Inelastic neutron scattering study of proton dynamics in Cs3H(SeO4)2 and Rb3H(SeO4)2

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Inelastic neutron scattering study of proton dynamics in Cs3H(SeO4)2 and Rb3H(SeO4)2

A. Belushkin, J. Tomkinson, L. Shuvalov

To cite this version:

A. Belushkin, J. Tomkinson, L. Shuvalov. Inelastic neutron scattering study of proton dynamics in Cs3H(SeO4)2 and Rb3H(SeO4)2. Journal de Physique II, EDP Sciences, 1993, 3 (2), pp.217-225.

�10.1051/jp2:1993124�. �jpa-00247825�

Oassification Physics Abstracts

63.20 64.70K

Inelastic neutron scattering study of proton dynaudcs in Cs3H(Se04)2

and Rb3H(Se04)2

A-V-

Belushkin(~<*),

J.

Tomkinson(~)

alld L-A-

Shuvalov(~>*)

(~) ^Rutherford Appleton Laboratory, Chilton, Great-Britain (~) ^{Institute of} Crystaflography, Moscow, Russia.

(Received

18 August 1992, revised 19 October 1992, acceptec 10 November

1992)

Abetract. The proton dynamics of the

Cs3H(Se04)2

and

Rb3H(Se04)2

have been studied by inelastic neutron scattering in

a temperature _range from 5 K _to 60 K. The results

are discussed in comparison with the isostructural acid sulphates, however the dynamics of the selenates is quite different. The splitting of selenate bands at low temperatures for both Cs and Rb

salts indicate _a phase transition to low symmetry. The anomalous temperature dependence

of hydrogen bond bending modes in the Cs salt is discussed in the framework of interactions between strongly anharmonic stretching modes and bending vibrations.

1. Introduction.

The tricaesium and trirubidium

hydrogen

selenates

belong

to _a

family

of

crystals

with the

general

formula

M3X(A04)2 (M=K, Rb, Cs, NH4i X=H, D; A=S, Se).

These

crystals

in

common with

compounds

of formula

MXA04

reveal _a number of

interesting physical

_prop erties:

ferroelectricity, ferroelasticity, high protonic conductivity

etc. In these

compounds

the three dimensional

hydrogen-bond

network characteristic of

KDP-type crystal

is absent. At _room

temperature

_a ^number

of, symmetry related,

proton

positions

_are

unoccupied.

This is because

they

_are

energetically

unfavorable. The _room

temperature

structure becomes unstable at _non ambient temperatures or pressures and the

crystals undergo

a

large variety

of

phase

transitions.

These transitions _are

thought

to be connected with the reconstruction of the

hydrogen-bonds

network

[1-4].

According

to dielectric measurements [5]

Cs3H(Se04)2 (referred

to below _as the Cs

salt) undergoes

_a second-order

phase

trallsition at 50 K.

Upon

deuteration the temperature ^{of this} transition increases

dramatically

to 168 K.

Analogous

studies _on

ltb3II(Se04)2 (referred

to below _as the Rb

salt)

have shown _no such anomalies in the dielectric

properties

below _room

temperature [6,

7].

However deuteration of the Rb salt leads to the _appearance of _a

>-type

(*) On leave from laboratory of Neutron Physics, JINR, Dubna, Russian Federation.

JOURNAL DE PHYSIQUE 't -T 3. N'2, FEBRUARY tW3 9

218 JOURNAL DE PHYSIQUE II N°2

c1

. , a

b

Recently X-ray

diffraction

experiments

have been

performed

to establish the structure of the low

temperature phases

of these

crystals.

In the deuterated ltb salt the deviations of the

heavy-atom positions

from the

A21a

_{space group} were too small to be detected below the transition temperature

[iii.

However

large

deuterium temperature ^factors were

reported

both at 110 K and 25 K. This observation is

probably

an indication that the deuterium atoms _were not

actually

located.

(Deuterium positions

_are

notoriously

difficult to determine

by X-ray diffraction.)

In the deuterated Cs salt small

changes

in the lattice constants at the transition

temperature _were

reported

[12]. ^The

P2i/m

_{space group was} obtained for the low

temperature phase. Analysis

of the atomic coordinates indicates that the low temperature

phase

transition is connected with _an

ordering

of the protons in

hydrogen

bonds while the

changes

in atomic

coordinates of the

heavy

atoms _{are more} subtle

[13, 14].

3.

Experiment.

Poly-crystaline powders

of the

samples

_were obtained

by

slow

evaporation

of _{an aqueous} solu- tion of rubidium

(or caesium)

carbonate and selenic acid [5].

The inelastic neutron

scattering

spectra

(INS)

_were recorded _on the TFXA spectrometer

at the

spallation

neutron _source

ISIS,

Rutherford

Appleton Laboratory,

UK

[15].

^{TFXA is}

an inverted

geometry

inelastic neutron

scattering

spectrometer ^which

provides good (ca.

2

ill)

_energy resolution _{over a} wide _energy transfer

(2

to 500

mev).

The

energies

of incident neutrons in the white neutron spectrum which illuminates the

sample

_are defined

by

the time-

of-flight

between moderator and

sample.

^{The final} neutron energy is fixed

by graphite analysers crystals.

The difference between initial and final _neutron

energies

^{defines the} _energy ^of the

exitations.

The

samples (in

aluminium foil

sachets)

_were in _a variable temperature cryostat ^and the temperature ^{of the}

samples

was determined

by

_a ^Rd-Fe

thermometer,

^the temperature

stability

was ca. 0.i K.

The INS spectra were recorded _at 5

K,

40 K and 60 K for Rb salt and 5 K, 25

K,

40

K,

50 K alld 60 K for Cs salt. The spectra were normalized to the monitor counts and converted from the neutron

time-of-flight

scale into the

scattering

^law

S(Q,w ) using

standard _programs

[15].

4. Data

analysis.

The

intensity

to very low _energy transfer is well scaled

by (see

e-g-

[16]):

si(Q,w) ~~

~

exp(-2w)wf(w), ⁽¹⁾

where

~~' _"

~~ /

4~w

^~°~~~

ii~

^~~~~°~~~°' ~~~

is the

Debye-Waller

factor and

~~~~ ~

U~g(W) W(I exP(W/T))'

~~~

U~ _{is the}

mean square

displacement

of the

scattering

atom in _a

particular

vibrational mode and

g(w)

is the

density

of

phonon

states. Here _we have

assumed, reasonably,

that the

only

significant scattering

cross section is that of the

hydrogen

atom.

220 JOURNAL DE PHYSIQUE II N°2

Assosiated with the

particular

vibrational transition observed

by

INS _are

multiphonon

_ex-

citations,

combinations between the local mode and the external

density

of _states. These _are also known _as

phonon wings

[17]. ^This contribution _can be modelled _as

Sn(Q,W)

+~

exP(-W) ($)~ _{~"))~, (4)}

(5)

where

~~~~~ =

f _f~-i(w')

@

f(W W')~~"

Due to the temperature

dependent

terms in the

equations (1), (2)

^and

(4)

for _{w »} T the total

intensity

of

single

and

multiphonon scattering

will be temperature

independent.

Also the relative energy

separation

of the fundamental and

multiphonon peaks

should remain _constant.

The

intensity

of the

multiphonon wing

_on the fundamental line is

proportional

to the

intensity

of the fundamental

provided

that there is _a

large

_{energy gap} between the lattice vibration

region

and fundamental line

position.

All these conditions _are satisfied in _{our case.}

5. Results and discussion.

The inelastic neutron

scattering

spectra ^{of the Cs} and Rb

salts,

at different temperatures,

are shown in

figure

2. The observed band

positions,

with

approximate

mode

descriptions,

_are

given

in table I. The spectra can be

conveniently

divided into three

frequency regions. Firstly

below _ca 10 mev is the

density

of states of the lattice vibrations. From 20 to 120 mev the

region

is associated with the

Se04

vibrations. Above 120 mev the local _70H and

boH

modes

are

expected.

5.I THE _{HYDROGEN BOND} viBRATioNs. The two acid salts have

consistently

similar _spec-

tra at each temperature. The most intense features observed _are at _ca 130 and 190 mev. These

correspond

to the

anticipated positions

^for _70H and

boH.

These

positions

_can be correlated with the

reported

Roo distances. From the well known correlation of Novak [18] we estimate for

Rcs(oo)

# 2.54

1

a 70H of132

mev,

and

RRb(oo)

# 2.514

I

a 70H of140 mev. These values _are close to but

slightly

lower than those

reported

in table I. The

discrepancies might

be accounted for

by

temperature differences. The

Roo

distances _are from _room temperature

measurements but the results in table I _are all obtained below 100 K. There _{are no} similar correlations for

boH

modes but the

assignement

of this mode to the

region

of190 _mev is not unusual. Because of the

strength

of the

boH mixing

with other

(Se04)

modes cannot be _very

important.

The _use of Novak's correlations to estimate

R~oo) 1mnlediately

suggests their _use to estimate voH. The value of _voH obtained is _ca 140 mev

(at

_room

temperature).

This

corresponds

_rea-

sonably

well with the ambient temperature IR spectrum of the Cs salt [20]. ^{The IR} spectrum shows _{a very}

intense,

_very

broad,

_response which reaches _a maximum at ca 140 mev. In _our spectra however there _{are no} other

important

bands

remaining

to be

assigned.

There is the

possibility

of

degeneracy

between _70H and _voH. However this _can be dismissed

immediately

because the _70H is

only

_as intense _as boH. A

doubly degenerate

band will be twice _as intense

as a

singly degenerate

band

(calculated

in the harmonic

approximation).

Indeed there _{are no} other bands in the spectrum ^that can be

reasonably assigned

to _a

simple

harmonic _voH. In the _case of the

isomorphous

acid

sulphates

a series of

low-energy, intense, sharp

lines _were

assigned

to

"tunneling" along

the OHO coordinate [8]. ^In our case the

Roo

distance is too

long

to

produce

^the low inter-well barriers calculated for

sulphates. Any tunneling

lines would

CS~H(SeO~)~

i ,

5 K

~

$

₂₅

I

^~'~ ₄₀

O

~i

60 K

~ ⁱ Rb~H(SeO~)~

~

~ 5 K

jj

B

~

40 K 3

d

~ 60 K

0 50 loo 150 200 250

Energy transfer (mev)

Fig.2.

INS spectra ^of

Rb3H(Se04)2

and

Cs3H(Se04)2

at diierent temperatures. ^From top to bottom: CS salt; 5 K, 25 K, 40 K, 60 K and Rb salt; 5 K, 40 K and 60 K.

Table I. Observed band

frequencies (in

mev

)

and their tentative

assignements

for

Rb3H(SeO~)2

and

Cs3H(SeO~)2 (1

mev ₌ 8.066

cm~~)

5 K 40 K 60 K 5 K 10 25 K 40 K 60 K

40.7 41.2 40.3 40.5

42.3 42.9 41.8 42.1 40.9 42.1 42.0 41.3

u2(Se04)

41.5

49.2

50.7 50.9 50.7 49.7 50.1 49.8 50.3 50.6

v4(Se04)

52.7

136.0 136.2 135.9 128.9 129.6 130A 133.8 _70H

190.3 190.5 190.1 184.3 184.9 185.9 188.2

boH

(*) Raman data after reference [20].

therefore be at

relatively high energies,

_as in the _case of KIIC03 [19].

Unfortunately

there _are

no

suitably sharp

candidates. One

possible

choice is the line _{at ca} 13 mev in the Cs salt. But this has been

previously assigned

to the external lattice modes [21] ^{and is} most

probably

the

222 JOURNAL DE PHYSIQUE II N°2

~~~ ^~---

°---~

'f

~OH

E »

-~ /

~ /

~ ^/

j ,'2

c ,'

UJ »

1' ,' --"

~--'

~---4---j

~_~

70H

~ ₁₃₄

E ,'.)

"

)/

il132

, ~

[ ,,

~

130

~,--'~

~-""

128

0 20 40 60

Temperature (K)

Fig.3.

The temperature dependence of _70H and 60H bending modes in

Rb3H(Se04)2

(1) and

Cs3H(Se04)2 (2).

The lines _are only _a guide to the _eye.

Se04 librational motion. Its

intensity

in _our spectrum must arise from _a

riding

motion of the

hydrogen

atom. This

intensity

falls

consistently

_as the temperature

rises,

and has its

largest

decrease around

phase

transition in the Cs salt. Its

position

in energy remains

unchanged.

(This

is

explained below).

Here _we should _stress that _voH

certainly

exists in _our spectra but

unfortunately

_{we are} unable to

identify

it

directly.

This is

probably

because it is

severely

anharmonic. The effect of its

changing

_{energy as} the temperature rises is demonstrated below.

The

hydrogen

bond modes _were each modelled

by

two Gaussians _{on a}

sloping

baseline. The Gaussian

lineshape

is _a

good

first

approximation

of the convolution of the intrinsic

lineshape

of the mode and the instrument resolution function. Where _{we assume} little

dispersion

which is reasonable in the _case of

hydrogen

bond modes. In the _case of the Rb salt the two Gaussians

were

independently adjusted.

This

procedure

however failed when

applied

to the Cs salt at

temperatures ^above 25 K. In this _case the

intensity

ratio of the local mode to its

multiphonon wing (fitted

to the 5 K

data)

_was used to

supliment

the _70H data at other

temperatures.

The correcteness of the

procedures

is confirmed

by

the

good

fits alld consistent results.

(The analogous

treatment of the Rb spectra _gave within

experimental

errors the _same result _as the

independent adjustment

of the Gaussians. This also supports the

validity

of _our

procedures).

In the _case of the boH vibrations of the Cs salt the situation is _more

complicated

because this vibration is

usually

mixed with other modes [8]. ^{For this band} we defined

only

the

position

of it's centre of

gravity

and

so there _are fewer details for

boH

vibration.

The results of the data

analysis

are shown in

figure

3 and detailed in table II. From the table it is _seen that the Cs salt band

origins

of _70H and

boH

_{move to}

higher energies

_as the temperature ^{is raised. The}

frequency displacement

of _70H with

temperature

^is an

identify- ing

characteristic of this mode [18]. ^{As the} temperature ^{falls and the}

hydrogen

bond becomes

both shorter and stronger, the _70H mode

characteristically

moves to

higher frequencies.

This is in

complete

contrast to _our observations where the

frequency

falls

as the temperature decreases.

Table II. Parameters of the _70H vibration of the proton

pos. Multiphonon wing Multiphonon wing

Mb. units intens.

s

25 129.6+0.1 3.7+0.2 0.76+0.03 1.17+0.06 137.3+0.7

40 130.4+0A 7.3+0.7 0.74+0.04 1.14 138.7+0.6

50 132.0+1.0 8.0+0.9 0.78+0.05 1.20 140+1

60 133.8+0.5 9.0+0.7 0.79+o.03 1.22 140.2+0.7

pos. wing

arb. units intens. peak _pos.

5

40 136.2+0.2 6.5+0.5 1.24+0.08 1.7+o.2 141.7+o.8

60 135.9+0.3 8,1+0.5 1.26+0.09 1.8+0.1 142.6+0.6

Band movement was not observed for the 70H and

boH

bands in the Rb salt. Below _we shall

associate this with the Roo ^value of the Rb salt.

The

displacement

of _a band to

higher frequency

_as the

hydrogen

bond

weakens,

_or

lengthens,

is characteristic of _voH. Indeed the IR data from the _upper temperature

phase

of the Cs salt

clearly

show such _a temperature

displacement

for the _voH maximum [20]. ^The

displacement

is

approximately

Au

/AT

+~ 0.16

mev/K.

This value _can be

compared

_{to our} observations for 70H and

boH A7/AT

_+~ 0.17

mev/K

and

Ab/AT

_+~ 0.ii

mev/K.

Furthermore diffraction

results from the

high

temperature

phase

have

provided ARoo/AT

+~

8.2x10~~l/K _[13].

Therefore _{we can} calculate

A((7

+

b)/2)/ARoo

~1735.7

mev/I.

_This value _compares well with

expectations

for the _voH of

strong hydrogen bonds;

where

AvoH/ARoo

~1487.7 mev

Ii

[18].

On the basis of the above discussion _we

interpret

the unusual

softening

of the

hydrogen

bond

bending

modes _as

a result of the strong resonance between the anharmonic weak _voH

band,

and the _70H and

boH

bands. There is _a stronger interaction with the _70H because it lies closer to voH. This is shown

by A7/AT

>

Ab/AT.

The _voH mode softens _as the

temperature ^{decreases and due to the}

proposed

interaction of _voH with the

bending

modes these latter also show _a

softening

with temperature. ^The

changes

ⁱⁿ temperature ^behaviour of the

bending

modes _are observed _ca. 10 K below the

phase

transition temperature defined

by

dielectric measurements. The _reasons for these

discrepancies

_are

a)

different

dynamical

responses

probed by

dielectric and neutron

methods;

and

b)

the observed

softening

is not

simply

_a trivial effect of the

phase change.

The _70H

frequency

falls in both

phases,

but the rate of descent is less in the low temperature

phase.

The detailed examination of this

effect,

to

study

the

microscopic

mechanism of mode

softening

is

planned.

224 JOURNAL DE PHYSIQUE II N°2

Incidentally

the

ordering

of protons in

hydrogen

bonds below the

phase

transition

explains

the

strengthening

of the 13 mev band. As the protons order the _roH distance shortens to

significantly

less than half of Roo. The

hydrogen

atom is _more

clearly

associated with _a

particular

_oxygen atom and the

riding

motion is

improved.

In the _case of the Rb

salt,

with its shorter Roo distance _uoH lies

significantly

below either

70H or

boH.

Here _resonance is absent and _no temperature ^variation is observed.

5.2 THE _SELENATE viBRATioNs. The

region

from about 20 mev to 120 mev _covers the

usual

Se04

vibrations. These vibrations show _{up very} well in the Raman data of Lautid _et al.

[20].

^Indeed our

reported frequencies,

table

I,

_are in

remarkably good

_agreement with the

equivalent optical

values.

Only u2(Se04)

and

u4(Se04)

_are identified in _our spectra. At the lowest

temperatures

_v2 ^is

split

in both the Cs and Rb salts. This is

obviously

due to the

phase change

in the Cs salt

and it

disappeares

at

higher

temperature. It

provides

strong support for the _occurence of _a similar low temperature

phase

transition in the Rb salt between 60 and 40 K. No

splitting

is observed for the low

frequency

_v4 component in _our Cs salt spectra.

(Although

such

splitting

is _seen in the low

frequency

Raman

component).

Our _v4 band

peaks

at the _mean value of the v4 Raman bands. We

assign

this band to the

in-phase

_v4 vibration of the linked

Se04

ions. A

weak

dispersion

of this mode would

disguise

_an

optically

visible

splitting.

6. Conclusions.

We report the first INS spectra from the Cs and Rb acid selenates.

Although structurally

related to the acid

sulphates

no transitions

specifically

associated with _voH could be

certainly

identified and

only

_70H and boH _were

assigned.

The influence of _{voH was} however observed in the temperature ^{variation of} the _70H and boH modes of the Cs salt. The Rb salt has _{a voH} too low to interact with 70H ^or boH and _no temperature variation _was observed.

Split

selenate bands indicate _a

low-symmetry low-temperature phase

^{for both} Cs and Rb salts.

Acknowledgements.

We would like to thank D.

Abramich,

A.

Lautid,

F. Remain and A. Novak for the _{open access}

they provide

to their results and M.

Ichikawa,

T. Gustafsson and I. Olovsson for structural data

prior

to

publication.

Our thallks _are also due to Mrs. N-M-

Shchagina

for

sample preparation

alld the SERC for _access to the ISIS facilities.

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