Discontinuities in Elastic Properties of CsH2PO4 at the Superionic Transition

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Discontinuities in Elastic Properties of CsH2PO4 at the Superionic Transition

Y. Luspin, Y. Vaills, G. Hauret

To cite this version:

Y. Luspin, Y. Vaills, G. Hauret. Discontinuities in Elastic Properties of CsH2PO4 at the Superionic Transition. Journal de Physique I, EDP Sciences, 1997, 7 (6), pp.785-796. �10.1051/jp1:1997192�.

�jpa-00247362�

Discontinuities in Elastic Properties of CSH2P04 at the

Superionic ^Transition

Y.

Luspin (*),

^Y.

^Vaills

^and

^G.

^Hauret

Centre de Recherches _sur la

Physique

des Hautes

Tempdratures,

Centre National de la Recherche

Scientifique,

45071 Orldans

Cedex,

France

(Received

23 December 1996, received in final form 18

February

1997, accepted ²¹

February 1997)

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. An

investigation

of the elastic properties ^of CSH2P04 has been

performed by

Brillouin spectroscopy

throughout

a temperature _range which includes the superionic transition at Ts _+~ 233 °C. At Ts, discontinuities have been observed for elastic constants

Cii, C22,

C33 and C* =

(Cii

+C22

+2C66)/4+ [((Cii

C22)~

+4(C12 +C66)~)~/~]/4.

Above Ts, the

corresponding

Brillouin lines show _a

broadening

without

pretransitional

features. In the

conducting phase,

a domain structure is revealed

by

the spectra. The observed elastic anomalies _are similar to

those obtained in other

hydrogen-bonded crystals,

such MHSe04

(with

M

=

NH4, Rb, Cs)

_or CsH2As04. In the

conducting

phase. ^{it has been}

show/hat

a bilinear

coupling

between strains and mobile protons neither contribute to a

significant

variation of the elastic _{constants nor can}

explain

the values of the observed

broadenings.

It is concluded that the experimental results could reflect _a strong

general anharmonicity

of the lattice

dynamics

in the

conducting phase.

R4sumd. Une dtude des

propridtds dlastiques

de CsH2P04 _a dt6 faite _par

spectroscopie

Brillouin sur un intervalle de

temp6rature

qui indut la transition

superionique

h Ts _+~ 233 ^°C.

I

Ts, des discontinuitds sont observdes _pour les constantes dlastiques

Cii, C22,

C33 et C*

=

(Cii

+ C22 +

2C66)/4

+

[((Cii

_C22)~ +

4(C12

+

C66)~)~/~]/4.

Au dessus de Ts, les rates Brillouin correspondantes

pr6sentent

_un

dlargissement

sans effet prdtransitionnel. Dans la phase conductrice, _une structure en domaines est mise _en dvidence par les spectres. Ces _ano-

malies 6Iastiques ressemblent h celles qui ont 6t6 observ6es dans d'autres cristaux h liaisons

hydrogAne

tels que MHSe04

(avec

M

= NH4, Rb,

Cs)

_ou CsH2As04. Dans la phase conductrice,

nous avons montrd qu'un

couplage

biIin6aire entre Ies ddformations et Ies protons mobiles _ne

pouvait _pas contribuer h _une variation

significative

des constantes

dlastiques

ni rendre compte des valeurs obtenues pour les

dlargissements.

Il _a dtd conclu _que les rdsultats

expdrimentaux

pourraient refldter _une forte anharmonicit6

g6ndrale

de la dynamique de r6seau dans la

phase

conductrice.

(*)

Author for

correspondence (e-mail: yluspin©univ-orleans.fr)

Q

Les

#ditions

_{de Physique 1997}

1. Introduction

Potassium

dihydrogen phosphate, KH2P04 (abbreviated KDP),

and its alkali

phosphate

and

arsenate

isomorphs

form _an

important

_group of

hydrogen-bonded crystals.

In the last

decades,

these substances have been

extensively

studied with

respect

to their

ferroelectric-paraelectric transition,

which _occurs at low

temperature.

^Above room

temperature,

_many

crystals

of this KDP group

undergo

other

phase

transitions

ill

but

they

have seldom been studied.

Cesium

dihydrogen phosphate CSH2P04,

^hereafter abbreviated

CDP,

is

generally

considered

as a

compound

of this group,

although

its

paraelectric phase

does _not exhibit the

tetragonal

structure of the

prototype

KDP. This

paraelectric phase

is monoclinic _as is that of

RbD2P04

_(2]

and

CSD2P04

_(3];

therefore,

CDP is considered _{as a}

low-symmetry representative

of the KDP group. The low

temperature

ferroelectric transition in

CDP,

which _occurs at 153

K,

has been

intensively

studied due to the unusual

pseudo

one-dimensional character of the

properties _[4].

Above _room

temperature,

two

phase

transitions have been

reported

_11,

5, 6],

but _a

controversy

still remains about the existence and the

temperature

^{of the lower} one

[7,8].

It has been shown [9] ^{that the}

highest

temperature

phase

is _a

protonic superionic

one.

Among

the alkali

phosphate

and arsenate

compounds belonging

to the KDP group which exhibit _a

phase

transition above

room temperature,

only

CDP and CDA

(CsH2As04)

have been found to become

superionic

conductors

[10].

The

properties

of both these

compounds

above _room

temperature, particularly

in the

vicinity

of the

superionic transition,

have been

scarcely

studied to date.

Therefore,

_we have

planed

to

investigate

their elastic

properties by

Brillouin

spectroscopy

and have

recently reported

the results obtained in CDA

ii Ii.

We present here _a similar

study

_on CDP. Such _a

study

is _a

priori justified by

the structure difference of these

compounds.

The _room

temperature paraelectric (PE) phase

^{of CDA is}

tetragonal,

like that of

KDP,

with the _{same space} group

IT2d

while the

room

temperature

^PE

phase

of CDP is monoclinic with space group

P21/m.

The PE

phase

of CDP is

isomorphic

to the _one of

TIH2P04 (TDP)

which has however _a

slightly

different _space

group

(P21la).

This last

compound,

also

belonging

to the KDP _group,

undergoes

_a ferroelastic transition above _room

temperature

which has been

recently

refined

by

neutron diffraction

[12].

2.

Experimental

and Brillouin Data

Brillouin

scattering

spectra have been obtained with _a

spectrometer

which is _{a pressure}

scanned, triple passed Fabry-Perot

interferometer

(effective

finesse

70, resolving

power

760000).

The

spectra

are

frequency

checked

by

a Michelson interferometer in

parallel.

We worked with the

~o

= 514.5 _nm line of _a

single frequency

Ar ion laser and the

stability

of the line is controlled

by

_an iodine cell.

The

samples

have been cut from

monocrystals

obtained

by

seed

growth

from _aqueous solution

by

_very slow

cooling.

As noted in the

introduction,

the _room temperature structure of CDP is

monoclinic,

not

piezoelectric,

with space group

P21/m (C(~) [13].

^{The latest} measurements of the cell _pa- rameters

[14] give

_a

= 7.9072

I,

b

= 6.3869

I,

c = 4.8792

I

_and

fl

= 107.712°. There _are two formula units per cell. It has been

pointed

out that the structure is

quasi-orthorhombic

with the choice a'

= 2a _{+ c,} b'

= b and c'

= c since it

gives fl'

= 90.22°

[15].

Unlike the _case of

KDP,

for which all

hydrogen

bonds _are

symmetry related,

there _are two

crystallographically

_non

equivalent hydrogen

bonds in the structure at _room temperature

related to

Hill

and

H(2)

atoms

[13,15].

The

longer bonds, involving Hill

_atoms, form chains of

P04

tetrahedrons

along

the _c axis and

they

are ordered _at that

temperature.

^{The other}

H(2)

hydrogen

bonds make

zigzag

chains

running along

the b axis and the

corresponding protons

x

a

b,y

C Z

Fig.

1. Relation between the chosen frame _{~, y, z,} to which the elastic constants are referred and the

crystallographic

_axes of the monoclinic _room temperature

phase.

are found to be disordered _on two off-centre sites with

significant

correlations [3] ^{and to become} ordered below the ferroelectric transition. These two kinds of connected chains make

layers parallel

to

(100) planes

which

correspond

to the observed

cleavage plane [16].

^This structure

strongly

resembles that of TDP at _room

temperature [17].

Above _room

temperature

two

phase

transitions have been found _near 149 °C and 230 °C

by

differential

scanning calorimetry [1,5]. However, contradictory

results exist for the lower transition. In _{a recent}

study _[18],

this transition did _{not appear} in DSC but _a broad heat

capacity anomaly

has been detected _near 149 °C. An

X-ray

diffraction

investigation [19]

^has revealed that _no

change

of the _{space group occurs} at 149

°C; only

_a weak feature in _one of the thermal

expansion

coefficients has been observed. In _an earlier work

[6],

^it was

reported

that

a

monoclinic-tetragonal change

_near 150-160 °C is

possible

_{as a} result of

prolonged heating

in this temperature range. In other

experiments performed

above _room

temperature,

^such

as

conductivity

measurements

[9,10]

_or ^Raman

spectroscopy [20],

^{the lower transition has}

not been detected. It has been also claimed

[7, 8] that, by appropriate pretreatments

of the

samples,

_a transition _{can occur} at 107 °C which is much lower than the

temperature

149 °C cited above.

Thus,

it _can be considered _up to date that _no definitive conclusion is avalaible

about the existence of that transition.

The second transition _near

Ts

_+~ 230 °C is well marked in every

experiment.

The

high

temperature

phase

has been identified _{as a}

protonic superionic

one

[9,10],

^but

contradictory

data exist about its structure. From

polarization microscopic

observations Baranov et al.

[10]

^concluded to _a cubic structure. In _an

X-ray investigation performed

_on

samples

in

air,

Bronowska et al.

[19]

^obtained a monoclinic structure 7 °C above

Ts

which is found to coexist with other

phases coming

from the

decomposition

of CDP

by

successive water

losses;

but in

new

experiments performed

in _a

H20 atmosphere by

the

powder method,

_a cubic structure has been found with Pm3m

(O()

_{space group}

_[21].

At _room

temperature,

_we have verified

that,

in the

(010) plane,

the

angle

between _one axis of the refractive index

ellipsoid

and the _c axis is

+~ 4.5° _as

previously reported [22].

The small value of that

angle

shows

that,

in this

plane,

the

ellipsoid

_axes almost coincide with the

crystallographic

_axes ^a' and _c. At _room

temperature,

we have measured the indices at

~o

with

light polarized along a',

b and _c; the

following

values have been obtained: _{na, =}

1.518,

nb = 1.512 and _nc

= 1.537.

For all the

phases

above _room

temperature,

^{the elastic constants have been referred to} a set of

orthogonal

_{x, y} and _{z axes} with y _ii b, z ii c, x I y and _z

(Fig. I).

It _can be remarked that x, y and _{z axes} almost coincide with the

crystallogaphic

_axes of the

quasi-orthorhombic

^cell.

Table I. Characteristics

of

the

investigated scattering geometries.

^{The ~s~al} convention

depicting

wavevector and

polarization

directions

of

the incident and scattered

light

beams has been ~sed.

Scattering geometries

Direction of _q

pV~

I

I-x+z)iv,vilx+z) [loo] Cii

2

(x vi [z, z](x

+

pi _[010] C22

3

(x

+

z) _{[001] C33}

4

(-v)iz>zi(x)

C*

The _mass

density

_p

= 3.254 g

cm~~

_{has been deduced from cell parameters}

[14].

^Due to the weak

change

of unit cell volume between 20 °C and 207 °C

[19],

^{the lack of data about} the _mass

density

above 207 °C and about the

temperature dependence

of refractive

indices,

we used the _room

temperature

values of both

density

and refractive indices in

computing

the elastic constants from Brillouin shifts at any temperature. ^{It is}

usually

considered that the

variations _versw

temperature

^of these two

quantities

_may

partially compensate.

During measurements,

^the

samples

_were immersed in silicon oil _as index

matching liquid

to decrease the

stray light;

another

advantage

is _a better

homogeneity

of the

temperature

ⁱⁿ the

sample.

To avoid

hysteresis effects,

all measurements have

only

been

performed

_on

heating.

Above

Ts,

the

samples keep

their

optical quality;

but _an irreversible deterioration _can be observed

when

temperature

decreases

through Ts

from the

conducting phase.

Due

probably

to the appearance of _numerous

microcracks,

the

samples

become

milky, retaining

the

integrity

of their external

shapes,

but the laser beam _{can no}

longer

enter them. These results _agree with

previous

observations

[10].

^After

cooling

down to _room

temperature,

if the

samples

are heated for _a second

time,

the

opacity

does _not

disappear

above

Ts.

Contradictory

data exist about the onset of

decomposition

of CDP in

experiments performed

in air. It has been

reported

that _a thermal

decomposition

starts in the range 175-225 °C

[19, 23],

in contradiction with others observations made _up to 250 °C

[5,18];

Romain et al.

[20],

which worked with

samples

in sealed

glass tubes,

did not detect _any

decomposition compounds

up to

+~

250 °C. For _our

samples,

heated in oil _up to 260

°C,

_no start of bubble has been

observed;

that would indicate that _no obvious loss of water occured below that

temperature.

To _ensure this

result,

_we have

performed

_an

X-ray

diffraction

analysis

_{on a}

sample

which has

been heated _up to 260 °

C,

after it _was cooled down to room temperature, and _we have checked that the recorded

spectrum

^{is identical to the standard} one of CDP at room

temperature [14].

3. Brillouin

Experiments

In the

right angle scattering geometry,

which has been

used,

the

velocity

V of _an acoustic _wave is related to the

corresponding

Brillouin

frequency

shift _u

by:

V

=

~ou/(n)

₊

_n))~/~

where _nj and _{ns are} the refractive indices for the incident and scattered

light

beams

respectively.

Parallelepipedic samples

have been cut and oriented _so that the acoustic _wave vector q lies

along

_{x, y} and _{z axes.}

Investigations

uersw

temperature

have been focused _on Brillouin

lines which

correspond

to

longitudinal

_or

pseudo-longitudinal (pL)

acoustic _~v-aves

(see

Tab.

1).

For these waves,

pV~

is related to elastic constants

by:

q ⁱ z

pvj

=

jail

+

c55

+

(jail c55)~

₊

4C15)~/~l/2 q[[y pV/=C22

q ⁽ Z

pV/

"

(C33

+

C55

+

((C33 C55)~

+

~~15)~~~j/~.

If _{we assume} that

C15

and

C35

_are small with

respect

to

Gil C55

and

C33 C55,

_we have:

pV/

_Q

Cii, pV/

=

C22, p(~

R

C33.

This

assumption

_can be

justified by

the fact that the chosen _{axes x, y} and _z almost _co- incide with the directions of the

pseudo-orthorhombic

_axes

a',

b and _c.

Nevertheless,

to check it more

quantitatively

at room

temperature,

we have made additional measurements on

pseudo-transverse (pT)

acoustic _waves in the

samples

described above and in another

sample

cut with

edges along

_{x, y} and _z. We have measured the values of

pV/~

^and

pV/~

along [100], [001], [101]

^and

[10i] (among

which

pV?

₌ 32.8 GPa and

pV/

= 67.2

GPa).

From these

values,

those related to the last two directions

being only

used in the relation

p(V/~[101]

+

V/T[101] V/~[10( V/~[10()

₌

2(C15

+

C35),

the

following

results have been obtained

(in GPa):

Cii

=

32.4, C22

₌

29.6, C33

₌

67.0, C55

₌

4.73, C15

₌

3.3, C35

= 3.2

with _an accuracy estimated _to

2%, except

^for

C15

and

C35

for which it is

equal

to

20%.

It _can be concluded that

pI[~

^and

pV/

coincide with

Cii

and

C33

within the measurement accuracy.

We have also

performed

_a

temperature investigation

of the

pseudo-longitudinal

wave with q

along [l10].

The related

expression

of

pV~

is _very

cumbersome;

within the

assumption

of _a

quasi-orthorhombic symmetry (I.e.

if _we consider that

C15, C35

and

C46

are Gt

0),

_we have:

PV~

# C* it

(Cll

₊

C22

+

2C66)/4

+

(((Cll C22)~

+

4(C12

+

C66)~)~~~j/4.

It is to be

emphasized that,in

the

high temperature phases,

_we have named the elastic constants

Cii, C22, C33

and C* in

keeping

^{with the} nomenclature used in the _room

temperature phase.

Indeed, they represent

the values of

pV~ corresponding

to acoustic _waves which

propagate along

the directions

[100], [010], [001]

^and

[l10]

defined with

respect

to the chosen frame at

room

temperature,

^because neither the structure _nor the

crystallographic

axes are known.

4. Results

4.I. ELASTIC CONSTANTS. The

temperature dependences

of

Cii, C22, C33

and C* _are

reported

in

Figures

2 and 3. No obvious features _are detected around 107 °C _or 149 °C

corresponding

to the uncertain transition discussed above. On the

contrary,

discontinuities

occur in every elastic constant at the

superionic

transition which _we have found to _occur at

Ts

= 233.1+ 0.I °C. Between 20 °C and

Ts,

the four _curves exhibit _a downward

bending

which is _{more or} less

marked, depending

_on the constant.

Above

Ts, unexpected

results _are obtained for

Cl1, C22,

and C*. In _a

given scattering

_geom-

etry,

^{when the}

sample

is translated to

modify

the

position

of the

scattering

volume

(cylindrical shape

with _a diameter of 0.I _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 value for the

frequency shift,

the

broadening

and the

intensity.

The

spatial

extension of the

regions

^related to _a

given

doublet _can be very

different, depending

_on both the dou- blet and the

sample;

therefore it is difficult _to

perform

_a

complete exploration

of the

samples

34

o

~ii

32 °

o

~~ ~ C22

. .

~°° °°°aaa _C*

z 30

~

° O

°

~ °

«

° °

.

°

° o

~

7

₂₈ X ~ ~~« ° ~~~°

z ~

~ xx

"

~

26 ^~

~

«

)o~

z

~ , « o

o

.,~«~ _,D 2~

~~« " ~

~

22

"..,

w ~,

©Rpoo'~

20

~-~4D2

18

0 50 100 150 200 250 300

TEMPERATURE(°C)

Fig.

2. Temperature

dependence

of the elastic constants

Cii,

C22 and C*. Di, D2 and D' _{refer to} the different doublets observed in the

conducting

phase. Di

(D2) corresponds

to the

highest (lowest) frequency

shift.

65 .

~ C~~

f

60

' '

' .

.

~ ^' .

~ 55 ^'

.

I

,

$

50 .,

)

28

v~

~j 26

',,,~

24

"

0 50 100 150 200 250

TEMPERATURE(°C)

Fig.

3.

Temperature dependence

of the elastic constant C33.

and _{we are never sure to} have detected all the

possible

different

regions.

^{The number of}

observed doublets

depends

_on the direction of _q: two

(Di, D~)

for

[100]

^and

[010],

three

(Di, D', D2)

for

[l10],

but _a

single

_one for

[001]

ⁱⁿ

spite

of _a careful

exploration,

within the

reserve noted above. The lines of _every doublet have been found to be

polarized

with the _same

polarization (VV)

_as the

corresponding

doublet below

Ts. Taking

into account the

polarization

and the cross-section of the

lines,

_we think that

they

^have to be attributed to

longitudinal

or

pseudo-longitudinal

elastic _waves. The

corresponding

elastic constants show linear decreases

uersw

temperature

^{in the}

conducting phase.

Table II. Characteristics

of

the Brillo~in

spectra j~st

above the

s~perionic

transition. Po- lar. is the

polarization of

the

light

beams

(V,

H stand

for

vertical and horizontal

respectively,

the

scattering plane being horizontal).

_r is the ratio

ill

where I and I _are the recorded lines

integrated

intensities

of

the additional do~blet and main do~blets

respectively.

Main doublet Additional doublet

Scattering

geometries pV~(GPa) r(GHz)

existence

polar. pV~(GPa)

_r

Di

26.0 1.8 yes VV 3.9 0.05

1

D2

20.7 0.55 _no

Di

25.2 1.75 yes VV 4.0 0.04

2

D2

20.1 0.58 _no

3 26.3 1.63 yes VV 3A 0.04

Di

24.64 1.75 yes VV 3.6 0.06

4 D' 21.76 1.0 _no

D2

19.94 0.61 yes VH 3.7 0.05

In _some

spectra,

^besides the main

doublet,

_an additional doublet is

unambiguously

detected with _a very small

intensity

and with the same

polarization

_as that of the main

doublet, except

for

D2

^of

C*,

for which it appears in crossed

polarization (VH).

The characteristics of the

spectra just

above

Ts

_are

reported

in Table II.

4.2. BRILLOUIN LINEWIDTHS. Below

Ts,

no

broadening

of Brillouin lines _can be

detected;

but above

Ts,

_every line related to _a main doublet exhibits _a

broadening.

The full widths at half maximum

(FWHM) ri, r2, r3

and r* of the lines

corresponding

to

Cii, C22, C33

and C*

are

reported

in

Figure 4,

after deconvolution. The

uncertainty

is estimated to 0.2 GHz and the instrumental width is 0.9 GHz.

The

broadening

of _a line

significantly depends

_on the type of doublet

(Di, D2

_or

D'),

but for _a

given doublet, Di

_or

D2,

similar values _are obtained whatever the elastic _constant

Cii, C22

_or C*. No

pretransitional

features _{appear near} the

transition,

but _a smooth increase of

ri (Di), r2(Di), r*(Di

and

r3

takes

place

_on

heating,

while

ri (D2), r2(D2)

and

r*(D2) keep nearly

constant values.

4.3. ELASTIC AND

QUASI-ELASTIC

SCATTERING. The unshifted

Rayleigh peak

has been

recorded in every spectrum

by

_mean of calibrated attenuators. At

Ts,

its

intensity generally

shows _an

abrupt

increase in most of the

scattering geometries, except

^{in the} case of

Cii(D2),

for which _a small decrease is observed.

Figure

5 shows

typical

variations of the

Rayleigh peak intensity.

In

spite

of _an almost _{very same} behaviour

consisting

of _an increase of the

intensity,

at

Ts,

to a value which remains

nearly unchanged

with further

heating,

it _seems difficult to draw any conclusions about the existence of _an additional contribution to the elastic

scattering

in the

conducting phase, having

in mind the

major

role

played by

the static defects and the

difficulty

to

predict

its

temperature dependence.

3,0 fi

~ r2

2.5

' fi (, r~, r* for Dj

r*

/

q2.0

~

y ~ ~

° «,

Z

~

° ox

" ~ _. ^"

~ f . j

Z ~

j

~

#

_l,0

,

. °

.

. - r* for

o~ ^{SO "} ° ^O'O ^{O O O}Q ,

K

~ K K ~ K K ~ K

' ( r~,r~ for D

0,0

230 240 250 260 270

TEMPERATURE(°C)

Fig.

4. Temperature

dependence

of

ri, r2,

r3 and

r*,

FWHM of the Brillouin lines related to elastic constants

Cii, C22,

C33 and C*

respectively.

For Di, D2 and D': _as in

Figure

2.

300

o

oo oo

o

_250

fi ^° ~ ^"

~ _. R~

(

₂₀₀

)

I150

ill

I ° D

j

loo ^~°°° °

lD

#

₄

~

50 a

.

~

o°Z~~ o O D

. ~o

°

.°'"

T

~

oa j ^"

~

o' ^' ~

0

50 loo 150 200 250

TEMPERATURE(°C)

Fig,

5.

Examples

of temperature

dependence

of the

Rayleigh

line

intensity.

RI and R3 correspond

to the spectra related to Cii and C33

respectively,

For Di and D21 as in

Figure

2.

We also observed that the

Rayleigh peak profile

does not

change

at

Ts

and that _no obvious

background

_appears in the spectra above

Ts. So,

it _can be concluded that there is _no evidence

for the _occurence of _a

quasi-elastic scattering

in the

conducting phase.

5. Discussion

5.I. EXISTENCE oF DOMAINS _{IN THE} CONDUCTING PHASE. As in CDA

[11],

the obser-

vation of _more than _one doublet in _some

scattering geometries

above

Ts obviously _suggests

the existence of domains in the

conducting phase.

In that

phase,

_we recall that

Cii, C22, C33

and C*

represent

"effective" elastic

constants, equal

to

pV~,

related to elastic _{waves propa-}

gating along

directions which have been defined with

respect

to the

crystallographic

_axes of the _room temperature

phase.

We must take into account

that,

above

Ts,

the

symmetry

^class may have

changed

and

that,

for _a

given domain,

the

crystallographic

_{axes may} have rotated.

A relation between the cubic and the monoclinic structures has been

proposed

in the latest

X-ray investigation [21],

ⁱⁿ which two _axes of the cubic

phase

_are rotated

by

+~ 45° in the

(001) plane,

but _no

possibility

of _a domain structure has been

suggested.

When _q lies

along [001],

^{the fact that} a

single

doublet is observed

implies

that the

[001]

direction is _common to the different domains _or that the values of

pV~

_{are very} similar in the different domains. When _q lies

along [100]

or

[010],

^{the close values of}

Gil

and

C22

for

Di

and

D2

and of the

corresponding

linewidths _are consistent with the

assumption

that the

crystallographic

_{axes are} oriented _as described in

[21]

ⁱⁿ one

type

of

domain,

while

they

_are

rotated

by

45° around _an axis

perpendicular

to the

(001) plane

in the other

type.

Within the latter

assumption,

in the _case 4 of Table

I,

the observation of two doublets is

expected

with values of

pV~

which should be close to those obtained for

Gil

and

C22.

The doublets

Di

and

D2

for C* _are consistent with that

prediction. However,

another doublet D' has also been detected with intermediate values for

pV~

and linewidth. This

implies

the

existence of _a third

type

^{of domain which should also be observed} in _cases I and 2. This fact shows the

difficulty

in

detecting

all the

types

of domain. From the Brillouin

results,

the domain

structure appears to be not

simple,

since three

types

of domain at least have been revealed.

The existence of _an additional doublet in _some

spectra

is also

compatible

with _a cubic

structure. Such _a doublet is

expected

when _q is not

parallel

to _a face of the cubic

cell,

_a

situation which exists in the

possible

domains described above.

In

conclusion,

_we will

emphasize

that _a domain structure is

unambiguously

established

by

the Brillouin

spectra.

^These

spectra

are

compatible

with _a cubic structure of the domains

but

they

cannot corroborate this structure. We think that there is

only

_a few domain

types,

although

the exact number cannot be

given.

The

crystallographic

orientations of the domains

cannot be

determined,

but

they

_appear well defined with

respect

to the monoclinic _axes. We

have verified that the _same doublets _are still

recorded,

whatever the

investigated sample

in _a

given scattering geometry.

5.2. ELASTIC ANOMALIES. The elastic behaviour of CDP

strongly

resemble that of CDA

[iii.

At

Ts,

the

abrupt jumps

of elastic constants and the simultaneous appearance of

signif-

icant

broadening

of the lines indicate _a

sharp

first order transition in both

compounds.

Such

a

similarity

_{was a}

priori

not

expected, owing

to the difference of the structures at room tem-

perature,

even in the presence of _an intermediate

phase.

A

comparison

of the results shows that the

anisotropy

of elastic

properties

is reduced at

Ts

in both

compounds,

with the _same range of values

(20-26 GPa)

for the elastic constants

just

^above

Ts.

For the

linewidths,

the range appears

greater

in CDP than in CDA: 0.5-1.9 GHz and 0.5-1 GHz

just

above

Ts,

_re-

spectively.

It _can be

pointed

out that such _an elastic behaviour has been also observed in the

MHSe04 compounds (with

M

=

NH4, Rb, Cs) [24-26].

A downward

jump

of elastic constants is

generally

observed in all these

protonic superconductors

_on

heating through Tsi however,

it

can be

pointed

out that the

present

result for

C22 (Di doublet)

shows that this

type

^of

jump

does not

systematically

_occur.

This _common elastic behaviour is in

keeping

with _a

similarity

of the conductive

properties

which appears in all these

compounds _[10; 27-30].

Such _a

similarity

_was also

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

sites is

just equal

to that of

protons.

Whatever the

domain,

the

jumps

of elastic constants have to be related to the break of

hydrogen

bonds at

Ts

which would

probably

_occur with _a simultaneous modification of the

structure. Such _a transition may either be induced

primarily by

the

protons,

as

proposed

in

CSHSe04

_type

crystals [31],

or be of the structural

type

^related to _a loss of

stability

of the

rigid sublattice,

_as

suggested

for the

superionic

transition in

Rb3H(Se04)2 _(32],

the

disappearance

of the protons

mobility

below

Ts being

_a consequence of the structural modification.

An

analysis

of the transition first

requires

_an examination of the

symmetry change.

In

CDP,

the _room

temperature

space group

P21/m

is _a

subgroup

of the cubic group Pm3m.

However,

there is _a

difficulty

due to the

possible

existence of _an intermediate

phase

between the monoclinic _room

temperature phase

and

Ts.

This

phase

has been

clearly

evidenced in the

study

of the

phase diagram ill, although

not detected in the latest

X-ray analysis _[21].

A detailed

study

of the

symmetry change

^is

beyond

the scope of this. paper and we think that such _a

study might

be undertaken when the structure data will be refined and confirmed.

Nevertheless,

it _can be

emphasized that,

if _a

group-subgroup

relation holds for the

superionic transition,

it is difficult to understand the existence of domains in the

high temperature phase,

which is the most

symmetric

_one.

Conversely,

if there is _no such

relation,

it is difficult _to understand

why

the

crystallographic

orientations of the domains appear well defined with

respect

to the monoclinic _room

temperature phase

structure.

Among

the

compounds MHSe04 (with

M

=

NH4, Rb, Cs)

and

CSH2A04 (with

A

=

As, P),

it _can be remarked

that,

below

Ts,

_{a non} linear

temperature dependence

for elastic constants

only

_appears in CDP. If _an order parameter ^exists for the

transition,

a

possible explanation

of these evolutions with

temperature

is the

biquadratic coupling he~o~

between _a strain _e

(ei,

_e2

and

e3)

and the order

parameter Q,

which is

generally

allowed whatever the

symmetry

of the

prototype- phase.

In the low

symmetry phase,

this

coupling gives

_a static contribution /hC _to the

anomaly

of _an elastic constant

C,

which is

proportional

to the square of the average value

Qo

of the order

parameter:

/hC = C

Co

=

2hQ(

where

Co

is the bare elastic constant.

Thus,

the

temperature dependence

of elastic constants would

reflect,

at least

partially,

the evolution of

Q(

far from the

stability

limit of the low

temperature phase, taking

^into account the first order character of the transition.

In the

conducting phase, couplings

between elastic _waves and mobile protons are

expected

to take

place.

A

general study

of

couplings

between these _waves and mobile atoms has been

given by

Huberman _et al.

[33].

^{From that}

study,

it _can be deduced that _a bilinear

coupling

kes between _a strain _e, related to _an acoustic wave, and _a

pseudospin

variable _s,

describing

the

mean values of proton

occupation

numbers _on their

possible sites,

leads to a

complex frequency

w

ill

for the acoustic wave, I.e. to _a

damped

_wave. If the

damping

is weak:

fl

« w, the elastic constant

C(w)

and the linewidth

r(w)

_can be written _as follows:

C(UJl

=

PM~/q~

=

Co ~211/((is fll~

+ uJ~)

rl~°)

_"

2fl

j~~

"

(~~/P)Q~'fs/(('fs fl)~

+ ~°~)

where

Co

is the bare elastic

constant,

~ _a constant related to

k,

_is the relaxational

frequency

for the variable _s. When _w ~

0,

we have also _{q ~} 0 and

fl

_~

0;

therefore the static variation

/hCo

of the elastic constant is

/hCo

_"

Co C(0)

=

~~

_and

(I)

_can be

expressed

as follows:

c(~u)

₌

^co /hcoil/((is _fl)2

_{+ ~u2)}

r(~u)

₌

isi/hco/ci~u)1~u2/1(is fl)2

+ ~u21 ~~j

No measurement of _i~

by

RMN

investigation

of the protons has been made in CDP. An

estimation of _{i~ can} be obtained

by comparison

with

CSHSe04 (29, 34], taking

into account

the

similarity

of the

conducting characteristics;

the order of

magnitude

is is +~ 0.5 GHz. If several

broadening

mechanisms

simultaneously

_occur, the

experimental

linewidth

rexp

verifies

rexp

> r

=

2fl

with

rexp

_{= ai~,} a

being

a factor between I and

4;

therefore _we have 0 <

fl

<

21~

and 0 <

(is fl)~

<

ij,

Since

w is

+~ 10 GHz for _every

line,

_we have

consequently (i~ fl)~

« w~

and the relations

(2), adapted

to the

present

^{results become:}

C(w)

=

Co /hCoi~/~v2

e

co

F(Ld)

=

7s(/~Co/Co~ ⁽³⁾

The first relation

(3)

shows that the influence of the

coupling

_on the elastic constant is relaxed.

If _{we assume} that

rexp

₌

r,

I-e- if there is

only

the contribution of the

coupling kes,

the

second relation

(3) gives

for

/hCo/Co

_a value between I and 4,

Consequently,

^the static elastic constant

C(0)

=

Co /hCo,

obtained from the first relation

(2)

takes _a null _or

negative value,

a result which must be

rejected.

The conclusion is that the

experimental

linewidth

rexp

must be

greater

^than

r,

which

implies

the presence of other

broadening mechanism(s).

The observed

broadenings

_are

temperature independent

_or

only slightly

^increased

by heating,

without

pretransitional

evolutions _near

Ts.

This

might

be _an

argument

^{in favour of} a

strong general anharmonicity

of the lattice

dynamics

in the

conducting phase,

as one

possible

other

mechanism. This

assumption

is consistent with _a Raman

study

in CDP

[20],

which concluded in favour the existence of _an

important

structural disorder in this

phase.

The mobile

protons

are

expected

to

give

_a contribution to the unshifted

peak

with _a width of the order of _i~, which is

slightly

lower than the apparatus width. This

explains why

no

quasi-

elastic

scattering

_can be detected in the Brillouin

spectra,

_even in the _case of _a

significant

contribution.

Experimentally,

this contribution cannot be

distinguished

from the elastic

peak

and is hidden

by

^it as discussed in Section 4.3.

6. Conclusion

In this Brillouin

investigation,

_we have observed _a

sharp

modification of the lattice

dynamics

for the acoustic modes in the

vicinity

^{of the Brillouin} zone

centre,

at the

superionic

transi-

tion. At

Ts,

the elastic constants

Cii, C22, C33

and C* show discontinuities and

broadenings

of the related Brillouin lines

abruptly

take

place.

These anomalies of the elastic

properties strongly

resemble those of

compounds

of the

MHSe04 family (M

₌

NH4, Rb, Cs)

and those of

CsH2AsD4,

which

belongs

to the KDP

family

_as CDP does. In the

conducting phase,

the spectra ^{have revealed the existence} of _a domain structure which is difficult to understand with

respect

to the structure data avalaible to date.

In the

conducting phase,

_we have shown that _a bilinear

coupling

between strains and mobile

protons

cannot contribute

significantly

to a modification of the elastic _wave characteristics. We have

proposed

_a

strong general anharmonicity

of the lattice

dynamics

_{as a}

possible explanation

of the line

broadenings. Therefore,

_we think that further

investigations

ⁱⁿ

CDP,

such _as

structure refinements and lattice

dynamics

studies

by

other vibrational

spectroscopies,

will

improve

the

knowledge

of the transition mechanism in that

compound and, possibly,

in the other

compounds

above cited.

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