Optical absorption spectrum of dilute U4+ impurities in incommensurate ThBr4 : lineshape analysis

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Optical absorption spectrum of dilute U4+ impurities in

incommensurate ThBr4 : lineshape analysis

P. Delamoye, R. Currat

To cite this version:

Optical absorption

spectrum

of

dilute

U4+

_impurities

in incommensurate

_{ThBr4 :}

_{lineshape analysis}

P.

_Delamoye

Laboratoire de _Radiochimie, Institut de

_Physique

Nucléaire, B.P. _1, 91406 _Orsay, France

and R. Currat

Institut

_{Laue-Langevin,}

156X, 38042 Grenoble _Cedex, France

(Re.Cu le 24 mai 1982, revise le 13 _{juillet, accepte} le 19 _{juillet 1982)}

Résumé. 2014 Les transitions de

champ cristallin des ions U4+ dilués dans

_ThBr4

donnent lieu à des bandes

_{d’absorption}

caractérisées _{par des}

_{singularités}

de bord. On montre _que les spectres observés

sont

_compatibles

avec l’existence d’une distorsion sinusoidale

_qui

module les

_{positions d’équilibre}

des ions Br- et réduit la

_symétrie

du site de l’ion actinide de

_D2d

à

_D2.

L’observation de

_{singularités}

spectrales correspondant

à des sites de

_{symétrie D2d}

résulte de

_{l’accrochage partiel}

de l’onde

incom-mensurable sur les ions U4+.

Abstract. 2014

Crystal-field

transitions associated with U4+

_impurities

diluted in

_{ThBr4 give}

rise

to broad

_absorption

bands characterized

_{by edge singularities.}

We show that the

_experimental

spectra are consistent with the known occurrence of a sinusoidal distortion which modulates the Br- ion

_{equilibrium positions,}

thus reducing the actinide

_{site-symmetry}

from

_D2d

to

_D2.

The obser-vation of _{spectral singularities corresponding} to

_D2d-sites

is

_interpreted

as

_resulting

from the

_partial

pinning

of the incommensurate modulation

_by

the U4+

_impurities.

Classification

Physics Abstracts 78. 50E

Pure

_{p- ThBr4}

is

_diamagnetic

and free of

optical absorption

over a wide _range of

_wavelengths.

Thus,

it is often used as a host material for

tetrapositive

actinide ions in

magnetic

and

optical

studies.

U4+

is most

_frequently

used because of its

relatively simple

electronic structure

_(5f2)

as well as for

_practical

reasons. In one such

_{study [1],}

the

_complete

visible and infrared

absorp-tion

_{(and emission)}

_spectra

of dilute

U4+

_impurities

have been examined. The

_spectra,

obtained

at low

_temperature

_{( ~}

4

_K),

could not be

_interpreted

on the basis of the «

_{accepted » ~3-ThBr4}

structure

_(space

_group

_D’9).

_Many

more lines were observed than could

_possibly

be due to

crystal-field

transitions associated with the

5f2

electrons on the

U4+

ions.

Furthermore,

instead

of the usual

(sharp) zero-phonon

transition

_lines,

broad bands with two

_{edge singularities}

were

observed.

Subsequently,

Raman

_[2]

and neutron diffraction

_[3]

studies have established that

_ThBr4

undergoes

a

_{displacive phase}

transition,

at

_7~

= 95

K,

from the

_{room-temperature}

p-phase

into an

incommensurately-modulated

structure.

656 JOURNAL DE _{PHYSIQUE -} LETTRES

The

_object

of this letter is to show that the observed

U4+

absorption

spectra are consistent

with the known wavevector and

_{point-symmetry}

characteristics of the condensed modulation. The situation here is similar to that encountered in the discussion of

NMR,

NQR

and EPR

lineshapes

in incommensurate _systems

_[4],

as both the

_{light-absorption}

and the resonance

tech-niques

are sensitive to the local value of the

_phase

of the frozen

_{wave. ,Unfortunately,}

the

_optical

technique,

which

_operates

on a _very short characteristic

_time-scale,

is

_only

useful at low

tempe-ratures, where thermal

_broadening

of the

_{spectral lineshapes}

is still tolerable

_(T

15

_K).

From the

_analysis

_below,

it _appears that the

U4 +

ions do not

_sample

the same distribution

of «local

_{phases »}

as the

Th4+

ions,

which

_{they replace.}

This illustrates another basic

_difficulty,

inherent to the use of

impurity probes

in incommensurate _structures,

_namely

that the local value of the

_phase

is influenced

_by

the nature of the

_impurity

_itself,

the latter

_acting

to some

degree

as a

_{phase-pinning}

centre.

-1.

_{Experimental absorption}

_spectra.

-

Figure

1 shows the essential features of the

U4 +

electronic

_absorption

_spectra

measured at 4.2

K,

in thorium tetrabromide

_{single-crystals.}

Two distinct sets of

_absorption

bands are obtained

depending

_upon the electric

_polarization

of the

incident radiation :

-i)

When the incident

_light

is

_{polarized along}

the

_{crystallographic}

four-fold axis

_(E))),

the

absorption

spectrum

consists of doublet-lines with two

_{edge-singularities.}

The

_frequency

sepa-ration between the

_{singularities (i.e.}

the

_bandwidth)

is

_typically

of the order of 8

cm-1.

ii)

When the incident

_light

is

_polarized

in the basal

_{plane (E1),}

the

_absorption

bands are

broader

₍₄₀

to 80

_{cm-1 )}

and consist of three

_peaks

_with,

as in the E

_{I I -case,}

two

_{edge-singularities.}

Fig.

1. -

Typical absorption

bands from U4+ in

_ThBr4

at

_liquid

helium _temperature. The

_{incident-light}

Fig.

2. - Primitive unit cell of

p-ThBr4 : (a) perspective view;

(b) looking down the

_tetragonal

axis. The

arrows in

_{(b ) correspond}

to the unit vectors _{ek in}

_{equation (1).}

2.

_Crystal

structure below

_~.

- The

high-temperature

structure

_[5]

of

_{ThBr4 (~-structure)}

is shown in

figure

2. Below

_7~,

neutron diffraction data show that the modulation wavevector

qs is directed

along

the

tetragonal

c-axis .

with C.

= 0.310 ± 0.005.

No

_appreciable

variation

_of

is observed _upon

_cooling,

down to 4 K. The combined

ana-lysis

of Raman,

infrared and inelastic neutron

_scattering

data

_(T

>

_{rj, together}

with the

obser-vation of

systematic

satellite-reflection extinction rules

_(T

_7~),

allows the

_symmetry

_[3]

of the soft

_optic

branch to be identified

_(’t4

in Kovalev’s notation

_[6]).

Furthermore,

since

higher-order satellite-reflections are

_hardly

visible

_(even

at 4

_K),

one _may assume a

_purely

sinusoidal

modulation,

in which case the atomic

displacements

below

_Tc,

_{Ulk, may} be written

_simply

in

658 JOURNAL DE _{PHYSIQUE -} LETTRES

The

_{quantities appearing}

in the

_expression

above are defined as follows :

r k

(=

I +

_r~)

is the

_position

vector of the kth atom in the Ith

_primitive

unit cell. Each such cell contains two Th4+ ions at

_(0,

_0,

₀₎

and

_(0,

_1/2,

_1/4)

and 8 Br- ions. Since the

_positions

of the

Th4+

ions are

_{unaffected by}

a modulation of

_~4-symmetry,

we need

_only

consider the

Br-displacements

in

_{equation (1),}

i.e. k = 1.8. As shown in

figure

2a,

the 8 Br - ions may be chosen

in such a _way as to

_generate

the

_complete

first and second

_{nearest-neighbour}

shells around the

Th4 +

ion located at the

_{origin. q}

is a

_{temperature-dependent amplitude}

factor which _may be taken as the order

_parameter

of the modulated

phase,

and _ek is a unit vector in the x or _y

direc-tion

_{(cf. Fig. 2b).}

0 is a

_parameter

entering

the

expression

of ’the soft-mode

eigenvector.

Its value

is a

_priori

unknown. Since _Ek is defined as +

_{1 ( - 1)}

for k = 1 to 4

(5

to

8),

0 is _{seen to} control

the

_phase

difference between the

_{displacements}

of the Br - ions located above and those located below the

Th4 +

ion at the

_origin.

3. Actinide

_{site-symmetry}

below

_7~.

- In the

_{high-temperature phase}

the

Th4 +

_{site-symmetry}

is

_D2d.

This is seen most

_clearly

in

_figure

_2a,

_{by considering}

the two

_{pseudo-tetrahedra generated}

by

the Br - ions labelled

_(1,

_2,

7,

8)

and

_(3,

_{4, 5,}

_{6) respectively.}

Each tetrahedron is

_separately

invariant under the

_{point-symmetry operations S’, 4 C2, C2y (= C~)}

and _{a d.} As a result of the

Br -

_{displacements given}

in

_{equation (1),}

each tetrahedron

_experiences

both a rotational

dis-placement

as well as a twist-deformation :

i)

The twist

_component

of the

_{displacements destroys}

both

_S4

and _{a d} for each tetrahedron.

ii)

The rotational

_component

of the

_{displacements}

rotates the

_{C~-axes by}

different amounts

for the two tetrahedra. Thus

_C~,

in

_{general disappears}

as a

site-symmetry

element. The

resulting

actinide

_{site-symmetry}

is thus

_C2.

If

_however,

the rotational

_components

_happen

to be

_equal

for the two

_tetrahedra,

_C2

sur-vives as a

site-symmetry

element,

and the actinide

site-symmetry,

to the extent that it is deter-mined

_by

the

_{surrounding eight}

Br- ions

_alone,

is

_D2

rather than

_C2.

The condition for this

to

_happen

_may be written as :

where _p. stands for the distance of ion k to the

4-axis.

With the

_help

of table

I,

we find that

condi-tion

₍₂₎

is

_satisfied,

_{simultaneously for}

all values

_of

_I,

if :

It is remarkable that the

_{preliminary analysis}

of the satellite-reflection intensities

[3],

measured

at 55

_K,

_{yields :}

in excellent

_agreement

with the condition

_expressed

in

_{equation (3).}

We do not wish to

_elaborate,

here,

on the

_{possible significance}

of this

_apparent

« coincidence _»,

_only

to

_point

out that it would appear to

_suggest

that the

_concept

of local

symmetry

plays

an

_important

role,

at least in this

type

of incommensurate structures.

Table I. _{- Cartesian components}

_of

the Br-

_position

vectors

_{rk 0}

and rotational

_eigenvectors

_ek. The R.T. values

_of

the

_parameters

x and z below are 0.311 and -

_0.08,

_{respectively [7].}

Fig.

3. - Character of Br-

displacements

for ~ = 0 (a) and (fJ, =

n/2 (b). The

_resulting

actinide

660 JOURNAL DE _{PHYSIQUE -} LETTRES

have

_only

considered the actinide site at

_(0,

0,

0).

Similar _arguments can be

_put

forward

con-cerning

the

_symmetry

of the

_{(0, 1/2,}

_1/4)

sites. Since no new

_physical

result is introduced

_by

including

these latter sites we shall

_ignore

them

_altogether.

With the

_help

of table I and

_introducing

the local

_{phase angle}

_{~o, :}

we obtain :

Inserting (4)

into

(1),

it _{is easy} to

_study

the character of the site-distortion as a function of cell

index I

_{(cf. Fig. 3) :}

- for sites such that

~pl ^_r

0,

the Br-

displacements correspond

to a _pure

_rotation,

_by

the

same

_angle,

of the two Br- tetrahedra. For such sites the

_D2d-symmetry

is

_preserved,

or

nearly

so;

-

for sites such that ~pl ~ ±

n/2,

we obtain a _pure twist-deformation and the

resulting

site

symmetry

is

_{D2 ;}

- for intermediate values of

~pj, both

components

are _present in

comparable

amounts and

the

_{site-symmetry}

is

_{again D2.}

,

4.

_{Crystal-field}

_energy. - Since

Th4 +

and

U4 +

have almost identical ionic radii the strain field associated with the substitution of one

_by

the other _may be

safely neglected.

Also,

for

dilu-tion levels of the order of 1

_0/00’

the

U4+

ions _may be treated as isolated

_{impurities, randomly}

distributed

throughout

the host lattice.

_Neglecting

second-order

_{perturbations,}

the

U4 +

elec-tronic

_levels,

_E(j),

_may be written as :

where

_{E~, E (i)}

and

8~~

are the

_{electrostatic,}

_spin-orbit

and

crystal-field energies,

the latter

being

defined as :

where the

_anm’s

are numerical coefficients and the

_B~s

are

crystal-field

_parameters

which

depend

upon the

position

rk of the

surrounding ligand (Br- )

ions. The values of n and m to be included in the summation on the

_right-hand

side of

_{equation (5)}

are restricted

_by

the

_symmetry

of the

free-ion electronic state under consideration and

by

the

_symmetry

of the

_ligand

field

_potential.

For f-electrons in a

D2d-field,

referred to its

_principal

_axes, we have

(T

>

_{Tc) [7] :}

The

_{corresponding crystal-field}

states are either

_{singlet-states}

_(fi,

_{r2, r3}

and

r4)

or

doublet-states

_(r5).

Below

_Tc,

the substitution :

in

_{equation (6) gives}

rise to a

_{cell-dependent}

correction _term,

å1E:j),

to

_8~.

Furthermore the

lifts the

_degeneracy

of the

_{restates :}

where

As

_expected

from

_{perturbation theory}

_arguments

_å1tP)

_(å2tp)

varies

_{quadratically (linearly)}

with the modulation

_amplitude

_’1-

_Moreover,

since

_å2t~j)

must _{vanish for lp,} =

0,

_{we may} write

to lowest-order in _{yy :} :

where

_x~

_{Pi and yj}

are

coefficients,

_{and yj}

vanishes for

_{non-degenerate}

_(T

>

_Tc)

states.

Although equation (7)

has been obtained here in a semi-intuitive

fashion,

it may be

_formally

derived

_{by considering}

the

_{explicit dependence}

of the

_B~

coefficients _upon the

_displaced

Br

-coordinates.

Figure

4 shows the various

_types

of « _{energy bands »}

_resulting

_from

_{equation (7).}

On each site the

_possible

electronic transition

_frequencies

vii’

are

_{given by :}

Fig.

4. -

Examples

of energy levels

8~

obtained from

equation (7) : (a)

singlet-state ~

> 0

(ground-state) ; (b)

doublet-state ~

> _{0; (c)}

_{singlet-state P}

0. Vertical arrows

_correspond

to transitions _giving

662 JOURNAL DE _{PHYSIQUE -} LETTRES

and the

_{spectral density}

of the

_{corresponding absorption}

bands as :

where the

_{superscript (0)}

refers to the electronic

_{ground-state.}

The observed

_spectral

singula-rities

_correspond

to the condition :

From Zeeman

_absorption

_spectroscopy

and

_{by analogy}

with what is found in other host

mate-rials we know that the

U4 +

_ground-state

is

_{non-degenerate}

in

_{D2d-symmetry.}

_Thus,

we see in

figure

4,

that condition

₍₈₎

is satisfied when :

i)

(~

= 0,

± -r

for

initially

(i.e.

T >

_Tc)

_{non-degenerate}

excited states.

2

ii)

91 =

± ~

for

_{initially degenerate}

excited states.

2

In both cases

_only

two

_{(edge-) singularities}

are found. We note in

_passing

that the

_simplicity

of the _present result

_{depends strongly}

on condition

_{(2) being}

fulfilled : the above

_analysis

carried

out

_taking

_C2

as the actinide

_{site-symmetry}

below

_{T c predicts}

that the

_spectral

_{singularities}

should not, in

_{general correspond}

to

_simple

values of _9,.

5. Discussion. - For T >

_{7~, group-theoretical}

_arguments

show that electronic transitions

involving

a

_{degenerate (non-degenerate)}

final-state are obtained with the

_E1(E~~)

_{incident-light}

polarization.

Thus the model

_presented

here accounts for the

_following

two observations :

i)

The occurrence of

_relatively

narrow doublet-lines in the

Ell -polarization,

as bandwidths in

that case are

_proportional

to the _square of the modulation

_amplitude

_q

_(a

small

_quantity,

even

at 4

_K).

ii)

The occurrence of broad bands in the

_{E1-polarization}

the bandwidths in that case

_being

proportional

to r~

rather than

_r~2.

Implicit

in the above statement is the

_assumption

that the coefficients

_{{ ~3~ ~}

and

_{

_{y~ }}

in

equation (7)

are of same order of

_magnitude.

In fact these coefficients are

_complicated

functions

of the

_~/s

and of the

_spatial

derivatives of the

_B=(rk)’s,

all

_quantities

whose numerical values

are

_largely

unknown.

_However,

there appears to be no fundamental reason

_why

the

_/3~’s

((/)

=

7B, F2, ~3’ r 4’

r 5)

should be

systematically larger

than the

y/s

((/)

=

7~),

and thus

we feel

justified

in

assuming

that

they

are in

_{general comparable.}

In addition a number of

_{previously unexplained experimental}

_features,

can now be accounted

for. For

_instance,

it is

_{possible, using}

a tunable

_laser,

to excite certain sites

_selectively

and to

observe the

_{corresponding}

fluorescence

_spectrum.

This

_technique

allows one to

_identify

the

transitions,

and in

_particular

the

_{singularities,}

which

_originate

from the same sites. Not

sur-prisingly,

the

_{experiment [8]}

shows that one of the two

_{singularities (marked}

_A)

in

_figure

la

is associated with both

_edge

_{singularities}

in

_figure

_Ib,

while the other

_{(marked ~)}

is associated with the third

_peak

in

_figure

lb.

_Clearly

the former

_corresponds

to sites

_{with 9,}

= ±

n/2

while

the latter

_corresponds

to _9, = 0. What is _not clear _at this

point

is

why

the additional

peak

in

figure

Ib occurs at

_all,

since the

_{corresponding}

transitions do not

_satisfy

condition

_(8).

Nevertheless,

the occurrence of the third

_peak

in the

_E1-spectra

is

_systematic.

Additional

proof

that _{it arises from T,} = 0 transitions may be obtained

by applying

_a

magnetic

field in

the

_crystal

basal

_plane,

whose effect is to lift the final-state

_{degeneracy :}

as

expected,

the third

A

_{possible interpretation}

for this anomalous «third

_{peak »}

is to

_postulate

that the

U4+

ions

pin

the

_phase

of the

_modulation,

in such a _way as to minimize their _energy. This _energy, or at

least that _part of it which is

_dependent

_upon the

_phase

of the

_modulation,

can be

_approximated

by

the 5f

_{crystal-field}

_{energy and with} our

(ad hoc)

choice of

_~o

>

_0,

this situation leads to an

excess of

U4+

sites with _{~o, - 0 :} this is

_{qualitatively}

what is needed in order to account for the

occurrence of the third

_peak

in

_figure

lb.

The last

_question

which must be answered is

why

the

_pinning

_{process remains}

_{incomplete :}

if it were

_complete

one would

_only

observe

_sharp

lines

_{corresponding}

to _cp, = 0. Here _{we must}

invoke some

_competition

between the

U4+

ions and other

phase-pinning

defects,

or

competi-tion between the individual

U4 +

ions themselves : even for a dilution level of 1

_0/0,,

the _average

U4+-U4+

distance is

_only

of the order of 2

_wavelengths

of the modulation

_(~

6

_c)

and it is

quite plausible

that

_they

are not able to minimize their

_{energies independently}

of one another.

This last

_point

is

_{strongly supported by}

the

_finding

that a

sample

with a dilution level of -

10-4,

rather than

10- 3,

exhibits a

_{comparatively}

_stronger «third

_{peak ».}

Further work on the

iso-morphous ThCl4

system,

where the

U4+

concentration _may be varied over a much wider _range,

is in progress.

A more detailed account of this work will be

_given

elsewhere.

,

Acknowledgments.

- One of

us

_{(P. D.)}

wishes to

_acknowledge

the assistance of M.

Husson-nois in the

_preparation

of the

_doped

_ThBr4

_samples

and of S. Lefrant in the

_magnetic

field expe-riment.

We thank R. Guillaumont and C. Vettier for useful

discussions,

K. A. McEwen for his critical

reading

of the

_manuscript

and L. Bernard for his collaboration in the

_analysis

of the neutron

results.

References

[1] GENET, M., DELAMOYE, P., EDELSTEIN, N., CONWAY, J., J. Chem. _Phys. 67 (1977) 1620.

[2] HUBERT, S., DELAMOYE, P., LEFRANT, S., LEPOSTOLLEC, M., HUSSONNOIS, M., J. Solid State Chem. 36

(1981) 36.

[3] BERNARD, L., CURRAT, R., DELAMOYE, P., ZEYEN, C. M. _{E., HUBERT, S.,} DE _{KOUCHKOVSKY, R.,} to be

published.

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