CONNECTION BETWEEN THE LOW TEMPERATURE THERMAL PROPERTIES OF GLASSES AND THEIR GLASS TRANSITION TEMPERATURE

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CONNECTION BETWEEN THE LOW

TEMPERATURE THERMAL PROPERTIES OF GLASSES AND THEIR GLASS TRANSITION

TEMPERATURE

T. Klitsner, A. Raychaudhuri, R. Pohl

To cite this version:

T. Klitsner, A. Raychaudhuri, R. Pohl. CONNECTION BETWEEN THE LOW TEMPERATURE THERMAL PROPERTIES OF GLASSES AND THEIR GLASS TRANSITION TEMPERATURE.

Journal de Physique Colloques, 1981, 42 (C6), pp.C6-66-C6-68. �10.1051/jphyscol:1981620�. �jpa- 00221286�

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JOURNAL DE PHYSIQUE

CoZZoque C6, suppZ6ment a u nO1 2, T m e 42, de'cembre 1981 page C6-66

CONNECTION BETWEEN THE LOW TEMPERATURE THERMAL PROPERTIES OF GLASSES AND T H E I R GLASS T R A N S I T I O N TEMPERATURE

T. K l i t s n e r , A.K. ~ a ~ c h a u d h u r i * a n d R.O. P o h l

Laboratory of Atomic and S o l i d S t a t e P h y s i c s , Come22 U n i v e r s i t y , Ithaca, NY 14853, U.S.A.

Abstract. Water doping of n i t r a t e glasses lowers t h e i r thermal conductivity.

The e f f e c t , however, i s smaller than expected on the basis of the increased density of s t a t e s of anomalous s t a t e s observed in specific heat measurements.

Addition of foreign atoms or molecules t o c r y s t a l l i n e s o l i d s changes t h e i r l a t t i c e vibrational spectrum, resulting in localized modes, resonances, and t u n - neling s t a t e s . We a r e exploring whether similar e f f e c t s can a l s o be caused in amorphous solids. As host g l a s s , we have chosen n i t r a t e glasses of the composition 40 mole % Ca(NO3l2 and 60 mole % KN03. Doping with LiN03 and KN02 up t o t h e i r s o l u b i l i t y l i m i t s , 6 x lo2' and 4.4 x lo2' respectively, caused no discernible e f f e c t on the low temperature s p e c i f i c heat of the glass ( < 2% change),' in c o n t r a s t t o t h e doping of a l k a l i halide c r y s t a l s with ~ i + or NO; ions, which r e s u l t s in low energy tunneling s t a t e s in many hosts.2 Doping the glass with water, however, a t concentrations between 1 ^{and 3}x loz1 increased the low temperature s p e c i f i c heat anomaly known to be c h a r a c t e r i s t i c f o r the amorphous s t a t e . ' The increase in entropy was found t o scal e with the water concentrations', but was approximately four orders of magnitude small e r than i t would be i f every water molecule would con- t r i b u t e one tunnel ing s t a t e . Thus, tunnel ing ( o r some other kind of low energy vibration) of t h e water a l s o appears t o be very unlikely in t h i s case.

We did observe, however, t h a t the s p e c i f i c heat anomaly of t h e water-doped glass scales with the reciprocal glass t r a n s i t i o n temperature TG, i . e . ,

a

-

T ~ - ' , with

exc ( 1 )

,.I. 16

'exc = 'v - ' ~ e b ~ e = aexc , ( 2 ) see Fig. 1. _Eq. (1) suggests t h a t the low temperature anomalous s t a t e s a r e a measure of the disorder frozen-into the glass a s i t s o l i d i f i e d , a s has a l s o been proposed independently by Cohen and rest,^ based on t h e free-volume theory of glasses.

In the present study, we have searched f o r a change in the low temperature thermal conductivity in water-doped n i t r a t e glass. Sample preparation, determina- tion of Tjiatid of the thermal conductivity have been described previously. 1,294

"present address : Max-Planck-Institut f u r Festk6rperforschung, Heisenbergstr. 1, D-7000 S t u t t g a r t 80, F.R.G.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981620

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F i g . 1. The anomalous s p e c i f i c heat o f 40/60 Ca(N03)2KN03 g l a s s increases w i t h decreasing TG r e s u l t i n g from doping w i t h wate a f t r Ref. 1. Water concentrations:

# I , 1.1; #2, 2.4; #3, 3.8; #4, 3.3, a l l i n loh cmqQ. A l s o shown i s t h e thermal r e s i s t i v i t y A-1 a t 0.1 K, see r i g h t hand ordinate. The dashed l i n e connecting t h e two data p o i n t s , obviously, i s o n l y an a i d f o r t h e reader. F o r equal changes i n TG, aexc increases approximately f o u r times more than A-1. TG f o r t h e c o n d u c t i v i t y samples i s 339 K (undoped), 292 K (doped).

To (K) 400

-

⁸⁰

s 'i'

* & 70

e, a

-

P

60

50

F i g . 2. Percent r e l a t i v e d e v i a t i o n , d e f i n e d as (Aexp - A f i t , u n ~ o p e ~ ) / ~ f i t , u n d o p e d o f t h e measured c o n d u c t i v i t y of t h e undoped ( " d r y " ) and t h e doped ("wet") samples.

The b e s t f i t t o t h e d r y sample, kit, undoped = 1.82 x T ~ (W cm-I ' ~K-I, ~ w i t h T measured i n K).

375 350 325 300 275

1 I I

A SAMPLE # 3 0 SAMPLE I 2

- ^{SAMPLE #}^I ^Y

A 40/60 CO(NO,)~-KNO, 0 %/SO CO(NO,)~-KNO, V SAMPLE 6 4

-

- ^a"U)

- 5

1 I I I I

+8

+ 4

s

g

.-

'f - 4 t -8

.;o -

Q)

a-12

2.5 ^-L 3.0 3.5

x IO'(K-\

TQ

, I I I I I ^I ¹ I

-0 -

- 0 -

- ^O O O o o O o O o O -

o 0 O r ,

yDry ^{( O '}

0

O O

0 -

0 0 "

- ⁰ ₀ ⁰⁰ ⁰ ⁰

- ⁰ O

..*. ...

^-

n O O

_{. .} . .

^--

Wet ( 0 )

> * . .

^•

:i _.*

_. . . _.

^-

- -

- 8 .

4 0 / 6 0 Ca (NO,) K N 4 -

-

1 I I I 1 I I 1 1 ^*

100 2 0 0 300 ₄₀₀ 500

Temperature, m K

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C6-68 JOURNAL DE PHYSIQUE

The conductivity A , measured between 0.1 and 0.5 K, followed a power law f o r both the doped and the undoped sample. For t h e undoped sample, A = 1.82 x 10- 4 T1.96 ( i n W cm-' K - ~ ) , while f o r the undoped sample, A = 1.69 x 10- i . e . , 7%

smaller. The qua1 i t y of the power law f i t t o the conductivity of the undoped sample i s shown in Fig. 2, which a l s o shows the r e l a t i v e deviation of t h e data obtained on the doped ("wet") sample r e l a t i v e t o the power law f i t f o r the undoped ("dry") sample. The data f o r the doped sample a r e lower, on average, by 7% than the data f o r the undoped sample. Both s e t s of data show a peak near 0.25 K, which we believe t o r e s u l t from an e r r o r in c a l i b r a t i o n of our thermometer.

In Fig. 1, we have plotted the thermal r e s i s t i v i t y A-l, a t 0.1 K , f o r the two samples. The e r r o r bars a r e those of the accuracy with which the sample geometry was measured ( * 5%). I t i s seen t h a t the increase of aexc, i . e . , of the density of s t a t e s in the water-doped sample, i s l a r g e r than the increase in thermal resistance, the l a t t e r being j u s t barely outside the experimental e r r o r . Conceivably, the increased density of s t a t e s of the s c a t t e r i n g centers i s partly o f f s e t by an increase of t h e speed of sound (which would increase the low temperature thermal conductiv- i t y ) , and/or by a decrease of the coupling constant in the doped sample. Measure- ments of the speed of sound in these glasses, in progress i n our laboratory, will shed some 1 ight on these questions.

This research was supported in part by the National Science Foundation under Grant #DMR-78-01560 and through the Cornell Materials Science Center.

References

1. A . K. Raychaudhuri and R. 0. Pohl, Solid S t a t e Comm. 37, 105 (1980), and submitted t o Phys. Rev.

2. V . Narayanamurti and R. 0. Pohl, Rev. Mod. Phys. 42, 201 (1970).

3 . M . H. Cohen and G. S. Grest, Phys. Rev. Lett. 45, 1271 (1980), and Solid S t a t e

Corn., in p r i n t .

4. A . K. Raychaudhuri, Ph.D. Thesis, Cornell University, August 1980, unpublished.

Cornel 1 Materials Science Center Report #4284, 1980.