Temperature dependence of the 306 and 227 cm-1 Raman lines in hexagonal ice between 250 and 80 K

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Temperature dependence of the 306 and 227 cm-1 Raman lines in hexagonal ice between 250 and 80 K

A. Ermolieff, A. Chosson, P. Faure

To cite this version:

A. Ermolieff, A. Chosson, P. Faure. Temperature dependence of the 306 and 227 cm-1 Raman lines in hexagonal ice between 250 and 80 K. Journal de Physique, 1976, 37 (12), pp.1457-1459.

�10.1051/jphys:0197600370120145700�. �jpa-00208548�

1457

TEMPERATURE DEPENDENCE OF THE 306 AND 227 cm-1 RAMAN LINES

IN

HEXAGONAL ICE BETWEEN 250 AND 80 K

A. ERMOLIEFF

(*)

Institut

Laue-Langevin, ^{B.P. 156,}

³⁸⁰⁴¹

^Grenoble,

^France

and

A.

CHOSSON,

^{P. FAURE}

Centre Universitaire de

Savoie,

^Faculté des Sciences et des

Techniques,

^B.P.

^143,

⁷³⁰¹¹

Chambéry,

^France

(Recu

^le

23 février 1976,

^{révisé le}

26 juin

^1976,

accepté

^{le 7}

juillet 1976)

Résumé. ²⁰¹⁴ Par diffusion Raman l’évolution de la fréquence ^en fonction de la température ^{a été}

étudiée entre 250 K et 80 K pour les modes de vibration 227 cm-1 et 306 cm-1 dans la

glace

^hexa-

gonale.

Le but était de déceler l’existence

possible

^d’un

couplage

^{entre modes}

optiques

^{et modes}

acoustiques

dans la région ^de température ^{où les} constantes élastiques présentent ^un comportement ^anormal.

Abstract. ²⁰¹⁴ The Raman spectra ^{of the} translational vibrational modes at 227 cm-1 and 306 cm-1 in hexagonal ^{ice were studied as a} function of temperature between 250 K and 80 K. The aim of the

experiment ^{was to detect a}

possible coupling

between acoustic and optical

phonons

in the range of temperature ^where the elastic constants display ^an anormal behaviour.

LE JOURNAL DE PHYSIQUE TOME 37, ^DTCEMBRE 1976, ^P

Classification

Physics ^Abstracts

8.800

1. Introduction. ^- Various

experimental

^observa-

tions in

hexagonal

^{ice show the} presence of anomalies around 100 K. These are measurements of

specific

heat

[1],

^thermal

expansivity [2], birefringence [3],

ultrasonic velocities

[4], polarization

^currents

[5]

and neutron diffraction measurements

[6].

The existence of this

anomaly

^has also been confirm- ed

by

^Brillouin

scattering

measurements

[7].

^A

range of

temperature

^was found between 70 K and 130 K where the elastic constants Clb C33 and _c44

display

^an anomalous behaviour. The several authors

attempt

^to

explain

^the

anomaly usually by

^{either a}

partial

structural transition

(hexagonal

^{ice - cubic}

ice)

^or

hy

^a

partial protonic

order-disorder transition.

A

coupling

between acoustic and

optical phonons

occurs in most structural or order-disorder transi- tions

[8].

^{It seems} useful therefore to

study

^{the fre-}

quency variation of translational

optical

^{modes as}

a function of

temperature. Moreover,

internal strains

producing

domains of cubic structure, ^or

large proton readjustments

^{related to local}

ordering,

induce distor- tions of the

oxygen-tetrahedra.

These distortions

can act on the behaviour of the lowest

frequency optical

^mode

(in hexagonal

^{ice the 227}

^{cm -1} line)

which

depends strongly

^{on the} temperature ^and becomes lower at the critical

temperature [8].

On the other

hand,

^{the 306}

^{cm -1}

line has been

explained by taking

^{into account the} proton

posi-

tions

[9, 10] (1).

An anormal behaviour of this line is to be

expected

^if

protons

^cause the observed ano-

malies in

hexagonal

ice around 100 K.

2.

Experimental

results and discussion. ^- The

single crystal

^{of ice Ih was of the same}

origin

^as those studied

by

^Brillouin

scattering [11].

The

impurity

^{content was less} than 1 ppm and the ratio

D/H

^about 142 ppm. The

sample

^{was inserted}

into an

optical

cryostat ^{under a}

nitrogen atmosphere,

with the c axis

perpendicular

^{to the}

scattering plane.

The incident laser beam was

polarized parallel

^to

the c axis.

A

Coderg

^PHI double monochromator with cooled

photomultiplier

^{and a SP164} argon ion laser were

used in these

experiments.

The

temperature

^was decreased and then raised at the controlled rate of 0.1

K/min.

^{The error in the}

frequency

measurements was about 0.15

%.

(*) Present address : C.E.N.G., L.E.T.I./E.P.A., ⁸⁵ X, 38041 Grenoble Cedex, France.

(1) Villain, J., ^Private communication, ^C.E.N.G. Grenoble, France.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0197600370120145700

1458

2.1 FREQUENCY VARIATION. ^- No

anomaly

^{in the} temperature

dependence

^{of the}

frequency

^{was found}

around 100 K either for the 227

cm -1

line or for the 306

cm-1

line

(Fig. 1

^and

2).

^The

frequencies

^{of these}

vibrations decrease as the

temperature

rises and the lines broaden.

The

slope

^{of the 227}

^{cm -1}

^line

(0.06 cm-’/K)

is half that of the 306

cm-’ one (0.12 cm -1 jK)

^and

seems to increase

abruptly

^for

temperatures

^above 190 K

(0.075 cm - 1 jK).

FIG. 1. - 227 cm-1 ¹ and 306 cm-’ ¹ Raman bands at different temperatures.

FIG. 2. ^- Temperature dependence ^{of 227 cm-1 and 306 cm-1 1}

lines (0.1 K/min) : ^x increasing temperature, 9 decreasing tempe-

rature.

2. 2 INTENSITY VARIATION. ^- We also studied the variation of the

intensity

^{of the Raman} lines with

temperature.

Intensity

measurements are

notoriously

^difficult.

Care was taken to ensure the

stability

of the incident laser

intensity.

^{The fact}

that,

^within

experimental

error, the intensities ^at the same temperature ^were found to be the same from one

temperature cycle

^to

another is an indication that the

optical

^{state of the}

sample

^and windows remained constant.

If the 227

cm -1

and 306

cm -1

lines have lorentzian

shapes, they

may be considered

independently

^{on the}

assumption

that each of them

corresponds

^{to an}

optical phonon

^{with a definite}

frequency. Figure

³

shows that the 306

cm-1

can be fitted

reasonably

well to a lorentzian

shape.

The fit is not as

good

^at

227

cm -1

but the difference between theoretical and

experimental

^curves may be due to the

overlap

^{of the}

172 cm - 1

line.

FIG. 3. - Comparison ^{of the} experimental ^{curves at 306 and}

227 cm-1 with lorentzians.

The

background

between the 227 and 306

cm -1 lines, probably consisting

^of disorder-allowed tran- sitions

[12]

^{is a}

complex composition

^{of vibration}

modes from which it is difficult to extract a

simple lineshape.

^The

assumption

that the Raman 227- 306

cm -1

band is the sum of the 227

cm -1

and the 306

cm -1 together

^{with a}

background

^is

adopted

here for the sake of

simplicity

^{and allows us to com-}

pare the different

intensity

variations.

The measurement of the line intensities was done

by weighing

^{the areas} of the lorentzian curves. The

background intensity

^{is estimated}

by subtracting

the contribution of the 227

cm -1

and 306

cm -1

lines from the whole Raman band. Thus we obtained the curves of

figure

^{4. The} intensities of the 227

cm -1

1459

FIG. 4. - a) Temperature dependence ^{of the} intensity ^{of the}

227 cm-’ and 306 cm-1 lines and of the background. - experi-

mental _curve, ^- theoretical curve. b) Temperature variation of the

intensity of the whole band.

and 306

cm -1

lines increase with temperature, ^while that of the

background

^decreases.

In

theory,

the scattered

intensity

of the Stokes line is

proportional

^to

(1

⁺

n),

where n is the Bose-Einstein

population

^factor

[14]

n=

ehv/kT -

¹

⁽¹⁾

v ⁼

frequency

of the studied

line,

h ⁼ Planck’s constant,

k ⁼ Boltzman’s constant.

Although

^{the observed}

intensity

variation is not in agreement ^with

equation (1),

^{this cannot be taken}

as evidence for an anormal behaviour since such

discrepancies

^are

commonly

observed in the intensities of Raman lines from other substances

[14-15].

^{A few}

points lying

^{above the mean}

intensity

^{curve of the}

227

cm-’

line are observed between 120 K and 140 K.

It is

possible

^{however to} conclude that within the

uncertainty

^{in the}

intensity

measurements no detec- table

anomaly

^exists.

3. Conclusion. ^- The curves of the

frequency

^varia-

tion with

temperature

of the translational vibrations at 227

cm-1

and 306

cm-1

show no

sign

^{of the ano-}

maly

^detected

by

^other

experiments

around 100 K.

The smooth behaviour of the 306

cm -1

line indi- cates that the protons ^{are not} concerned with the

anomaly

ⁱⁿ the elastic constants. This is in agreement with the Brillouin

scattering experiments

which show- ed no

isotopic

^{effect in} the critical

region [7].

Moreover,

^{these Raman}

experiments

^{show that}

the

anomaly

^{has no effect on}

long

range forces : either those

proposed by Wong, Klug

^and

Whalley [10]

in order to outline an

explanation

of the 306

cm -1

line or those worked out

by

^Faure and Kahane in their mixed Coulomb-Valence

dynamical

^model

[9].

Alternatively,

^{the curves} of intensities versus tem-

perature show that the

density

of the well defined modes increases with temperature, but decreases for those modes with a

frequency spread (background).

Therefore the

degree

of order associated with the molecular orientations should be greater ^{above 100 K} than below.

This conclusion would be in agreement ^{with the} results of Peterson and

Levy [6]

which show that the deuterium atoms on the bonds

parallel

^and

oblique

to the

optical

^c axis differentiate at

high

temperature.

References

[1] GIAUQUE, ^{W. F. and} STOUT, ^J. W., ^{J. Am. Chem. Soc. 58} (1936) 1144.

[2] DANTL, G., Z. Phys. 166 (1962) 115 ;

LA PLACA, S. and BEN POST, ^Acta crystallogr. ¹³ (1960) ^503.

[3] KAHANE, A., ^Thèse (1962) ^Paris.

[4] HELMREICH, D., Physics of ^Ice (Plenum Press, ^New York) 1969, p. 231.

[5] SIXOU, ^{P. and} JENEVEAU, A., Physics ^and Chemistry of ^Ice (Royal Society ^of Canada, Ottawa) 1973, p. 295.

[6] PETERSON, ^{S. W. and} LEVY, A. A., ^Acta Crystallogr. ¹⁰ (1957) 70 ;

HALTENORTH, H., ^Thèse (1974) Münich ;

WITLOCK, R. G., Submitted as part ^{of the} requirements ^for

the degree ^{of M. Sc.} Birmingham University.

[7] ERMOLIEFF, A., ^Solid State Commun. 17 (1975) ^1013.

[8] Structural phase transition and soft ^modes (Samuelsen, ^Andersen and Jens Feder, Universitets forlaget, Oslo) ^1971.

[9] FAURE, P. and KAHANE, A., ^Phonons (Flammarion Sciences, Paris) 1971, p. 243.

[10] WONG, ^{P. T.} T., KLUG, ^D. D., WHALLEY, E., Physics ^and Chemistry of ^Ice (Royal Society ^of Canada, Ottawa) 1973, p. 87.

[11] KLINGER, J., Thèse (1974) ^Grenoble.

[12] BERTIE, J. E. and WHALLEY, E., J. Chem. Phys. ⁴⁶ (1967) ^1271.

[13] LONDON, R., ^Adv. Phys. 13 (1964) ^423.

[14] STEKHANOV, ^{A. I. and} CHISLER, ^E. V., ^Sov. Phys. Solid State 3 (1962) ^2549.

[15] BOBOVITCH, Yo. S. and TULUB, ^T. P., Opt. Spectrosc. ^U.S.S.R.

9 (1960) ^392.