
placed between two quartz windows, approximately 1
cm in diameter, pressed to obtain a transparent layer,
and placed in an Oxford Instrument model CF-1204 cry-
ostat, mounted in the cell compartment of the
spectrophotometer.
ðkÞ
ðkÞ
C
¼
C ðiÞ;
ð4Þ
q
q
i
k
while B are crystal-field parameters. For the C symme-
q
s
k
try the crystal-field Hamiltonian includes 15 real Bq
parameters, out of which 14 are independent (see Table
2
1
2
). The B parameter was therefore arbitrary set to zero.
In the fitting procedure the full (364 · 364) SLJM ma-
J
3
trix for the f electronic configuration was diagonalized.
The calculations have been performed by applying the
f-shell empirical programs written by Reid [17] and
running on a PC under the Linux Mandrake operating
system.
3. Phenomenological model for description of the
electronic transitions
Energy-level calculations were carried out by apply-
ing a phenomenological model, based on the effective
Hamiltonian approach [14,15]. The eigenvectors and
eigenvalues of the crystal-field levels were obtained by
simultaneous diagonalization of the combined free-ion
and crystal-field energy matrices. The applied Hamilto-
nian includes the following terms:
4
. Results and discussion
4
.1. Chemical properties
K Li UF forms a fine crystalline redish-brown solid
5
2
10
and is one of the most stable uranium (III) compounds,
considerably less hygroscopic and sensitive to oxidation
by atmospheric oxygen than, e.g., chloro- or bromo-
complexes of uranium (III). Nevertheless, after a few
hours of exposition to air it becomes green, due to
hydrolysis and oxidation to uranium (IV). The com-
pound is insoluble in methanol, while in water it under-
goes decomposition within several hours. In
concentrated HCl, it is soluble with the formation of
^
^
^
H ¼ H þ HCF:
ð1Þ
A
^
H
A
contains the spherically symmetric (atomic) parts of
^
H and is defined as:
X
k
^
H
^
^
^ ^
A
¼ Eave
þ
F ðnf ; nf Þf þ f ASO þ aLðL þ 1Þ
k
5f
k¼2;4;6
X
i
^
^
T t
^
i
þ bGðG
2
Þ þ cGðR
7
Þ þ
X
i¼2;3;4;6;7;8
3ꢀn
X
the characteristic unstable UCln ð3 < n 6 6Þ complex
j
k
þ
M m^
j
þ
P ^p ;
ð2Þ
k
anions.
j¼0;2;4
k¼2;4;6
where Eave is the spherically symmetric one-electron part
4.2. X-ray powder diffraction analysis and crystal
structure
k
of the Hamiltonian, F (nf,nf) and f represent the radial
5
f
integrals of the electrostatic and spin–orbit interactions,
ˆ
ˆ
while f and A are the angular operators correspond-
The powder pattern of K Li UF was indexed on
k
SO
5
2
10
ing to these interactions, respectively. The a, b and c
the basis of an orthorombic cell with a = 20.723(1),

M. Karbowiak et al. / Chemical Physics 310 (2005) 239–248
241
Table 1
Observed and calculated d spacings and observed relative intensities for K
5
Li
2
UF10
h k l I/I
d
obs
d
calc
0
h k l
d
obs
d
calc
I/I
0
2
2
0
2
4
4
0
4
0
2
2
6
2
6
1 0
0 1
1 1
1 1
1 0
0 1
2 0
1 1
0 2
0 2
2 1
0 1
1 2
1 1
6.259
5.775
5.185
4.643
4.325
4.155
3.906
3.670
3.467
3.290
3.232
3.090
3.031
2.875
6.235
5.763
5.181
4.636
4.317
4.151
3.903
3.665
3.467
3.288
3.232
3.092
3.030
2.874
84
100
91
12
22
11
30
36
64
24
98
70
60
36
4 2 1
7 0 1
6 2 0
2 2 2
6 0 2
0 3 1
2 3 1
4 2 2
0 1 3
4 3 1
8 2 0
6 2 2
4 1 3
2.835
2.719
2.584
2.511
2.442
2.423
2.369
2.316
2.263
2.200
2.159
2.076
2.041
2.843
2.723
2.587
2.515
2.447
2.436
2.371
2.318
2.252
2.205
2.158
2.073
2.038
18
34
35
92
60
90
20
42
18
40
18
19
56
3
˚
˚
b = 7.809(2), c = 6.932(2) A and V = 1121.89 A . The
observed and calculated d spacings and observed rela-
tive intensities are listed in Table 1. There are four mol-
ecules per unit cell. The calculated and pyknometrically
ꢀ
3
measured densities are equal to 3.77 and 3.69 g cm
,
respectively. The diffraction data reveal, that the com-
pound is isostructural with the analogous K Li NdF
10
5
2
[
18] and K Li LaF [19] fluorides, which have been as-
5 2 10
(a)
16
signed to the space group D2h ꢀ Pnma. Hence, one may
presume that the characteristic feature of the crystal
structure of K Li UF are also sheets perpendicular
4
000
6000
8000
10000
12000
14000
5
2
10
-
1
Energy (cm )
to the a-axis formed by isolated UF dodecahedra and
8
LiF tetrahedra [19]. The U polyhedra are isolated from
4
each other and one may assume, that the distance be-
˚
tween uranium ions should be not shorter than 6.72 A,
which is the Nd–Nd distance determined for
K Li NdF [18]. The relatively large distance between
5
2
10
adjacent uranium ions limits interion interactions and
reduces the probability of cooperative effects induced
by direct metal–metal interactions. The point symmetry
for the central metal ion sites was determined to be Cs.
(
b)
4
.3. Absorption spectra and CF calculations
1
4000 16000 18000 20000 22000 24000 26000
A survey absorption spectrum of the compound is
Energy (cm-1)
ꢀ
1
presented in Fig. 1. In the 4000–18,200 cm range the
spectrum consists of sharp and well separated absorp-
tion lines, which arise from intraconfigurational
Fig. 1. Survey absorption spectra of thin films of K
at 4.2 K.
5 2
Li UF10 recorded
3
3
5
f ! 5f transitions from the lowest Stark component
2
3
S + 1
of the ground multiplet to excited states of the
L
J
3
3+
multiplets. Above this spectral region, the 5f ! 5f
U
sites in the crystal. As a result of the low site sym-
3
+
transitions are obscured by strong and broad
metry of the U ion, the CF levels are non-degenerate,
except of KramerÕs degeneracy and are not accompanied
by distinct vibronic sidebands. Fig. 3 shows the absorp-
3
2
1
5
f ! 5f 6d bands. Fig. 2 presents a high resolution
4 2 4 4
spectrum in the I ! H and I ! F absorp-
9
/2
9/2
9/2
5/2
4
4
tion ranges. As one may expect for an undiluted sample,
the lines are somewhat broader, e.g., the line at 9425
tion spectrum in the I ! I
transition range re-
11/2
9
/2
corded at 298 and 4.2 K. The indicated by arrows hot
ꢀ
1
ꢀ1
cm has a half width of 7 cm . The number of ob-
bands have been assigned as transitions from the second
and the third excited component of the I
multiplet to the two lowest components of the I
3
3
4
served lines in the 5f ! 5f transition range do not ex-
ground
/2
9
4
ceeds the (2J + 1)/2 value, which is indicative for single
1
1/2

242
M. Karbowiak et al. / Chemical Physics 310 (2005) 239–248
4
4
*
I9/2
F5/2
(
b)
*
*
4
2
I9/2
H9/2
*
(
a)
4200
4400
4600
Energy (cm )
4800
5000
9400
9600
9800
10000 10200 10400 10600
-1
-
1
Energy (cm )
4
2
4
4
Fig. 3. The 4.2 K (a) and 298 K (b) absorption spectrum of K
5
Li
9/2 ! I11/2 transition range. Asterisks indicate hot bands
assigned as transitions from the second and third excited level of the
2
UF10
Fig. 2. A detailed view of the
I
9/2 ! H29/2 and
I
9/2 ! F5/2
4
4
in the
I
absorption transitions at 4.2 K. Arrows indicate absorption lines
assigned as transitions of U and included in crystal-field calculations.
3+
4
ground
I
I
9/2 multiplet to the two lowest energy components of the
4
11/2 multiplet.
multiplet. On this basis one could establish the energies
4
ꢀ1
of the two lowest Stark components of the I ground
In the 0–18,200 cm range, the theory predicts 80
9
/2
ꢀ1
multiplet at 153 and 295 cm . Since emission transi-
tions are completely quenched in undiluted uranium
intraconfigurational f ! f transitions. From analysis of
the absorption spectrum we could determine and include
in the CF calculations as many as 71 experimental crys-
(
III) compounds, the energies of the two highest energy
2
S + 1
components of the ground multiplet could not have
been determined experimentally.
tal-field levels, originating from 20
L
J
multiplets.
Since, for U ions at the low symmetry sites of poly-
crystalline K Li UF10 one cannot obtain information
3
+
Figs. 4–6 present details of absorption spectra
recorded in 11,000–12,500, 13,200–14,300 and 14,500–
5
2
on the irreducible representation of the levels, they were
assigned by adjusting the experimental wavenumbers
with the calculated ones within a particular multiplet,
in terms of increasing energies. In cases where the num-
ber of levels was smaller than that predicted by theory,
ꢀ
1
1
8,500 cm
energy range, respectively. The lines
3
+
assigned as absorption transitions of U and included
in crystal-field analysis are in Figs. 2–6 marked with
arrows.
1
1000
11200
11400
11600
11800
12000
12200
12400
12600
-1
Energy (cm )
4
4
4
4
4
Fig. 4. Absorption spectra in the I9/2 ! ( I15/2 + G5/2 + S3/2 + F7/2) transition range of K
5 2
Li UF10 at 4.2 K. Arrows indicate absorption lines
3+
assigned as transitions of U and included in crystal-field calculations.

M. Karbowiak et al. / Chemical Physics 310 (2005) 239–248
243
13200
13400
13600
13800
14000
14200
14400
-1
Energy (cm )
4
4
Fig. 5. Absorption spectra in the I9/2 ! G7/2 transition range of K
5
Li
2
UF10 at 4.2 K. Arrows indicate absorption lines assigned as transitions of
3+
U
and included in crystal-field calculations.
the experimental levels were assigned to the nearest cal-
culated values.
details and reliability of the method is discussed else-
where [16,21–24].
3
+
To the best of our knowledge, so far CF calculations
of any lanthanide or actinide ion in compounds of the
K Li MF type, have not been performed. Thus, due
Owing to the lack of symmetry at the U site in the
K Li UF compound as many as 14 independent
5
2
10
parameters are describing the CF potential. A least-
squares procedure with so many parameters may lead
to a false minimum of no physical meaning. In order
to reduce the space of possible solutions we have applied
one of the commonly accepted among the simplified phe-
nomenological CF models – the angular overlap model
(AOM), known to be especially efficient in cases of
low symmetry systems [7,20,23]. In this approximation,
the whole CF effect is described by the three e , e and
5
2
10
to the absence of reference data for initial values of
the CF parameters, we have utilized those obtained
from ab initio calculations. For this purpose we have
applied a perturbation approach, comprising leading
terms of direct electrostatic, exchange, multipole polar-
ization, and inter-ionic renormalization contributions.
This type of calculation has already been employed,
among others, in our previous papers [7,8,20]. The
r
p
14500
15000
15500
16000
16500
17000
17500
18000
18500
-
1
Energy (cm )
5 2
Li UF10 at 4.2 K. Arrows indicate absorption lines assigned as transitions of U and included in crystal-field
3+
Fig. 6. Absorption spectra of K
calculations.

244
M. Karbowiak et al. / Chemical Physics 310 (2005) 239–248
ed AOM parameters, only. Thus, in the early phase of
Table 2
Free-ion and crystal-field parameters for K
cm , except n)
5
Li
2
UF10 (all values in
calculations, the three AOM parameters with the initial
ꢀ1
ꢀ
1
values of e = 800, e = 400 and e = 100 cm , were
r
p
d
a
bc
k
Parameter
AOM
Fitted value
freely varied. In addition the free-ion F and f param-
5
f
eters were also varied. As initial values for the free-ion
parameters were taken those obtained for U :LaCl3
E
ave
19,752 (25)
38,407 (75)
34,185 (102)
20,031 (95)
27.4 (6.6)
ꢀ1005 (47)
[1317]
1627 (15)
1618 (76)
922 (79)
2
4
6
3+
F
F
F
a
[
(
9], while the remaining parameters of the Hamiltonian
Eq. (2)) were fixed at values characteristic for the U
3
+
ion [25]. The final values of the AOM parameters were
b
c
f5
equal to e = 1192 (± 66), e = 403 (± 67) and e = 28
r
p
d
ꢀ
1
f
2
(
± 53) cm . During the fitting procedure the AOM
P
parameters were stable and except of the last one, they
were determined with relatively small errors. A small va-
2
0
2
2
4
0
4
B
B
B
705
139
783 (60)
lue for e was expected, since this parameter has been
ꢀ482
ꢀ750 (106)
d
proved to be lattice-dependant and usually less impor-
tant [23]. One may state that the AOM model has de-
scribed the energy levels structure relatively well. The
B1
185
26 (122)
4
B
2
30
41 (135)
4
B
3
1699
2550
172
1424 (149)
2463 (116)
241 (138)
321 (97)
ꢀ49 (148)
1293 (125)
631 (165)
ꢀ114 (148)
37
4
B
4
ꢀ
1
r.m.s error was 55 cm and differences between exper-
imental and calculated energy values were not larger
6
B
0
6
B
1
964
ꢀ1
6
than 100 cm . The next stages of the fitting procedure
B2
ꢀ330
6
B
3
k
q
843
were performed with the application of the B crystal-
6
B
4
157
ꢀ642
field parameters. The obtained, final values of the
6
B
5
AOM parameters, were used for the determination of
d
a
n
k
q
e
the initial values of the B parameters by applying the
71
equation [16]:
a
The Bk parameter values calculated from the AOM parameters:
q
1
ꢀ
p d
= 1192, e = 403 and e = 28 cm .
X
e
r
k
l
kq
B ¼
W e
l
;
ð5Þ
b
i
q
The T parameters were during a fitting procedure kept at the
2
3
4
6
7
l¼0;1;2
constant values: T = 306, T = 42, T = 188, T = ꢀ242, T = 447
8
ꢀ1
j
4
6
and T = 300 cm . The M as well as P and P parameters were
where
0
constrained by the Hartree–Fock determined fixed ratios: M = 0.67,
2
0
4
0
4
2
6
2
ꢄꢂ
ꢃꢅꢀ
M = 0.55M , M = 0.38M , P = 0.5P , P = 0.1P .
1
2
k þ 1
3
k
3
0
X
c
l
kq
l
Numbers in parentheses indicate errors in determination of the
W
¼
ðꢀ1Þ ð2 ꢀ dl0
Þ
al
7
ꢂ
3
0
0
parameter values.
d
P
2
1=2
ꢃ
ꢂ ꢃ
Root mean square deviation: r ¼
½ðD Þ =ðn ꢀ pÞꢃ , where D is
i
i
i
k
3
R
k
ꢂ
t
the difference between the observed and calculated energies, n is the
number of levels fitted and p is the number of parameters freely varied.
ꢁ
C ðH ; U Þ
ð6Þ
q
t
ꢀ
l
0
l
R
t
t
e
Number of levels included in the fitting procedure.
are the coefficients determined by the ligand coordinates
R , H , U and the power exponents a are characterizing
t
t
t
l
the distance dependence of the intrinsic parameters for
the U –F linear ligator. We accepted the values of
level energy values has been found for the second com-
3
+
ꢀ
4
ponent of the G multiplet. The calculated splitting of
7
/2
2
ꢀ1
a from [23]. The e in Eq. (6) is defined for the average
the H2 multiplet is equal to 463 cm , which is signif-
l
l
9/2
metal–ligand distance R.
icantly lower than the experimentally observed value of
601 cm . However, in an one-electron Hamiltonian
k
q
ꢀ1
In the last stage of the fitting procedure fourteen B
k
crystal field parameters as well as the F , f , a, b and
model, the splitting value of this mutiplet is usually
underestimated. A similar tendency has been noticed
5
f
2
P free-ion parameters were freely varied and simultane-
3
+
ously determined. In this step of calculations the AOM
for U :LaCl , where the calculated splitting value is
3
ꢀ
1
parameters have served as a constraint on the physical
more than by 100 cm [9] smaller than the experimental
one whereas after inclusion of the two-particle correla-
tion crystal-field (CCF) operators into the semiempirical
Hamiltonian, a considerable improvement in the fitting
results could be noticed. However, in the case of
K Li UF this procedure may be not applied, as the
k
q
reasonableness of the B parameters, such as the basic
features of the metal–ligand bond [16,23]. The final
parameter values are shown in Table 2, whereas the
experimental and calculated energy levels are listed in
Table 3. The final r.m.s. deviation (37 cm ) is relatively
small as for an actinide ion in a strong crystal field. For
comparison, in the CF analysis of U :LiYF forty en-
ergy levels were fitted to six B parameters with a
ꢀ
1
5
2
10
number of one-electron CF parameters is so large, that
the inclusion of additional adjustable parameters would
make the calculations untracteable.
3
+
4
k
q
1
r.m.s. deviation of 50 cm [12]. The largest difference
The values of the obtained free-ion parameters are
ꢀ1
3+
k
(
82 cm ) between the experimental and calculated CF
typical for the U ion. The B parameters retain stable
q

M. Karbowiak et al. / Chemical Physics 310 (2005) 239–248
245
Table 3
Calculated and experimental energy levels for K
5
2
Li UF10
2
S + 1
a
b
ꢀ1
ꢀ1
exp ꢀ Ecalc (cmꢀ1
ꢀ12
ꢀ12
ꢀ42
–
L
J
Eigenvectors
Calculated energy (cm
)
Experimental energy (cm
)
E
)
4
4
2
I
9/2
84 I9/2 + 14 H29/2
12
165
337
584
715
4426
4522
4564
4669
4925
4947
7222
7372
8124
8219
8266
8386
8493
8785
8801
9499
9613
9702
9811
9962
10,198
10,401
10,490
11,121
11,270
11,316
11,364
11,514
11,601
11,641
11,720
11,803
11,872
12,064
12,139
12,246
12,310
12,374
12,448
12,548
13,628
13,726
13,900
13,989
14,793
14,867
14,960
15,051
15,111
15,296
15,465
15,581
15,636
15,698
15,737
15,830
15,867
15,925
0
153
295
–
–
4464
4507
4577
4615
4950
4980
7220
7430
8147
8223
8261
8417
8473
8775
–
9425
9614
9701
9828
10026
–
10,433
10,461
11,158
11,279
11,309
11,357
11,507
11,581
11,644
11,773
11,807
11,848
12,071
12,101
12,231
–
4
2
8
8
8
8
5 I9/2 + 11 H29/2
4
2
3 I9/2 + 14 H29/2
4
2
1 I9/2 + 13 H29/2
4
2
0 I9/2 + 14 H29/2
–
38
4
4
2
I
11/2
91 I11/2 + 4 H211/2
4
2
9
9
9
9
9
2 I11/2 + 2 H211/2
ꢀ15
4
2
2 I11/2 + 3 H211/2
13
4
2
4 I11/2 + 3 H211/2
ꢀ54
25
33
4
2
4 I11/2 + 3 H211/2
4
2
2 I11/2 + 5 H211/2
4
4
4
2
F
3/2
60 F3/2 + 22 D13/2
ꢀ2
4
2
5
6 F3/2 + 21 D13/2
58
4
2
I
13/2
86 I11/2 + 6 K13/2
23
4
4
2
8
8
8
8
9
9
6 I11/2 + 5 K13/2
4
2
6 I11/2 + 7 K13/2
ꢀ5
4
2
7 I11/2 + 4 K13/2
31
4
2
7 I11/2 + 7 K13/2
ꢀ20
ꢀ10
–
4
2
0 I11/2 + 6 K13/2
4
2
0 I11/2 + 7 K13/2
2
2
2
H29/2
28 H29/2 + 18 G19/2
ꢀ74
2
2
2
3
2
3
8 H29/2 + 15 G19/2
1
2
2
1 H29/2 + 16 G19/2
ꢀ1
17
64
–
32
2
2
9 H29/2 + 15 G19/2
2
2
3 H29/2 + 16 G19/2
4
4
4
4
F
5/2
55 F5/2 + 22 G5/2
4
4
6
5
3 F5/2 + 12 G5/2
4
4
8 F5/2 + 8 G5/2
ꢀ29
4
4
4
4
4
I15/2 + S3/2 + G5/2 + F7/2
54 G5/2 + 19 F5/2
36
4
4
2
4
3
4
2
3
2
4
3
5
4
2
4
3
6
4
7 G5/2 + 16 I15/2
9
4
4
9 I15/2 + 12 S3/2
ꢀ7
ꢀ7
ꢀ7
ꢀ20
3
4
4
4 I15/2 + 8 F7/2
4
4
3 I15/2 + 13 F7/2
4
4
6 I15/2 + 18 F7/2
4
4
8 I15/2 + 16 F7/2
4
4
6 I15/2 + 15 G7/2
53
4
4
4
3 I15/2 + 13 F7/2
4
4
4 I15/2 + 19 F7/2
ꢀ24
4
4
7 I15/2 + 11 F7/2
7
4
4
5 I15/2 + 8 F7/2
ꢀ38
ꢀ15
–
4
4
6 G5/2 + 18 I15/2
4
4
7 I15/2 + 21 F7/2
4
4
4 I15/2 + 17 F7/2
12,380
12,430
–
6
4
2
2 I15/2 + 11 K15/2
ꢀ18
4
4
2 I15/2 + 20 F7/2
–
4
4
4
4
G
7/2
67 G7/2 + 17 F7/2
13,601
13,644
13,933
13,973
14,786
14,851
14,956
14,980
15,096
15,316
15,465
15,547
–
ꢀ27
ꢀ82
33
ꢀ16
ꢀ7
ꢀ16
ꢀ4
ꢀ71
ꢀ15
20
4
4
6
6
5
5 G7/2 + 16 F7/2
4
4
2 G7/2 + 21 F7/2
4
4
9 G7/2 + 20 F7/2
4
2
F
9/2
57 F9/2 + 21 H29/2
4
2
4
5
4
4
9 F9/2 + 16 H29/2
4
2
0 F9/2 + 20 H29/2
4
2
5 F9/2 + 21 H29/2
4
2
8 F9/2 + 20 H29/2
2
2
2
H211/2
27 H211/2 + 36 K13/2
2
2
3
3
2
2
3
7 H211/2 + 17 K13/2
0
2
4
6 H211/2 + 16 G11/2
ꢀ34
2
2
1 H211/2 + 35 K13/2
–
2
2
6 H211/2 + 38 K13/2
15,702
15,768
15,841
15,890
15,912
4
31
11
22
2
4
8 H211/2 + 16 G11/2
2
4
2
2
K13/2 + D3/2
49 K13/2 + 20 H211/2
2
2
5
2
6 K13/2 + 15 H211/2
2
2
1 K13/2 + 36 H211/2
ꢀ13
(
continued on next page)

246
M. Karbowiak et al. / Chemical Physics 310 (2005) 239–248
Table 3 (continued)
2
S + 1
a
b
ꢀ1
ꢀ1
exp ꢀ Ecalc (cmꢀ1
5
L
J
Eigenvectors
Calculated energy (cm
)
Experimental energy (cm
)
E
)
2
2
2
1
1
7
7
6
5 K13/2 + 35 H211/2
16,020
16,071
16,194
16,256
16,474
16,535
16,869
17,082
17,206
17,292
17,346
17,469
17,516
17,550
17,671
17,779
17,870
18,152
16,025
16,095
16,170
16,219
16,430
16,545
16,832
17081
–
17,347
17,386
17,495
17,530
17,561
17,685
–
4
2
4 D3/2 + 13 H211/2
24
4
4
2 D3/2 + 13 H211/2
ꢀ24
ꢀ37
ꢀ44
10
ꢀ37
ꢀ1
–
55
40
26
14
2
4
0 K13/2 + 6 I13/2
2
4
2 K13/2 + 5 I13/2
2
4
9 K13/2 + 4 I13/2
4
4
4
2
D
G
1/2
35 D1/2 + 33 P1/2
2
4
2
9/2 + G17/2
57 G9/2 + 6 G17/2
4
2
5
3
4
3
5
2
2
2
9 G9/2 + 4 G17/2
4
2
7 G9/2 + 12 G17/2
4
2
6 G9/2 + 9 G17/2
4
2
3 G9/2 + 16 G17/2
4
2
9 G9/2 + 8 G17/2
4
2
6 G9/2 + 17 G17/2
11
14
–
2
4
5 G17/2 + 16 G9/2
2
4
6 G17/2 + 15 F7/2
4
2
4
2
D5/2 + L15/2
31 D5/2 + 16 D25/2
17,839
18,197
ꢀ32
2
2
2
8 L15/2 + 22 K15/2
45
a
Nominal quantum numbers for the atomic state associated with group.
The leading eigenvector components, in percentage.
b
3
+
in the fitting procedure and are in general accordance
ger than those reported for U doped in chloride host
ꢀ
1
with the calculated ones on the basis of the e , e and
crystals for which the CF is weaker (451 cm
U :LaCl [9] and 626 cm for U :Cs NaYCl [26]).
In fluoride matrices the total splitting of the ground level
of U ions have been determined for CaF , SrF and
for
r
p
3
+
ꢀ1
3+
ed parameters, obtained from the AOM step. Therefore,
we may conclude, that the achieved values retain their
physical meaning and that we have avoided in the calcu-
3
2
6
3
+
2
2
lations a pitfall of a local minimum. Since, the errors in
LiYF crystals, and are equal to 667, 460 and 1113
cm , respectively [11,12]. The splitting of the ground
multiplet can be directly related to the magnitude of
the total crystal-field strength, which may be expressed
4
k
ꢀ1
the determination of those of the B parameters which
q
4
4
6
are displaying small values, i.e., B , B and B , are larger
1
2
2
than the parameter values itself, one ought to consider
the fixing of the values, either at zero or at those result-
by the scalar parameter N , defined as [27],
v
ing from the AOM step. However, the value obtained
"
#
1
=2
4
X
from the fitting procedure for B parameter corresponds
2
4p
2
k
q
N
v
¼
ðB Þ
:
ð7Þ
well with the calculated one from the AOM step, and
should be therefore regarded as a well determined, in
spite of the relatively large error. The absolute values
ð2k þ 1Þ
k;q
ꢀ
1
For K Li UF , N = 4334 cm
U :LiYF , N = 5529 cm [12]. The difference in the
4 v
,
while for
5
2
10
v
4
6
3+
ꢀ1
of the B and B parameters are lower than those calcu-
1
2
lated in AOM step, but the inclusion of these parameters
in the fitting procedure has been found important for the
stability of the overall fit and they were therefore freely
varied in the adjustment, also.
crystal-field strength results mainly from differences in
3
+
U–F distances in both compounds. In LiYF , the U
4
3
+
ions substitute for Y and the Y–Cl distances are equal
˚
to 2.244(4x) and 2.297(4x) A [28]. For K Li UF the
5
2
10
4
The total splitting of the I9/2 ground multiplet could
U–F distances have not been determined, but assuming
that they are similar to those of La–F in K Li LaF
not be experimentally determined from emission spectra,
since these cannot be recorded for an undiluted sample.
However, as has been shown in [7], a relatively accurate
determination of a possible large number of CF level re-
sults also in a relatively accurate determination of the
energy level structure of the ground multiplet. Further-
more, for K Li UF only the two highest energy levels
5
2
10
3+
3
+
(the ionic radius of La is very close to that of U
)
one may expect that they adopt values between
˚
2.30–2.48 A [19].
It has been shown [27] that one may expect a linear
dependence between the scalar crystal-field strength
parameter (N ) and the maximum Stark splitting
5
2
10
v
4
of the I multiplet could not have been determined
(DEmax) of J-terms with small J-mixing. It is the case
9
/2
experimentally. The two lowest energy levels of the
ground multiplet could be determined from the observa-
tion of hot absorption bands. The calculated value of
of the ground multiplet. Fig. 7 shows the maximum
4
3+
splitting of the I ground multiplet of U ions in
9
2
hitherto studied hosts, versus the N parameter. In this
v
ꢀ
1
the total splitting is 715 cm which is, as expected, lar-
figure, the dash line presents a linear fit to all experi-

M. Karbowiak et al. / Chemical Physics 310 (2005) 239–248
247
1200
1000
800
600
400
200
2000
3000
4000
5000
6000
-
1
N (cm )
v
4
3+
parameter for the U ion in different matrices. The dash line resulted from
Fig. 7. Maximum Stark splitting of the I9/2 ground multiplet versus N
v
the linear fit to all experimental points, whereas the solid line presents the best linear fit obtained for chloride hosts, only.
mental points. As one may notice, the experimental
points do not match very well the linear dependence
and the most significant deviations from the predicted
trend are observed for hosts with relatively large CF
strength. If one takes into account the chloride hosts
only, the variation of the N parameter with DE
Acknowledgements
The authors thank Dr. J. Janczak of the W. Trzebia-
towski Institute of Low Temperature and Structure Re-
search of the Polish Academy of Sciences in Wrocław,
for the X-ray powder diffraction measurements as well
Dr. Michael Reid (University of Canterbury, New Zea-
land) for providing his f-shell programs.
v
max
4
(
I9/2) may be well approximated by the linear depend-
ence, shown with the solid line in Fig. 7. The experi-
mental points for fluoride hosts are located above,
and those for bromide and iodide hosts below the line
determined for chlorides, and the deviations are larger
for iodides than for bromides. This may indicate that
the predicted linear relation is obeyed only for hosts
with a similar covalency. However, due to a limited
experimental data set additional analyses are required
in order to state whether the observed regularity is
not an accidental trend.
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2
10
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3
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ues to those of experimental ones. For the I ground
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1
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