Study of the Global Thermal Hysteresis in D-BCCD with Elastic Neutron Scattering

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Study of the Global Thermal Hysteresis in D-BCCD with Elastic Neutron Scattering

O. Hernandez, J. Hlinka, M. Quilichini

To cite this version:

O. Hernandez, J. Hlinka, M. Quilichini. Study of the Global Thermal Hysteresis in D-BCCD with Elastic Neutron Scattering. Journal de Physique I, EDP Sciences, 1996, 6 (2), pp.231-236.

�10.1051/jp1:1996144�. �jpa-00247179�

Short Communication

Study of the Global Thermal Hysteresis in D-BCCD with Elastic Neutron Scattering

O. Hernandez

(*),

J. Hlinka and M.

Quilichini

Laboratoire Léon Brillomn

(C.E.A.-C.N.R.S.), C.E.A.lsaclay,

91191 Gif-sur-Yvette cedex, France

(Received

3 November 1995, received and

accepted

in final form 24 November

1995)

PACS.05.70.Fh Phase Transitions:

general

aspects

PACS.64.70.Rh Commensurate-incommensurate transitions

PACS.77.80.Dj

Domain structure;

hysteresis

Abstract. We have

studied,

with elastic neutron

scattering,

the temperature

dependence

on

heating

and _on

coohng

of the _wave vector of the modulation in the two mcommensurate

phases (INCI

and

INC2)

of

fully

deuterated betaine calcium chloride

dihydrate (D-BCCD).

A

large (2-3 K) global hysteresis

_{appears m} these two

phases

_up to T,. Moreover, the

study

of the

higher

order satellites intensities suggests ^the non-sinusoïdal character of the modulation

below T~-20 K. These

phenomena

coula be the

experimental

signature ^of the

"complete

DeviI's staircase" regime.

Résumé. Nous _avons étudié _par diffusion

élastique

de neutrons la

dépendance

_en tempéra-

ture _au refroidissement et _au

chauffage

du vecteur d'onde de la modulation dans les deux

phases

incommensurables

(INCI

et

INC2)

du chlorure de bétaine et de calcium

di-hydraté complète-

ment deutéré

(D-BCCD).

Une

large (2-3 K)

hystérésis globale

apparaît

dans

ces deux phases,

et _ce

jusqu'à

T~. De

plus,

l'étude des intensités des satellites d'ordre

supérieur suggère

le _carac- tère _non sinusàidal de la modulation _en dessous de T~-20 K. Ces

phénomènes

pourraient être la

signature expérimentale

du

régime

de type "escalier du Diable

complet".

1. Introduction

BCCD

((CH3 )3NCH2COOCaCI2(H20)2

is _a dielectric

compound

with _a

phase diagram

~vhich bas been described _{as an}

incomplete

Devil's staircase after

Aubry

_[2] and Bak [4]. At atmo-

spheric

_pressure and from tue _room

temperature

normal

phase (space

_group

Pnma)

stable up ^to T

= T~, fifteen modulated commensurate

(COM) phases,

with incommensurate

(INC) phases inserted,

_are detected with

decreasing temperature [23].

^{For all of these}

phases

tue

wave vector of the modulation is

given by

_{q =} ^ôc*. In the low

temperature

ferroelectric

phase

of this

diagram,

à is _zero.

Up

to now two _main mcommensurate

phases

have been

distinguished

in BCCD. The INCI

phase

_is stable between T~ and the commeiisurate step at

)

and the INC2

phase

st.abilizes in the temperature range bet~v.een the and

( phases.

From

already

known results _we may wonder

(*)

Author for

correspondence je-mail: hernandfibah.saclay.cea.fr)

Q

Les

Éditions

_de

Physique

1996

232 JOURNAL DE

PHYSIQUE

I N°2

about the true nature of the INC2

phase.

To be _more

specific,

the sinusoidal

approximation

is

accepted

_{as a}

good

_one to describe the modulation in the INCI

phase;

whereas in the INC2

phase,

_one has observed the loss of the linear

temperature dependence

for

à(T)

and the presence of rive

higher

order commensurate

phases là

=

), (, (, (, [)

with _a very

narrow

temperature

range of existence

[23]. These, apparently,

two different behaviours have

motivated the present

experimental

elastic neutron

study;

its results _were

expected

for _a better

understanding

of

dynamical properties.

After the works

by Aubry

_{[2] we} know that for _{an one} dimensional

epitaxial

mortel

(based

_on

the Frenkel-Kontorova

mortel),

in the limit of _a

large amplitude

of the

modulation,

the Devil's staircase _can become

"complete".

This _means that it contains _an

infinity

of commensurate

phases

which _are not all

expenmentally

visible.

So,

in

spite

of _an

apparently

continuous

à(T)

_curve

(which

characterizes de

facto

_a true mcommensurate

phase),

the

"complete

Devil's

staircase"

regime

^has two distinctive features which _are accessible

experimentally

_[2]:

. The

hysteresis

of each step

generates

a

global hysteresis

of

à(T) (different

from the

"obvious"

hysteresis

observed

dunng

_a first order transition with coexistence of

phases).

. The

phase

mode has _a gap.

In the present ^work we shall concentrate on the evidence of the first

item,

thus _we shall

study

the

temperature dependence ion cooling

and _on

heating runs)

of the misfit

parameter

^à. So far this theoretical model has been refined

by

Axe] and

Aubry

_[3] and has obtained _a nice

qual-

itative

experimental

illustration for thiourea

[12,16],

which is the structural incommensurate

compound

the _most

comparable

with BCCD.

However,

_{we are aware} that the

problem _gets complicated

if _we consider the fact that the

origm

of _a

global hysteresis during

_a

phase

transition INC-COM _{is not}

only

_an intrinsic _one

(pinning

of the

phase

modulation

by

the discrete

underlying

lattice

[6], [18]),

but coula also be connected with _an extrinsic effect due to the

pinmng by crystal

^defects. Such extrinsic

hysteresis

has been studied

expenmentally

_on

doped

materials

(where

the defects concentration is

known)

or on irradiated

compounds.

Exhaustive _{reviews on} this matter have been

proposed by

Hamano

[14]

^{and Strukov}

[22].

^{These authors estimate that intrinsic}

phenomena

atone cannot

explain

the

experimental

results of the whole mcommensurate

phase,

but account

only

for the results

near the lock-in transition at

T~.

Furthermore the behaviour of incommensurate

phases

is very sensitive to the _presence of

crystal

defects

(vacancies, impurities

and

dislocations).

The

difliculty

is to estimate their number and their _nature and therefore their real influence _on intrinsic effects.

So,

_{m any} real

sample (whatever

its

quality is),

defects contribution _can not be avoided in the

signature

of the

global hysteresis.

2.

Experimental

Details

The expenment was

performed

_on the two _axis spectrometer ^3Tl located at _a thermal _source of the

Orphée

_reactor,

Saclay,

France. We have used _as monochromator _a Germanium

crystal III

1

1) reflection,

that is k~ ₌ 2.662

À~~

or

E~

₌ 14.68

mev),

_{a primary} beam collimation oo =21' and _a

pyrolytic graphite

filter in order to increase the

elliciency

of

filtering

of second

order contaminations. The monodomam

single crystal IV

_ci 2

cm3)

of

completely

deuterated BCCD

(mosaic spread

^of ci

là')

has been _grown

by

slow

evaporation

^from _a ^saturated

D20

solution of

fully

deuterated _pure chemicals

(the

betaine molecule is

prepared

with D

atoms).

The

scattenng plane

was the

il

0

0) plane, allowing

_us to examine

(0

_{k 1)}

Bragg

and satellite reflections. The

sample,

enclosed in _an aluminium

container,

_was mounted _on the cold

finger

of _a

displex

closed

cryostat (Helium exchange gas).

The temperature ^{could be determined with}

la) jbj

deduced from first order satellites deduced from third order satellites

°~ heating _Ti ^°~~ . heating

~ ^~ ~

°~~

D cooling

a,~

C cooling ^{° °}

.°'°~fi

032

~

° ^"

.

~~~ 028 ^~

~

f .

D o

030 ^~ D

~ .

, ~ , D '

f ₂₉ 2/7 i

o 27 ~

o'

Cr =~jéJ Cr

o

028 D," = °

027 )

/

026 026

1/4~

02S zW

ÎNCI

~~À09 _l14

l19 124 129 134 139 144 149 154 lS9 184 169

~~ils

l17 l19 121 123 12S 127 129

T(K) T(K)

Fig.

1.

Temperature dependence

_on

cooling

and _on

heating

of the misfit parameter deduced from satellites

[(0

4

+à)j (ai

and

[(0

⁴

36), (0

4

2-36)] (b).

a

precision

of /hT

= 0.01

K,

but the thermal

stability during

_a

complete

_run does not exceed 0.05 K. The average time of stabilization of the

crystal

before each measurement was

equal

to 45 minutes.

The

temperature dependence (on cooling

and _on

heating runs)

of the first order satellite

peaks

around

(0

4

0)

_was studied from _T~ down to 78 K

(deep

inside the commensurate

phase

à

=

).

We could also

observe,

with _a reasonable

counting

rate,

higher

order satellite reflec-

tions, mainly

second and third order _ones. At each

temperature,

the modulation _wave vector

à(T)c*

and the modulation

amplitude (the intensity

of the satellite

peak being proportional

to the

squared

modulus of the order

parameter)

_were deduced from data treatment. The fit

procedure

_was based _{on a} least _squares fit refinement between the data

profiles

and the _ana-

lytical

function which takes _{into account} instrumental resolution and describes the diffraction

peaks.

In order to reduce

systematic

_errors linked with the

alignment

of the spectrometer,

we have taken the average value between the

positions

^of the two

symmetrical

satellite

peaks (0

4

à)

and

(0

4

-à)

to calculate the modulation _wave vector. We have

applied

the _same

method with the two third order satellites

(0

4

36)

and

(0

4 2

-36).

The two

à(T)

_curves

so deduced _{are very}

similar,

but in the latter _case, trie

precision

_on the determination of _q~ is mcreased

by

_a ^{factor of} 3.

3. Results

The

à(T)

_curves deduced from

positions

^{of first} and third order satellites _are

reported

in

Figures

la and 16

respectively (black

_squares

correspond

_{to a}

heating

_{sequence, open squares}

to a

coohng one).

The

plateau corresponding

to the

phase

à

=

already

_seen with

X-rays scattering by

Brill _et ai.

[5],

is

clearly

visible. It is

according

to _our

knowledge

the first lime that this

phase

is _seen with neutron

scattering

without extemal field

applied (electrical

field

[7, loi,

or

hydrostatic

_pressure

[9]). Furthermore,

_a remarkable

global hysteresis

_{appears m} the INC2

phase

and in the INCI

phase

_up to T~. We notice that

. The first order satellites _emerge around 166.4 K.

234 JOURNAL DE

PHYSIQUE

I N°2

integrated inte$lies

on

cooling co~Ing

0 os _{~ ---~~ l}

30 ₁ -~.-~

+ +

l 120 ~

~

jj

+ 5*(

~~~

° l

~

04 2

~

lÙ*(ÎjÎ~

~ _~ +/ _z 5*( IOC

~ C

~ ~

+ ~+

+ ~$ ^~ ₉₀

_O03 + 80

~

)

~

~ é ₇₀

E ~ ^OE _~~ ~ l14

~ c

002 ^°

~

V ~~

~~ l14 ~

~~ ^~ ~q

+

~~~

)

jj

^~ +

~

i+~~

< ~ c

"' ,

$ lO[ _{.._}

_,~

_{j $}

~~~70 ₈₀

90 100 ÎIO ₁₂₀

130 140 150 160 ~70 ^~70

É~

90 ~IOO ÎIO 120~ lé

140 150 160

T(K) ^' T(K)

Fig.

2.

Integrated

intensities of satellites

(0

4

à),

(0 4

26), (0

4

3é) (a),

and

)(T)

for

n = 2,3

(b)

~ ⁱ

on

coohng.

Aiiows mark the

plateau

at à

= ~ and the

beginnmg

of the

phase

à

=

(.

. The second and third order satellites _are detectable belo~v. about 146.5 K.

. The linear character of

à(T)

in the INCI

phase

is found _agam with _a

global hysteresis

of about 2 K. This

hysteresis

is

large compared

with the 0.5 K _one observed in thiourea

[17].

. The

phase

à

=

)

is stable in the

temperature

_{ranges :}

j126-122.05 Kj

_on

cooiing

[125-128.9 Ill

_on

heating, respectively.

The

hysteresis

is thus

equal

to 3 K in

agreement

with results

proposed by

Chaves et ai.

[loi,

but in

apparent

contradiction with others measurements of dielectric _constant

[23].

This controversial situation coula be due to different

experimental protocols.

Moreover

~ve have not detected

dunng

this

phase

transition any coexistence of the locked

phase

~vith the INCI

phase.

This confirms the idea of _a continuous lock-in transition

expressed by

Ribeiro et ai.

[21].

. In the INC2

phase,

this

global hysteresis

without coexistence of

phases

_persists, but around 116.6 K and II 7.1 K _on

cooling

and _on

heating respectively,

the transition toward the

phase

à

= takes

place.

Ii is _a

typical

^first order transition with coexistence of

phases

and "obvious"

hysteresis

of 0.5 K. It must be noticed that the rive

higher

order

commensurate

phases lé

=

), (,), ), ()

characterized

by

dielectric and thermal measurements have temperature range of existence too narrow to be individualized here.

Finally,

_~ve have _not observed thermal

hysteresis

in the

integrated

intensities of satellite

peaks, contrary

to thiourea for which such _a

phenomenon

has been discovered _over three

degrees

above tue commensurate

phase

^à ₌

_[16].

What about the relative intensities of

first,

second and third order satellite

peaks (Fig.

2a and

2b)?

We know that in the _case of _a static sinusoidal

distorsion,

the Bessel's functions

development

of the

scattenng amplitude gives

^for an

n~~

_order diffraction satellite _an intensity

In

_«

J((K.1~

_cf

() )~*( §f)~n

_for

_K.1~

_<

_1,

_{with K the}

_scattering

_{vector and}

1~ the modulation

amplitude Ill].

Therefore

)

is with this

hypothesis

insensitive to the temperature, ^with

)

1

= 9 _*

).

In

Figure 2a,

the

temperature dependence

of the

integrated intensity

^of the

i i

first order satellite presents a clear

anomaly

around the first order transition at while the

intensity

^{of the third order satellite} is shown to increase

steeply

below this

phase

transition.

Furthermore,

from these _two

plots (a, b)

we see that the third order satellite has

roughly

the

same behaviour with temperature in the two INC

phases,

_even

though

it increases more

rapidly

m the INC2

phase

than in the INCI _one. We _can also notice that the

intensity

^of the third order satellite becomes

higher

than the second order _one

approximately

below 120 K.

Figure

2b

clearly

shows that the ratio

jf

is

roughly

constant all _over the measured

temperature

range,

i

while

jf _presents

a very clear

change

of

regime

from the lock-in _at

( _(T

cf l17

K).

This

clearly

demonstratesi that the third order satellite contains not

only

_a diffraction

harmonic,

but also _a distorsion harmonic with _{a wave} vector

3qo.

This _non sinusoidal character of the modulation

is established at least below 146.5

K,

where

)

is

already higher

than

).

i 1

4. Conclusions

The results

presented

in the previous section have demonstrated the existence of _a

large (2-3 K) global hysteresis

which extends _over the INCI and INC2

phases,

from the lock-in transition at up to T~

(where

à has _a value of

0.332,

_{very near}

)).

This

global hysteresis

observed does not

depend

_on the number of

temperature cycles

and could be the

experimental signature

of the

complete

Devil's

staircase,

_even ^{if the} rote of

crystal

^defects

notably

around _T~ should not be

neglected.

In thiourea the

global hysteresis

has also been observed up ^to T~.

In addition _we have

given

the behaviour with temperature of the third order satellite. We have _seen that its

intensity

becomes measurable at

roughly

145

K,

in the INCI

phase.

Therefore

we can say that this

phase

starts to

present

a non sinusoidal character below 145 K which remains weak in the INCI

phase.

The INC2

phase

lias _{a non} smusoidal character too,

slightly

more

pronounced

than the _one of INCI _even

though

there _{is no} marked difference between the

two rates. This is _m

agreement

^with

previous

E-P-R- data

[20]

^{where the}

hyperfine

structure

below 140 K has to be

analysed assuming

_a soliton

regime.

Furthermore ail these results corroborate the Landau

interpretation

based _{on a} soliton regime

proposed

to

explain

several dielectric constant anomalies

(corresponding

to the lock-in at and at

) _[8])

and the

à(T)

curve deduced from neutron measurements

iii. Finally,

others E-P-R- measurements

[13]

^have

shown also that the soliton

density (which

is related to

à(T)) _presents

in trie INCI

phase

above the transition _a thermal

hysteresis

of about 2 _or 3

degrees

in

agreement

^with our results.

It remains to correlate _our measurements with inelastic

scattering

results. Inelastic neutron

experiments performed

_on the _same

sample

_as the _one used

here,

have shown that at 145 K the

phason

mode has _no gap ^at the satellite

position;

this statement is

obviously

limited

by

the resolution of the three _axis

spectrometer

used for the measurements which had _a value of 0.04 THz

[19], [15]).

^This

support

^{the sinusoidal}

description

of the modulation in the INCI

phase

_m the

(T~,

T~ 20

K) temperature

_range. For lower

temperature,

ⁱⁿ the _non sinusoidal

regime, the results

presented

^here should be

supported by

the

study

with temperature of the

phason

mode gap.

Acknowledgments

One of the authors

(O.H.)

is

financially supported by

the Ministère

Français

de

l'Enseignement

Supérieur

et de la Recherche. We _{are very} much indebted to Dr. J. M. Godard

(Labora-

236 JOURNAL DE

PHYSIQUE

I N°2

toije

de

Physique

des

Solides, Orsay, France)

for

providing

excellent

single crystals,

and to P.

Boutrouille for technical

support.

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