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Crystal Growth ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
1) Introduction ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Applications ,[object Object],[object Object],[object Object],[object Object]
Methods for Crystal Growth ,[object Object],[object Object],[object Object],[object Object],[object Object]
a.) Growth from the melt: ,[object Object],[object Object],[object Object],[object Object]
Advantages of solidification: ,[object Object],[object Object]
b.) Growth from solution: ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
b.1) Molten salt (flux) growth: ,[object Object],[object Object],[object Object],[object Object],[object Object]
b.2) Metallic solution growth: ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
b.3) Hydrothermal growth: ,[object Object]
c.) Growth from the vapor phase: ,[object Object],[object Object]
2) Processes for crystal growth from the  melt : ,[object Object],[object Object],[object Object]
 
It’s a Boy!! Born May 8, 2001 at 10:35 p.m. Weight:  14 lbs, 9 oz Length:  15 inches Crystal growth furnace for SUBSA investigation, destined for Space Station Alpha in May 2002.
Directional Solidification, i.e. Vertical Bridgman Growth ,[object Object],[object Object],[object Object]
[object Object],[object Object]
Advantages of the Bridgman Process: ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Liquid   Encapsulation Advantages: Properties of a good encapsulant -  Prevents contact between the crystal and the melt  -  Reduced nucleation - Thermal stresses are reduced -  Reduced evaporation - Melting temperature lower than the crystal - Low vapor pressure - Density lower than the density of the melt - No reaction with the melt or the crucible Best encapsulans: - B 2 O 3 - LiCl, KCl, CaCl2, NaCl Crucible Encapsulant Melt Crystal
Bridgman growth with the Submerged Baffle ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Gr  g     T  H 3  2
2.2 Czochralski Method (CZ): ,[object Object],[object Object],[object Object],[object Object]
Advantages: ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Drawbacks: ,[object Object],[object Object],[object Object],[object Object]
Drawbacks (continued): ,[object Object],[object Object],[object Object],[object Object]
Liquid encapsulated Czochralski method (LEC) ,[object Object],[object Object],[object Object],[object Object]
Drawbacks: ,[object Object],[object Object],[object Object],[object Object]
2.3 Zone melting and floating zone: ,[object Object],[object Object],[object Object],[object Object]
Advantages : ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Drawbacks : ,[object Object],[object Object],[object Object],[object Object]
3) Convection and segregation
Enclosure Heated from Below
Natural buoyancy forces moving  boundary less difficult  predict  (at S/L interface) hard  to  predict, model and control Magnitude: Features:  V ~  w L unsteady:  Gr > 5,000 turbulent:  Driving  mech. Forced Convection L  and   T  = f (time)  ° f (time) Growth  process: all CZ, FZ Comparison of Natural and Forced Convection
c)   Impose  forced convection -  Accelerated Crucible Rotation Technique -  Coupled Vibrational Stirring -  Rotating Baffle Control of Crystal Homogeneity a)   Reduce  natural convection: -  Reduced gravity (µg) -  Magnetic fields   -  Submerged baffle b)   Enhance  natural convection -  centrifuges
No motion of phase boundary Beginning of motion Mass Transfer: Solid-Liquid Interface
Diffusion-controlled segregation Tiller et al.
Perfect Mixing Scheil (1942), Pfann(1952) ∆  f S  = change in solid fraction Solidified Fraction, f S •  no steady state •  axial inhomogeneity (k<<1)
Burton, Prim and Slichter’s  BPS Model •  assumption: 1-D flow (?) •  Stagnant solute layer, at y = 0,  v=0  C L  = C 0   at  x =   BPS   at  x = 0
Burton, Prim and Slichter’s  BPS Model, cont. Levich: Kodera (1953): measurement of D [cm2/s] Levich soulution  -Czochralski only -crucible = finite melt -natural convection,  -couterrotation -turbulence
Solute Conservation in CV: Ostrogorsky & Müller: Integral CV approach
Ostrogorsky and Müller: Integral control-volume approach (cont.) ,[object Object],[object Object],a = 1/6 Table  1   D  and V ∞  for several important melt growth techniques   (CZ=Czochralski, FZ = Floating Zone, Gr = Grashof number)       Driving  Mechanism Growth Method  D V ∞ Crystal rotation Cz, FZ V∞     L Natural Convection Bridgman V ∞   ~Gr (  /L) Weak natural convection in microgravity Bridgman V ∞ ~Gr(  /L) 1/2
•  Cochran's ∞ rotating disc: J.Appl.Phy. 27(1956)686 •  Levich (Sparrow and Gregg) Model of Ostrogorsky  and  Müller and Data of Bridges k eff  versus growth rate R and    for Czochralski grown crystals.
Microscopic Inhomogeneity  (1  m to 1 mm) ,[object Object],[object Object],[object Object],[object Object]
Bridgman growth with the Submerged Baffle ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Gr  g     T  H 3  2
Micro-segregation (a) Bridgman and (b) Baffle   Spreading Resistance in 6 cm diameter Ga-doped Ge-2%Si alloy Measurements conducted by M. Lichtensteiger at NASA-MSFC [9]

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Tufts Rpic Crystal

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  • 14. It’s a Boy!! Born May 8, 2001 at 10:35 p.m. Weight: 14 lbs, 9 oz Length: 15 inches Crystal growth furnace for SUBSA investigation, destined for Space Station Alpha in May 2002.
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  • 19. Liquid Encapsulation Advantages: Properties of a good encapsulant - Prevents contact between the crystal and the melt - Reduced nucleation - Thermal stresses are reduced - Reduced evaporation - Melting temperature lower than the crystal - Low vapor pressure - Density lower than the density of the melt - No reaction with the melt or the crucible Best encapsulans: - B 2 O 3 - LiCl, KCl, CaCl2, NaCl Crucible Encapsulant Melt Crystal
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  • 30. 3) Convection and segregation
  • 32. Natural buoyancy forces moving boundary less difficult predict (at S/L interface) hard to predict, model and control Magnitude: Features: V ~ w L unsteady: Gr > 5,000 turbulent: Driving mech. Forced Convection L and  T = f (time)  ° f (time) Growth process: all CZ, FZ Comparison of Natural and Forced Convection
  • 33. c) Impose forced convection - Accelerated Crucible Rotation Technique - Coupled Vibrational Stirring - Rotating Baffle Control of Crystal Homogeneity a) Reduce natural convection: - Reduced gravity (µg) - Magnetic fields - Submerged baffle b) Enhance natural convection - centrifuges
  • 34. No motion of phase boundary Beginning of motion Mass Transfer: Solid-Liquid Interface
  • 36. Perfect Mixing Scheil (1942), Pfann(1952) ∆ f S = change in solid fraction Solidified Fraction, f S • no steady state • axial inhomogeneity (k<<1)
  • 37. Burton, Prim and Slichter’s BPS Model • assumption: 1-D flow (?) • Stagnant solute layer, at y = 0, v=0 C L = C 0 at x =  BPS at x = 0
  • 38. Burton, Prim and Slichter’s BPS Model, cont. Levich: Kodera (1953): measurement of D [cm2/s] Levich soulution  -Czochralski only -crucible = finite melt -natural convection, -couterrotation -turbulence
  • 39. Solute Conservation in CV: Ostrogorsky & Müller: Integral CV approach
  • 40.
  • 41. • Cochran's ∞ rotating disc: J.Appl.Phy. 27(1956)686 • Levich (Sparrow and Gregg) Model of Ostrogorsky and Müller and Data of Bridges k eff versus growth rate R and  for Czochralski grown crystals.
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  • 44. Micro-segregation (a) Bridgman and (b) Baffle Spreading Resistance in 6 cm diameter Ga-doped Ge-2%Si alloy Measurements conducted by M. Lichtensteiger at NASA-MSFC [9]