VILA VÍLA - VItrum LAugaricio Joint Glass Center of Institute of Inorganic Chemistry of SAS, A....

VILA

VÍLA - VItrum LAugaricioJoint Glass Center

of Institute of Inorganic Chemistry of SAS, A. Dubček University of Trenčín, and RONA, j.s.c.

Študentská 2, Trenčín, SK-911 50, Slovak Republic

VILA & FU AVČR & UPCE

KLASICKÁ NUKLEAČNE RASTOVÁ TEÓRIA A JEJ APLIKÁCIE

Marek Liška, Mária Chromčíková, Miroslava Rodová, Karel Nitsch, Zdeněk Černošek

OUTLINE

• Gibbs energy controls the [P, T] world

• Driving force for crystallization

• Crystal nucleation - embryo

• Crystal growth

• Nucleation and growth – TTT

• Mathematical model

• Application to ZnCl2

PERSISTING WARNING

NOT

TOO

MUCH

THEORY!!!!!!!!!!!!

GIBBS ENERGY

S

S

S

L

L

L

As2Se3 - G vs T(K)FACT53 - FACT53 - FactSage 5.3 compound database (Jan. 2007)

T(K)

G(K

J/m

ol)

300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500-650

-600

-550

-500

-450

-400

-350

-300

-250

-200

-150

-100

-50

Tliq

Undercooling

VOLUME VERSUS SURFACE23 4

34

rSrV

fpmelt,crystal, 0

)()(TT

V

TGTGG

m

mmV

0 SG

23 434

)( rGrGSGVrG VSV

2484d

)(d 2 VV GrrrGr

rrG

VV G

rGrrG 2

20max)( ***

Critical nucleus – critical radius r*:

VOLUME

VERSUS

SURFACE

Thermodynamic activation barrier:MISSION IMPOSSIBLE

Entropy of mixing decreases G:

N

N

N

NkTrGN

NN

N

NN

N

NN

N

NN

NkTrGNG

rrr

rrr

r

r

rr

ln)(

lnln)(

kTGN

kT

GNN r

2V

3*

*

3

16expexp

2mfpmfp

2fp

3

2V

3*

3

16

3

16

VTTH

T

GG

Vmfpfpmfpmfpmfpmfp )( GVTTTHSTHTG

Proportional to # of neighbors, Ns, frequency, kT/h, Boltzman factor of kinetic activation energy, and Nr*:

HOMOGENEOUS NUCLEATION RATE

kTHT

TVN

kT

G

h

kTNI

2mfp

2fp

2m

3

as

3

16expexp

2fp

as

11)/ln()ln(ln

TTTB

Tk

GhkTNNI

kHTVB 2mfp

2fp

2m

3 316

HOMOGENEOUS NUCLEATION RATE

TTT fp

kTHT

TV2

mfp

2fp

2m

3

3

16exp

kTG

hkT aexp

Decreases with T

Increases with T

Increases with T

= 0 for T=Tfp

RATE OF CRYSTAL GROWTH

kTNGGfNdt

dnAmfpas exp)lc(

kTGfNdtdn

as exp)cl(

hkT

f

uNRTGkTGfNdt

dn

dt

dns mfpas exp1exp)lc()cl(

fp

fpmfpa exp1exp

TTR

TTHkTG

h

kTu

NUCLEATION vs CRYSTAL GROWTH

T Tfp fpGm 0 u 0T 0 u 0

Tfp

Tg

NUCLEATION AND GROWTHConstant p, T, single component => u, I = const.

31 34

utV Volume after growth from to t

dutIVtVt

0

3liqcr 3

4)( Vcr<<Vliq=> Vliq= const

43

0

33

liq

cr

3

1d

3

4

)0(

)()( tuItuI

tV

tVt

t

TTT = Temperature – Time – Transformation

.)0(

)()(

liq

cr consttV

tVt

TTT DIAGRAMS

TTT diagram of salol

(A) = 10-6 (B) = 10-8

THE MODEL

)3/ln(ln4)10ln()ln( exp6

exp3 tIu

TC

TTTBAWIu

11)ln( 2

fp

exp3

fp

2fpmfpexp1ln3)/ln(4TTR

TTHhkTW

3ss lnln3ln3ln3 NNNNA

k

GC a4

kHTVB 2

mfp2

fp2

m3 316

64expexp

3 1031

)( tuIt

REGRESSION TREATMENT

3ss lnln3ln3ln3 NNNNA

k

GC a4

CzBxAWIuy )ln( 3

kHTVB 2mfp

2fp

2m

3 316

2fp1 TTTx

Tz 1

RESULTS

A = - 49.11

B = 46916278

C = 46795

Ga = 97 kJ/mol

sapr = 3.4 K

RESULTS

2 3 4 5 6 7 8 9150

200

250

300

Calculated Experiment

T /

oC

log(t / s)

CONCLUSION

The plausible semi-empirical method (e.g. the general form of the regression

function)was proposed for the quantitative description of the TTT diagrams.

GENERAL CONCLUSIONSSome people do not like theory...

AT LEASTONE

EXPERIMENTPLEASE!!!

(Prayerof

MiaFarrow)

Photo

© Z. Černošek

THANK YOU FOR YOUR PATIENT ATTENTION