Brillouin Spectroscopy Investigation of the Superionic Transition in CsH 2AsO 4

(1)

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Brillouin Spectroscopy Investigation of the Superionic Transition in CsH 2AsO 4

Y. Luspin, Y. Vaills, G. Hauret

To cite this version:

Y. Luspin, Y. Vaills, G. Hauret. Brillouin Spectroscopy Investigation of the Superionic Transition in CsH 2AsO 4. Journal de Physique I, EDP Sciences, 1996, 6 (7), pp.941-948. �10.1051/jp1:1996108�.

�jpa-00247224�

(2)

Brillouin Spectroscopy Investigation of the Superionic Transition in CsH2As04

Y.

Luspin (*),

Y. Vaills and G. Hauret

Centre de Recherches _sur la Physique des Hautes Tempdratures, Centre National de la Recherche

Scientifique, 45071 OrI6ans Cedex. France and

Universit6 d'OrI6ans, 45067 OrI6ans Cedex 2, France

(Received

23 January 1996, received in final form 13 March 1966, accepted 2 April 1996)

PACS.64.70.-p Specific phase transitions PACS.62.20.-x Mechanical properties of solids

PACS.78.35.+c Brillouin and Rayleigh scattering; other light _scattering

Abstract. A Brillouin scattering investigation in CsH2As04 has been performed _over _a temperature _range 20 200 ^°C which includes the superionic transition at Ts _+~ 167 °C. At Ts, large discontinuities

are observed for elastic constants Cii1 C33 and C*

=

(Cii

+ C12 +

2C~)/2

and, above Ts, _a broadening of the corresponding fines takes place. In the conducting phase

above Ts, the spectra ^reveal _a domain structure. The results _are discussed by comparison with compounds of CSHSe04 type. ^It is shown that _a linear coupling between strains and mobile protons in the conducting phase _can neither contribute to modification of elastic constants _nor to broadening of lines. The experimental results reflect _a strong general anharmonicity of the

lattice dynamics in the conducting phase.

Rdsum4, Une 6tude _par diffusion Brillouin de CsH2As04 _a 6t6 faite _sur I'intervalle de tem-

p6rature 20 200 ^°C qui contient la transition superionique h Ts

+~ 167 ^°C.

I

Ts, d~importantes

discontinuit4s sont observ6es _pour [es _constantes Cii, C33 et C*

= (Cii + C12 +

2C$)/2

_et~

au-dessus de Ts, _un 4Iargissement des raies correspondantes apparait. Dans la phase conductrice au-dessus de Ts, [es spectres ^r6vbIent une structure _en domaines. Les r6suItats sont discut6s _par comparaison _avec [es compos6s du type CSHSe04. On montre qu'un couplage Iin6aire entre _une

d6formation et [es protons mobiles dans la phase conductrice _ne peut _pas contribuer h la

mo-

dification des constantes 6Iastiques ni h I'6Iargissement des rates. Les r6suItats exp6rimentaux

r6vbIent pIut6t _une forte anharmonicit6 g6n6raIe _pour la dynamique de r6seau dans la phase conductrice.

1. Introduction

Cesium

dihydrogen

arsenate CsH2As04, hereafter abbreviated CDA,

belongs

to the KDP

(KH2P04) family

which has been the

object

of intense research for

generally

focused _on the low temperature

ferroelectric-paraelectric

transition, over three decades.

(*) Author for correspondence

(UFR

Facult6 des Sciences, Laboratoire

d~(tudes

_Physiques _des Mat6riaux, B-P. 6759, Universit6 d'Orl6ans, 45067 Or16ans Cedex 2, France)

(ditions

_de _Physique ₁₉₉₆

(3)

942 JOURNAL DE PHYSIQUE I N°7

Above _room temperature, two

phase

transitions have been detected _near 123 ^°C and 165 ^°C

respectively [1-5].

The lower transition appears

only

ⁱⁿ

X-ray

and _some DTA

investigations,

while the _upper _one is

systematically

detected whatever the type of

investigation.

It has been

recently

established _[6] that the

highest

temperature

phase

is _a

protonic superionic

conductive

one. CDA and cesium

dihydrogen phosphate (CDP)

_are the

only

two

compounds

in the KDP

family

which _are

known,

to

date,

to exhibit such _a conductive

phase

_[6].

The properties of CDA above _room temperature ^have

only

been

scarcely investigated.

We report here _an

investigation

of the elastic behaviour

by

Brillouin spectroscopy over a tem-

perature range which includes the two transitions cited above. The interest of such _a

study

is enhanced

by

the fact that conductive

phases

also exist in

other,

but

structurally different,

families of

hydrogen

bonded

compounds

such _as MHSe04

(with

M

=

NH4,

Rb and

Cs)

that

we have

recently investigated by

Brillouin

scattering [7-9].

2.

Experimental

and

Crystal

Data

The Brillouin

scattering

experiments were

performed

with _a spectrometer ^which ^is a pressure

scanned, triple passed plane Fabry-Perot

interferometer

(effective

finesse 70,

resolving

power

760000).

The spectra are

frequency

checked

by

_a Michelson interferometer in

parallel.

The

light

_source is the

lo

₌ 514.5 _nm line of _a

single frequency

Ar ion laser.

The

samples

were cut from

monocrystals

which _were obtained

by

seed

growth

from _aqueous solution

by

slow

evaporation.

At _room temperature, the structure is

tetragonal

with space group IT2d

(the

_same _as KDP _at

room

temperature).

The most recent measurements of cell parameters

give

a = b

= 7.9865

I

and _c

= 7.8979

I

_[10].

The first transition _near 123 °C has been observed

by

DTA in _some

experiments

[2, 3], ^but

not

systematically

_{[4], and}

by X-ray diffraction'[3,4].

The structure of the

phase

above 123 ^°C is

given

as monoclinic but without data about parameters [4].

It has been

suggested

that the

superionic phase,

which takes

place

above the second transition

near Ts _" 165 °C, has _a monoclinic structure [2].

However,

in _an

X-ray investigation

_[4], the

structure has been found to be orthorhombic with parameters which _are different from those

at _room temperature.

Recently,

Baranov et al. have claimed _a cubic structure on the basis of

optical

observations [6].

Thus,

_we think that no definitive data _are _now available about that structure.

At _room temperature, we have measured the refractive indices at lo and obtained the values na = 1.5749 and _n~ ₌ 1.5525 which _are in excellent agreement with those cited in [11]. ^The

mass

density

_p ₌ 3.610 g cm~~ has been deduced from cell parameters at room temperature [10].

In

computing

the elastic constants from Brillouin

frequency shifts,

_we have used the _room temperature values of _mass

density

and refractive indices at any temperature. No data _are available about their temperature dependences and it is

usually

considered that their evolution with temperature may

partially

_compensate _one another.

In every measurement, the

sample

was immersed in silicon oil _as index

matching liquidj

the

advantages being

a reduction in the _amount of stray

light

and _a _more

homogeneous

temperature of the

sample.

To avoid

hysteresis effects,

all measurements were

performed by heating

^the

^crystals.

^Above

Ts,

the

samples

still have _a

good optical quality (identical

to that between _room temperature

and

Ts),

but _an irreversible deterioration takes

place

when temperature decreases

through

Ts from the

conducting phase.

The

samples

become

milky, retaining

^the

integrity

of their external

shapes,

but the laser beam _can _no

longer

enter them.

(4)

Table I. Characteristics

of

the

investigated scattering

geometries. ^The itsitai convention

x))a, g))b(= a)

and

z))c

and that

depicting

_wave vector and

polarization

directions

of

the incident and scattered

light

beams have been itsed.

Scattering

_geometry direction of _q

expression

of

ii

+

,

+ Cii

2 ₊ ₊

y)

[100] Gil

3

1-z -g)[x,x](-g+z) [ool]

C33

4 C*

#

(Cll

+ C12 +

5

jx+z)jj-x+z),yjj-x+z) jiooj

Above

Ts,

for

sample

immersed in oil, _we observed in oil _no bubble

starting

from the

samples.

That would indicate that _no obvious water loss _occurs in the studied temperature _range. It is to be noted that for

experiments performed

in air, there _are

significant disparities

about the

temperature oi the onset oi water elimination

,

which is found between 150 and 250 °C

[2,4].

In order to corroborate _our observations, we have

performed

_an

X-ray

diffraction

analysis

_on _a

sample

which has been used in Brillouin

investigations,

^alter

cooling

down to room temperature and verified that the obtained spectrum is identical to the standard _one oi CDA

[lo].

3. Brillouin

Experiments

We used

right angle scattering

geometry (or the

experiments:

in this _case the

velocity

V of _an acoustic _wave is related to the

corresponding

Brillouin

frequency

^shift _u

by:

v =

>ou/jn)

₊

n])1/2

where _n, and _ns are the retractive indices (or the incident and scattered

light

^beams

respectively.

The

scattering geometries

_are

reported

in Table I

along

with the direction of the acoustic

wave vector q and the

expression

of

pV~

in terms of elastic constants in the

tetragonal

_room

temperature

phase.

The

piezoelectricity

of the

tetragonal phase

introduces _no distinction between elastic _con- stants at constant electric

displacement Cf

and elastic constants at constant electric field

C(

for

Cii, C33,

and C12. On the contrary,

C(

and

Cl

have to be

distinguished;

the values oi the

piezoelectric

modulus d36 ₁₁_{2] and} ^{oi the} dielectric constant _e33 lead to _a relative difference

of15% between them at _room temperature.

We have focused _on Brillouin lines

corresponding

to

longitudinal

^elastic waves which _are intense lines, as

usual,

and for which

pV2

is _a

simple

expression in terms of elastic constants

(the

four first

scattering geometries).

On has been

investigated

in two

scattering geometries

in order to detect _a

possible splitting

in the

high

temperature

phase.

We have also studied the Brillouin line

corresponding

to the transverse elastic _wave related to

C(

for two reasons;

firstly,

its

intensity

_appears to be _as

large

_as that of _a

longitudinal

_wave and

secondly,

it is the

constant

CA

which exhibits the famous decrease to _zero at the low temperature ferroelectric

phase

transition, _common to all the KDP

family compounds.

It must be pointed out

that,

in the

superionic phase,

the elastic constants have been named

Cii,

C33 and C* in

keeping

with the nomenclature at _room temperature. ^The structure of this

phase

is not

clearly

established and _our data

only

represent the ,~alues of

pV2 corresponding

to acoustic _waves

propagating

along

the directions

[loo], [ool]

^and

[llo]

defined _at _room temperature.

(5)

5( j ^. lx+z)ly,yll-x+zl

ii o lx+y)lz,zll-x+y) 52

~

lh so

~i

I )

~~

§~

ti 2j i~

22

~/

20

~

50 100 150 200 1°)

Fig. 1. Temperature dependence of elastic constant Cit. Di and D2 refer to the two observed doublets

(see text).

Lines _are guides for the _eye.

4. Results

4.1. ELASTIC CONSTANTS. At _room temperature, the

following

values have been obtained

(in GPa)

_:

Gil

" 54.5 C33 _" 41.8

C$

= 1.82 C*

= 29.7 C12

" 1.3

with _an _accuracy estimated to

I%,

except ^for C12 ^for which the _accuracy

drops

to

loo%,

due to its indirect determination. These values agree

satisfactorily

with

although they

_are

systematically higher.

This fact _can be

explained by

the lower value of the

mass

density

^which ^has been taken in [13].

The temperature

dependences

of

Cii, C33, C(

and C* _are

reported

in

Figures

^and ^2.

They

show _no obvious feature around the first transition _near 123 °C.

Abrupt

and relative

large

downward

jumps

for each elastic constant appear ^at the superionic transition, ^which we

have found to _occur at Ts

" 167.3 + 0.1

°C,

without

pretransitional

evolution below Ts.

Above

Ts, unexpected

results _are obtained. In _a

given scattering

geometry, ^if the

sample

is translated in order to

change

the

position

of the

scattering

volume

(of cylindrical shape

with _a diameter of 0.1 _mm and _a

length

of 0.2

mm)

the spectrum,

involving initially

a

given

Brillouin

doublet,

_may

change quasi-discontinuously, exhibiting

_a _new doublet with _a different

frequency

shift and _a different _cross section. Such _an

exploration

of the

samples

is tedious because the

spatial

extensions of

regions giving

^different spectra can be very

different, depending

on the

samples.

^In the

sample

cut to _measure

C*, only

_one type of spectrum ^has ^been

detected,

while for every other

scattering

geometry two types of doublet have been observed which _we have named Di and D2

(Di being

the doublet with the

highest frequency shift).

The lines for Di and D2 have been found to be well

polarized

with the _same

polarization

_as that of

the

corresponding

doublet below

Ts. Taking

into account their

intensities,

it is reasonable _to associate them with

longitudinal

acoustic _waves. In _some spectra, an additional doublet with very small

intensity

and small

frequency

shift is

unambiguously observed,

with _a

polarization

which is the _same _as that of the main doublet. The characteristics of the spectra obtained

just

above

Ts

_are

reported

in Table II.

(6)

~i

iii

39

j*

%i+

29

$~

ti 27

§

25

fi

~~

~

w 23

[*

~

i

~

21

C66

Iii °2

50 100 150 200 1°[)

Fig. 2. Temperature dependence of elastic constants C33, C*, and

C~.

For Di and D2: _as in

Figure 1. Lines _are guides for the eye.

Table II. Characteristics

of

Briiiouin spectra

jitst

^above Ts. R is the ratio

of

^the recorded line

height

^H with respect to that

of

the

corresponding

line

jitst

below

Ts,'r

is the ratio

h/H,

h

being

the recorded line

height of

the additional weak doitbiet.

Scattering

Main doublet Additional doublet

geometry ^R ^existence r

Di 25.7

unchanged

_yes 3.5 2.6 _x

D2 21.7 enhanced

by

~w 2 yes

iv. weak)

4.0 2.2 _x 10~2

2 Di 25.7

unchanged

_yes 3.9 3.6 _x

D2 21.2 enhanced

by

~w 2 yes

iv. weak)

4.7 2.o _x 10~2

3 Di 23.3

unchanged

_yes 4.0 4.0 _x

D2 20.9 enhanced

by

~w 2 no

4 21.6 enhanced

by

~w 2 _no

When the temperature increases, the doublet related to

C( _disappears _abruptly

_at Ts.

Above

Ts

_no line with the _same

polarization

_can be detected in spite of careful research. This result shows that either the line

height

is reduced

by

_a ^factor greater than 100 _or the

frequency

shift

(at

constant

height)

is lower than 1.10

GHz, corresponding

to _a value of

pV2 equal

to 0.25 GPa.

4.2. BRILLOUIN LINEWIDTHS. Below

Ts,

_no

broadening

of lines has been detected. But

above

Ts,

_every line related to _a main doublet exhibits _a

broadening.

The full widths _at half maximum

(FWHM) Pi,

T3 and T* of lines

corresponding

to elastic constants Cii, C33 and C*

are

reported

in

Figure 3,

^after deconvolution. No critical behaviour appears near the

superionic

transition, but smooth increases take

place

when temperature ^increases.

(7)

lx+z)ly,yl(-x+z) . 01 » 02

~l lx+yllz,zll-x+y) O01 A02

~

,o ^~

~

o.$.~

⁸ ^* ^.

.~

iSJ

,' ^>

~~~~ ^' > & ^>

'

,

a ~

lIr

/§

r3

. 01 '02

~

~ r~ _~

~ ~

, o

~ o

~

°O,

>o

170 180 190 200

(8)

The set of results show that the directions of the

crystallographic

_axes in the domains _are not related in _a

simple

_way to those of the

tetragonal phase

since it appears that neither of them remains _common to the various domains.

Furthermore,

the existence of _an additional weak doublet with the _same

polarization

_as the main

doublet,

in almost all the

scattering geometries,

would indicate that the acoustic _wave _vector _q _never lies

along

a

crystallographic

axis in _an

orthorhombic, tetragonal

_or cubic structure _or that _q lies

along

_a

non-binary

axis of _a monoclinic _or triclinic structure. On the basis of the Brillouin _results

only,

_we think that

no definitive conclusion _can be obtained about the number of domain types ^and about the orientation of their

crystallographic

axes.

The domain structure revealed

by

Brillouin

scattering

_can be related to the

changes

^which

have been

reported

in visual observation _[2] and _can

explain

the fact

that, apparently,

the

crystal

becomes

optically isotropic [2,6].

5.2. ELASTIC ANOMALIES. The

abrupt jumps

ôf êlastic constants at Ts ând ^the ^simulta-

neous

broadening

of lines indicate _a

sharp

first order transition. From that point ^of view, ^the

elastic behaviour of CDA

strongly

resembles that of the

compounds NH4-,

Rb- and CSHSe04 of the MHSe04

family [7-9].

These results _are in

keeping

with the

similarity

of conductive

characteristics between the KDP

family

and the MHS04 closed to the MHSe04 _one, which has been

previously emphasized

_[6]. Such _a

similarity

_was _a priori

unexpected

since in the

MHSe04 family

the number of protons is half that of their

possible equivalent sites,

whilst in the KDP

family

the number of

possible equivalent

sites is

just equal

to that of protons.

The

abrupt jumps

of elastic constants, whatever the

domain,

^have to be related to the break of

hydrogen

bonds at Ts which would reduce the lattice cohesion. However, _a

complete understanding

of the results first requires the symmetry

analysis

of the transition and therefore the

knowledge

of the structure above Ts. If _a

group-subgroup

relation

holds,

the presence of

domains in the

conducting phase

would indicate that the low symmetry

phase

is the

high

temperature

phase,

_a situation which has been rather

scarcely

observed. Another

possibility

is that the symmetry _groups ^of the low and

high

temperature

phases

_are

subgroups

of the _same parent _group. In this _case, the transition would _occur between two

phases

which may or may not be related

by

_a

group-subgroup

relation. No definitive conclusion _can be drawn about the connection between the existence of domains and the symmetry

change,

since the structure of the

conducting phase

is not known at present.

In the

conducting phase, couplings

between elastic _waves and mobile protons are

expected

to take

place.

A

general study

of these

couplings

has been

given by

Huberman et al. [14]. ^From that

study,

it _can be deduced that _a linear

coupling

les between _a strain _e and _a

pseudospin

variable _s, related to the _mean values of proton occupation numbers _on their

possible

sites, leads to a

frequency dependent

elastic constant

C(~a)

and Brillouin linewidth T(~a) ^which are

given by

_[9]:

cjw)

=

p~J2/q2

₌

co zico~slis fl)/l~l

₊ _ca~)

T(~a) =

2fl

=

(/hCo/C(~a))~a~~s/(~)

₊ _~a~)

where ~s is the relaxation

frequency

for fluctuations _{of s,} Co the bare elastic constant,

fl

the

damping

of elastic _wave and

/hCo

" Co

C(o)

₌ ^l~.

No NMR

investigation

about the measurement of _~s has been

performed

till _now.

Taking

into account the

similarity

of the

conducting

characteristics

[6,15]

if _we _assume that the value of _~~ for CDA is of the _same order of

magnitude

_as that for

CSHSe04, namely

_~s

~w

o.5

GHz,

the _same conclusion _as in that

compound

_can be reached for CDA _as well since

~)

< ~a~ holds.

On _one

hand,'the

influence of the

coupling

on the elastic constant is relaxed

and, consequently,

(9)

no decrease of that constant will _occur; _on the other hand, the

expected broadening

is much smaller than the

experimental

_one.

Therefore,

the observed

broadening

would reflect other

mechanism(s).

From this point ^of

view, investigations

of lattice modes other than acoustic modes _are suitable. The fact that _no critical behaviour of the

broadening

_appears _near

Ts might

be _an argument in favour of _a strong

general anharmonicity

of the lattice

dynamics

in

the

conducting phase.

5.3.

QUASI-ELASTIC

SCATTERING. The estimated value for _~s would

explain why

_no quasi- elastic

scattering

appears in the Brillouin spectra. ^The contribution oi the mobile protons is

expected

to

give

_an unshifted

peak

with _a width similar to that oi the apparatus. ^Therefore this

contribution,

if it takes

place

with detectable

intensity,

would be hidden

by

the elastic

Rayleigh peak.

6. Conclusion

Our Brillouin

investigations

have shown that

important

discontinuities of elastic constants hold at the

superionic

transition in

CsH2As04,

without

pretransitional

features. In the

conducting phase,

_a

broadening

is observed for each

investigated

Brillouin

line,

without critical evolution

near the transition. All these results

strongly

resemble those of the MHSe04

family

of _com-

pounds, although

these

compounds

_are

structurally

^different ^from ^CDA. In the

conducting phase,

the results show the existence of _a domain structure, _a ^result

which, unfortunately,

_can-

not be discussed in relation to the structure

change,

due to the lack of data _on the

conducting phase.

It _seems that the

broadening

of lines above the transition would reflect

a strong an-

harmonicity

of the lattice

dynamics,

_a

suggestion

that needs to be corroborated

by

_a widened

study

of the lattice

dynamics.

References

ill

Nicholson J-Y- and Soest

J-F-,

J. Chem.

Phgs.

60

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715.

[2] Goffman

V-G-,

Ivchenkova

M.D.,

Mishchenko A-V- and Shaimerdinov

B-U-,

Sov.

Phys.

Crystaiiogr.

22

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631.

[3] Hart

S.,

Richter P-W- and Clark

J-B-,

J. Solid State Chem. 37

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302.

[4]

Zhigamovskii

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Polyakov Yu.A., Bugakov V-I-,

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M-A-,

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K.,

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Y.,

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Y.,

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[8]

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Vaills Y. and Hauret

G.,

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Y.,

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[lo]

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