ULTRASONIC PROPERTIES OF Se - Ge GLASSES, BETWEEN 1 K AND 100 K

HAL Id: jpa-00225483

https://hal.archives-ouvertes.fr/jpa-00225483

Submitted on 1 Jan 1985

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

ULTRASONIC PROPERTIES OF Se - Ge GLASSES, BETWEEN 1 K AND 100 K

J. Duquesne, G. Bellessa

To cite this version:

J. Duquesne, G. Bellessa. ULTRASONIC PROPERTIES OF Se - Ge GLASSES, BETWEEN 1 K AND 100 K. Journal de Physique Colloques, 1985, 46 (C10), pp.C10-445-C10-448.

�10.1051/jphyscol:19851098�. �jpa-00225483�

JOURNAL DE PHYSIQUE

C o l l o q u e C10, s u p p l 6 m e n t a u n 0 1 2 , Tome 4 6 , dbcembre 1 9 8 5 p a g e C10-445

ULTRASONIC PROPERTIES OF Se

-

Ge GLASSES, BETWEEN 1 K AND 100 K

J . Y . DUQUESNE AND G. BELLESSA

L a b o r a t o i r e d e P h y s i q u e d e s ~ o l i d e s * B d t . 510, U n i v e r s i t e P a r i s - S u d C e n t r e d ' o r s a y , 91405 O r s a y , F r a n c e

E s d

-

Nous avons 6tudi6 quelques propri6t6s Qlastiques e t an6lastiques de verres de s6lQnium-germanium, e n t r e 1 K e t 100 K e t vers 100 MHz, qrZice 2 des m6thodes de propagation d'ondes ultrasonores. Nous constatons que ces p r o p r i 6 t 6 s sont sensibles 2 l a r i g i d i t 6 du r6seau e t nous 6tablissons un p a r a l l s l e avec l e s calculs th6oriques bas& sur le concept de mode de fr-ence nulle.

Abstract

-

^We have studied some e l a s t i c and a n e l a s t i c properties of selenium- germanium glasses, between 1 K and 100 K and around 100 MHz, w i t h ultrasonic propagative methods. We e s t a b l i s h t h a t those properties a r e sensitive t o t h e r i g i d i t y of t h e network and we compare them with theoretical computation based upon the zero frequency mode concept.

We have investigated t h e e l a s t i c and anelastic p r o p r t i e s of m r p h o u s SeI_Gex glasses (x = 0 ; 0.1 ; 0.25 ; 0.40 ; 1 ) , by mean of a standard ultrasonic pu s e m- thod (in t h e 100 MHz range) and between 1 K and 100 K (typically).

The amorphous selenium is a polymeric material with weak interactions between the chains (of Van der Waals type). In such a m t e r i a l , crankshaft-type motion /1/ shows that one conceives continuous deformations of p a r t s of the network (localised on the chains) involving very l i t t l e cost i n energy. The network i s then quite "soft". A t t h e opposite, t h e m r p h o u s germanium has a very r i g i d structure since its coordina- t i o n number is 4 and since both t h e bond angles and the bond lengths a c t a s cons- t r a i n t s imposed upon t h e set of atoms. Then, t h e e l a s t i c properties are expected t o be q u i t e d i f f e r e n t i n a-Se and a-Ge. I n t h a t respect, t h e study of m r p h o u s Se-Ge glasses i s interesting since t h e structure changes from a s o f t one t o a r i g i d one, a s t h e concentration of germanium increases. H e and T h o r p have perforfwd t h e o r e t i c a l calculations of the e l a s t i c d u l i of random networks with d i f f e r e n t man ccordina- t i o n numbers /2/. Their r e s u l t s a r e then compared w i t h our exprimental results. The anelastic properties a r e a l s o expected t o depend on t h e r i g i d i t y of the network.

Kurjian and a 1 have shown t h a t the acoustic attenuation in Ge-As-S glasses i s sensi- t i v e t o t h e degree of crosslinking of t h e network /3/. Gilroy and P h i l l i p s have stu- died S-Ge and Se-Ge glasses in the 10' Hz range and have pointed out t h e correlation between the number of constraints per atom and t h e mchanical losses /4/. We present here r e s u l t s on Sel-xGe glasses (from Se t o Ge) i n t h e 10' Hz range and we compare them w i t h the calculate3 number of zero frequency modes i n glasses. The concept of zero frequency mode was f i r s t introduce by A h , Weaire e t a 1 /5/. It i s a localized mode in which part of t h e network can be continuously deformed without any c o s t in energy /6/. Recently, He and Thorps have derived t h e number of such modes as a func- tion of t h e mean ccordination number /2,6/.

W e have measured t h e sound velocity a t 4 K. In u n i t of l~~cm.s-', we find (respec- t i v e l y ) : v T = 1 . 0 5 ; 1 . 2 4 ; 1 . 4 4 i n S e , Se @ Se Ge (shearwaves) ; l T ~ = 2 . 0 ; 2.16 in Se, GeqnGel (longitudinal waves) _{- - --} ;

'GR

^z5;.2

3

d O ( ~ a y l e i g h waves)

.

^{Zhe elas-}

t i c modul US C4* is p vT2 ( p is the volumic ma&)

.

The figure (1) shows t h e exprimm- tal variation of C44 a s a function of the man coordination number < r > = 2x

+

2 of

* ~ a b o r a t o i r e a s s o c i b a u C e n t r e N a t i o n a l d e l a R e c h e r c h e S c i e n t i f i q u e .

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19851098

C10-446 JOURNAL DE PHYSIQUE

Se Ge glasses. (In the case of 0

4 sel-& we ass- : VT = 1/2 ;

t vT92 1)P; vR). The f u l l l i n e in f i g

(1) i s the theorical calculation of He and Thorpe /2/ normalised t o the

0 experimental value in a*. The o-

x

verall aqreemsnt between the theore-

* p

t i c a l and experimental variations of

C44 i s rather good. Below <r> ⁼ 2 . 4 ,

2 2

the e l a s t i c modulus i s not zero. In-

deed, the theoretical calculation predicts a zero value but with over- s i r p l i f i e d hypothesis (in particular,

0 0 0

the i n t e r chain forces are not mn-

2 < r ' 4

^sidered).

We have also masured the acous- f i g (1)

.

e l a s t i c modulus C44 in Se-Ge glasses t i c attenuation in the 108Hz range

versus the man coordination n d x r . in Se-Ge glasses. The figure (2) The f u l l l i n e i s the calculation of displays our results. The internal He and Thorpe /2/ (See t e x t ) . friction peak of a-Se has been ex-

plained, f ram a phenollwological pint of view, by t h e m 1 activated processes exhibiting a wide distribution of acti- vation energies E extending down to very small values (typically ^: 0 < E < 1 0 - ~ e ~ ) /7,8/ The magnitude of the peak is reduced when the chains are crosslinked and the peak only appears a s a shoulder in Se75 Ge25 o r Se60 Ge40. In a-&, no such peak o r shoulder i s revealed a t low temperature. (The shoulder localised around 7 K a r i s e f m the tunnelling relaxation processes /9/ and, so, is different from the shoulders here considered). In order

to

estimate the magnitude of the peaks (or shoulders), vx?

extramlate down t o 0 K the lin- variations that we observe a t low t-awe /9/.

In the case of Sego Gel0 t h a t extrapolation i s not possible since our data do not extend down to sufficiently low temperatures. The f i g

(3) displays the magnitudes a s a function of the mean coordination number <r> and

the

f u l l l i n e i s the calculated number N of zero frequency lrodes (in arbitrary u n i t s

( f r m /2/. The overall variations are similar but those of N are steeper than those of the magnitude of internal f r i c t i o n .

I

^{.7h.'*k., (164 MHz)}

[email protected]*---

~,/.**~w~e,h5(150 MHz) Sa Ga (250 MHz) J 60 40

A-. ^- .... ...*..- ... -. ".. .-... .. ..

P* ^...

- G O (220 MHz)

I

0 50 100 150

f i g (3)

.

Magnitude of the internal f r i c t i o n peak (or shoulder) in Se-Ge glasses versus

the

I mean cmrdination n*.

TEMPERATURE

⁽

K >

The f u l l l i n e is the calcu- lated n m h r N of zero fre- f i g (2)

.

internal f r i c t i m in Se-Ge glasses suency mode (/2/)

.

versus t a p z a t u r e , in the 100 MHz range.

The figure ( 4 ) displays the variation of the sound velocity with temperature in Se-Ge glasses. Those variations are linear over a wide range of temperature. Such linear variations have been revealed in many m r @ o u s materials but t h e i r origin is s t i l l unknown. In particular, they cannot be attributed t o the t h e m 1 activated pro- cesses responsible for the internal frictiy-peaks

/lo/.

The slopes of

the

linear va- riations are respectively (in unit of -10- K ) : 3.2 ; 1.4 ; 0.46 in Se, Se75p25, Se60Geqo (shear waves) and 0-3 i n Ge (Rayleigh Wave). Those values are gathered m fig. ( 5 ) a s a function of the mean coordination number <r> and the f u l l l i n e is the calculated nuther of the zero frequency modes /2/ (in arbitrary u n i t s ) . Again, the overall behaviours are similar.

TEMPERATURE I N KELVIN

f i g ( 4 )

.

r e l a t i v e variation of sound velocity f i g (5)

.

slope of the linear va- in se-Ge glasses, versus temperature. r i a t i o n of velocity in

Se-Ge glasses, versus the man coordination number. The f u l l l i n e is the calculated nmber N of zero frequency modes

(/2/)

.

Conclusion : The e l a s t i c and anelastic properties of Se-Ge glasses are sensitive t o the degree of crosslinking of the network and our experiments agree with the previous studies. Similitudes and differences are found concer- ning

the

cornparaison between those properties and the theoretical deri- vation of the number of zero frequency modes.

JOURNAL DE _PHYSIQUE

1 . See for example

:

Roberts, G.E.,

White, E.F.T.,

The Physics of Glassy Polymers, Appl. Sci. Publ.

LTD

(London) ,

^{ELI. by}

^R.N.

^Haward,

⁽¹⁹⁷³⁾ ,

^p.

^153.

/2/ . He, H., 'Ihorp,

M.F.,

Phys.

Rev.

Lett., (1985), 54, 2107

/3/ . Kurjian, C.R., Krause, J.T., Sigety, E.A., P m . 9th

Int.

Glass Conf.

(Versailles, 1971), 1972, p. 503

/4/

. Gilroy, K-S., Ehilipps,

W.A.,

Phil.

Mag.

B, (1983), - ^{47, 655.}

/5/ .

^{Alben, R.,} Weaire, D., Smith, D.E.

Jr, Brcdsky, M.H., Phys. Rev. B, (1975), 11,

2271

/6/ . Thorp, M.F., J. of non Cryst.

Solids,

(1983), 57, 355.

/7/

. ^{Duquesne, J.Y.,} Bellessa, G., J. Phys. C

:

Solid St. Phys. 2, L-215, 1980 /8/ . Duquesne, J.Y., Bellessa, G., Physics Letters, (1985), 107 A , ^221.

/9/ . Duquesne, J.Y., Bellessa, G., Phil.

Mg.

(1985), to

be

published.

/lo/ . Bellessa G., Phys. Rev. Lett., (1978), 40, ^1456.