Kinetico-thermodynamic aspect of glass formation and critical cooling rates in chalcogenide systems

Mat. Res. Bull., Vol. 16, pp. 505-511, 1981. Printed in the USA. 0025-5408/81/050505-07502.00/0 Copyright (c) 1981 Pergamon Press Ltd.

KINETICO-THERMODYNAMIC ASPECT OF GLASS FORMATION AND CRITICAL COOLING RATES IN CHALCOGENIDE SYSTEMS

S. A. Dembovsky and E. A. Chechetkina

The Kurnakov Institute of General and luorganic Chemistry, the Academy of Sciences of the USSR Lehinsky Prospect 3I, Moscow II707I,USHR

(Received March 5, 1981; Communicated by R. Roy)

ABSTRACT Crystallization barrier estimate d by means of the empirical theory of glass formation (I-3) is shown to be activation enthalpy, relating to the elementary stage which limits crystallization process. This stage is assumed to correspond to the initial reorientation of particles in glass or melt followed by nucleation and growth. The dependencies connecting the enthalpy and the free activation energy of initial reorientation are obtained. The simple method of calculation of critical cooling rates of glass forming melts is suggested.

In the framework of the ideas, n a m e d b y the author "an empirical theory ox gAass zormatio~' (I-3), the expression is found which connects the energetic barrier aEcr with the structural and thermodynamic properties of a substance: mEcr = C Ed/VEC = ~ ( A

+ U) E d ~ / 2

(T)

ere C is glass fgrming ability. E d i s aver ag.e binding energy, • s valenw e±ec~ron concen~rawlon, ~ is a~mensionless coefficient related to the liquidus temperature ( ~ = ~ T i ~ / ~ , where Tm is a melting temperature of individual substances), 505

506

S.A.

DEMBOVSKY, et al.

Vo]. 16, No. 5

A is a number of different atoms, U is a number of different structural;mlts, W=(VEC-K)/VEC is a share of lone-pair electrons (K is an average coordination of the melt, (VEC-K) is a lone-pair electron concentration). As it was shown in (3) substances with ~Ecr< 20 R ~ are incapable of glass formation under usual cooling and quenching conditions, which nearly coincides with Turnbull-Cohen criterion (@), obtained from the kinetic theory of glass formation. The simple dependence of the characteristic crystallization time on the value of mEcr(fig.I) has been proposed in (3) as well.

7

T/h

-2

3. o+i -i, / -2' ( i

,

o

+o

i

i

&

" m

m

"

+E++(RT.) FIG. I Characteristic crystallization time as a barrier of crystallization. I - GeSe, 2 4 - e(GeSe2-GeBe) , 5 - As2Se 3, 6 - Se, 7 -GeSe2), 9 -e(Se-As2Se3). Here and below eutec~ic of the system.

function of energetic - GeSe2, 3 - As2Te 3, - AsSeI, 8 - e(Sesymbol "e" means the

The fracture of the lg ~ r = f ( a E ~ ) straight line was con~ nected with the change of the v v+ crystallization mechanism. For the substances farther than the fracture the value of aEcr is larger than the average chemical binding energy, and crystallisation is likely to proceed by means of bond breaking and not by switchlng. Being a complicated and multistaged process, crystallization is finally limited by the stage with energy barrier ~Ecr. This fact is indicated by the relation between ~ r and ~Ecr. Applying the Eyrimg's equation to this stage and assuming the first order of the process we obtain: lg~

-- lg~-2,3031g(I -~)~ - I0,319 - lgT + AG~/2,303RT

(2)

where ~ is crystallization time, o( is crystallization degree (volume fracture crystallized by moment ~ ) , ~ G ~ is a free energy of active complex formation.

Vol. 16, No. 5

CHALCOGENIDE SYSTEMS

507

Introducing values ~ = % ' T =(Tm-I00) and ~ = 0,99 into e9.(2) we are able to calculate the values AG ~ for substances in fmg.I. Then, as seen in table I, ~E does not coincide w i t h ~ G ,~ the difference between these two Crvalues being either positive or negative. If ~Ecr is the activation enthalpy: ~ E c r = ~ H ~ ~ ~G~+ T a S ÷

(3)

the negative differences ( ~ E ~ - ~G ) correspond to % S < 0 and positive ones to ~S~>0, that ~ is consistent with order or disorder of the structure when active complex is formed. For the substances, crystallization of which may proceed with chemical bonds breaking (~E > Ed) , the crumbly structure of the active or complex and accordingly large positive ~ S * values should correspond. It is really observed - see table I and fig.2.

I

o_o / ' ! 1 0

20

/~0

60

"Ecz(RTm)

80

t00

FIG. 2 Free energy and entropy of active complex formation versus energetic barrier of crystallization (enthalpy of active complex formation). As seen in f'ig.2 the following relations between the values ~Ecri ~ H * , ~ G # and S~are established. Firstly, the value ~H#= ~G~= 28 RTm, corresponding to the zero me~nlng of activation entropy, actually coincides with Turnbull-Cohen criterion. Secondly, ~S # being equal to 8R, the fracture of straight lines occurs, dividing the substances into two groups: AH~E d. For good glass formers two conditions are fulfilled simultaneously - ~H'>E d and a great contribution of the entropy member T a S ~. Therefore, crystallization of the substances of this group, unlike thr group with %H*
Vo]. 16, No. 5

CHALCOGENIDE SYSTEMS

509

As seen in table I, it is the enthalpy in the form of AEcr/R~,including the entropy member, that characterizes glass forming ability, because the change of AG ~ is comparatively small for the substances with various capacity for glass formation.On the other I~ud the free energy ~G ~ determines the kinetics of crystallization and, as stated below, critical cooling rates as well. Therefore the knowledge of its value is of great importance. Values of ~G ~ for substances with known ~Ecr and are found by means of diagram in fig.2. The values ~Ecr~ ~H ~, ~G ~ and T ~ S ~ are assumed to be independent on temperature in the considered temperature interval. The discussed activation barrier with free energy aG ~ seems to be attributed neither to the nucleation barrier A G " nor to the growth barrier ~G ~ since from the scant information (b~ (6) for A s ~ e z ~G"= 29±0,9; ~H'= 38±0,4 and ~H#=32±2 kcal/mol}

~G ~? ~

~G". and ~ c r ~ ~H ~ ~ ~ ' ~ ~H"

(~G% ~I and ~Ecr= ~5

Kcal/mol lot As2Se ~ ~ see table I). It is supposed that the barrier ~ ~G should be related to the initial reorientation of particles in glass (melt) after which nucleation and crystal growth follow as it shown by the scheme:

~G ~ I)

A --~A

2)

A

3)

W*+ ~G' ° ---~An

u

~GI--~ ~G'I o ~G~ aG~, ~" Acr A - ~ A° ~ Acr

(~

~

~o )

(3)

(~ ~ o )

where A, Ao, ~ u and Act is the particle state in the initial glass or melt, in reorientated state, in nucleus and in crystal accordingly; W ~ is the thermodynamic barrier of crystal nucleus formation.

/

/ / I I 0

%

0

FIG. 3 Crystallization degree o6versus crystallization t i m e ~ by eq. (2) . . . . by scheme (3) ..... experimental curve.

510

S.A.

DEMBOVSKY, et al.

Vol. 16, No. 5

This scheme is illustrated in fig.3. On the first stage the cess.of crystal.li~a~ion i~ l'^zmi.ted by. formation and growth of CrlNlCS.i nuclei L~w + ~ ) ; ~ ]. un ~ne secona s~age reorientated particles which were accumulated before are rapidly spend with variable velocity corresponding the barrier change from aG' to ~G #. Begining with To and up to the end of crystallization the process is limited by the initial reorientation. At partial superposition of stages one obtains the S-form crystallization curve which is experimentally observed.

~

If ~G ~ corresponds to the initial stage of crystallization, the critical cooling rate (CCR), e.g. the minimal rate at which the melt must be cooled to prevent its crystallization, should be the exponential function of the barrier %G~: (@) •

V = V 0 exp(-aG~/RT~) TABLE 2 Critical Cooling Rates of some Chalcogenides ~) Experiment-~x)

Substance

V after (7)

igV

Calculation igVoe q. (J+) i g v e q.

(~+)

V

,, ,,

GeSe GeSe 2 As2Te 3 e(GeSe2-GeSe)

m

I0

m

I

m

-I

I0

II, 8

As2Se 3 Se

0,02

-I,7

II,2

AsSel e (Se-GeSe2)

0,005

-2,3

12,2

e (Se -A s2 Se 3 )

300 m

1,0

m

0,I

2,5

I2,8

m

-I,8

0,016 m

-2,2 n

-2,7

0,006 m

0,002

~)Critical cooling rates V in K/sec ~ ) T h e experimental CCR curve from (7) was obtained in a quantitative zorm by introducing the following values of cooling rates that presumably correspond to the adopted in (7) cooling conditions: water quenching - I0 K/sec, air quehching - 0,I K/sec, slow cooling - 0,0I K/sec. As seen in table 2, the factor V o is practically constant: lg Vo = I2,0+0,8 that close to the thermal vibration frequencies of atoms or atom groups. Assuming l g V ~ 12 one can calculate CCR for substances with known ~Ecr, as it ~as been done for a number of chalcogenides in table 2.

Vol. 16, No. 5

CHALCOGENIDE SYSTEMS

511

The cooling rate I00-200 K/sec is known to be related to sharp quenching and the cooling rate~ O , I - O , O I K/sec - to standard cooling conditions. In accordance with this fact, GeSe with V = 300 K/sec would not form glass and, on the contrary, the eutectic of the (Se-As2Se~)-system with V = 0,002 K/sec would not crystallize. J Cooling rate V = O,I K/sec, achieved by simple cooling of a massive block in the air, corresponds to the Turnbnll-Cohen criterion. The obtained dependencies between ~E.~, AG @ and CCR appear to be applicable to the broad range of V'substances, including substances with the negative values of ~ that are typical for elements and ionic compounds with %v
1_8, 33 (1975)

Thibierge and A. Brenac, J. Non-Cryst. Solids

8. D. R. Uhlmann, J. Non-Cryst. Solids 7, 337 (I972). 9. J. C. A. Vreeswijk, R. G. Gossink and J. M. Stevels, J. Non-Cryst. Solids, I6, 15 (I97~).