Crystal Growth Rate BCF Spiral Calculator

Crystallization surface physics: Calculate face growth rate ($G$) across parabolic low-supersaturation and linear high-supersaturation regimes using the Burton-Cabrera-Frank (BCF) spiral and 2D Birth-and-Spread models.

Growth Regime & Kinetic Parameters

Relative Supersaturation σ (S - 1): σ = (C - C*)/C*

Crystallization Temp T (°C):

Step Height h (nm): Lattice monomolecular step

Linear Kinetic Coeff C_lin (μm/s):

Spiral & Surface Dislocation Properties

Critical Transition Supersat σ_1: BCF transition from σ² to σ¹

Surface Diffusion Length x_s (nm):

Crystal Face Growth Rate Output

BCF Growth Rate G:

μm / minute

Growth Regime:

Kinetic mechanism

Spiral Step Spacing:

y₀ (nm)

Face Velocity:

nm / s

Overlapping Steps:

x_s / y₀ ratio

Empirical Power Law Equivalent ($G = k_g \sigma^g$)

Local Apparent Growth Order $g$: --

Apparent Rate Constant $k_g$: --

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Crystal Growth Rate BCF Spiral Calculator

Growth Regime & Kinetic Parameters

Spiral & Surface Dislocation Properties

Crystal Face Growth Rate Output

Empirical Power Law Equivalent ($G = k_g \sigma^g$)

Frequently Asked Questions