Phase Transformation All Formulas For Numerical Problems | Material Science Formula For Numerical Problems

In this place, you will get all types of numerical problem-solving formulas on the topic of "PHASE TRANSFORMATION" on one page. This formula will help you to solve different types of problems on "PHASE TRANSFORMATION" very easily. Check out all this formula given below before solving Numerical Problems on "PHASE TRANSFORMATION" given on this site or anywhere.

PHASE TRANSFORMATION

FORMULA

Formula 1

Used to Calculate: Total change in free energy during phase transformation

∆G = (4/3)πr³∆G_v + 4πr²γ

Where,
∆G = Change in free energy during phase transformation
∆G_v = Volume free energy or Free energy difference between the solid and liquid phase
r = radius of the nucleus
γ = surface free energy

Formula 2

Used to Calculate: Critical radius for stable solid particle during homogeneous nucleation

r^*_homo = - 2γ/(∆G_v)

Where,
r^*_homo = Critical radius of the nucleus for homogeneous nucleation
γ = surface free energy
∆G_v = Volume free energy or Free energy difference between a solid and liquid phase

Formula 3

Used to Calculate: Critical activation free energy for the formation of a stable solid particle during homogeneous nucleation

∆G^*_homo = [(16πγ³)/{3(∆G_v)²}]

Where,
∆G^*_homo = Critical activation free energy for the formation of a stable solid particle during homogeneous nucleation
γ = surface free energy
∆G_v = Volume free energy or Free energy difference between a solid and liquid phase

Formula 4

Used to Calculate: Critical radius in terms of latent heat of fusion and melting temperature during homogeneous nucleation

r^* = [{- (2γT_m)/(∆H_f)} {1/(T_m - T)}]

Where,
r^* = Critical radius of the nucleus
γ = surface free energy
T_m = Equilibrium solidification temperature (K)
T = Temperature (K)
∆H_f = Latent heat of fusion

Formula 5

Used to Calculate: Critical activation free energy in terms of latent heat of fusion and melting temperature during homogeneous nucleation

∆G^* = [{16πγ³T_m²} / {3(∆H_f)²}] [1 / {(T_m - T)²}]

Where,
∆G^* = Critical activation free energy of the nucleus
γ = surface free energy
T_m = Equilibrium solidification temperature (K)
T = Temperature (K)
∆H_f = Latent heat of fusion

Formula 6

Used to Calculate: Different interfacial energies and contact or wetting angle for homogeneous nucleation

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γ_IL = γ_SI + γ_SLcosθ

Where,
γ_IL = Liquid-surface interfacial energy
γ_SL = Solid-liquid interfacial energy
γ_SI = Solid-surface interfacial energy
θ = Wetting angle (angle between γ_SI and γ_SL vectors)

Formula 7

Used to Calculate: Critical radius for stable solid particle during heterogeneous nucleation

r^*_het = - 2γ_SL/(∆G_v)

Where,
r^*_het = Critical radius of the nucleus for heterogeneous nucleation
γ_SL = Solid-liquid interfacial energy
∆G_v = Volume free energy or Free energy difference between a solid and liquid phase
θ = Wetting angle (angle between γ_SI and γ_SL vectors)

Formula 8

Used to Calculate: Critical activation free energy for the formation of a stable solid particle during heterogeneous nucleation

∆G^*_het = [(4πγ_SL³)/{3(∆G_v)²}] {2 - 3cosθ + cos³θ}

⇒∆G^*_het = (1/4)[(16πγ_SL³)/{3(∆G_v)²}] {2 - 3cosθ + cos³θ}

⇒∆G^*_het = (1/4) (∆G^*_homo) (2 - 3cosθ + cos³θ)

Where,
∆G^*_het = Critical activation free energy for the formation of a stable solid particle during heterogeneous nucleation
∆G^*_homo = Critical activation free energy for the formation of a stable solid particle during homogeneous nucleation
γ_SL = Solid-liquid interfacial energy
∆G_v = Volume free energy or Free energy difference between a solid and liquid phase

Formula 9

Used to Calculate: Fraction of transformation (Avrami Equation)

y = 1 - exp(-ktⁿ)

Where,
y = Fraction of transformation
k, n = Time-independent constants

Formula 10

Used to Calculate: Transformation rate

rate = 1 / t_0.5

Where,
t_0.5 = Time required for a transformation to proceed to 50% completion

REFERENCES:

Materials Science and Engineering: an Introduction (9E) by William D. Callister, Jr., and David G. Rethwisch.

Click here to know details about this book and download it in pdf format.

Materials Science and Engineering: A First Course by Raghavan.

Click here to know details about this book and download it in pdf format.

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