Plane Front Solidification

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Plane Front Solidification
Growth of Single Crystals
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Single Crystals
Planar
Cellular
Dendritic
Turbine Blades
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Constitutional Supercooling
Criterion for Plane Front
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Single Crystals
Growth Parameters
Operationally
Establish Temperature Gradient
Move Interface through Temperature Gradient
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Bridgeman (Modified)
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Bridgeman (Modified)
Vertical
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Thermal Balance at S/L Interface
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Selection
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CzochralskiCrystal Pulling
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CzochralskiCrystal Pulling
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Floating Zone
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Illustrative Heat Flow AnalysisFloating Zone

• Circular cross section, dia.2a.
• Heat loss coeff., hconstant.
• Moving coordinate, Z0 _at_ freezing interface.
• Steady state, relative to freezing interface.
• Consider resolidified rod
• Rod is thin, , negligible radial
  temperature gradient

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Enthalpy Balance on Thin Slice of Solid Floating
Zone
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Axial Conduction
Conduction In
Conduction Out
Net
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Axial Convection
Convection Out
Convection In
Net
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Circumferential Heat Loss
Cicumferential Loss
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Governing PDE Boundary Conditions
Axial Conduction
Moving Coordinate (Convection)
Loss to Surroundings
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Solve for l using quadratic formula.
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Solution