HYPERSONIC INVESTIGATION OF THE λ-TYPE PHASE TRANSITION IN AMMONIUM-CHLORIDE

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HYPERSONIC INVESTIGATION OF THE λ-TYPE PHASE TRANSITION IN AMMONIUM-CHLORIDE

M. Gross, D. Gerlich, S. Szapiro

To cite this version:

M. Gross, D. Gerlich, S. Szapiro. HYPERSONIC INVESTIGATION OF THE

λ-TYPE PHASE

TRANSITION IN AMMONIUM-CHLORIDE. Journal de Physique Colloques, 1979, 40 (C8), pp.C8-

203-C8-206. �10.1051/jphyscol:1979834�. �jpa-00219539�

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HYPERSONIC INVESTIGATION OF THE A -Ty pE P HASE TRANSITION IN AMMONIUM-CHLORIDE M. GROSS - D. GERLICH - and S. SZAPIRO

Department of Physios and Astronomy, Tel Aviv University, Ramat Aviv, Tel Aviv Solid State Physics Department, Soreq Nuclear Research Center Yavne, Israel.

Abstract . - The well known order-disorder X-type phase transition in NH.CJl has been investigated, using the Brillouin Scattering method.The hypersonic sound velocities and elastic constants have been measured in the immediate vicinity of, as well as far away, both above and below the transition point.

The velocities of the longitudinal modes along the < 100 > and < 110 > directions are in a good agreement with existing experimental results and show the expected dip when temperature is lowered through the X -point.However no significant change is observed in the temperature region of 120°K - 150°K as is indicated by previous NMR measurements. The difference between the present hypersonic measurement and previous ultrasonic results is accounted for by a'dispersion mechanism. Under the assumption of a single-relaxation model, the temperature variation of the relaxation strengths and relaxation times is deduced and interpreted in terms of critical exponents and scaling laws.

1. Introduction. - The order-disorder phase transition in NH^CX, as well as that in NH^Br has generated much experimental and theoretical interest. At 242°K ammonium-chloride undergoes aX-type'phase transition from a disordered cubic (CsCA type) structure to an ordered tetragonal l a t t i c e . Above the transition temperature the tetrahedra of the ammonium groups are randomly distributed between the two equi- valent orientations in the cubic unit cell whereas below the transition point the tetrahedra assume a ferromagnetic-like ordering, while the cubic structure is maintained.

Previous hypersonic measurements IV havs con- centrated on the temperature region near T^. The data for longitudinal phonons along the < 100 > d i - rection have been analyzed / 2 / in terms of a single- relaxation model using existing ultrasonic results / 3 / / 4 / . Similar analysis has been carried out for NH4Br / 5 / / 6 / .

The present study was mainly concerned with hypersonic acoustic properties of NH^CA both in the

near vicinity of, as well as far away from the transition temperature, with the temperature-dependent dispersion along both < 100 > and < 110 > direc- tion as a primary goal.

2. Experimental Procedure. - Brillouin Scattering was used for the measurement of hypersonic longitudinal velocities along the < 100 >and < 110 > directions of the crystal in the disordered phase and similar measurements in the ordered phase.

The experimental set-up consisted of four main components.

a- An argon ion laser operated at 5145 A, in single- mode. This resulted in a laser line width of appro- ximately 130 MHz and power of 500 MW, which was

appreciably reduced, using neutral density f i l - ters to avoid crystal damages and to secure thermal equilibrium in the scattering c e l l .

b- A scattering c e l l , designed for right-angle- scattering geometry. Temperature-controlled l i - quid-nitrogen cryostat supplied the adequate JOURNAL DE PHYSIQUE Colloque C8, supplément au n°ll, tome 40, novembre 1979, page C8-203

Résumé . - La transition de phase ordre-désordre du type X, bien connue dans NH^Cl, a été étudiée, en utilisant la méthode de diffusion de Brillouin. Les vitesses et les constantes élastiques du son hy- personique, ont été mesurées dans le voisinage immédiat ainsi que plus loin, au dessus et au dessous du point critique. Les vitesses des modes longitudinaux le long des directions <100> et < 100 > sont en bon accord avec les résultats expérimentaux existants et exhibent la-singularité attendue lorsque

la température est abaissée en passant par le point X . Cependant aucun changement notable n'est observé dans la région de 120°K - 150°K comme c'est indiqué par les mesures de NMR réalisées. La dif- férence entre les mesures hypersoniques actuelles et les résultats ultrasoniques disponibles, est at- tribuée à un mécanisme de dispersion. Sous l'assomption d'un modèle de relaxation singulier la varia- tion de température des forces de relaxation et des temps de relaxation est déduite et interprétée en termes d'exposants critiques et de lois de transformation d'échelle.

Article published online by EDP Sciences and available at

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979834

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~ 8 - 2 0 4 JOURNAL D E PHYSIQUE

cooling and thermal s t a b i l i t y . The crystal wasgrown shed. The suspected existence /7/ of a c r i t i c a l beha- from a saturated aqueous solution of NH4C% w i t h

Urea a s a habit modifier. In the s c a t t e r i n g c e l l the crystal was immersed i n Isopentane (C5H12) t h a t served both f o r index matching and the e s t a - blishment of thermal equilibrium in the c e l l . c- A piezoelectri cal l y scanned Fabry-Perot i nterfe-

rometer with mirror spacing of 0,45 cm.

d- Detection and recording devices. The scattered l i g h t a t r i g h t angle was focused on a pinhole

-

aperture on the face of a water-cooled photo- mu1 t i p l i e r , and recorded together with t h e vol- tage of the Fabry-Perot and the temperature, on a magnetic tape f o r f u r t h e r data processing.

The Brillouin spectra were obtained with the polarizations of both the incident and scattered beams perpendicular t o the s c a t t e r i n g plane. The spectra were f i t t e d t o a theoretical function cons- i s t i n g of a sum of Lorentzians. The Brillouin s h i f t s yielded the frequency (vS) of the phonons involved which was in range of 21-25 GHz. The longitudinal

velocities (VL) were calculated using the formula :

where Xo i s the incident l i g h t wavelenght and n the index of refraction. -The 1 ongitudinal e l a s t i c cons- t a n t ( c L ) was obtained by

where cL = cll f o r phonons along < 100 > and C 1 1 + C 1 2 t 2 C 4 4 f o r p h o n o n s 'L = ' e f f = 2

along < 1 1 0 > .

3.

-

Results and Discussion.

-

The measurements were made f o r the longitudinal mode along both < 100 >

and < 110> between room temperature and 130' K.

They agree well w i t h existing data /1/ covering a narrower temperature region, and contribute f u r t h e r information regarding the region below and away from TI. In t h i s temperature-region the present re- s u l t s confirm the vanishing of t h e dispersion which, though expected, was not p r y i o u s l y establ i

-

viour below 150' K was not observed. The measured hypersonic sound velocity and e l a s t i c constant along both directions displayed t h e expected dip,upon ap- proaching the t r a n s i t i o n and a normal r i g i d - l a t t i c e - l i k e variation with temperature away, both above and below TX.

The wavelength of the phonons in question cor- respond t o the l i n e a r region of the acoustic dispersion curve, where the sound velocity i s expected to be independent of the frequency. However, t h e comparison between our measured hypersonic e l a s t i c cons- t a n t s and previously reported /3/ ultrasonic data y i e l d s a considerable difference. This dispersion in- creases as the temperature approaches TX, which i ndi

-

cated i t s connection t o the phase t r a n s i t i o n . Both t h e temperature dependence of the hypersonic e l a s t i c constant and the dispersion have been accounted f o r by existing theories /8/, /9/, / l o / . These theories involve the mechanism of energy exchange between the sound wave and reorientation process of the ammonium group.

Assuming a single-relaxation model a t low-fre- quencies, the re1 axation strength, C , and the r e l a - xation time, T, were obtained f o r the longitudinal phonons in both d i r e c t i o n s from :

and

where measured hypersonic data were used t o estimate cLm and ultrasonic data / 3 / , /4/, /11/ were used f o r t h e low frequency limiting value of the velocity vO, e l a s t i c constant cllO, and attenuation aO.

The use of ultrasonic data f o r the low-frequency-limiting values of v 0

,

cl10 and aO, and hypersonic data f o r the high-frequency-limiting values

OD

of cll was found t o ,be i n t e r n a l l y consistent w i t h

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M. GROSS, and a l . c8-205

the f i n a l values obtained f o r T in the temperature ^{2 00} range used ( i .e. u 2 ~ 2 << 1 f o r the ultrasonic mea-

surements / 3 / , / 4 / , /11/ and u 2 ~ 2 >> l f o r the pre- s e n t hypersonic investigation).

The inverse relaxation strength calculated f o r

$

^o,m

the longitudinal modes along < 100 > and < 110 >

-

-bo..,o

directions showed a 1 inear variation with temperatu-

re. both above and below the t r a n s i t i o n ( s e e f i g u r e 1 ) .

-!::.>,

^{m o}!&?50 250.0 2550 2600 2650 2700 2750 280.0 285.0 , 2900

Though the behaviour of C i s not too well unders- ^{T I}^{K )}

tood t h e o r e t i c a l l y /2/ two phenomena are observed : Fig. 2.

-

Inverse relaxation time a s a function of The d i s c o n t i n u i t y i n t h e inverse relaxation strength the temperature for the longitudina1 Inode

<loo> in NH CR. Solid curve i s a non-linear-least- a t Tl and t h e marked increase in the r a t e of change square f i t

80

a power law :

-

¹

of C-' w i t h the temperature ( t h e slope i n the orde- r (T) = r - l ( ~ ~ )

+

a [(T

-

Th) / T ~ ] "

red phase i s appreciably higher than t h a t in t h e disordered phase).

a single re1 axation model. These exponents should equal y ( t h e exponent characterizing the temperature variation of the inverse s u s c e p t i b i l i t y ) i f an anisotropic Heisenberg Model i s expected, / 2 / , /12/, /13/. The exponerats found i n the present work do not agree with the scaling law /14/ f o r y : y = ( 2

-

^q)v^{b u t}r a t h e r with the scaling law /14/

f o r y ' : 3 y 1 / ( 2 ~

+

y ' ) = 2

-

^qand an experimental r e s u l t /15/

p

⁼0.15. (See Stanley /14/ f o r the exact

3.0 d e f i n i t i o n of 0 , v , ~ a n d y ' . )

Fig. 1.

-

Inverse relaxation strength a s a function of the temperature f o r the longitudinal mode along

<loo>

in NH4CL

The re1 axation time, T , and i t s temperature variation were obtained using existing data /4/ on ultrasonic attenuation which was assumed t o be equal /11/ f o r longitudinal phonons along both directions.

The relaxation time (see figure 2) i n the disordered phase was found t o f i t a power-law of the form :

which yielded TI = 242.1' K and similar exponents (0.58 and 0.56) were found f o r the

<loo>

and <110>

d i r e c t i o n s (respectively). The simi 1 a r i t y between the exponents i s consistent with the assumption of

Through the use of another s e t of data /11/ f o r the attenuation of the longitudinal phonons along

<110>, a higher value f o r n (0.8) i s obtained. This exponent agrees w i t h t h e scaling law f o r y and as such confirms the assumption of an anisotropic Heisenberg ferromagnet-like behaviour. However the existence of d i f f e r e n t exponents f o r d i f f e r e n t d i - rections of the longitudinal acoustic mode, contra- d i c t s t h e assumption of a single-relaxation-model.

Clarifying t h i s question c a l l s f o r a reinvestiga- tion of the ultrasonic attenuation and a thorough comparison of data obtained in t h e

<loo>

and <110>

directions.

The r e s u l t s of t h e present work bring out s i g n i - f i c a n t differences between acoustic p r o p e r t i e s of ammonium-chloride and previous r e s u l t s / 5 / , /6/, / l o / concerning ammonium bromide. The differences a r e manifested in t h e magnitude and variation of the e l a s t i c constants measured, and the c r i t i c a l behaviour of the relaxation strength and relaxation time.

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JOURNAL DE PHYSIQUE

Although t h e s t r o n g s i m i l a r i t y between the two c r y s - t a l s suggests

/lo/

t h a t some u n i v e r s a l mechanism i s

References

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Spectra o f S o l i d s , e d i t e d by G.B. Wright t i o n time, i n d i c a t e a d i f f e r e n c e i n t h e n a t u r e o f (Springer, New York, 1969) pp. 593.

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(1966) 1130.

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Hamiltonian f o r b o t h NH4Br and NH4CR and f u r t h e r development of t h e dynamical t h e o r i e s of c r i t i c a l

14/ Garland, C.W. and C.F., J , Chm. Phys.

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44 (1966) 3678.

Acknowledgements.

-

The authors wish t o express t h e i r g r a t i t u d e t o J. Azoulay f o r h i s c o n t r i b u t i o n and t o M. Wolf f o r t e c h n i c a l assistance.

Key words : Ammonium c h l o r i d e , Phase T r a n s i t i o n s , Acoustic Dispersion, B r i l l o u i n S c a t t e r i n g .

Code Number (Subject C l a s s i f i c a t i o n ) : 64.70 K 62.20 D

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