On the ferroelectric phase transition in (CH3)4 NCdBr 3 (TMCB)

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On the ferroelectric phase transition in (CH3)4 NCdBr

3 (TMCB)

G. Aguirre-Zamalloa, M. Couzi, N.B. Chanh, B. Gallois

To cite this version:

Short Communication

On

the

ferroelectric

_phase

transition in

_(CH3)4

_NCdBr3

_(TMCB)

G.

_{Aguirre-Zamalloa(1),}

M.

_Couzi(1),

N.B.

_Chanh(2)

and B.

_Gallois(2)

(1)

Laboratoire de

_{Spectroscopie}

Moléculaire et Cristalline

_(URA

124 -

_CNRS),

Universitd de Bor-deaux

_{I, 33405 Talence Cedex,}

France

(2)

Laboratoire de

_{Cristallographie}

et de

_Physique

Cristalline

_(URA

144 -

_CNRS),

Université de Bordeaux

I, 33405

Talence

Cedex,

France

(Received

on

_July

_{S, 1990,}

_{accepted infinalfonn on July}

_{18, 1990)}

Résumé. 2014 La transition de

_{phase ferroelectrique}

de

_(CH3)4

_NCdBr3

_{(TMCB) à ~}

156 K est étu-diée _par diffraction des _rayons

X ;

on montre _que le _groupe

_d’expace

de la

_phase

_{paraélectrique}

est

P63 /m,

avec des

_parametres

de maille a, a, c, et _que celui de la

_phase

_{ferroélectrique}

est

_{P61 (ou}

_P65)

avec _pour

_paramètres

_{a, a,} 3c. La transition est

_analysée

a l’aide de la theorie de Landau. En

parti-culier,

le

_changement

de

_symétrie

observé

_implique

l’existence d’invariants d’ordre trois

_(transition

du

_premier

_ordre).

Un

_{ddveloppement}

_classique

de

_l’énergie

libre de

_Landau,

incluant les termes de

couplage

avec les

_composantes

du vecteur

_polarisation

_{(ferroélectrique impropre)}

rend _compte d’une manière satisfaisante de la

_dependance

en

_temperature

de la

_polarisation

_spontanée

et des

suscepti-bilités

_{diélectriques,}

mesurées

_{précédemment.}

Abstract. - The ferroelectric

phase

transition in

_(CH3)4

_NCdBr3

_(TMCB)

at ~ 156 K is studied

_by

X-ray

diffraction measurements; it is shown that the _{space group} of the

_{paraelectric phase}

is

_P63/m,

with lattice _parameters a, a, c, and that of the ferroelectric

phase

is

_P61

_(or

_P65)

with lattice

param-eters a, a, 3c. The transition is

analyzed

in the framework of the Landau

_theory.

In

_particular,

the observed

_symmetry

_{change implies}

the _presence of cubic invariants

_(first-order

_transition).

A

classi-cal Landau _type

_expansion

of the

_{free-energy, including coupling}

terms with the

_polarization

vector

components

(improper ferroelectric)

is able to account

_{satisfactorily}

for the _temperature

_dependence

of the spontaneous

polarization

and dielectric

_{susceptibilities}

which have been

_previously

measured. Classification

Physics

Abstracts

61.14F - 61.SOE - 64.70 - 77.80

The

_crystals

with formula

_(CH3)4

NMX3

(M

=

_{Mn, Cd;}

X =

_Cl,

Br)

are

_hexagonal

at room

temperature,

with

_space-group

_P63/m

and Z = 2 formula units

per

unit-cell

[1-4].

The structure is made of infinite linear chains of

_face-sharing

_MX6

octahedra and the

_space

between the chains is

occupied by

the

_{tetramethylammonium}

_groups

_{(TMA) exhibiting}

an orientational disorder

_of

dy-namic nature

_[5,6].

The chlorides

_(CH3)4

_NMnC13

_(TMMC)

and

_(CH3)4

_NCdC13

_(TMCC)

un-dergo

a number of structural

_phase

_transitions,

_{governed essentially by}

the reorientational

dynam-ics of the

TMA,

and

_leading

to different

_non-polar

ordered

_phases

with monoclinic

_symmetry,

sta-ble at low

_temperatures

_([5-10]

and cited

_references).

The controversial case of

_(CH3)4

NMnBr3

2136

(TMMB) [4,

11,

12]

has been solved in favour of a monoclinic low

_temperature

_phase

_[12],

which is

_probably

also

_non-polar.

In this series of

_compounds,

_(CH3)4

_NCdBr3

_(TMCB)

exhibit a

_particular

_behaviour,

since

re-cently

the low

_temperature

_phase

has been found to be ferroelectric

_[13].

A first-order

_phase

tran-sition from

_P63/m

to the

_{polar phase}

occurs around 156

_K;

it is characterized

_{by a}

marked

lambda-shaped anomaly

of the dielectric constant

_along

the c direction

_{(polar axis)}

[13, 14],

whereas a _very

small discontinuous

_change

of the dielectric constant

_along

a is observed

[13]

_(Fig.l).

In

addi-tion,

the ferroelectric

_phase

is

_optically

uniaxial,

which means that it has a

_hexagonal

or

_trigonal

symmetry,

with

_point

_group

other than

6/m

_{[14] .}

Fig.

1. - Schematic

representation

of the

_temperature

_dependence

of

_(a)

the _spontaneous

_polarization

Pz

and of

_(b)

the dielectric constant

_along

the a and c directions

_(frequency

100

_kHz,

on

_cooling).

Data

_points

are taken from

_{[13] ;}

note that a similar curve for êc has been obtained in

_{[14] .}

In this short

_paper

we

_present

_X-ray

diffraction measurements made on TMCB at low

tem-peratures

allowing

an

_unambiguous

determination of the

_space-group

of the ferroelectric

_phase.

Then,

the

_phase

transition will be described in the framework of Landau

_theory.

Singe crystals

of TMCB have been

_prepared

from saturated

_aqueous

_solutions,

as described

previously

[3] .

Small

_needles,

_{elongated along}

the c

_direction,

with dimensions of about 0.12 x 0.4 x 0.8

mm3

have been selected for

_X-ray

diffraction measurements, after examination

_through

a

polarizing microscope.

’

The

_phase

transition is first evidenced on

_{powder photographs}

obtained with a Guinier-Simon camera,

_operating

between 80 and 300

_K;

it is characterized

_by

small discontinuities in the thermal evolution of a number of reflection

lines,

and

_by

the

_appearance

of new reflections in the low

temperature

phase.

The data are consistent with the occurence of a weak first-order transition

around 160

_K,

as found

_already

_[13,14].

photographs

at 110 K

_{(ferroelectric phase),}

with

_{crystal rotating}

around the c

axis,

_clearly

show

a

_triplication

of the lattice

_parameter

_along

_c, as evidenced

_by

the

_presence

of

_{surperstructure}

reflections

_along

c* which were absent at room

_temperature.

A similar result has been obtained

already

with TMCC at low

_temperature

_[7,8].

With

_TMCB,

the

_Weissenberg

_photographs

of the

_(hk0)

and

_(hkl)

_planes

at 110 K show that the

_hexagonal

_symmetry

is

conserved,

with no

change

of the lattice

_{period along}

a and b. This is now in contrast with TMMC and TMCC where

superstructure

reflections have been observed at low

_temperature

in those

_{planes, together}

with a

splitting

of the main reflections due to a monoclinic distortion

[8] .

In the low

_temperature

_phase

of

TMCB,

the

_only

_systematic

absence of reflection is observed for the

_[00£]

row line

_(reflection

condition £ =

6n)

on

_{precession photographs}

of the

_(hO£)

_plane.

Thus,

the

_space-group

for the low

_temperature

_phase

can be either

P61

(or

equivalently

P65)

or

_P6122

_(P6522).

Since

P6122

is not a

_polar

_group,

the

_{space group}

of the ferroelectric

_phase

of TMCB is then

_{unambiguously}

determined as

_P61

_(P65).

Note that the

_polar

axis

_{of P61 lies}

_along

the c

_direction,

as observed

_{experimentally}

_{[13] ;}

also, P61

is a

_sub-group

of

_{P63/m (paraelectric}

phase),

which is not the case for

P6122.

It should be also

_pointed

out that Raman

_{scattering experiments}

with TMCB

_[15]

show that the

doubly

degenerate

lattice modes. with

_E2g

_symmetry

in the

_{paraelectric phase}

are not

_split

in the ferroelectric

_phase,

as

_expected

for an uniaxial structure

_[14]

such as

_P61.

_Again,

this is in contrast

with TMMC and

TMCC,

where the

_{corresponding}

_E2g

modes showed a doublet structure at low

temperatures

owing

to the monoclinic

_symmetry

of the ordered

_phases

_{[9] .}

The

_hexagonal

unit-cell of the ferroelectric

_phase,

with lattice

_parameters

such as _{a, a,} 3c de-termines a lattice

_{instability occurring}

at a

_point

_A(0,

_0,

_a)

inside the

_hexagonal

Brillouin zone

of the

_{paraelectric phase (a,}

a,

c)

[16] ;

the

_{triplication along}

c is obtained for the

_particular

value

a =

1/3.

In the

P63/m

space-group,

the wave-vector

_group

for all

_points

à

_lying

on the r - A line is

C6

[16] ,

of which the four little

_{representations}

are denoted as

_{Ai/A, A2/B}

_{(one-dimensional)}

and

_{A3/Ei, A4/E2}

_(these

are short-hand notations for the

_{complex conjugate physically}

degen-erate

_{El(1), El(2)}

and

_{EZ(1), Ez(2)}

_{representations}

_{[16] ).}

_Following

classical

_group

theoretical

procedures

[17] ,

we have

_performed

a

_systematic

search for all

_sub-groups

of

P63/m

issued from

point

A(0,

0,

1/3).

It turns out that

_P61

_(or

_P65)

is induced

_by

_{03/El .}

_Now,

the full

_{representation}

(03/El j

P63/m)

is of dimension four since there are two arms in the star of the wave-vector at

_point

à

_{[16] ;}

it follows that the order

_parameter

has four

_components

_{ql, q2, q3} and _q4 such as q,

= 9â

and q2 =

_q3.

The

_P61

_space-group

_corresponds

to such solutions as

_{qi #}

_0,

_{q4 e}

_0,

_q2 = _q3 = 0 and

P65

to

_equivalent

solutions where

_{q2 #}

_0,

_{q3 #}

_0,

_{ql = q4} = 0. The

_symmetric

and

_{anti-symmetric}

powers

of the

representation

03/El T

P63/m

(with

a

_{= 1/3)}

_give

in

_particular:

According

to

_(2),

there is a Lifschitz invariant since the

_{anti-symmetric}

_square

contains the vector

representation

Au (z);

on the other

hand,

the relation

₍₃₎

determines the _presence of two cubic invariants

_{(2Ag) .}

After these

_{group-theoretical}

_{considerations,}

the Landau

_free-energy

_expansion

is

_fully

2138

where w = _p ±

_nm-/3

_{(n integer),}

but for convenience we shall consider a real form

_expansion

using

order

_parameters

_1Ji

_(i

= 1 to

₄₎

defined as:

Then,

the Landau

_free-energy

_developed

_up

to the fourth order writes:

In this

_expression

_{xo( [ [ )}

and

_xo{1)

are the free dielectric

_{susceptibilities}

_parallel

and

perpendic-ular to the c

_axis,

_{respectively,}

and

P,

_{Py (Elu symmetry)}

and Px

(Au symmetry)

are the three

components

of the

_polarization

_vector; for

convenience,

only

coupling

terms of lowest order

be-tween

_{the 1Ji}

and

_Pj

_components

have been included.

_Coupling

terms with the strain tensor

com-ponents

have been

omitted,

since the transition is

_{non-ferroelastic; also,}

the Lifschitz invariant and other

_gradient

terms have been

omitted,

since

_according

to

_{calorimetric,}

dielectric

_[13,14J

and Raman

_scattering

_[15]

_experiments,

there is no hint of existence of an intermediate

_(possibly

incommensurate) phase.

As usual we

_put:

all other coefficients

_{being supposed}

_temperature

_{independent (improper}

ferroelectric transition

[18]).

So,

the effective

_potential

for the ferroelectric

_phase

_{P61 (q #}

_{0, q’}

=

0)

can be written as:

Of _course, a similar

_expression

can be obtained for

_{energetically equivalent}

_P65

domains

_{( q}

=

0, q’ f:. 0).

_

Minimizing

A-* with

_respect

_top

_yields:

and the minimization

_equations

Then,

the transition

_temperature

Te

is

_given

_by:

and the

_equilibrium

value of the order

_parameter

_by:

where:

and where qc is the

jump

value of

q(T)

at

Te

(first-order transition):

Now,

in the

_{paraelectric phase}

_(T

>

_Te)

the static dielectric

_{susceptibilities}

are:

and in the

P61

ferroelectric

_phase

_(T

_Te),

it comes

[18,19] :

where the

_Xij’s

are the

_"high

_{frequency" suceptibilities}

of the order

_parameters

[19]

_given

_by:

i.e. :

In

_figure

2,

we have

_represented

a numerical simulation of the characteristic

_{quantities given by}

the relations

_{(11), (13), (16)}

and

_(17),

with coefficients chosen so as to

_{reproduce qualitatively}

the

expérimental

results

_{[13,14] .}

So,

the

_general

trends observed for the

_temperature

_dependence

of the

_spontaneous

_polarization

_Pz

and dielectric

_{susceptibility}

_{X(1) [13]}

can be simulated in a

2140

can be

_reproduced,

but

the

_experimental

data exhibit an additional downward variation that makes

xf(11)

to reach values lower than

_xo([[)

at low

_temperature

_[13,14]

_{(Fig.l). Obviously,}

such an

observation cannot be accounted for

_(Fig.2)

with

_only

a

_coupling

term of the form

_{q2 Pz}

₍₈₎

_[18],

but as shown from

_{(3), higher}

order

_coupling

terms of the form

_{q3 Pz}

are allowed

_by

_symmetry,

since

_[A3/El

contains 2

_A"(z);

also,

a

_coupling

term of the form

_{q2 P;}

can

_always

be added.

Clearly,

this latter term is able to introduce an additional downward variation of

xf(11) provided

that the

_coupling

coefficient is

_positive

_[18],

as shown here for

_{Xf (-L)}

_{(Fig. 2).}

Note however that

introducing

such terms

as q3 Pz

and

_{q2 P;}

in

₍₆₎

is

_equivalent

to consider an effective

_potential

for the ferroelectric

_phase

_developed

_up to the siJCth order

_{in q}

_including

cubic terms

_{(already present)}

and fifth order _terms, which is not _{very easy} to

_apprehend.

Fig.

2. - Numerical simulation for the

temperature

dependence of (a)

the order

_{parameter q}

and the spon-taneous

_polarization

Pz and of

_(b)

the dielectric

_{susceptibilities}

_x(11)

and

_x(1),

_according

to the model po-tential

_(6).

The

_following

coefficients have been chosen: Te = 156

_K,

_{To =}

₁₁₉

_K,

1Jc =

2.43, c’

=

1,

XO(IL)

=

7.5,

XO(J-)

=

4.75, g

=

0.18, h

=

_0.0006;

_{for convenience we}

put

ce = 0.

Thus,

we conclude that the

_phase

transition

_{P63/m o}

_P61

_(P65)

of TMCB at - 156 K is

im-proper

ferroelectric;

it is of first order because of the existence of third order invariants and it can

be accounted for in a

_satisfactory

_way

with a classical Landau

_free-energy

_expansion,

as far as the

static

_properties

are concerned. The

_dynamical

_aspects

of this

_phase

transition will be considered

Acknowledgements.

The authors wish to thank Professor R Vanek et al.

_(Institute

of

_Physics,

Czechoslovak Acad. Sci in

_Prague)

for communication of their results

_[14]

_prior

to

_publication.

References

[1]

MOROSIN B. and GRAEBER

E.J., Acta

Cryst.

23

₍₁₉₆₇₎

766.

[2]

MOROSIN

B., Acta

Cryst.

B28

₍₁₉₇₂₎

2303.

[3]

DAOUD

A.,

Bull Soc. Chim.

_France,

Part I

₍₁₉₇₆₎

751.

[4]

ALCOCK N.W and HOLT

_{S.L., Acta Cryst.}

B34

₍₁₉₇₈₎

1970.

[5]

PEERCY

_P.S.,

MOROSIN B. and SAMARA

G.A.,

Phys.

Rev. B8

₍₁₉₇₃₎

3378.

[6]

MANGUM B.W and UTTON

_{D.B., Phys.}

Rev. B6

₍₁₉₇₂₎

2790.

[7]

BRAUD

M.N.,

COUZI

_M.,

CHANH

N.B., MERESSE A.,

HAUW C. and GOMEZ-CUEVAS

_A.,

Ferroelectrics 104

₍₁₉₉₀₎

367.

[8]

BRAUD

M.N.,

COUZI

M.,

CHANH

N.B.,

COURSEILLE

C.,

GALLOIS

B.,

HAUW C. and MERESSE

A., J.

Phys.:

Condens. Matter

_{(in press).}

[9]

BRAUD

_M.N.,

COUZI

_M.,

CHANH N.B. and GOMEZ-CUEVAS

A., J.

Phys.:

Condens. Matter

_{(in press).}

[10]

BRAUD

M.N.,

COUZI

M.,

CHANH

N.B., J.

Phys.:

Condens. Matter

_{(in press).}

[11]

TANAKA

H.,

TSURUOKA

F,

ISHII

T,

IZUMI

H.,

Iio K. and NAGATA

_{K., J.}

_Phys.

Soc.

_Jpn

55

₍₁₉₈₆₎

2369.

[12]

VISSER D. and MCINTYRE

G.J.,

Physica

B 156-157

₍₁₉₈₉₎

259.

[ 13J

GESI

_{K., J.}

_Phys.

Soc.

_Jpn

59

₍₁₉₉₀₎

432.

[14]

VANEK

_P.,

HAVRANKOVA

_M.,

SMUTNY F and

BREZINA B.,

Ferroelectrics

_{(in press).}

[15]

AGUIRRE-ZAMALLOA G. and COUZI

_M.,

in

_preparation.

[16]

BRADLEY C.J. and CRACKNELL

_A.P,

The Mathematical

_Theory

of

_Symmetry

in Solids

_(Clarendon

Press,

Oxford)

1972.

[17]

PEREZ-MATO

J.M.,

MANES

J.L.,

TELLO M.J. and ZUNIGA

FJ., J.

Phys.

C: Solid State

_Phys.

14

₍₁₉₈₁₎

1121.

[18]

DVORAK V.,

Ferroelectrics 7

₍₁₉₇₄₎

1.

[19]

COWLEY

R.A., Adv

Phys.

29

₍₁₉₈₀₎

1.