Critical Free Energy for Nucleation Calculator

Calculate Critical Free Energy









Formula

The formula to calculate the critical free energy for nucleation is:

\[ \Delta G = \frac{16 \pi \gamma^3 T_m^2}{3 \Delta H_f^2 \Delta T^2} \]

Where:

Definition

Critical free energy is the energy required for the formation of stable nuclei during the phase transition.

Surface free energy is the energy required to create a solid–liquid phase boundary during solidification.

Melting temperature is the temperature at which a metal or alloy transitions from solid to liquid.

Latent heat of fusion is the heat released during solidification, measured in Joules per cubic meter.

Undercooling value is the difference between the melting temperature and the temperature under consideration, also known as supercooling.

Example Calculation

Let's assume the following values:

Using the formula:

\[ \Delta G = \frac{16 \pi (0.2)^3 (1000)^2}{3 (1,200,000,000)^2 (100)^2} \approx 9.30842267730309 \times 10^{-18} \, \text{J} \]

The critical free energy is approximately \(9.30842267730309 \times 10^{-18}\) Joules.

Conversion Chart

Surface Free Energy (J/m²) Melting Temperature (K) Latent Heat of Fusion (J/m³) Undercooling Value (K) Critical Free Energy (J)
0.1 900 1000000000 50 0.000000000000000005
0.1 900 1000000000 100 0.000000000000000001
0.1 900 1000000000 150 0.000000000000000001
0.1 900 1100000000 50 0.000000000000000004
0.1 900 1100000000 100 0.000000000000000001
0.1 900 1100000000 150 0.000000000000000000
0.1 900 1200000000 50 0.000000000000000004
0.1 900 1200000000 100 0.000000000000000001
0.1 900 1200000000 150 0.000000000000000000
0.1 900 1300000000 50 0.000000000000000003
0.1 900 1300000000 100 0.000000000000000001
0.1 900 1300000000 150 0.000000000000000000
0.1 900 1400000000 50 0.000000000000000003
0.1 900 1400000000 100 0.000000000000000001
0.1 900 1400000000 150 0.000000000000000000
0.1 900 1500000000 50 0.000000000000000002
0.1 900 1500000000 100 0.000000000000000001
0.1 900 1500000000 150 0.000000000000000000
0.1 1000 1000000000 50 0.000000000000000007
0.1 1000 1000000000 100 0.000000000000000002
0.1 1000 1000000000 150 0.000000000000000001
0.1 1000 1100000000 50 0.000000000000000006
0.1 1000 1100000000 100 0.000000000000000001
0.1 1000 1100000000 150 0.000000000000000001
0.1 1000 1200000000 50 0.000000000000000005
0.1 1000 1200000000 100 0.000000000000000001
0.1 1000 1200000000 150 0.000000000000000001
0.1 1000 1300000000 50 0.000000000000000004
0.1 1000 1300000000 100 0.000000000000000001
0.1 1000 1300000000 150 0.000000000000000000
0.1 1000 1400000000 50 0.000000000000000003
0.1 1000 1400000000 100 0.000000000000000001
0.1 1000 1400000000 150 0.000000000000000000
0.1 1000 1500000000 50 0.000000000000000003
0.1 1000 1500000000 100 0.000000000000000001
0.1 1000 1500000000 150 0.000000000000000000
0.1 1100 1000000000 50 0.000000000000000008
0.1 1100 1000000000 100 0.000000000000000002
0.1 1100 1000000000 150 0.000000000000000001
0.1 1100 1100000000 50 0.000000000000000007
0.1 1100 1100000000 100 0.000000000000000002
0.1 1100 1100000000 150 0.000000000000000001
0.1 1100 1200000000 50 0.000000000000000006
0.1 1100 1200000000 100 0.000000000000000001
0.1 1100 1200000000 150 0.000000000000000001
0.1 1100 1300000000 50 0.000000000000000005
0.1 1100 1300000000 100 0.000000000000000001
0.1 1100 1300000000 150 0.000000000000000001
0.1 1100 1400000000 50 0.000000000000000004
0.1 1100 1400000000 100 0.000000000000000001
0.1 1100 1400000000 150 0.000000000000000000
0.1 1100 1500000000 50 0.000000000000000004
0.1 1100 1500000000 100 0.000000000000000001
0.1 1100 1500000000 150 0.000000000000000000
0.2 900 1000000000 50 0.000000000000000043
0.2 900 1000000000 100 0.000000000000000011
0.2 900 1000000000 150 0.000000000000000005
0.2 900 1100000000 50 0.000000000000000036
0.2 900 1100000000 100 0.000000000000000009
0.2 900 1100000000 150 0.000000000000000004
0.2 900 1200000000 50 0.000000000000000030
0.2 900 1200000000 100 0.000000000000000008
0.2 900 1200000000 150 0.000000000000000003
0.2 900 1300000000 50 0.000000000000000026
0.2 900 1300000000 100 0.000000000000000006
0.2 900 1300000000 150 0.000000000000000003
0.2 900 1400000000 50 0.000000000000000022
0.2 900 1400000000 100 0.000000000000000006
0.2 900 1400000000 150 0.000000000000000002
0.2 900 1500000000 50 0.000000000000000019
0.2 900 1500000000 100 0.000000000000000005
0.2 900 1500000000 150 0.000000000000000002
0.2 1000 1000000000 50 0.000000000000000054
0.2 1000 1000000000 100 0.000000000000000013
0.2 1000 1000000000 150 0.000000000000000006
0.2 1000 1100000000 50 0.000000000000000044
0.2 1000 1100000000 100 0.000000000000000011
0.2 1000 1100000000 150 0.000000000000000005
0.2 1000 1200000000 50 0.000000000000000037
0.2 1000 1200000000 100 0.000000000000000009
0.2 1000 1200000000 150 0.000000000000000004
0.2 1000 1300000000 50 0.000000000000000032
0.2 1000 1300000000 100 0.000000000000000008
0.2 1000 1300000000 150 0.000000000000000004
0.2 1000 1400000000 50 0.000000000000000027
0.2 1000 1400000000 100 0.000000000000000007
0.2 1000 1400000000 150 0.000000000000000003
0.2 1000 1500000000 50 0.000000000000000024
0.2 1000 1500000000 100 0.000000000000000006
0.2 1000 1500000000 150 0.000000000000000003
0.2 1100 1000000000 50 0.000000000000000065
0.2 1100 1000000000 100 0.000000000000000016
0.2 1100 1000000000 150 0.000000000000000007
0.2 1100 1100000000 50 0.000000000000000054
0.2 1100 1100000000 100 0.000000000000000013
0.2 1100 1100000000 150 0.000000000000000006
0.2 1100 1200000000 50 0.000000000000000045
0.2 1100 1200000000 100 0.000000000000000011
0.2 1100 1200000000 150 0.000000000000000005
0.2 1100 1300000000 50 0.000000000000000038
0.2 1100 1300000000 100 0.000000000000000010
0.2 1100 1300000000 150 0.000000000000000004
0.2 1100 1400000000 50 0.000000000000000033
0.2 1100 1400000000 100 0.000000000000000008
0.2 1100 1400000000 150 0.000000000000000004
0.2 1100 1500000000 50 0.000000000000000029
0.2 1100 1500000000 100 0.000000000000000007
0.2 1100 1500000000 150 0.000000000000000003
0.3 900 1000000000 50 0.000000000000000147
0.3 900 1000000000 100 0.000000000000000037
0.3 900 1000000000 150 0.000000000000000016
0.3 900 1100000000 50 0.000000000000000121
0.3 900 1100000000 100 0.000000000000000030
0.3 900 1100000000 150 0.000000000000000013
0.3 900 1200000000 50 0.000000000000000102
0.3 900 1200000000 100 0.000000000000000025
0.3 900 1200000000 150 0.000000000000000011
0.3 900 1300000000 50 0.000000000000000087
0.3 900 1300000000 100 0.000000000000000022
0.3 900 1300000000 150 0.000000000000000010
0.3 900 1400000000 50 0.000000000000000075
0.3 900 1400000000 100 0.000000000000000019
0.3 900 1400000000 150 0.000000000000000008
0.3 900 1500000000 50 0.000000000000000065
0.3 900 1500000000 100 0.000000000000000016
0.3 900 1500000000 150 0.000000000000000007
0.3 1000 1000000000 50 0.000000000000000181
0.3 1000 1000000000 100 0.000000000000000045
0.3 1000 1000000000 150 0.000000000000000020
0.3 1000 1100000000 50 0.000000000000000150
0.3 1000 1100000000 100 0.000000000000000037
0.3 1000 1100000000 150 0.000000000000000017
0.3 1000 1200000000 50 0.000000000000000126
0.3 1000 1200000000 100 0.000000000000000031
0.3 1000 1200000000 150 0.000000000000000014
0.3 1000 1300000000 50 0.000000000000000107
0.3 1000 1300000000 100 0.000000000000000027
0.3 1000 1300000000 150 0.000000000000000012
0.3 1000 1400000000 50 0.000000000000000092
0.3 1000 1400000000 100 0.000000000000000023
0.3 1000 1400000000 150 0.000000000000000010
0.3 1000 1500000000 50 0.000000000000000080
0.3 1000 1500000000 100 0.000000000000000020
0.3 1000 1500000000 150 0.000000000000000009
0.3 1100 1000000000 50 0.000000000000000219
0.3 1100 1000000000 100 0.000000000000000055
0.3 1100 1000000000 150 0.000000000000000024
0.3 1100 1100000000 50 0.000000000000000181
0.3 1100 1100000000 100 0.000000000000000045
0.3 1100 1100000000 150 0.000000000000000020
0.3 1100 1200000000 50 0.000000000000000152
0.3 1100 1200000000 100 0.000000000000000038
0.3 1100 1200000000 150 0.000000000000000017
0.3 1100 1300000000 50 0.000000000000000130
0.3 1100 1300000000 100 0.000000000000000032
0.3 1100 1300000000 150 0.000000000000000014
0.3 1100 1400000000 50 0.000000000000000112
0.3 1100 1400000000 100 0.000000000000000028
0.3 1100 1400000000 150 0.000000000000000012
0.3 1100 1500000000 50 0.000000000000000097
0.3 1100 1500000000 100 0.000000000000000024
0.3 1100 1500000000 150 0.000000000000000011
0.4 900 1000000000 50 0.000000000000000347
0.4 900 1000000000 100 0.000000000000000087
0.4 900 1000000000 150 0.000000000000000039
0.4 900 1100000000 50 0.000000000000000287
0.4 900 1100000000 100 0.000000000000000072
0.4 900 1100000000 150 0.000000000000000032
0.4 900 1200000000 50 0.000000000000000241
0.4 900 1200000000 100 0.000000000000000060
0.4 900 1200000000 150 0.000000000000000027
0.4 900 1300000000 50 0.000000000000000206
0.4 900 1300000000 100 0.000000000000000051
0.4 900 1300000000 150 0.000000000000000023
0.4 900 1400000000 50 0.000000000000000177
0.4 900 1400000000 100 0.000000000000000044
0.4 900 1400000000 150 0.000000000000000020
0.4 900 1500000000 50 0.000000000000000154
0.4 900 1500000000 100 0.000000000000000039
0.4 900 1500000000 150 0.000000000000000017
0.4 1000 1000000000 50 0.000000000000000429
0.4 1000 1000000000 100 0.000000000000000107
0.4 1000 1000000000 150 0.000000000000000048
0.4 1000 1100000000 50 0.000000000000000354
0.4 1000 1100000000 100 0.000000000000000089
0.4 1000 1100000000 150 0.000000000000000039
0.4 1000 1200000000 50 0.000000000000000298
0.4 1000 1200000000 100 0.000000000000000074
0.4 1000 1200000000 150 0.000000000000000033
0.4 1000 1300000000 50 0.000000000000000254
0.4 1000 1300000000 100 0.000000000000000063
0.4 1000 1300000000 150 0.000000000000000028
0.4 1000 1400000000 50 0.000000000000000219
0.4 1000 1400000000 100 0.000000000000000055
0.4 1000 1400000000 150 0.000000000000000024
0.4 1000 1500000000 50 0.000000000000000191
0.4 1000 1500000000 100 0.000000000000000048
0.4 1000 1500000000 150 0.000000000000000021
0.4 1100 1000000000 50 0.000000000000000519
0.4 1100 1000000000 100 0.000000000000000130
0.4 1100 1000000000 150 0.000000000000000058
0.4 1100 1100000000 50 0.000000000000000429
0.4 1100 1100000000 100 0.000000000000000107
0.4 1100 1100000000 150 0.000000000000000048
0.4 1100 1200000000 50 0.000000000000000360
0.4 1100 1200000000 100 0.000000000000000090
0.4 1100 1200000000 150 0.000000000000000040
0.4 1100 1300000000 50 0.000000000000000307
0.4 1100 1300000000 100 0.000000000000000077
0.4 1100 1300000000 150 0.000000000000000034
0.4 1100 1400000000 50 0.000000000000000265
0.4 1100 1400000000 100 0.000000000000000066
0.4 1100 1400000000 150 0.000000000000000029
0.4 1100 1500000000 50 0.000000000000000231
0.4 1100 1500000000 100 0.000000000000000058
0.4 1100 1500000000 150 0.000000000000000026
0.5 900 1000000000 50 0.000000000000000679
0.5 900 1000000000 100 0.000000000000000170
0.5 900 1000000000 150 0.000000000000000075
0.5 900 1100000000 50 0.000000000000000561
0.5 900 1100000000 100 0.000000000000000140
0.5 900 1100000000 150 0.000000000000000062
0.5 900 1200000000 50 0.000000000000000471
0.5 900 1200000000 100 0.000000000000000118
0.5 900 1200000000 150 0.000000000000000052
0.5 900 1300000000 50 0.000000000000000402
0.5 900 1300000000 100 0.000000000000000100
0.5 900 1300000000 150 0.000000000000000045
0.5 900 1400000000 50 0.000000000000000346
0.5 900 1400000000 100 0.000000000000000087
0.5 900 1400000000 150 0.000000000000000038
0.5 900 1500000000 50 0.000000000000000302
0.5 900 1500000000 100 0.000000000000000075
0.5 900 1500000000 150 0.000000000000000034
0.5 1000 1000000000 50 0.000000000000000838
0.5 1000 1000000000 100 0.000000000000000209
0.5 1000 1000000000 150 0.000000000000000093
0.5 1000 1100000000 50 0.000000000000000692
0.5 1000 1100000000 100 0.000000000000000173
0.5 1000 1100000000 150 0.000000000000000077
0.5 1000 1200000000 50 0.000000000000000582
0.5 1000 1200000000 100 0.000000000000000145
0.5 1000 1200000000 150 0.000000000000000065
0.5 1000 1300000000 50 0.000000000000000496
0.5 1000 1300000000 100 0.000000000000000124
0.5 1000 1300000000 150 0.000000000000000055
0.5 1000 1400000000 50 0.000000000000000427
0.5 1000 1400000000 100 0.000000000000000107
0.5 1000 1400000000 150 0.000000000000000047
0.5 1000 1500000000 50 0.000000000000000372
0.5 1000 1500000000 100 0.000000000000000093
0.5 1000 1500000000 150 0.000000000000000041
0.5 1100 1000000000 50 0.000000000000001014
0.5 1100 1000000000 100 0.000000000000000253
0.5 1100 1000000000 150 0.000000000000000113
0.5 1100 1100000000 50 0.000000000000000838
0.5 1100 1100000000 100 0.000000000000000209
0.5 1100 1100000000 150 0.000000000000000093
0.5 1100 1200000000 50 0.000000000000000704
0.5 1100 1200000000 100 0.000000000000000176
0.5 1100 1200000000 150 0.000000000000000078
0.5 1100 1300000000 50 0.000000000000000600
0.5 1100 1300000000 100 0.000000000000000150
0.5 1100 1300000000 150 0.000000000000000067
0.5 1100 1400000000 50 0.000000000000000517
0.5 1100 1400000000 100 0.000000000000000129
0.5 1100 1400000000 150 0.000000000000000057
0.5 1100 1500000000 50 0.000000000000000451
0.5 1100 1500000000 100 0.000000000000000113
0.5 1100 1500000000 150 0.000000000000000050
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