Energy spectrum of binary graphite intercalation compound acceptor-acceptor type C12FeCl3(ICl)0.75

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Energy spectrum of binary graphite intercalation compound acceptor-acceptor type C12FeCl3(ICl)0.75

V. Kulbachinskii, S. Ionov, S. Lapin, V. Avdeev

To cite this version:

V. Kulbachinskii, S. Ionov, S. Lapin, V. Avdeev. Energy spectrum of binary graphite intercalation

compound acceptor-acceptor type C12FeCl3(ICl)0.75. Journal de Physique I, EDP Sciences, 1992, 2

(10), pp.1941-1948. �10.1051/jp1:1992257�. �jpa-00246674�

Classification

Physics

Abstracts 71.25T

Energy _spectrum of binary graphite intercalation compound acceptor-acceptor type CI~FeCJ~(ICI)o~~s

V. A. Kulbachinskii, S. G.

Ionov,

S. A.

Lapin

and V. V. Avdeev

Low

Temperature Physics

Department, Moscow Lomonosov

University,

119899, Moscow, Russia

(Received 25

May

1992, accepted 15 June J992)

Abstract. Here _we report ^{the results of} a

study

_on the Shubnikov-de Haas effect (SdH) in the first

synthesize binary graphite

intercalation

compound (GIC) Ci~fecl~(ICI)o,75

of the first stage acceptor-acceptor type ^{and of the second} stage ^GIC C12FeC13 and

C16ICl.

The _stricture and the phase transition order-disorder type ^{also have been}

investigated.

Introduction.

The

widespread

interest in the

study

^of

graphite

intercalation

compounds

was stimulated

by

the

possibility

^of

studying charge

_transport in

quasitwo-dimensional

structures. The

high degree

^of

perfection

of the GICS

presently produced

allows _one to use quantum

oscillatory

effects to

study

their energy spectrum ^{and derive} information _on the

shape

and dimensions of the Fermi

surface,

concentration of carriers and effective _masses. New

possibilities

for

understanding

the

physical properties

of the GIC _are

opened by

_a

complex

intercalation in which there _are

sequential layers

of

graphite,

an intercalate

I,

and _an intercalate 2. Such

compounds

referred to as heterointercalated _or

binary [1-9]

_can be divided into _some classes _: those with

acceptor~

acceptor, acceptor

donor _or donor-donor intercalate _sequences. Here _we report ^{the results of} a

study

on the Hall

effect,

Shubnikov-de Haas

effect, phase

transitions in the first

synthesized acceptor-acceptor

type ^{hetero-GIC of the first} stage ^{and the second} stages ^{of ICI}

GIC, Fecl~~

GIC. The chemical formulas of the

compounds investigated

_are

Ci~fecl~(ICI)o_75, C12FeCl~

and

C16ICl.

Experimental.

Highly

oriented

pyrolitic graphite

annealed at T

~ 3 300 K with _an

angle

of disorientation less than 1°

along

C-axis in the form of

quasi single crystals plates

was used. Ferric trichloride

(FeC13)

and iodine monochloride

(ICI)

were

synthesized

from elements and refined

by

multiple

distillation in _a

dry

chlorine flow _or

multiple recrystallisation correspondingly.

Fecl~-GIC

and

C16ICl-GIC

_were

synthesized

from gaseous

phases

as was described in

[9].

1942 JOURNAL DE PHYSIQUE I N° 10

The

compound Ci~fecl~(ICI)o_~5

_was

synthesized

in _two steps. ^To

begin

with the second stage

Ci~fecl~

_was

produced.

The introduction of the iodine monocloride resulted in the

filling

of all free

interlayer

_spaces and the formulation of _a

first-stage

GIC with

altemating layers

of different intercalates and

graphite.

The sequence of

layers

in

C12FeC13(ICI)075

_are

C-Fecl~-C~ICI-C-FeCI~~C-ICL-

etc.

Chemical

compositions

of GICS _were determined

by gravimetric analysis

and chemical

analysis. X-ray analysis

_was carried out _{on a} diffractometer URD-6

(Germany)

Cu

K~ irradiation,

Ni filter. The families of 001 lines _were obtained. The second stage ^GIC

Ci~fecl~ samples

of

equal geometric dimensions, weights

and

compositions

were

placed

into melted ICI in thermostat and every 24 hours

X-ray analysis

_was carried _{out on one}

sample.

Some

diffractograms

_are shown in

figure

I. When the time of

synthesis

was about 70

hours,

a mono

phase sample

of hetero-GIC

Ci~FeC13(ICI)o.75 containing layers

of

FeC13

and ICI _was

produced (fig.

I, curve

3).

Under

exposition

of _more than 150 hours the first stage ^of

C~ICI

e

~ o

o o

o

o o

is so 70 60 50 40 ya 20 <o

2

o o

o oo

o ~

2 9 80 70 do 50 40 >o 20 <o

~

i-Q 80 70 60 50 40 yo 20 40

e

, o

~ O

~ a

'LB'8b '7b 6b '>b Ah yb '2'o 11

~

5

o

t 9 80 70 60 >o ^do ,o to <o

Fig.

I.

Diffractograms

of _a second stage

C12FeCl~

in ICI at different time of

synthesis

t, hours 1) 24 2) 48 3) 72 4) 120 5) 172.

Open

circles

correspond

to peaks of the second stage C12FeC13 and full circles

correspond

to

peaks

of the second stage ^of

C16ICl.

may be obtained. The

single-phase samples

had _a repeat

period

of

10.471

_for

_C16ICl, 12.751

_for

_C12FeCl~

_and

16.531

_for

C12FeCl~(ICI)o_~5.

The C-axis

charge density

_{p~ may} be calculated from the Fourier transform of the _structure factors

F~oi

as it _was done in

[101.

The

experimental

_structure factors

F~oi

are related to the

integrated

intensities

I~oi

^{of the}

X-rays

diffracted from atomic

planes perpendicular

to the

graphitic

c-axis

by

the well known

expression

)F~oi)

=

(I~oi/KLPA)~'~ (l)

where K is _a scale

factor, L,

P and A _are the

angle-dependent

Lorentz

factor, polarization

factor and the

absorption factor, respectively.

The theoretical _structure factor

F~oj

in

equation (I) depends

_on the

position _(z~)

and the atomic

density (n~)

^{of the atomic}

layers according

to the well known

expression

M

F~oi

₌

£

n~

f~ ^{[cos (2} grlz~)

+ I sin

(2 grlzj)I

_D~

(2)

j =1

where the _sum extends _over the M

planes

in the

cell, f~

^and _D~ represent ^{the atomic}

scattering

factor and the

Debye-Waller

temperature ^{factor for the}

j-th layer.

The

integrated intensity

data has been

analyzed by comparing

the

experimentally

derived structure factors

F)i (Eq. (I))

with _structure factors calculated

according

to

equation (2)

which _we will henceforth refer _{to as}

F~oj.

The

layer

parameters n~, z~, in

equations

are

simultaneously adjusted

in

computer

program ^to minimize the

weighted

residual function

R,

_were R is

given by

z

M F

hi F~oi

)~ wi ^~'~

R

=

'"°

~

(3)

£ _)F~oi)~wi

i=o

The _sum in

equation (3)

extends _over all the observed diffraction

peaks

and wi is the statistical

weight

of the I-th

experimental

structure factor. The statistical

weight,

_wi, is

inversly proportional

to the square of the standard deviation in the structure factor. A C-axis

charge density,

_p~, can be calculated from the Fourier transform of the structure factors. In the _case of

a

centrosymmetric

structural model for the intercalate

layer

^{which has} a central Fe

layer

localised at z ₌

oh,

the

expression

for p~ takes the form

Pz -

1( _F1°1

C°S

~

i~~ ⁽⁴⁾

where

d~

^{is the} repeat ^{distance for the c-axis}

charge

distribution. Other atomic

layers

_appear as

pairs

of

layers

in the unit cell

positioned

with mirror symmetry ^about z =

01.

_{We found}

non-

centrosymmetric layer

models to be in poor agreement ^with

experimental

data. The function

was constructed from the measured _set

()F~oi))

of structure factors. In this _case, the

magnitude

F

hi

is determined

directly

from the data

(I[oi ),

but the

phase (sign)

must still be extracted from _a structural

analysis.

In

figure

2 _we

plot

^{the results of the Fourier}

synthesis (Eq. (4))

_{as a} function of _z for the stage ^{I hetero-GIC}

C12FeC13(ICI)o.75.

The width of

figure

2

corresponds

to one repeat distance for the c-axis

charge density.

Peaks in the function p~ seen in

figure

2

correspond

to the atomic

layers

of

C, Fe, ICI,

Cl- which lie

perpendicular

to the

graphitic

c-axis. Our

analysis

indicate that the ferrum chloride molecular

species

in the intercalate

layer

of the

1944 JOURNAL DE

PHYSIQUE

I N° 10

~o-

i2

,~j

20

' ~

je

^{Cl ~}

~

l

0

20

~ -~~~r,, ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

-20,00 _{~10,00 0~00} 10,00

(

Fig.

^2. C~axis

charge density

_{pz vs. z} for the stage ^{I GIC} Ci~FeC13(ICI)o_~5. Peaks in the function

p~(2

_seen in the

figure correspond

to the atomic

layers

of C, Fe and Cl- which lie

perpendicular

to the

graphitic

C-axis.

compound

_are oriented in such _a way as to generate ^Cl-

layers

^that contact the

bounding

carbon

layers.

The Fe has been found to be located in _a central

layer (z

=

0).

We studied the Shubnikov-de Haas

(SdH)

effect in the second stages

C12FeC13, C16ICl

and

the first stage

Ci~fecl~(ICI)o_75.

The SdH oscillations of the second stages

C12FeC13,

C16ICl

are shown in

figure

3.

Only

_one oscillation

frequency

is observed for every

compound.

The

angular dependence

of the oscillation

frequency and, hence,

the

angular dependence

of the

extremal cross-section of the Fermi-surface S

corresponds

to the formula

S(o

=

S(0

cos~

(o ).

Here o is the

angle

between C-axis and the

magnetic

field B.

Thus,

the

C12FeCl~, C16ICl

Fermi-surfaces _{are a} smooth

(or slightly undulating) cylinder.

The Hall coefficient R does not

depend

on the

magnetic

field up ^to B

=

lo tesla. The concentration of

Pa

l/

0 2 B,T

Fig.

3.

Dependence

of the

oscillatory

part ^of the transverse

magnetoresistance

_p~ on

magnetic

field I) graphite, 2) CI6ICL 3) Cj2FeC13.

holes _was determined from Hall effect

(P

~

)

and from SdH effect

(P

s~~ data

independently by using

formulas

~~

R

e

'

~~~~

(2 grfi)~

_*

[/~

(N

I

d~]

^~~~

were

d~=3.351,

N is _a stage

number,

_d~ is the width of the intercalate

layer,

d~ ⁺

(N

I

d~ being

the

repeat period

of GIC

investigated.

In

C12FeC13, C16ICl

the value of

P~

=

Ps~~

=

2.6 _x

10~~ m~~

and 2.I _x 10~~

m~~ correspondingly

and hence

they

have

only

one group of holes. The extremal Fermi surface cross-section in

C12FeC13

is

S

=

(295-310)

_x 10~~

(sm)~~

and in GIC

C16ICl

is S

=

(260-290)

x 10~~

(sm)~~.

Compared

to the

original Ci~fecl~ compound

in which

only

_one oscillation

frequency

18

observed,

the energy

spectrum

^{of the}

Ci~fecl~(ICI)o.75

is much _more

complicated.

The SdH oscillation of the first stage

compound

are a

superposition

of three

frequencies

in all of which beats _{are seen,} evidence of _two close

frequencies

in each harmonic

(Fig. 4a).

In the Fourier spectra ^{of SdH} oscillations three modulated

frequencies

dominate

(Fig. 4b).

The extremal

iQ

5 6 7 8 9

B,T

A

,2

0 1000 2000

f,T

Fig.

4.

Dependence

of the

o8cillatory

_part of the _tran8verse

magnetore818tance

_p~ on

magnetic

field of hetero-GIC C12FeC13(ICI)075 (a) and the Fourier transform of the oscillations (b).

JOURNAL DE PHYSIOUEI -T 2. N' lo, OCTOBER 1992 69

1946 JOURNAL DE PHYSIQUE I N° lo

Fermi surface cross-section in GIC

C12FeCl~(ICI)o_~5

are

Si

=

(60-80) x10~~(sm)~~

S~ ₌

(860-920

x 10~~

(sm)~~

and S~ ₌

(280-300

_x 10~~

(sm)~~

The extremal Fermi-sur- face cross-sections

correspond undulating

^coaxial

cylinders

oriented

along

the C-axis. The

reason for the appearance of several

isoenergetic

surfaces in the form of

undulating cylinders

in

the

binary

GIC is _an additional indirect interaction between carbon atoms in

neighboring layers

of carbon

separated by

_an intercalate

layer, according

to the model of energy spectrum ^of

hetero-GIC, proposed

in

[4, 9]. Assuming

_a

layer

_sequence ABAB.. for the GIC

Ci~fecl~(ICI)o_~5

_{we get}

[4, 9]

_a

dispersion

relation for _two bands _:

Ei

~ ⁼ ± y

f

cos 4S

(yf~ cos~

_4S

+ _7~ *~

k()~'~ ⁽⁶⁾

where a

=

k~1/2, I~

^is the repeat

period

of the GIC

along

the

C-axis,

_~J *

=

3~'~ _ao

y$~/2,

k~ ^{is the}

in-plane

_wave vector. The value of the extremal _cross sections in

k-space Si

~ ⁼

grkj

ⁱⁿ the k

=

0

plane perpendicular

to the C-axis is

equal

to

gr x

)E~)

x

()E~)

±2

yf)

Si

~ ⁼

(7)

'1*~

An

expression

for the carrier effective _masses

mi(~

is

equal

to 4

fi~()E~)

_±

yi*)

mi*2

_"

~ ~

(8)

3 an

y$

The energy spectrum

(6)

thus leads to a Fermi surface in the

shape

of _two

undulating

coaxial

cylinders

oriented

along

the C-axis.

Using

the

experimental

values for the Fermi surface _cross section and the

cyclotron

_mass, one can find

using equations (6-8)

the parameters ^{of the} energy

spectrum

^of GIC which _are shown in the table1.

Table I. Parameters

of

the energy spectrum

of

GIC.

~°~P°~~~"~

~

~,

1°~~ Clfl~~ _~l~*/~l~o

EF, Yi,

_e Yi*,

2 270 0.140 0.31 2.7 0.3

2 300 0.145 0.33 2.7 0.3

880 0.26 0.6 2.3 0.26

63 0.09

Thus,

_{as a} result of

heterointercalation,

the

original Ci~fecl~

GIC Fermi

surface,

_a smooth

(or slightly undulating) cylinder

is transformed into _a Fermi surface

consisting

of _two

undulating

coaxial

cylinders

oriented

along

the C-axis.

The existence of ABAB...

regions

leads _to the creation of _two branches in the energy

spectrum,

^described

by equation (6).

We find a

representation

of the spectrum ^{of the AAA..}

stack of

layers [4, 9].

The new energy sub-band arises from the

possible

AAA...

layer

stack in

Ci~fecl~(ICI)o_~5.

We find for the third extremal Fermi surface cross-section the

expression

qr x

()E~)

+ 2

yf)~

S~ =

(9)

'1*~

The

experimental

value of

53

₌

(280-300

x 10~~

(sm)~~ approximately

coincides with the Fermi surface cross-section of the second stage ^GICS

CI~ICI

and

Ci~fecl~

and may

belong

to

regions

of this GIC in the volume of the

sample,

but

according

to the

X-ray

data all

investigated samples

were

monophase

of

Ci~fecl~(ICI)o_~5.

Thus _a

composite

_structure of the type ^ABAB... and AAAA... may lead _{to a} three-band

structure. For such _a spectrum ^{the Fermi surface consists of three}

undulating

coaxial

cylinders

along

the C-axis.

It is known that when GICS _are cooled down _{to a} certain temperature a

phase

^transition

occurs due _to the solidification of the intercalate

layer.

In the mono-GICS of iodine

monochloride disorder-order transitions _occur for To ₌ ^{305-315 K}

(To

_grows as the GIC stage number

increases)

and is

easily registered by

the

discontinuity

in

resistivity along

the C-axis. In

figure

5 the relative

change

in the C-axis

resistivity

is shown for the hetero-GIC

C12FeC13(ICI)o.75 (curve I)

and for the second stage ^GIC

C12FeCl~ (curve 2).

The transition in

C12FeC13(ICI)o.75

_occurs at a lower

temperature

To =

302 K than in

CI~ICI (To

₌ ³¹²

K).

Note that the

resistivity discontinuity

for the transition in the hetero-GIC is less

by

_a factor 2.

The temperature ^{of the transition} To =

302 for the hetero-GIC

Ci~fecl~(ICI)o_~5

is

slightly

less than the temperature ^{of the transition for the first} stage ^{of GIC}

CSICI.

The temperature shift of the transition _means that _a

change

^of an ICI

layer

to

Fecl~

leads to reduced interaction in the

remaining

ICI

layers.

.8

~ i~l.4

j

'

£

~1.o

~~

0. 6

290 31

Fig. 5. - ^{lative ange}

and ⁱⁿ second stage ^16ICl

(2).

In conclusion _we would like to direct attention to the

following important

fact. The presence of intercalate molecules _creates the

possibility

of indirect interaction between carbon _atoms

separated by

intercalate molecules.

Therefore,

it is not

possible, strictly speaking,

to

neglect

interlayer

interactions and consider the GIC _as

purely

two-dimensional systems, ⁱⁿ

spite

of the

significant

increase in

interlayer

distance.

1948 JOURNAL DE

PHYSIQUE

I N° lo

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