Specific heat of solid deuterium in the region of the proposed rotational glass phase

~

S o h d State Communlcatlon~, Vol 44,No 4, pp 469-471, P r l n t e d in Great Brltaln

1982

0 0 3 8 - 1 0 9 8 / 8 2 / 4 0 0 4 6 9 - 0 3 5 0 3 00/0 P e r g a m o n Press Ltd

SPECIFIC HEAT OF SOLID D E U T E R I U M IN THE REGION OF THE P R O P O S E D R O T A T I O N A L GLASS P H A S E Davld G

Haase

Physlcs Department, North Carollna State U n l v e r s l t y Ralelgh, NC 27650, U S A (Recelved 17 June 1982 by A

G

Chynoweth)

The speclflc heat of solid d e u t e r i u m of 33% p a r a d e u t e r l u m c o n c e n t r a t i o n has been m e a s u r e d for i K > T > 0 II5K by a thermal r e l a x a t i o n technique No evidence of a phase transition was found in the samples in the temperature range associated wlth the m o l e c u l a r rotatlonal glass phase No thermal remanence effects were observed for c h a r a c t e r l s t l c m e a s u r e m e n t s tlmes greater than 30 seconds I n t e g r a t i o n of the specific heat indlcates that rotational entropy of the solid b e l o w 0 35 K e l v l n equals about 10% of the free rotator entropy, in agreement w l t h ~P/3T) V studies of solld H 2

II

The solld hydrogens, H 2 and D2, are formed of m i x t u r e s of the spherlcal ground state molecules para-H 2 or o r t h o - D 2 and the flrst excited rotatlonal state (J=l) molecules, o r t h o - H 2 or paraD2 The J=l m o l e c u l e s have an electrlc quadrupole (EOO) i n t e r m o l e c u l a r mnteractlon It has b e e n shown that at intermediate J=l m o l e c u l a r concentrations m o l e c u l a r r o t a t i o n in the hydrogens is quenched at low temperatures without long range o r l e n t a t l o n a l order I Thls b e h a v i o r has alternately b e e n described as the formatlon of a ~ u a d r u p o l a r glass 2, or a p a r a - o r l e n t a t l o n a l phase J The present paper describes speclflc heat m e a s u r e m e n t s of solid normal d e u t e r l u m (33% paraD2) in the t e m p e r a t u r e range of the glass phase, i e below 0 3 Kelvln The goal of thls w o r k was to seek any evidence of a b u l k thermodynamic phase transition assoclated w l t h the glass or of frozenin rotational defects analogous to those found in structurally amorphous solids 4 Previous w o r k on the D 2 glass state has involved studles of NMR r e l a x a t l o n and ~P/~T) V The NMR results quote several dlfferent transition temperatures5,6, 7 b e l o w 0 4K dependent upon measurement condltlons, but the evidence for any sort of d l s c r e t e transltlon is still a matter of controversy 8 M e a s u r e m e n t s of ~P/~T) V in solld normal D 2 have shown no ~vldence of a sharp phase transltlon to T = 125 m K The spec~flc heat of solid normal D 2 has been previously m e a s u r e d by Gonzales, et al , to T = 0 3K ~ In addition SP/~T) V results in 33% para-D 2 down to T = 0 $5K have been reported by Ramm, Meyer and Jarvls ±i Heat generated by para-D 2 to ortho-D 2 conv e r s l o n makes Joule type speciflc heat m e a s u r e ments of solld D 2 dlfflcult at the lowest temperatures In the present w o r k a thermal relaxatlon technique was used w h i c h allowed better temperature control The samples were m e a s u r e d using a copper w ~ r e thermal llnk b e t w e e n the sample cell and the d l l u t l o n refrigerator m l x l n g chamber The cell (see Figure i) was heated to a temperature 5 to 20 m K above that of the m l x l n g chamber and allowed to come to a thermal equ~iibrlum After v a r y l n g lengths of tlme the cell

D -

-

(i> Q c>

-

-

G

Figure I Schematic d l a g r a m of sample cell and thermal llnk A - M i x l n g chamber thermometer B Automatlcally controlled heater C - M 1 x l n g chamber D - C o p p e r - n l c k e l fill cap111ary, 0 010" ID E Sample cell, OFHC copper F - Sample cell heater, 4 lead G - Thermometer, Speer 220 ohm slab, 0 5 m m thlck H - Sample volume filled wlth I00 m l c r o n slntered copper powder I - Cell support, thln w a l l e d stalnless steel tube J - Thermal llnk, 0 03 cm copper w l r e s h e a t i n g was then stopped and the coollng of the cell m e a s u r e d as a function of tlme The heat capacity of sample and cell w e r e calculated from the thermal relaxatlon, followlng the analysls of Fagaly and Bohn 12 The samples w e r e grown from 33% para-D 2 gas at m e l t l n g pressures of 200 to 400 psl The 469

470

S P E C I F I C HEAT OF SOLID D E U T E R I U M

copper sample cell was filled w i t h a slntered copper sponge l e a v i n g a 0 15 cm 3 sample v o l u m e lnslde the sponge F r o m the n o m l n a l i00 m l c r o n d l a m e t e r of the copper particles the area of the D 2 - c o p p e r interface was estimated to be greater than 50 cm 2 Therefore the K a p l t z a r e s l s t a n c e b e t w e e n the D 2 sample and the cell w o u l d be n e g l i z i b l e of 0 1 K for these samples 13 The thermal r e l a x a t i o n time b e t w e e n the sample and the cell was c a l c u l a t e d to be less than 0 1 seconds at 0 1 K Rooas , et al ,14 n o t e d that such a sintered copper cell had a c a t a l y t l c effect upon m o l e c u l a r specles c o n v e r s i o n in their D 2 samples Although the c o n v e r s l o n rate could not be m e a s u r e d d l r e c t l y in the present w o r k a check was m a d e on catalytlc effects by m e a s u r e m e n t of the long range o r d e r t r a n s l t l o n in solid H 2 as a f u n c t i o n of tlme after sample growth The recorded transltlons w e r e c o n s i s t e n t w l t h a normal H 2 c o n v e r s l o n rate and so it is assumed the same case held for the n o r m a l D 2 samples The d a t a dlsDlayed here came from samples m e a s u r e d w i t h l n t w e n t y - f o u r hours a f t e r growth of the crystals The cell t e m p e r a t u r e was m o n l t o r e d w i t h Speer 220 ohm r e s i s t o r ground to a 0 5 ram slab and epoxled Into a slot In the cell The cell was supported from the m l x l n g chamber by a thln w a l l e d stalnless steel tube and thermally conn e c t e d to the m l x i n g chamber by three 0,03 cm d i a m e t e r copper w l r e s A 70 o h m m a n g a n l n w i r e firmly w r a p p e d and v a r n i s h e d to the cell provlded heat for the heat c a p a c l t y and thermal conductlvlty measurements The c o n d u c t i v l t y of the copper thermal link was m e a s u r e d by statlc m e t h o d s several tlmes d u r l n g the course of the experiments. The b a c k g r o u n d heat c a p a c l t y of the cell and h e a t e r compared w e l l w l t h p u b l l s h e d d a t a on copper and m a n g a n i n B e c a u s e of the small size and spongy n a t u r e of the sample volume the actual mass of the sample was p r e c l s e to only + 5% The cell t h e r m o m e t e r was m o n i t o r e d w i t h a 4-wire s e l f - b a l a n c e d c o n d u c t a n c e bridge The b r l d g e output was recorded w ~ t h a chart r e c o r d e r or by an ~nterface to a m i n i c o m p u t e r During the h e a t l n g and r e l a x a t i o n the m l x ~ n g chamber t e m p e r a t u r e was s e p a r a t e l y m o n i t o r e d and autom a t ~ c a l l y controlled to a stab~l~ty of less than 0 2 mK All of the thermal r e l a x a t l o n s of the cell, with and w ~ t h o u t D 2 sample, appeared to be e x p o n e n t l a l w ~ t h typical t~me constants In the range of 2 to 60 seconds The heat c a p a c i t y could then be calculated from the t~me constant ~ and the link thermal c o n d u c t i v i t y ~ as C = ~< Thls result applies regardless of any internal sample heating The results of the s p e c i f i c heat m e a s u r e m e n t s are s h o w n ~n Fmgure 2 and are compared w ~ t h prev i o u s m e a s u r e m e n t s by Gonzales, et al , and Ramm, et al The ~P/aT) V results have b e e n converted to Cv u s i n g the G r u n e l s e n r e l a t i o n V

=YLattice

Cv' Lattice + YEQQ Cv,EnO

w h e r e YEOQ = 1 62 and V = 19 8 cm3/mole, and a s s u m i n g that the l a t t i c e c o n t r i b u t i o n Y L Cv,L IS n e g l ~ g ~ b l e at these low temperatures The results p r e s e n t e d and an e x a m l n a t i o n of the I n d i v l d u a l thermal r e l a x a t i o n s showed no e v l d e n c e of a f~rst or second order phase transition at any point F u r t h e r m o r e the data was re-

Vol

IOO

I

'

'

I

44, No i

i

f

~

~0

4

i

x

x x

#

O5O

x

og o

x

x

8 d 0

g 0

×

i "6 0 2 0 E

0 0

o

o o 010 o oo

8 005

-o I

OI

I

I

I

I

I

I

I

I

05 T E M P E R A T U R E (K)

02

Figure 2 Plot of Cv versus t e m p e r a t u r e for solid D2. 0 Present work, 33% para-D2 A Cv calculated from aP/aT)V data of Ramm, et al , 33% para-D2 X Cv d a t a of Gonzales, et al , 33% para-D2 p r o d u c i b l e after repeated cycllngs of the sample through the entlre temperature range The speclflc heat d a t a was v l s u a l l y smoothed e x t r a p o l a t e d to T=0 and integrated to calculate the r o t a t l o n a l entropy of the sample, o = X--Rln~ T=o w h e r e X = the para-D 2 c o n c e n t r a t l o n 0 33 The entropy is n o r m a l i z e d to the v a l u e XRIn3 expected for a freely r o t a t l n g p a r a - D 2 m o l e c u l e A plot of Cv/T versus temperature showed a peak at T = 0 35K allowing the e x t r a p o l a t i o n to T=0 In agreement w i t h similar c a l c u l a t i o n s from 3P/~T) V In solid H215 the entropy d i f f e r e n c e b e t w e e n T=0 and T=0 35 K is about 10% of XRIn3 This suggests that the G r u n e l s e n relatlon, e x p r e s s i n g a prop o r t l o n a l l t y b e t w e e n aP/~T)v and CV, is valid in the glassy region for the solld h y d r o g e n s In analogy with the e x p e r i m e n t s of Zlmmerman and W e b e r 4 one of the samples was cooled to a base t e m p e r a t u r e of 0 130 K and then several thermal r e l a x a t i o n s w e r e m e a s u r e d for dlfferent initial t e m p e r a t u r e d i f f e r e n c e s and heatlng times In these m e a s u r e m e n t s the inltlal temperature d l f f e r e n c e s varled from 5 to lO0 m K and the baklng times from 5 to 250 m l n u t e s The thermal relaxations under these v a r y l n g condltions were ident~cal and showed no evldence of low energy excltatlons or rotational defects having long r e l a x a t l o n times Thls is a somewhat d l f f e r e n t result than that in R e f e r e n c e s 5 and 7 w h l c h reported relaxatlon tlme of i0 to 15 m l n u t e s for the establlshment of a stable N M R r e l a x a t l o n tlme

Vol

44, No

SPECIFIC HEAT OF SOLID DEUTERIUM

4

The present results are consistent wlth a gradual freezing of the J=l rotational moments wlthout any discrete phase transltlon to the glass state From the comparlson to the H 2 ~P/$T)v results it appears that the Grunelsen relatlon-ls valld In the "glass" even though the Grunelsen relatlon is a result of equlllbrlum statistleal mechanics Rotatlonal defects havlng relaxation

471

times longer than 30 seconds were not observed down to 0 115 Kelvln Acknowledgement - Helpful dlscusslons with Dr M A Klenln are gratefully acknowledged, as is the communication by Dr P Meyer of results prlor to publicatlon Thls research was supported by Natlonal Sclence Foundatlon grant DMR 79-23202

REFERENCES ii

F

Sllvera, Rev

Mod

Phys

52, 393 (1980)

2N S Sulllvan, M. Devoret, B P Cowan and C Urbmna, Phys Rev BI7, 5016 (1978) 3S P H to

Washburn, M Calklns and H Meyer, Bull A S 27, 537 (1982) and S Washburn, M Calklns, Meyer and A B Harrls, J Low Temp Phys be published

4j Zlmmerman and G 46, 661 (1981)

Weber, Phys

Rev

Letters

5W T Coehran, J R Gaines, R P McCall, P E Sokol, and Bruce R. Patton, Phys Rev Letters 45, 1576 (1980) 6N J

S Sullivan, M Devoret and J de Physlque 40, L-599 (1979)

7N S Sulllvan and D 189 (1981)

M

Vasslere,

Esteve, Physlca 107B,

8S Washburn, R Schwelzer, and H Meyer, Solid State Commun 35, 623 (1980) 9D

G

Haase, unpublished

I00 D Gonzales, David White and H L Johnston, J Phys Chem 61, 773 (1957) llD1etolf Ramm, Horst Meyer and Robert L Phys Rev, BI, 2763 (1970) 12R L Fagaly and R G Bohn, Rev Instrum 48, 1502 (1977) 13C. L Reynolds, Jr and A C Phys Rev BI4, 4114 (1976)

M

Scl

Anderson,

14R J Roberts, E. Ro3as, and J G J Low Temp Phys 24, 265 (1976) 15D G Haase and A 189 (1981)

Mills,

Daunt,

Saleh, Physlca 107B,