LaMaV LaMaV Crystal Growth in Glass Crystal Growth in Glass Forming Liquids Forming Liquids Marcio Marcio Luis Ferreira Luis Ferreira Nascimento Nascimento Edgar Edgar Dutra Dutra Zanotto Zanotto Federal University of São Carlos, Brazil Federal University of São Carlos, Brazil Vitreous Materials Laboratory Vitreous Materials Laboratory www.lamav.ufscar.br www.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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LaMaVLaMaV
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
Properties required to test modelsor calculate growth rates
i) Diffusivity (or viscosity) vs. T;ii) Crystal-glass free energy vs. T
LaMaVLaMaV
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.
LaMaVLaMaV
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
LaMaVLaMaV
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
LaMaVLaMaV
950950ooCC
2min 30s
Growth in situ: Diopside
LaMaVLaMaV
950950ooCC
3min 00s
Growth in situ: Diopside
LaMaVLaMaV
950950ooCC
3min 30s
Growth in situ: Diopside
LaMaVLaMaV
950950ooCC
4min 00s
Growth in situ: Diopside
LaMaVLaMaV
950950ooCC
4min 30s
Growth in situ: Diopside
LaMaVLaMaV
950950ooCC
5min 00s
Growth in situ: Diopside
LaMaVLaMaV
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
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
LaMaVLaMaV
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)
LaMaVLaMaV
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
Validity of crystal growth models & StokesValidity of crystal growth models & Stokes--Einstein / Einstein / EyringEyring equation in a equation in a widewide temperature rangetemperature range