phase transformation

How to Calculate and Solve for Conversion of Volume Fraction to Mass Fraction | Phase Transformation

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The image above represents the conversion of volume fraction to mass fraction.

To compute for volume fraction to mass fraction, four essential parameters are needed and these parameters are α-phase Volume Fraction (Vα), β-phase Volume Fraction (Vβ), α-phase Density (ρα) and β-phase Density (ρβ).

The formula for calculating volume fraction to mass fraction:

Wα = Vαρα/(Vαρα) + (Vβρβ)

Wβ = Vβρβ/(Vαρα) + (Vβρβ)

Where:

Wα = α-phase Weight/Mass Fraction
Wβ = β-phase Weight/Mass Fraction
Vα = α-phase Volume Fraction
Vβ = β-phase Volume Fraction
ρα = α-phase Density
ρβ = β-phase Density

Let’s solve an example;
Find the conversion of volume fraction to mass fraction when the α-phase volume fraction is 4, the β-phase volume fraction is 7, the α-phase density is 11 and the β-phase density is 10.

This implies that;

Vα = α-phase Volume Fraction = 4
Vβ = β-phase Volume Fraction = 7
ρα = α-phase Density = 11
ρβ = β-phase Density = 10

Wα = (4)(11)/((4)(11)) + ((7)(10))
Wα = (44)/(44) + (70)
Wα = (44)/(114)
Wα = 0.38

Therefore, the α-phase mass fraction, Wα is 0.38.

Wβ = (7)(10)/((4)(11)) + ((7)(10))
Wβ = (70)/(44) + (70)
Wβ = (70)/(114)
Wβ = 0.614

Therefore, the β-phase mass fraction, Wβ is 0.614.

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How to Calculate and Solve for Transformation Rate | Phase Transformation

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The image above represents transformation rate.

To compute for transformation rate, one essential parameter is needed and this parameter is Halfway Time to Completion (t0.5).

The formula for calculating transformation rate:

Rate = 1/t0.5

Where:

Rate = Transformation Rate
t0.5 = Halfway Time to Completion

Given an example;
Find the transformation rate when the halfway time to completion is 20.

This implies that;

t0.5 = Halfway Time to Completion = 20

Rate = 1/t0.5
Rate = 1/20
Rate = 0.05

Therefore, the transformation rate is 0.05 s-1.

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How to Calculate and Solve for Particle Grain Growth | Phase Transformation

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The image above represents particle grain growth.

To compute for particle grain growth, four essential parameters are needed and these parameters are Temperature Constant (C), Activation Energy (Q), Boltzmann’s Constant (K) and Temperature (Kelvin) (T).

The formula for calculating particle grain growth:

G’ = C exp (-Q/KT)

Where:

G’ = Particle Grain Growth
Q = Activation Energy
C = Temperature Constant
K = Boltzmann’s Constant
T = Temperature

Let’s solve an example;
Find the particle grain growth when the activation energy is 4, the temperature constant is 8, the boltzmann’s constant is 1.380E-23 and the temperature is 10.

This implies that;

Q = Activation Energy = 4
C = Temperature Constant = 8
K = Boltzmann’s Constant = 1.380E-23
T = Temperature = 10

G’ = C exp (-Q/KT)
G’ = (8)exp(-(4)/(1.38064852e-23)(10))
G’ = (8)exp(-4/1.3806485199999997e-22)
G’ = (8)exp(-2.8971892136602593e+22)
G’ = (8)(0)
G’ = 0

Therefore, the particle grain growth is 0.

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How to Calculate and Solve for Avrami Equation | Phase Transformation

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The image above represents avrami equation.

To compute for avrami equation, three essential parameters are needed and these parameters are Time (t), Time Independent Constant for the Reaction (K) and Time Independent Constant for the Reaction (n).

The formula for calculating avrami equation:

y = 1 – exp(-Ktn)

Where:

y = Avrami Equation
K = Time Independent Constants for the Reaction
n = Time Independent Constants for the Reaction
t = Time

Let’s solve an example;
Find the avrami equation when the time independent constant for the reaction is 18, the time independent constant for the reaction is 10 and the time is 12.

This implies that;

K = Time Independent Constants for the Reaction = 18
n = Time Independent Constants for the Reaction = 10
t = Time = 12

y = 1 – exp(-Ktn)
y = 1 – exp(-(18)(12)10)
y = 1 – exp((-18)(61917364224))
y = 1 – exp(-1114512556032)
y = 1 – 0
y = 1

Therefore, the avrami equation is 1.

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