Continuous and discontinuous phase transitions in ammonium halides

Journal of Molecular Structure, 115 (1984) 169-172 Elsevler Science Pubhshers B.V., Amsterdam L Pnnted

l-t. YURTSNEN Department

and

W. F.

of Physics.

169 m The Netherlands

SHERMAN

Klng’s

College

London.

Strand.

London

WC2

Reman spectra of NH@ and NH4Br have been recorded as functions of The X-type phase transition In NH&l has been studted temperature and pressure. (ii) a trlcrltical and (ill) a second order transltlon. A as (1) a weakly first order, strongly first order transltlon has been studied in NH&. The analysis of the data has concentrated on the correlation of frequency shift wlih volume change across the phase change regions. Thls correlation has been establlshed for the frequencies of the uc and us Raman modes of NHACI at zero pressure (1st order) I. 6 .kbar ftricrltlcal) and 2 d kbar (2nd order) . an> the frequencies of the ~6 Raman mode of NH&r at zero pressure (1st order) _ A single Y (mode Grunelsen parameter) has been shown to describe each frequency shift right through the phase change region once an order-disorder contribution has been Introduced at and below the transltlon temperatures.

lNTFtODUCnOH The

A-type

phase

many techniques. applicability

translhons

They

temperatures one-another

involve


NH4CI

chain

fantlferro-ordered)

along

between

At zero

transltlon

.

the two

phase

above

possible

about

Is strongly

the observed

transltlon

Above

TX

the

order

siudled

to investigate

of the NHf they are

dlstrlbuted

the

At parallel

parallel

arrangement

Ions are

0022-2860/84/$03

to

along

wlthln the a essentially

orlentatlons.

1 6 kbar It becomes

In NH&l

2nd

Is weakly The zero

order

1st order pressure

1st order. that was Introduced frequency

In a previous

shifts to the volume

paper

changes

(ref. 1)

we

rlght across

regions.

RESULTS Raman

by

halldes.

ions.

Ions orientated

In NH4Br

NH:

been

In the ammonium

all the NH:

whereas

have

on which

It Is known that the X-transition

Ex-tendlng a formalism have related

systems

the c axls but have an antl-parallel

pressure

but for pressures

halldes

transltlons.

has virtually

It Is ferro-ordered)

b plane

good such

the loss of orlentatlonal

below TX.

any one

NHqBr

are therefore

of new ways of studying

the A-transltlons

randomly

of the ammonium

spectra

of NHqCI

00

0 1984

and

NHqBr

Elsewer

Science

were

recorded

Publishers

B.V.

under

fixed pressure,

the

170 variable NH4CI

temperature spectrum

1708 cm-l

spectrum

Observed

and

flgs. I to 6. various given

whereas

of the NH:

170 cm-l)

centre

frequencies

plotted as a function

flg. 6 shows

and

one

band

138 cm”).

for the band

the data

fixed temperatures.

in the

Ion at about

The

plotted

details

are

shown

of temperature as a function

In

at

of

of the calculations

are

below.

parameter where

AND

DIS4XSSIo#

our earlier

Yp

by:

where

of Yp can

However,

constant

discrepancy

equivalent

convenient

equatton

fret.41

are: have

usually

used

the two-value The

therefore

relatlonshlp condltlons. chosen more v=

general

to be a the phase

lntegrahngC1)

. . . . (2)

other

found

and

where nP

expressions

=

which

most

of the paramerers

slgnlflcantly

differently

A(p). (A(p)

to a volume

th6 same

and

+ alp

the change

Ln(V/VT) pressure

which

we have

+ a2pz).

The

5 Is therefore:

to obtain

In table

and

it is

(3)

....

required

Yp

Is Introduced = a,

and

frequency.

However

1 to 3.

above.

transltlon.

effects

to the observed

v for all temperature

for figs.4

condltlons

as described

In at the phase

Thus

In pressure.

given

Input parameters

tamblent

evaluated

see figs.

an extra term.

+ VT expf-Ypfin
or lattice-parameter

to the volume-change

to temperature.

required

to VT,

contrlbutlon

describe

2.3)

necessary

Yp,

that switches

pressure.

behave

as a pclynomlal

In figs. 1 lo 5 are

fiefs.

The

polntl

In addltlon

21 cannot

expression

+ A(P) shown

constant

To allow for this.

transmon

beyond

Thus

that we have

VT COrrespOndinQ

as the reference

Ap)

the phase

to what seems

Ln(V/VT)).

Yp

thrs assumption.

frequencies

several

data

be calculated.

frequency

as opposed

(equation

The values those

or

support

is Included. are

the phase

)

can

In paftlcular)

to express

%

purposes.

as an order-disorder

by pressure

A.

there

Griinelsen

eastly determined.

leads

calculaled

+ VT exp (-Yp

2 works well at zero


and

mode

away from

and

throughout

Y assumption

(Clearly

A appears

described

frequencies induced

(0

parameter

Equation

as constant

but that Is the form

2.

Well

flgs. 1 to 5 clearly

2 with the length-change

observed

been

coefficient.

term.

v =4

the frequencies

a single

and

observed

for TCTk.

to equation

an lsobarlc

(1)

both fatrly constant

an extra correction

for tabulation

Using data

between

AP*O

but

expansion

the constant

the term &rglves:

0 for PTA

we define

...

be regarded

maklng

unless

including

thermal

It Is assumed.

region. transltlon.

(ref. 1)

a and(dv/dT)are

be evaluated.

that the value

paper

Yp = -fdv/dTIp/(~,~>

a Is the volume

transition.

and

values

with two bands

mode

at about

at about

1 to 5 show the data

at two different

Following

are

Is concerned tnternel

lattice mode

v5 mode

calculated

Figs.

DALDUtATK)1yS

can

(the

fixed pressures.

pressure

paper

the symmetric-bendlng

~5 a translatlonal

and

In the NH4Br

This

condlttons.

(~2

I.

the calculated

frequencies

llke

171

Fig.3

Fig.5

v5 of NH,Br,

P=O,

v2 of NH4C1,P=1.6

(first

order)

Fig.4

kbar(tricritical)Fig.6

v2 of NH4C1,

P=2.8

v5 Of NH4C1*

kbar(2ndGrder)

Tz250 T%273

K ('ppr) K (lower)

172 TABLE

1

Fig. No.

v2 v5

Note

contatn


3Pfor

of of

AFfor

v5

AFfor

=

from

the

is

formalism

requires

an

tdv/dP)T/+.r))

where

B

is the

Followlng Y = AT For

+

volume-change

data

as

a

a0

a3

al

0.096 -0.141 0.096 -0 141

the

-1 111 -0.373 -1. Ill -0 373

character -

times

larger

cover

components

mcreases

pressure

10

5.

the

seems

than

variable

mode

of

which

the

A

are

small, since

transition)

but

surprlslng.

and

equivalent

pressure

Grunelsen

of

expected.

(as

studies

value

(Ii) it must

(lli)

the


the

NH4Cl.

at constant

parameter:

(4)

...

compresslbllrty.

same ~1

NH4CI

~2

calculated

.

Ar and

1st order

to

/cm-l

pressure

isothermal

Isothermal the

+ A(T)

about

of

as

wlth

1 to

NH4CI.

values

the

figs.

0.28 0 75 -8.67 0.22 1.30 0.10 1 41

others

the

for

4

0.001 0.001 0.001 1.6 1.6 2.8 2.8

decrease

Increase

Nl-i4Br

Extending temperature YT

v2

required

p/kbar

all

NH4CI

for

of

a contribatlon

values value

NH4Sr.

lndlcates

values

0.1347 2.523 I. 59 0.1347 2.523 0.1347 2.523

v2 u5

values

a2 Yp

u2 u5 v5=

4

I

and

Mode

1 2 3 5

the

al

A,_. a,.

YP.

type

of

argument

YT Z% 0 0266 and

and

appropriate

function

as

LntV/VTd

eXp[-YT

of

for AT

pressure

before.

__

as

.

(5)

u5NH4CI and

in

A(T)

fig

YT s

2 619.

terms

-

Using

values

of

these.

Y can

the

be

6.

CONCLUSIONS Raman A-transition or

discontinuous It Is

that

frequencies regions

change

nature

reasonable

relatively data

seem

for

easily In

the

6.

A Bonilla V &vi et

correlate

and

of

transitron.

to

the

believe

measured viclnlty

REFERENCES 1. H Yurtseven and W F France t 19921, ed. 2 C W Garland and 13 3. 6 8 Weiner and C W 4. Hovl, Mutlkalnen and

5.

to

NH4CI

of

NH4Sr.

that

this

frequency phase

with

volume

and

to

will shifts

be

true

may

changes

falthfully

be

for

other

used

rlght

lndlcate

to

through

the

the

continuous

systems

also.

deduce

volume-

and

transltlons.

Sherman. int. Conf. on Raman Spectroscopy. Bordeaux. J Lescombe and P W Huong. p.429. Aenard. J. Chem Phys ti (1966) 1130 Garland. J. Chem. Phys 56 (19721 155. Plrlnen, Ann. Acad Sclent. Fenn , Ser.AVI 404 (1973).

et nl. Actn Crystogr. A 26 (1970) nl. Ann. Acnd.Sci. renn.sr. 0 VI

156.

Un.791.

1 (1968).