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Crystal Growth in Glass Crystal Growth in Glass Forming LiquidsForming Liquids

MarcioMarcio Luis Ferreira Luis Ferreira NascimentoNascimentoEdgar Edgar DutraDutra ZanottoZanotto

Federal University of São Carlos, BrazilFederal University of São Carlos, BrazilVitreous Materials LaboratoryVitreous Materials Laboratory

www.lamav.ufscar.brwww.lamav.ufscar.br

Presented at the IMI-NFG US-Japan Winter School , Jan 14, 2008 and Reproduced by the International Materials Institute for Glass for use by the glass research community; Available at: www.lehigh.edu/imi

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•• IntroductionIntroduction•• Growth models?Growth models?•• Normal GrowthNormal Growth•• Screw Dislocation GrowthScrew Dislocation Growth•• Surface Nucleation GrowthSurface Nucleation Growth•• Some ExamplesSome Examples•• Experimental ResultsExperimental Results•• AcknowledgmentsAcknowledgments•• BibliographyBibliography

Outline

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i) The undercoolingundercooling, which is a measure of the driving force for crystal growth;

ii) The site factor, which is the fraction of sites on the crystal/ glass interface that can incorporate molecules;

iii) The effective diffusivity in the crystal/liquid interface, which is a measure of the resistance to molecular motion and rearrangement.

Crystal growth rates depend basically on three factors:Crystal growth rates depend basically on three factors:

Introduction

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Relevance

The development of glassThe development of glass--ceramics ceramics depend on the controlled depend on the controlled

crystallization of certain glassescrystallization of certain glasses

Crystallization kinetics allows or Crystallization kinetics allows or not the existence of vitreous statenot the existence of vitreous state

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THEORY

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How Crystals Grow?

Painting by Paolo Massacci

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Example of Crystal Growth

αα--phase growth on NS2 atphase growth on NS2 at780780ooCC / / 1 min 1 min intervalsintervals

NaNa22OO⋅⋅2SiO2SiO22

800 850 900 950 1000 1050 1100 115010-9

10-8

10-7

10-6

u (m

/s)

T (K)

Meling & Uhlmann

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ii) ) NORMALNORMAL

Three Classical MechanismsThree Classical Mechanisms

SiOSiO22 & GeO& GeO22

How Crystals Grow?

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iiii) ) SCREW DISLOCATION MODELSCREW DISLOCATION MODELNaNa22OO⋅⋅2SiO2SiO2 2 , Na, Na22OO⋅⋅4B4B22OO33 & & DiopsideDiopside

G. H. Gilmer, J. Crystal Growth 42 (1977)

How Crystals Grow?George Gilmer

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PbOPbO⋅⋅SiOSiO22 & & AnorthiteAnorthite

iiiiii) ) SURFACE NUCLEATION or 2DSURFACE NUCLEATION or 2D

How Crystals Grow?

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NORMAL GROWTH

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Normal Growth

λcrystal liquid

crystalcrystal--liquid interfaceliquid interface

⎟⎠⎞

⎜⎝⎛ Δ

−=RTGvv D

lc exp0

⎟⎟⎠

⎞⎜⎜⎝

⎛ Δ+Δ−=

RTGG

vv Dcl exp0

( ) ⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛ Δ−−⎟

⎠⎞

⎜⎝⎛ Δ−λ=

RTG

RTGvTu D expexp 10

( )cllc vvu −λ=

| |

Potential

Distance

ΔG l

ΔG c

ΔG

ΔGD

λcrystalliquid

vlc

vclKineticsKinetics

S. Glasstone, K. J. Laidler, H. Eyring, The Theory of Rate Processes (1941)

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( ) ⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛ Δ−−⎟

⎠⎞

⎜⎝⎛ Δ

−λ=RT

GRTGvfTu D expexp 10 f ≈ constantconstant ≈ 1

Harold A. WilsonHarold A. Wilson YakovYakov FrenkelFrenkel

Normal GrowthFraction of prefered

growth sites f

H. A. Wilson, Philos. Mag. 50 (1900)Ya. Frenkel, Phys. Z. Sowjetunion 1 (1932)

Main supposition: crystal growth front has a high concentration of growth sites f ~1

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SCREW DISLOCATIONGROWTH

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The screw dislocation mechanism was proposed by Burton, Cabrera & Frank.

Screw Dislocation

Frederick Frank Nicolás Cabrera

W. K. Burton, N. Cabrera, F. C. Frank, Trans. Roy. Soc. London A243 (1951)

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Screw Dislocation

( ) ( ) ⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛ Δ−−

ηλλ=

RTGTkTfTu B exp13

ThermodynamicTransport

ηλ= 3

Tkv B

dislocation linedislocation line⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛ Δ−−λ=

RTG

vfTu exp)( 1

Surface is smooth but imperfect at atomic level

m

m

TTTf

π−

≈2

SE

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SECONDARY SURFACE NUCLEATION2D-GROWTH

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Surface Growth: 2D⎟⎠⎞

⎜⎝⎛

Δ−

η=

GTBbCu exp

wherewhere:3λ

=Tkb B

3 2mA

m

VN

HΔα=σ

((largelarge crystal case)crystal case)

B

mkVB

2σπλ=

((smallsmall crystal case)crystal case)

B

mk

VB3

2σπλ=

0ANC Sλ≈

( ) ( )[ ]323 5

134

3 //exp/

/RTG

NC S Δ−−

Γ

λπ=

Surface is smooth but also imperfect at atomic level, but free of intersecting screw dislocations

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i) i) NormalNormal ((NN))

ii) ii) Screw DislocationsScrew Dislocations ((SDSD))

iii) iii) Surface NucleationSurface Nucleation ((2D2D))

Summary: Growth Mechanisms

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i) i) NormalNormal ((NN))

ii) ii) Screw DislocationsScrew Dislocations ((SDSD))

iii) iii) Surface NucleationSurface Nucleation ((2D2D))

( ) ⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ Δ

−−λ

=RT

GDTu u exp1

( ) ⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ Δ

−−λ

=RT

GDfTu u exp1

( ) ⎟⎠⎞

⎜⎝⎛

Δ−

λ=

GTBDCTu u exp2

ifif DDuu≈≈ DDηη

Summary: Growth Mechanisms

ηλ= 3

Tkv BDu

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EXAMPLES OF

CRYSTAL GROWTH CURVES

Properties required to test modelsor calculate growth rates

i) Diffusivity (or viscosity) vs. T;ii) Crystal-glass free energy vs. T

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800 900 1000 1100 1200 1300 1400 1500 1600 17000

1x104

2x104

3x104

4x104

5x104

6x104

7x104

ΔG (J

/mol

)

T (K)

Turnbull Hoffman Borisova

700 800 900 1000 1100 1200 13000,0

5,0x103

1,0x104

1,5x104

2,0x104

2,5x104

ΔG (J

/mol

)

T (K)

Turnbull Hoffman Burgner & Weinberg

Gibbs Free EnergyComparison of measured and calculated Gibbs free energies ΔG for LS2 and diopside in wide range of temperatures. Li2O⋅2SiO2

CaO⋅MgO⋅2SiO2

M. L. F. Nascimento, Thesis, Federal University of São Carlos (2004)

Both approximations are valid near Tm. For normal and screw dislocationgrowth ΔG does not have a strong influence on U compared to the transport term.

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Viscosity: Diopside

)/(.log 751396127410 −+−=η T

1000 1200 1400 1600 1800 2000

-2

0

2

4

6

8

10

12

14

16

Licko & Danek15

Kozu & Kani16

McCaffery et al.17

Neuville & Richet18

Sipp et al.19

Taniguchi20

Klyuev21

this worklog

η (P

a.s)

Temperature T (K)

M. L. F. Nascimento, E. B. Ferreira, E. D. Zanotto, J. Chem. Phys. 121 (2004)

CaOCaO⋅⋅MgMgOO⋅⋅22SiOSiO22

Eduardo Ferreira

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Arrhenius or Vogel-Fulcher-Tammann-Hesse (VFTH) equations describe viscosity data between Tgand Tm for many systems; but is the Stokes-Einstein/Eyring equation adequate to describe the rearrangements on the crystal growth front?

Svante Arrhenius Gustav TammannGordon Fulcher

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Growth in situ: Diopside

2min 00s

950950ooCC

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950950ooCC

2min 30s

Growth in situ: Diopside

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950950ooCC

3min 00s

Growth in situ: Diopside

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950950ooCC

3min 30s

Growth in situ: Diopside

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950950ooCC

4min 00s

Growth in situ: Diopside

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950950ooCC

4min 30s

Growth in situ: Diopside

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950950ooCC

5min 00s

Growth in situ: Diopside

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1100 1200 1300 1400 1500 160010-11

10-10

10-9

10-8

10-7

10-6

10-5

10-4

800 900 1000 1100 1200 1300 1400

10-11

10-10

10-9

10-8

10-7

10-6

10-5

10-4

CaO·MgO·2SiO2

Briggs & Carruthers Fokin & Yuritsyn Kirkpatrick et al. Nascimento et al. Reinsch & Müller ZanottoG

row

th ra

te U

(m/s

)

Temperature T (K)

screw

T (oC)

Growth rates: Diopside

( ) ⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ Δ

−−λ

=RT

GDfTu u exp1

λ ~ 1.5 ASD

1.1Tg

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1000 1100 1200 1300 1400 1500 1600 170010-13

10-12

10-11

10-10

10-9

10-8

10-7

10-6

10-5

10-4

R2 = 0.89a0 = (0.161 ± 0.004)ÅA = -2.0449B = 4330.54141 KT0 = 777.01529 KHm = 180 kJ/mol

Tm = 1623 (1350oC)

Reinsch & Müller's data

Gro

wth

rate

u (m

/s)

T (K)

CordieriteS. Reinsch, M. L. F. Nascimento, R. Muller, E. D. Zanotto, sub. JACS

The mechanismdepends on the Tmof μ−cordierite, a metastable phase...

If Tm = 1350oC ⇒ SD

If Tm = 1467oC ⇒ 2D

2MgO2MgO⋅⋅2Al2Al22OO33⋅⋅5SiO5SiO22

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Si−O bondbond1.62Å

O−O bondbond2.64Å

SiOSiO22 glassglass

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛ Δ−−

λη=

RTGTkTu B exp)( 1

Silica Type I

1600 1700 1800 1900 2000

-1,0x10-9

0,0

1,0x10-9

2,0x10-9

SiO2 Type I - Wagstff's data

Gro

wth

rate

u (m

/s)

Temperature T (K)

Normal growth

1.11.1TTgg

λ ~ 1 A

Nascimento & Zanotto, PRB (2006)

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700 800 900 1000 1100 1200 130010-13

10-12

10-11

10-10

10-9

10-8

10-7

10-6

10-5

10-4

u (m

/s)

T (K)

Barker et al. Burgner & Weinberg James Matusita & Tashiro Ota et al. Schmidt & Frischat Zanotto & Leite Fokin Soares Jr. Gonzalez-Oliver et al. Deubener et al. Ogura et al. Parcell Ito et al. Leontjeva

u(T) ajustado com λ = 1,3 Å

LiLi22OO⋅⋅2SiO2SiO22

2D2D

TTgg

1.11.1TTgg

LS2 ( ) ⎟⎠⎞

⎜⎝⎛

Δ−

λ=

GTBDCTu u exp2

B

m

kVB3

2σπλ=

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SummaryThree classical types: normalnormal, screwscrew & 2D2D

ΔG = TurnbullTurnbull or HoffmannHoffmannΔGD == via StokesStokes--Einstein / Einstein / EyringEyring

ΔHm = melting enthalpymelting enthalpyη = viscosityviscosity

Validity of crystal growth models & StokesValidity of crystal growth models & Stokes--Einstein / Einstein / EyringEyring equation in a equation in a widewide temperature rangetemperature range