The Temperature Dependent Shear-Strain of the (NbSe$\bf_4$)$\bf_{10}$I$\bf_3$ Compound, a Quasi-One-Dimensional Charge Density Wave System, below the Peierls Transition

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The Temperature Dependent Shear-Strain of the (NbSe_4)_10I_3 Compound, a Quasi-One-Dimensional

Charge Density Wave System, below the Peierls Transition

Z. Vučić, J. Gladić, C. Haas, J.L. de Boer

To cite this version:

Z. Vučić, J. Gladić, C. Haas, J.L. de Boer. The Temperature Dependent Shear-Strain of the (NbSe_4)_10I_3 Compound, a Quasi-One-Dimensional Charge Density Wave System, be- low the Peierls Transition. Journal de Physique I, EDP Sciences, 1996, 6 (2), pp.265-275.

�10.1051/jp1:1996147�. �jpa-00247183�

The Temperature Dependent Shear-Strain of the (NbSe4)ioI3 Compound,

_a

Quasi.One.Dimensional Charge Density Wave

System, below the Peierls lkansition

Z. Vuéié

(~>*),

^{J. Gladié}

(~),

C.

Haas (~)

^{and J-L- De Boer}

(~)

(~)

University

of

Groningen, Laboratory

of Chemical

Physics,

Materials Science Center,

Nijenborgh

4, 9747 AG

Groningen,

Tl~e Netl~erlands

(~) ^{Institute of} Physics of the University of

Zagreb, Bijeniéka

cesta 46, P-O-B. 304, ¹⁰⁰⁰⁰

Zagreb,

Croatia

(Received

19

July

1995, received in final form 24 October 1995,

accepted

3

November1995)

PACS.61.50.Ks

Crystallographic

aspects of

polymorphic

and order-disorder transformations PACS.71.45.Lr

Charge-density-wave

systems

PACS.61.66.Fn

Inorganic compounds

Abstract. An

X.ray study

of the quasi-one-dimensional

charge density

_wave

(CDW)

_sys-

tem

(NbSe4)ioI3

_{as a} function of temperature from _room temperature down to 130 K has been

performed by taking

oscillation and zeroth level

Weissenberg photographs.

A reversible trans- formation of the _room temperature tetragonal lattice into four

symmetrically-related

monoclinic domains has been observed at the Peierls transition temperature, TP m 285 K, with

a continuous

change

of the monoclinic

angle

from 90° _to 92.1° at 130 K. The monoclinic deformation of the

tetragonal lattice,

1-e- the shear-strain

along

the chain axis _seems to be _an elastic _response to the

long wavelength

transverse modulation of the 3D-CDW order which _can be

quahtatively

_ex-

plained by taking

into account the Coulomb interaction between CDWS _on

neighbouring

chains up to the

next-nearest-neighbours.

1. Introduction

More tl~an ten years ago a serres of _new

quasi-one-dimensional compounds

witl~

general

cl~emi- cal formula

(MSe4)~I;

M

=

Ta, Nb,

_{z =}

2, 3, 10/3

bas been

syntl~esized.

It is believed tl~at tl~e

investigation

of tl~ese

quasi-ID compounds migl~t

oifer _{a new}

insigl~t

into tl~e CDW

problems.

Structural data of

l~alogenated tetracl~alcogenides,

_as

compared

to

tricl~alcogenides,

reveal _a

stronger

one-dimensional cl~aracter

[1-3].

Tl~e intercl~ain distance _is found _to be enl~anced and tl~e average metal-metal distance _is sl~ortened. A In~eaker intercl~ain interaction _is indicated but not _an enl~ancement of tl~e

anisotropy

of tl~e

pl~ysical properties [4-7].

^{A furtl~er}

comparison

is less

straigl~tforward

since tl~ere _{is a}

great

^diiference between tl~e metal cl~ain environments in

l~alogenated tetracl~alcogenides

and

tricl~alcogenides.

Tl~e electronic

properties

^of tl~e tricl~alco-

genides

are

largely governed by

intracl~ain

cl~alcogenide pairing

_[7], wl~ereas for

l~alogenated tetracl~alcogenides

neitl~er tl~e

cl~alcogenide pairing

_nor tl~e influence of tl~e

l~alogenide

atoms

are still resolved.

(*)

Author for

correspondence:

Institute of Physics of the University of

Zagreb,

Bijenicka cesta 46.

P-O-B. 304, 10000

Zagreb,

Croatia

je-mail: vucic@olimp.irb.hr).

@

Les

Éditions

_de

_Physique

₁₉₉₆

However, according

to structural features

reported

for tl~e _z

= 2

compounds

_[8] and tl~e data from _our

preliminary investigation

_[9], it _seems tl~at in

(MSe4)~I

_group of

compounds

tl~e 3D- CDWs

ordering

is

accompanied

witl~ _{a transverse} modulation of tl~e CDW "lattice" and _a sl~ear strain of the lattice itself. Strain induced

by

CDWS has been

reported

for

(TTF)(SCN)o.s88 _Î10]

and

(TTF)(SeCN)o.s8 Il Ii.

These

compounds

have lattices

consisting

of two sets of chains: tl~e

conducting

one

(TTF)

and tl~e

nonconducting

_one

(XCN;

X

=

S, Se). Altl~ougl~

_very small

(less

tl~an

0.04$l)

_a similar shear-8train eifect _can be found in

(TTF)(TCNQ)

in wl~ich the bath sets of chains _are

conducting.

Electronic bond structure calculation

[12]

^of

(l/ISe4)~I (M

=

Nb, Ta)

bas sl~own tl~e existence of _a well

separated dz2

conduction band of the metal cl~ain

(l/ISe4)oo

wl~icl~ is

progressi,~ely

filled from

1/4

to

1/3

to

7/20

_{as ~} increases from _z

= 2 to 3 to

10/3, respectively.

It is aise sl~own tl~at tl~e

driving

force for metal ion distortion

along

tl~e

(MSe4)oo

cl~ain

sl~arply

diminisl~es _as tl~e

dz2

band

filling

deviates from

1/2.

Two of the

compounds;

those witl~ _x

= 2

and _~

=

10/3,

bave revealed _a Peierls transition associated ~vitl~ CD~i formation

(at

260 K and 285 K,

respectively) [13-15].

In tl~ese two, ^due to a

dz2

^baud

folding,

tl~e

following

Fermi

wave vectors ha,~e been

expected: kf

_m c*

/2

for the _z

= 2

(c

₌

4d;

d

being

_average metal- metal

distance)

and

kf

m c*

/4

for tl~e _~

=

10/3 (c

₌

10d). Experimentally

it is fourra tl~at

2kf components

^of tl~e distortion _wave vectors

(being (+0.05, +0.05, 2kf

₌

+0.085) (Ta)

_or

(+0.065,

+0.065.

2kf

=

+0.159) (Nb)

for _z

= 2 [8] and

(0,0,2kf

=

+0.487)

for _z

=

10/3 [16,1?i)

_are

net far from trie

expectation.

In botl~

compounds

tl~e CDW state is

accompanied by

nonlinear

conductivity, switcl~ing,

narrow-band _noise and remarkable

metastability [13-15]. Especially,

in tl~e _{x =}

10/3 compound

a

l~uge l~ysteresis

bas been fourra

recently

_m

tl~ermopower

vs

temperature measurements

[18].

In order to search for the structural

background

of tl~is

hysteresis

and first of ail to deter- mine tl~e structure of tl~e low

temperature phase,

_we

performed

_a CAD4

X-ray _scattering

data collection at several

temperatures

clown to 100 K.

During

the

low-temperature

lattice determi- nation _we faced tl~e

problem

of

l~aving

to deal witl~ tl~e

multiplicity

of most of

Bragg

reflections.

However,

_using restricted subset of reflections _we

managed

to determine tl~e monoclinic lattice

(a

= 9.405

À,

b ₌ 9.427

À,

_c

= 31.815

À,

_a

= ~y =

90.0°, fl

_m

92.3°)

at 100 K.

Starting

witl~ tl~is lattice the

intensity

data collected _were

quite

insuflicient for tl~e determination of

tl~e structure. Tl~e

multiplicity

of reflections _was found to be

temperature dependent

and

reversible, beginning

and

disappearing

_upon

crossing

tl~e Peierls

temperature.

^Tl~erefore we

decided,

_{as a} first step, to collect _as

complete

_as

possible reciprocal

_space information and to resolve tl~e "structure" of the

multiplicity by taking ~veissenberg

and oscillation

photographs

of tl~e _x

=

la/3 compound single crystal

as a function of

temperature

clown to 130 K.

2.

Exper1nlental

Procedure

Structural

investigations

were

performed

_on tl~e

(NbSe4)ioI3 single crystals kindly supplied by

Dr

Berger

and Prof.

Levy.

Most of

crystals

_are

needle-like, sl~aped

_as

trigonal

_prisms

witl~ tl~e

longest edge parallel

to tl~e

tetragonal

_{c axis.} Witl~in tl~e _same buncl~ several

single crystals

of

good quality

_were cut to the

typical

dimensions of10 _x 10 _x 20 _~lm. In order to take

Weissenberg

and oscillation

pl~otograpl~s, crystals

were mounted to a

glass

liber witl~ _a dot of vaseline _grease to minimize

restoring

^forces. The

glass

^liber was fixed to _a brass

pin

l~older of the Enraf-Nonius _{two arcs}

goniometer

l~ead. Tl~e

crystal

_was mounted _so that _{a or} b _{axis was}

collinear

(better

thon

+0.05°)

with the

goniometer

rotation _axis. The

low-temperature

Enraf- Nonius

Weissenberg

_{camera was} used witl~

X-ray

CuKo

grapl~ite-monocl~romatized

radiation and 1 _mm hole collimator. The horizontal slit _was set wide

enougl~ (3

_mm at

maximum)

to

cover a

temperature dependent spreading

of

Bragg

reflections

(due

_to tl~e

multiplicity)

_out of

the zerotl~

level,

witl~out

recording

_any

spots

^from

l~igl~er

^levels.

Tl~e

crystal

_was cooled

by

_a

liquid-nitrogen

_{vapor stream,} tl~e flow and

temperature

^{of wl~icl~}

were

regulated by

two

independent

l~eaters. Tl~e

apparatus

was

primarily

calibrated

using

a

copper-constantan (çi

= 20

~lm) tl~ermocouple

attacl~ed to tl~e

top

^{of tl~e}

goniometer

l~ead in

place

of tl~e

crystal.

Tl~e measured

temperature

shows +2.5 K oscillations witl~ _a là minutes

period

around stable

(better

tl~an o-à

K)

_average value. Tl~ese

periodic

oscillations _are inl~erent to tl~e construction of tl~e

cooling apparatus.

During

_a

cooling /l~eating cycle

tl~e

Weissenberg photographs

_were taken

approximately

_every

10 K. In order _to minimize the data collection time the full

(180°)

oscillation _was

performed only

at _a few selected

temperatures.

^{At all otl~er} temperatures a limited oscillation range

(60 -100°)

_,vas

cl~osen, large enougl~

to _caver tl~e relevant part ^of

reciprocal

_space. Trie oscillation

pl~otograpl~s

_were taken at tl~e _same

temperatures

and _are sl~o,vn at tl~e

edge

of the

Weissenberg pl~otograpl~s.

Tl~e most intensive and

relatively

distant reflection

(0,0,20)

is chosen to demonstrate tl~e

spreading

of

spots

^due to tl~e

multiplicity

eut of zeroth level. All distance measurements on a film _were clone _{using a} binocular

microscope (enlargement 50x)

witl~ _a built-in cahbrated scale and _a calibrated microdensitometer

appropriately adjusted

to

optimize signal-to-noise

ratio and tl~e lateral resolution.

3. Results

Weissenberg

and oscillation

pl~otograpl~s

sl~own in

Figure 1, together

with CAD4 data taken at room temperature, ^have confirmed the structural

investigation

results

published by

tl~e Nantes group

[3j.

^Tl~e room temperature

phase

of tl~e _z

=

10/3 compound

is found to be

tetragonal

witl~

P4/mcc symmetry (see Fig.

l and 2 in Ref.

[3]) l~aving

two metal cl~ains

(at 1/2,0,z

and

0,1/2,z)

oriented

along

tl~e _{c axis,} surrounded

by

two type of iodine _rows

(at 0,0,z

and

1/2,1/2,z) containing

4 and 2 iodine ions per c

lengtl~ (or

vice

versa), respectively.

In _an

NbSe4

infinite

cl~ain,

eacl~ metal atom is sandwicl~ed

by

two

rectangular

Se units stacked

along

tl~e cl~ain axis. Tl~e dil~edral

angle

between

adjacent rectangles

is

45°,

_so tl~e

stacking

unit is

a

NbSe8 antiprism.

In

Figure

la _an oscillation

pl~otograpl~

is

sl~own,

witl~ tl~e a-axis _as tl~e oscillation axis. A _serres of

layer

lines of

type

^nki _up to tl~e fourtl~ level

in

=

4)

_are observed.

A

Weissenberg photograpl~

of tl~e zerotl~ level _is shown _in

Figure

16 where tl~e two

mutually perpendicular

_axes, c* and

b*,

_are marked. Beside tl~e

tetragonal arrangement

^of reflections _in tl~is b*c*

plane,

_a

relatively strong

diffuse

scattering

around

Bragg

reflectioiis

lying

_{on or} close to the c* axis _is revealed. The

intensity

of diffuse

scattenng

^{is modulated}

by

the intensity ^of

Bragg

reflections and extends

exclusively

in

planes parallel

to a*b*

plane.

Tl~ere _are several

possible

_sources, botl~ static and

dynamic,

whicl~

migl~t

_cause sucl~ _an intensive diffuse

scattering.

Tl~e

particular reciprocal

_space distribution of tl~e diffuse

scattering

indicates disorder

along

tl~e _c-axis. Tl~e most

simple

_cause would be of

morpl~ological

_origin

since under

sligl~t

mecl~anical _pressure

perpendicular

to tl~e _c-axis tl~e

crystal disintegrates

into a buncl~ of tl~reads. This

might

_mean tl~at eacl~

crystal

consists of domains-tl~reads

weakly

bound

togetl~er

and

perl~aps

sl~ifted

randomly

witl~

respect

to _one anotl~er

along

tl~e c-axis.

Otl~er

possible

_{sources are} static disorder of tl~e iodine _{ions or}

low-energy pl~onon

modes. Tl~e static disorder of iodine _was detected

during

tl~e CAD4 refinement

procedure

wl~en it _was found that iodine

Debye-Waller (DW)

factor _is

unusually large (7:2

ratio to other DW factors

[3]).

A contribution of

low-energy phonon

modes is also

expected

_since neutron

scattering

data

(altl~ougl~

for _~

= 2

compound [19,20])

bave revealed _a TA

low-energy nearly dispersionless phonon branch,

with _wave vector

perpendicular

to c* direction and _a

polarization

vector

aloiig

c~ direction.

However,

_in this

experiment

we dia not observe any

significant temperature

dependence

of the diffuse

scattering,

as would be

expected

for the

phonon

contribution.

a)

)Î

Fig.

1.

-a) Oscillation-crystal photograph,

_room temperature, ^a-axis oscillation

(20°),

CuKcx

graphite-monochromatized radiation,

random oscillation _range location.

b) Weissenberg pl~otograph

of zeroth level, _room temperature, _a-axis oscillation

(188°),

CuKo

graphite-monochromatized

radiation, c* and b* _{axes are} indicated.

By decreasing

the temperature ^{below tl~e Peierls transition}

temperature (TP

_m 285

K)

eacl~

Bragg

^{reflection of tl~e} room

temperature tetragonal phase

_is

split

into 4 of almost tl~e _same

intensity.

Excluded from tl~is rule _are tl~e

(hk0) reflections,

wl~icl~ _are not

spht.

Tl~e magni- tude of tl~e

splitting

increases _as increases. An

example

of _a

Weissenberg (and oscillation)

pl~otograph,

taken at 131.5 K in tl~e low temperature

phase,

is sl~own _in

Figure

2. Com-

pared

to the _room temperature

Weissenberg photograph

it is

clearly

seen that ail reflections except ^tl~ose on tl~e b*

(a*)

_{axis are}

quadrupled.

Tl~e indexes of tl~e _new

Bragg

reflections _in tl~e

tetragonal

reference frame _are:

(h

+

ni(T),

k

,1), (h qi(T), k,

_1),

(h,

k ₊

ni(T),

₁₎ and

Fig.

2.

Weissenberg

and

oscillation-crystal photograph

of zeroth level taken at T

= 131.5 K, a-axis

oscillation,

CuKo

graphite-monochromatized

radiation.

Weissenberg photograph:

reduced oscillation range

(100°)

to _caver most of the spots of c*-axis and _a few

representative

_ones of b*-axis. Oscillation

pl~otograph (shown

_{as a}

strip):

20° oscillation range chosen to detect

representative

spots

(0,0,20)

and

(0,10,0)

the

split

and the

unsplit

_one,

respectively.

Note that each spot

(except

those of

b*-axis)

in

Weissenberg photograph

is

quadrupled.

(h,

k _ni

(T),

_{1). Tl~e}

magnitude

of

splitting

_ni

(T) changes

as a function of

temperature

contin-

uously

from _zero at

TP

_up to 0.olll at 130 K and back to zero upon

heating

above tl~e Peierls

temperature.

We _see tl~at eacl~ of tl~e reflections

previously

_on tl~e

tetragonal

c* axis is

split

into 4 _{new ones}

symmetrically placed

around tl~e

position

of tl~e old reflection. Tl~e distance between tl~e spots on tl~e

Weissenberg

film measured

parallel

to tl~e 1= 0 line reveals for eacl~

1, ^two

pairs

of reflections: _one for wl~icl~ tl~e

splitting magnitude

is

independent

of1 and tl~e otl~er witl~ linear

dependence

_on 1.

Since _{we are}

deahng

witl~ _a zerotl~ level

Weissenberg photograpl~

the

interpretation

of the observation is

straightforward.

The

pairs

of spots ^the distance of whicl~ is

independent

of1 form two _new c* _axes,

ci

~,

lying

in tl~e b*c*

tetragonal reciprocal plane,

tilted

symmetrically

from tl~e

tetragonal

c*

aiis

_and

_meeting

_at

an

angle

of

2Afl*(T).

Since tl~e a* and b* _{axes remain}

uncl~anged (untilted)

below

TP

tl~e _{two new}

reciprocal

lattice

angles

£

b*c(

~ are

(90

+

Afl)*

Fig.

3.

a)

Detail

(enlarged)

of

Weissenberg photograph

taken at T

= 250 K

showing quadrupled (0,0,6)

spot. Outer _pair of spots ^is

2Afl*

_apart while the distance of inner

pair

is

proportional

to and

m

2fÀc*Ap*RF Ii

₌

6). b)

Detail

(enlarged)

of oscillation

photograph

taken at T

= 250 K

shov~ing tripled (0,0,20)

spot

(see text).

The distance of outer pair of spots ^is 2Yoo20 " 2iÀc* AP" RF

Ii

₌

20).

Fig.

4.

a)

and

b)

the _{same as in} Figure 3 but at T

= 157 K.

and

(90 Ap)~, respectively.

Tl~e

pairs dependent

_on Î

belong

to two otl~er _new c* _axes.

c(

~,

lying

m tl~e a~c*

tetragonal plane, meeting

at tl~e _same

angle

_as tl~e former _ones. In

tl~ls

case tl~e two _iiew

angles (90

+

Ap)*

_are defined witl~

respect

to tl~e a* axis

(£a*c(~).

Consequently,

tl~e 4

reflections, originating

from any

single

reflection

lying

_on tl~e

tetragolal

c*

axis,

Will appear in oscillation

pl~otograpl~s

_as 3 spots due to tl~e

overlap

of two spots on tl~e film since tl~e film sl~o~vs _a

projection

of _a part of

reciprocal

_space

(limited by

3 _mm slit and 12° oscillation

angle)

auto tl~e a*c~

plane.

All otl~er reflections will appear

quadrupled.

Tl~e oscillation

pl~otograpl~s

taken at each

temperature

for the most intensive

(0,0,20)

reflection coiifirm the above

expectation (see

tl~e

strip

at the

edge

_in

Fig. 2).

Bath

Weissenberg (a)

and oscillation

16) pl~otographs

of the

(0,0,6)

and

(0,0,20) reflections, respectively

_are sl~own

enlarged

in

Figures

3 and

4,

taken at two diiferent

temperatures

250 K and là?

K, respectively.

From tl~ese observations _we conclude to tl~e existence of four _{new sets} of

Bragg

reflections

defining

four monoclinic lattice domains. Tl~ese _are related _to eacl~ otl~er

by

_a fourfold rotation

axis

(c-axis), scl~ematically

shown in

Figure

5. Therefore tl~e Peierls transition _is

accompanied

witl~ _a

tetragonal

to monoclinic transition and witl~ tl~e sl~ift of tl~e cl~ain

planes

of

(h00)

or

(0k0)

_type

along

c-axis. The relative shift _{or more}

precisely

tl~e lattice sl~ear strain _can be

simply

described

by

the

temperature dependent

monoclinic

angle fl

which is

changing

its

magnitude

from 90° at

TP

to 92.1° at 130 K.

Each

pl~otograpl~

taken below

TP

contains _a well

developed splitting

of

reflections,

both in

Weissenberg (W)

part of tl~e

pl~otograpl~ (seen

as

2Afl)

and in tl~e oscillation

(O) strip (seen

_as

2ÀRF

_ni

).

From

~veissenberg photographs

_{one can}

simply

read

angles

between _two monoclinic

T>Tp T<Tp

~--2_

0020

,

~ "~

m~,u

~*

3

colo

fl/2

ù-~

Fig.

5. Schematic presentation of

representative

_spots

lying

_on c* axis, ^above and below Peierls transition temperature, TP _m 285 K. Note that below TP each spot

having

f ~ 0 is

quadrupled

thus

forming

four

symmetrically

related monoclinic domains characterized

by

monoclinic

angle

fl.

c~ _axes which _are

lying

in tl~e

plane perpendicular

to tl~e oscillation _axis. Trie distance betweeii

trie extreme spots ^{measured in the} oscillation

photograph

is

2Y(mm)

whicl~ is related to the

splitting

_ni

by

the

expression

_{ni "}

il /RFA,

where

RF

" 28.65 _{mm is} the _camera radius aiid

= 1.54 is the

wavelengtl~

of tl~e CuKa radiation.

Furtl~er,

_{ni =} ic~

sin(Ap*),

where c~ is tl~e true monoclinic

reciprocal

_axis

lengtl~ (c*

=

cl cos(Ap)).

Tl~e

temperature dependence

of botl~

Afl

and _{n20 are} sl~own in

Figures

6 and

7, respectively.

4. Discussion

We bave observed tl~at tl~e lattice of tl~e

(NbSe4)ioI3 compound

exl~ibits _a structural transfor- mation from

tetragonal

to monoclinic _at tl~e transition

temperature Ts

= 285 K wl~icl~ coincides witl~ tl~e Peierls transition

temperature.

Belo~v"

TP,

tl~e

spontaneous

^{monoclinic strain}

produces

foui- domains

corresponding

to tl~e four

tetragonal

< 100 > directions wl~icl~ _con be chosen for the monoclinic b _axis. A monoclmic distortion _is

interpreted

as a relative

slip

of

NbSe4

chairs

along

the

chair,

_c axis. The

magnitude

of tl~e

slip

is measured

by

tl~e monoclinic

angle fl.

Trie

net

change

of

fl

in tl~e

temperature

^{interval from 285 K clown to 130} K is fourra _to be

small,

about 2.1°.

According

to tl~e electromc

conductivity

measurements

[19]

^{aiid tl~e} electron microscopy

superlattice

reflections detection

[16]

^{tl~e monoclinic distortion evolution} goes

along

witl~ _a 3D-CDW

ordering.

We bave first considered _a

possibility

tl~at tl~e monoclimc distortion _{is a} result of tl~e _con- densation of _a

doubly-degenerate

_transverse acoustic

(TA pl~onon

mode of _{wave vector}

(0,0,q)

and

ix, y) polarization.

In tl~at _case 4 satellites _ai-e

expected

to be recorded _on tl~e

Weissenberg pl~otograpl~s

around eacl~

Bragg

reflectioii except ^{around tl~ose witl~} tl~e index

(0,0,1).

Unfor-

tunately,

tl~e

experiment

shows

quite

tl~e

opposite:

below

TP

there _are 4 _new

Bragg

reflections around each previous one

except

around tl~ose with

= 0.

Since tl~e otl~er

possible

TA

pl~onon

mode of tl~e _wave vector

(q,0,0) orland (0,q,0)

and

(z)

~ ~, ^{c llUd~ ~~©}

~ ,' _J

~ UOÎ:lL

°.

Î bU

'.

/ '.

i

r,-

(Jo

0

, i»

'

-~

/90

Fig.

6.

Temperature dependence

of the monodinic

angle (from Weissenberg photographs,

spot

(0,0,6); (.) heating, (o) coohng.

Note that _errer bars _are shown

only

when greater than _size of the

symbols.

'io

° ni tuai

~

C coolifii

Il tilt _»

~

o fin

n in

~

/

o zu ^~ _(.

o on

-i-~-- i

' ?o z o z ho ziJo

Î

Fig.

7.

Temperature dependence

of transverse distance Yoo20 *

~20(T)ÀRF (mm)

of

one of four

spots

(0

+

~20(T),0, 20)

_or

(0,

0 +

~20(T),20) (from splitting

of

Bragg

spot

(0,0,20));

measured in oscillation

photographs

relative to the tetragonal c*-axis. (~20 # lc*

sin(Afl*)) (errer

bars _are shown

only

when greater ^than _size ^{of the}

symbols).

polanzation

is almost

certainly

ruled out

by

virtue of

arguments given

_in discussion related to

strong

^diffuse

scattering observed,

_an alternative mecl~anism

underlying

tl~e observed eifect sl~ould be

sougl~t

for.

A

question

arises wl~ether in

(NbSe4)ioI3

tl~ere is _a

coupling

between _a 3D-CDW

ordering

and tl~e lattice sl~ear strain. In order to answer tl~is

question

_one sl~ould first

reinvestigate

_in detail the

superstructure spots

below

TP seeking particularly

for _transverse

components

^{of tl~e} distortion _wave vector diiferent from the

commonly expected

values like 1

(or zero)

_or

Il?-

So

far,

_no transverse components of _q have been resolved for the _z

=

10/3 compound [16,1?i.

(TTF)(SCN)o_s8s

is _an

example

of _a

quasi-ID

CDW

system

in wl~ich both the 3D-CDW

ordering

and lattice monoclinic distortion _are observed

[loi.

The net

change

of the monoclinic

angle fl

from

TP

= 180 K to 4.2 K is measured to be _m

2.1°,

similar to _our results for the

(NbSe4)ioI3 compound.

Moreover it is shown that the monoclinic lattice distortion

(shear strain)

is

coupled

to the relative

phase

^{shift of} the CDW. Two

types

^{of interchain forces} are

discussed: the Coulomb force between CDWS which tends to induce _a

phase slip,

and the elastic force which resists

it, preferring

to minimize the

phase slip.

In the

comprehensive

work

on

(TTF)(TCNQ) [?Ii

it is shown that

competing

Coulomb interactions have to be

present

in order to

explain

_a deviation of _qi from the most common values

(or 0)

_or

1/2.

In the

case of

(TTF)(TCNQ)

the

competition originates

from _two

interpenetrating

^chain

subsystems;

(TTF)

and

(TCNQ) having

two diiferent Peierls transition

temperatures.

^In the group of isostructural

compounds (TTF)(SCN)o.s88, (TaSe4)21and (NbSe4)ioI3 only

_one

subsystem

is carrying the CDWS. The natural conclusion is that in order to

explain

_a CDW

phase

slip

_in these

compounds,

_a

competition

between CDWS _on the first and the _moi-e distant

neighbouring

chains must be assumed. As it is shown _in the work

[22]

^{which introduces the}

concept

^{that Coulomb forces} are the dominant mechanism for _a CDWS' _transverse

ordering,

the interaction with the nearest

neighbours

would favor _an

out-of-phase ordering.

^{On the}

other hand the next-nearest

neighbours (NN) (and

also _more distant

neighbours)

would

try

to

impose

^its own

out-of-phase ordering.

Whether the NN and _more distant

neighbours

should be taken into account _or not

depends _[22]

_on whether the

magnitude

of the

exponential

cut-off

parameter

_qjj

dl

is smaller _or

larger

than

1, respectively (dl

is transverse distance between the chains and qjj ⁼

2kf).

For the group of

compounds

under consideration the cut-cif

parameter

can be estimated from trie available data to be

0.64,

0.48 and 0.10 for

(TTF)(SCN)o.ss8, (~iSe4)21

and

(NbSe4)ioI3 compounds, respectively.

The conclusion is

straightforward;

in all these

compounds

the NN and _more distant

neighbours

should be included in order to take

into account

properly

the eifects of the Coulomb interaction. Whether _or not the deviation

from _qi

=

(or 0)

will _appear

depends

also _on the effective

strength

of the

screening by

iodine-atoms _rows which

separates

^the next-nearest

neighbouring

chains. For

(NbSe4j2I

and

(TaSe4j2I

value of the _qi diiferent from _zero

(or ₁₎

has been

reported.

The observed values of _{qi are very}

small;

_moreover for these

compounds

_{qia = qib, as may} be

expected

if the

Coulomb interaction of the next-nearest

neighbours

is not

strongly

screened

by

iodine _rows.

The

(NbSe4)ioI3 is, according

to the cut-off-limit _value

qjjdi

₌

0.10,

the best candidate to exhibit the eifect of _more distant

neighbours

to a transverse CDW

ordering.

A

good

indication is the observed shear strain

which,

if related to the transverse component of the distortion

wave

vector,

^{indicates that either} _qa ^should be diiferent from _zero

(with

_qb

#

0)

_or vice _versa.

This is in

agreement

^{with trie structural}

particularity

of the _z

=

10/3 compounds compared

to two other members of the group.

Namely,

the _~

=

10/3 compound

has _an intemal lattice anisotropy

having

two

nonequivalent

iodine _rows at

(0,o,z)

and

il /2,1/2,z).

The

suggestion

that there should be _transverse components of _q in the _~

=

10/3 compound

_emerges from the electron _microscopy observation

[16j. There, superstructure

reflections _in the a~c"

plane (see Fig.

3 in Ref.

[16j)

_are well locahzed

along

c* _axis

(qjj

^but

elongated

in a* direction up ^to

the o-1 a*. So when and if _transverse

components

^{of the}

superstructure

reflections would be

resolved,

the isolated

spots

^should appear

quadrupled along

transverse

reciprocal

_{axes in} both directions. This is _in

agreement

with the observed shear strain vectors _as well _as with the local

lattice

anisotropy

effective at the level of the

next-nearest-neighbours.

Acknowledgnlents

We

gratefully acknowledge illummating

and

clarifying

discussions with

prof.

A.

Bjeh§.

~Ve also thank Dr. K.

Biljakovié

who had

suggested

LT structural

investigation

and

supplied

_us

with

high-quality single crystals.

The

crystals

_1n"ere

origmally synthesized

in

prof.

F.

Levy's laboratory by

H.

Berger

to ~vhom _{,ve owe}

special

thanks. This

investigation

and the

stay

of

one of the authors

(Z. V.)

at

Laboratory

of Chemical

Physics

in

Groningen (during

which the

experimental,vork

_was

performed),

_was

financially supported by

Commission of the

EC,

DG

XII,

Contract number

B/CII*-913183,

_as ~vell _as

by

the

Ministry

of Science and

Technology

of

the

Republic

of Croatia.

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