Critical radius of nucleus Calculator

Calculate Critical Radius









Formula

The formula to calculate the Critical Radius of a Nucleus is:

\[ \text{Critical Radius} = \frac{2 \cdot \text{Surface Free Energy} \cdot \text{Melting Temperature}}{\text{Latent Heat of Fusion} \cdot \text{Undercooling Value}} \]

Definition

The Critical Radius of a Nucleus is the minimum size of a stable nucleus formed during solidification. Surface Free Energy is the energy to create a solid–liquid phase boundary during solidification. The Melting Temperature is the temperature at which the metal or alloy melts. Latent Heat of Fusion is the heat liberated during solidification. The Undercooling Value is the difference between the melting temperature and the temperature under consideration (below melting temperature), also known as supercooling.

Example Calculation

Let's assume the following values:

Using the formula:

\[ \text{Critical Radius} = \frac{2 \cdot 0.2 \cdot 1000}{1200000000 \cdot 100} \approx 3.3333E-09 \, \text{meters} \]

The Critical Radius is approximately 3.3333E-09 meters.

Conversion Chart

Surface Free Energy (J/m²) Melting Temperature (K) Latent Heat of Fusion (J/m³) Undercooling Value (K) Critical Radius (m)
0.1 900 1100000000 90 0.000000001818182
0.1 900 1100000000 95 0.000000001722488
0.1 900 1100000000 100 0.000000001636364
0.1 900 1100000000 105 0.000000001558442
0.1 900 1100000000 110 0.000000001487603
0.1 900 1200000000 90 0.000000001666667
0.1 900 1200000000 95 0.000000001578947
0.1 900 1200000000 100 0.000000001500000
0.1 900 1200000000 105 0.000000001428571
0.1 900 1200000000 110 0.000000001363636
0.1 900 1300000000 90 0.000000001538462
0.1 900 1300000000 95 0.000000001457490
0.1 900 1300000000 100 0.000000001384615
0.1 900 1300000000 105 0.000000001318681
0.1 900 1300000000 110 0.000000001258741
0.1 950 1100000000 90 0.000000001919192
0.1 950 1100000000 95 0.000000001818182
0.1 950 1100000000 100 0.000000001727273
0.1 950 1100000000 105 0.000000001645022
0.1 950 1100000000 110 0.000000001570248
0.1 950 1200000000 90 0.000000001759259
0.1 950 1200000000 95 0.000000001666667
0.1 950 1200000000 100 0.000000001583333
0.1 950 1200000000 105 0.000000001507937
0.1 950 1200000000 110 0.000000001439394
0.1 950 1300000000 90 0.000000001623932
0.1 950 1300000000 95 0.000000001538462
0.1 950 1300000000 100 0.000000001461538
0.1 950 1300000000 105 0.000000001391941
0.1 950 1300000000 110 0.000000001328671
0.1 1000 1100000000 90 0.000000002020202
0.1 1000 1100000000 95 0.000000001913876
0.1 1000 1100000000 100 0.000000001818182
0.1 1000 1100000000 105 0.000000001731602
0.1 1000 1100000000 110 0.000000001652893
0.1 1000 1200000000 90 0.000000001851852
0.1 1000 1200000000 95 0.000000001754386
0.1 1000 1200000000 100 0.000000001666667
0.1 1000 1200000000 105 0.000000001587302
0.1 1000 1200000000 110 0.000000001515152
0.1 1000 1300000000 90 0.000000001709402
0.1 1000 1300000000 95 0.000000001619433
0.1 1000 1300000000 100 0.000000001538462
0.1 1000 1300000000 105 0.000000001465201
0.1 1000 1300000000 110 0.000000001398601
0.1 1050 1100000000 90 0.000000002121212
0.1 1050 1100000000 95 0.000000002009569
0.1 1050 1100000000 100 0.000000001909091
0.1 1050 1100000000 105 0.000000001818182
0.1 1050 1100000000 110 0.000000001735537
0.1 1050 1200000000 90 0.000000001944444
0.1 1050 1200000000 95 0.000000001842105
0.1 1050 1200000000 100 0.000000001750000
0.1 1050 1200000000 105 0.000000001666667
0.1 1050 1200000000 110 0.000000001590909
0.1 1050 1300000000 90 0.000000001794872
0.1 1050 1300000000 95 0.000000001700405
0.1 1050 1300000000 100 0.000000001615385
0.1 1050 1300000000 105 0.000000001538462
0.1 1050 1300000000 110 0.000000001468531
0.1 1100 1100000000 90 0.000000002222222
0.1 1100 1100000000 95 0.000000002105263
0.1 1100 1100000000 100 0.000000002000000
0.1 1100 1100000000 105 0.000000001904762
0.1 1100 1100000000 110 0.000000001818182
0.1 1100 1200000000 90 0.000000002037037
0.1 1100 1200000000 95 0.000000001929825
0.1 1100 1200000000 100 0.000000001833333
0.1 1100 1200000000 105 0.000000001746032
0.1 1100 1200000000 110 0.000000001666667
0.1 1100 1300000000 90 0.000000001880342
0.1 1100 1300000000 95 0.000000001781377
0.1 1100 1300000000 100 0.000000001692308
0.1 1100 1300000000 105 0.000000001611722
0.1 1100 1300000000 110 0.000000001538462
0.15 900 1100000000 90 0.000000002727273
0.15 900 1100000000 95 0.000000002583732
0.15 900 1100000000 100 0.000000002454545
0.15 900 1100000000 105 0.000000002337662
0.15 900 1100000000 110 0.000000002231405
0.15 900 1200000000 90 0.000000002500000
0.15 900 1200000000 95 0.000000002368421
0.15 900 1200000000 100 0.000000002250000
0.15 900 1200000000 105 0.000000002142857
0.15 900 1200000000 110 0.000000002045455
0.15 900 1300000000 90 0.000000002307692
0.15 900 1300000000 95 0.000000002186235
0.15 900 1300000000 100 0.000000002076923
0.15 900 1300000000 105 0.000000001978022
0.15 900 1300000000 110 0.000000001888112
0.15 950 1100000000 90 0.000000002878788
0.15 950 1100000000 95 0.000000002727273
0.15 950 1100000000 100 0.000000002590909
0.15 950 1100000000 105 0.000000002467532
0.15 950 1100000000 110 0.000000002355372
0.15 950 1200000000 90 0.000000002638889
0.15 950 1200000000 95 0.000000002500000
0.15 950 1200000000 100 0.000000002375000
0.15 950 1200000000 105 0.000000002261905
0.15 950 1200000000 110 0.000000002159091
0.15 950 1300000000 90 0.000000002435897
0.15 950 1300000000 95 0.000000002307692
0.15 950 1300000000 100 0.000000002192308
0.15 950 1300000000 105 0.000000002087912
0.15 950 1300000000 110 0.000000001993007
0.15 1000 1100000000 90 0.000000003030303
0.15 1000 1100000000 95 0.000000002870813
0.15 1000 1100000000 100 0.000000002727273
0.15 1000 1100000000 105 0.000000002597403
0.15 1000 1100000000 110 0.000000002479339
0.15 1000 1200000000 90 0.000000002777778
0.15 1000 1200000000 95 0.000000002631579
0.15 1000 1200000000 100 0.000000002500000
0.15 1000 1200000000 105 0.000000002380952
0.15 1000 1200000000 110 0.000000002272727
0.15 1000 1300000000 90 0.000000002564103
0.15 1000 1300000000 95 0.000000002429150
0.15 1000 1300000000 100 0.000000002307692
0.15 1000 1300000000 105 0.000000002197802
0.15 1000 1300000000 110 0.000000002097902
0.15 1050 1100000000 90 0.000000003181818
0.15 1050 1100000000 95 0.000000003014354
0.15 1050 1100000000 100 0.000000002863636
0.15 1050 1100000000 105 0.000000002727273
0.15 1050 1100000000 110 0.000000002603306
0.15 1050 1200000000 90 0.000000002916667
0.15 1050 1200000000 95 0.000000002763158
0.15 1050 1200000000 100 0.000000002625000
0.15 1050 1200000000 105 0.000000002500000
0.15 1050 1200000000 110 0.000000002386364
0.15 1050 1300000000 90 0.000000002692308
0.15 1050 1300000000 95 0.000000002550607
0.15 1050 1300000000 100 0.000000002423077
0.15 1050 1300000000 105 0.000000002307692
0.15 1050 1300000000 110 0.000000002202797
0.15 1100 1100000000 90 0.000000003333333
0.15 1100 1100000000 95 0.000000003157895
0.15 1100 1100000000 100 0.000000003000000
0.15 1100 1100000000 105 0.000000002857143
0.15 1100 1100000000 110 0.000000002727273
0.15 1100 1200000000 90 0.000000003055556
0.15 1100 1200000000 95 0.000000002894737
0.15 1100 1200000000 100 0.000000002750000
0.15 1100 1200000000 105 0.000000002619048
0.15 1100 1200000000 110 0.000000002500000
0.15 1100 1300000000 90 0.000000002820513
0.15 1100 1300000000 95 0.000000002672065
0.15 1100 1300000000 100 0.000000002538462
0.15 1100 1300000000 105 0.000000002417582
0.15 1100 1300000000 110 0.000000002307692
0.2 900 1100000000 90 0.000000003636364
0.2 900 1100000000 95 0.000000003444976
0.2 900 1100000000 100 0.000000003272727
0.2 900 1100000000 105 0.000000003116883
0.2 900 1100000000 110 0.000000002975207
0.2 900 1200000000 90 0.000000003333333
0.2 900 1200000000 95 0.000000003157895
0.2 900 1200000000 100 0.000000003000000
0.2 900 1200000000 105 0.000000002857143
0.2 900 1200000000 110 0.000000002727273
0.2 900 1300000000 90 0.000000003076923
0.2 900 1300000000 95 0.000000002914980
0.2 900 1300000000 100 0.000000002769231
0.2 900 1300000000 105 0.000000002637363
0.2 900 1300000000 110 0.000000002517483
0.2 950 1100000000 90 0.000000003838384
0.2 950 1100000000 95 0.000000003636364
0.2 950 1100000000 100 0.000000003454545
0.2 950 1100000000 105 0.000000003290043
0.2 950 1100000000 110 0.000000003140496
0.2 950 1200000000 90 0.000000003518519
0.2 950 1200000000 95 0.000000003333333
0.2 950 1200000000 100 0.000000003166667
0.2 950 1200000000 105 0.000000003015873
0.2 950 1200000000 110 0.000000002878788
0.2 950 1300000000 90 0.000000003247863
0.2 950 1300000000 95 0.000000003076923
0.2 950 1300000000 100 0.000000002923077
0.2 950 1300000000 105 0.000000002783883
0.2 950 1300000000 110 0.000000002657343
0.2 1000 1100000000 90 0.000000004040404
0.2 1000 1100000000 95 0.000000003827751
0.2 1000 1100000000 100 0.000000003636364
0.2 1000 1100000000 105 0.000000003463203
0.2 1000 1100000000 110 0.000000003305785
0.2 1000 1200000000 90 0.000000003703704
0.2 1000 1200000000 95 0.000000003508772
0.2 1000 1200000000 100 0.000000003333333
0.2 1000 1200000000 105 0.000000003174603
0.2 1000 1200000000 110 0.000000003030303
0.2 1000 1300000000 90 0.000000003418803
0.2 1000 1300000000 95 0.000000003238866
0.2 1000 1300000000 100 0.000000003076923
0.2 1000 1300000000 105 0.000000002930403
0.2 1000 1300000000 110 0.000000002797203
0.2 1050 1100000000 90 0.000000004242424
0.2 1050 1100000000 95 0.000000004019139
0.2 1050 1100000000 100 0.000000003818182
0.2 1050 1100000000 105 0.000000003636364
0.2 1050 1100000000 110 0.000000003471074
0.2 1050 1200000000 90 0.000000003888889
0.2 1050 1200000000 95 0.000000003684211
0.2 1050 1200000000 100 0.000000003500000
0.2 1050 1200000000 105 0.000000003333333
0.2 1050 1200000000 110 0.000000003181818
0.2 1050 1300000000 90 0.000000003589744
0.2 1050 1300000000 95 0.000000003400810
0.2 1050 1300000000 100 0.000000003230769
0.2 1050 1300000000 105 0.000000003076923
0.2 1050 1300000000 110 0.000000002937063
0.2 1100 1100000000 90 0.000000004444444
0.2 1100 1100000000 95 0.000000004210526
0.2 1100 1100000000 100 0.000000004000000
0.2 1100 1100000000 105 0.000000003809524
0.2 1100 1100000000 110 0.000000003636364
0.2 1100 1200000000 90 0.000000004074074
0.2 1100 1200000000 95 0.000000003859649
0.2 1100 1200000000 100 0.000000003666667
0.2 1100 1200000000 105 0.000000003492063
0.2 1100 1200000000 110 0.000000003333333
0.2 1100 1300000000 90 0.000000003760684
0.2 1100 1300000000 95 0.000000003562753
0.2 1100 1300000000 100 0.000000003384615
0.2 1100 1300000000 105 0.000000003223443
0.2 1100 1300000000 110 0.000000003076923
0.25 900 1100000000 90 0.000000004545455
0.25 900 1100000000 95 0.000000004306220
0.25 900 1100000000 100 0.000000004090909
0.25 900 1100000000 105 0.000000003896104
0.25 900 1100000000 110 0.000000003719008
0.25 900 1200000000 90 0.000000004166667
0.25 900 1200000000 95 0.000000003947368
0.25 900 1200000000 100 0.000000003750000
0.25 900 1200000000 105 0.000000003571429
0.25 900 1200000000 110 0.000000003409091
0.25 900 1300000000 90 0.000000003846154
0.25 900 1300000000 95 0.000000003643725
0.25 900 1300000000 100 0.000000003461538
0.25 900 1300000000 105 0.000000003296703
0.25 900 1300000000 110 0.000000003146853
0.25 950 1100000000 90 0.000000004797980
0.25 950 1100000000 95 0.000000004545455
0.25 950 1100000000 100 0.000000004318182
0.25 950 1100000000 105 0.000000004112554
0.25 950 1100000000 110 0.000000003925620
0.25 950 1200000000 90 0.000000004398148
0.25 950 1200000000 95 0.000000004166667
0.25 950 1200000000 100 0.000000003958333
0.25 950 1200000000 105 0.000000003769841
0.25 950 1200000000 110 0.000000003598485
0.25 950 1300000000 90 0.000000004059829
0.25 950 1300000000 95 0.000000003846154
0.25 950 1300000000 100 0.000000003653846
0.25 950 1300000000 105 0.000000003479853
0.25 950 1300000000 110 0.000000003321678
0.25 1000 1100000000 90 0.000000005050505
0.25 1000 1100000000 95 0.000000004784689
0.25 1000 1100000000 100 0.000000004545455
0.25 1000 1100000000 105 0.000000004329004
0.25 1000 1100000000 110 0.000000004132231
0.25 1000 1200000000 90 0.000000004629630
0.25 1000 1200000000 95 0.000000004385965
0.25 1000 1200000000 100 0.000000004166667
0.25 1000 1200000000 105 0.000000003968254
0.25 1000 1200000000 110 0.000000003787879
0.25 1000 1300000000 90 0.000000004273504
0.25 1000 1300000000 95 0.000000004048583
0.25 1000 1300000000 100 0.000000003846154
0.25 1000 1300000000 105 0.000000003663004
0.25 1000 1300000000 110 0.000000003496503
0.25 1050 1100000000 90 0.000000005303030
0.25 1050 1100000000 95 0.000000005023923
0.25 1050 1100000000 100 0.000000004772727
0.25 1050 1100000000 105 0.000000004545455
0.25 1050 1100000000 110 0.000000004338843
0.25 1050 1200000000 90 0.000000004861111
0.25 1050 1200000000 95 0.000000004605263
0.25 1050 1200000000 100 0.000000004375000
0.25 1050 1200000000 105 0.000000004166667
0.25 1050 1200000000 110 0.000000003977273
0.25 1050 1300000000 90 0.000000004487179
0.25 1050 1300000000 95 0.000000004251012
0.25 1050 1300000000 100 0.000000004038462
0.25 1050 1300000000 105 0.000000003846154
0.25 1050 1300000000 110 0.000000003671329
0.25 1100 1100000000 90 0.000000005555556
0.25 1100 1100000000 95 0.000000005263158
0.25 1100 1100000000 100 0.000000005000000
0.25 1100 1100000000 105 0.000000004761905
0.25 1100 1100000000 110 0.000000004545455
0.25 1100 1200000000 90 0.000000005092593
0.25 1100 1200000000 95 0.000000004824561
0.25 1100 1200000000 100 0.000000004583333
0.25 1100 1200000000 105 0.000000004365079
0.25 1100 1200000000 110 0.000000004166667
0.25 1100 1300000000 90 0.000000004700855
0.25 1100 1300000000 95 0.000000004453441
0.25 1100 1300000000 100 0.000000004230769
0.25 1100 1300000000 105 0.000000004029304
0.25 1100 1300000000 110 0.000000003846154
0.3 900 1100000000 90 0.000000005454545
0.3 900 1100000000 95 0.000000005167464
0.3 900 1100000000 100 0.000000004909091
0.3 900 1100000000 105 0.000000004675325
0.3 900 1100000000 110 0.000000004462810
0.3 900 1200000000 90 0.000000005000000
0.3 900 1200000000 95 0.000000004736842
0.3 900 1200000000 100 0.000000004500000
0.3 900 1200000000 105 0.000000004285714
0.3 900 1200000000 110 0.000000004090909
0.3 900 1300000000 90 0.000000004615385
0.3 900 1300000000 95 0.000000004372470
0.3 900 1300000000 100 0.000000004153846
0.3 900 1300000000 105 0.000000003956044
0.3 900 1300000000 110 0.000000003776224
0.3 950 1100000000 90 0.000000005757576
0.3 950 1100000000 95 0.000000005454545
0.3 950 1100000000 100 0.000000005181818
0.3 950 1100000000 105 0.000000004935065
0.3 950 1100000000 110 0.000000004710744
0.3 950 1200000000 90 0.000000005277778
0.3 950 1200000000 95 0.000000005000000
0.3 950 1200000000 100 0.000000004750000
0.3 950 1200000000 105 0.000000004523810
0.3 950 1200000000 110 0.000000004318182
0.3 950 1300000000 90 0.000000004871795
0.3 950 1300000000 95 0.000000004615385
0.3 950 1300000000 100 0.000000004384615
0.3 950 1300000000 105 0.000000004175824
0.3 950 1300000000 110 0.000000003986014
0.3 1000 1100000000 90 0.000000006060606
0.3 1000 1100000000 95 0.000000005741627
0.3 1000 1100000000 100 0.000000005454545
0.3 1000 1100000000 105 0.000000005194805
0.3 1000 1100000000 110 0.000000004958678
0.3 1000 1200000000 90 0.000000005555556
0.3 1000 1200000000 95 0.000000005263158
0.3 1000 1200000000 100 0.000000005000000
0.3 1000 1200000000 105 0.000000004761905
0.3 1000 1200000000 110 0.000000004545455
0.3 1000 1300000000 90 0.000000005128205
0.3 1000 1300000000 95 0.000000004858300
0.3 1000 1300000000 100 0.000000004615385
0.3 1000 1300000000 105 0.000000004395604
0.3 1000 1300000000 110 0.000000004195804
0.3 1050 1100000000 90 0.000000006363636
0.3 1050 1100000000 95 0.000000006028708
0.3 1050 1100000000 100 0.000000005727273
0.3 1050 1100000000 105 0.000000005454545
0.3 1050 1100000000 110 0.000000005206612
0.3 1050 1200000000 90 0.000000005833333
0.3 1050 1200000000 95 0.000000005526316
0.3 1050 1200000000 100 0.000000005250000
0.3 1050 1200000000 105 0.000000005000000
0.3 1050 1200000000 110 0.000000004772727
0.3 1050 1300000000 90 0.000000005384615
0.3 1050 1300000000 95 0.000000005101215
0.3 1050 1300000000 100 0.000000004846154
0.3 1050 1300000000 105 0.000000004615385
0.3 1050 1300000000 110 0.000000004405594
0.3 1100 1100000000 90 0.000000006666667
0.3 1100 1100000000 95 0.000000006315789
0.3 1100 1100000000 100 0.000000006000000
0.3 1100 1100000000 105 0.000000005714286
0.3 1100 1100000000 110 0.000000005454545
0.3 1100 1200000000 90 0.000000006111111
0.3 1100 1200000000 95 0.000000005789474
0.3 1100 1200000000 100 0.000000005500000
0.3 1100 1200000000 105 0.000000005238095
0.3 1100 1200000000 110 0.000000005000000
0.3 1100 1300000000 90 0.000000005641026
0.3 1100 1300000000 95 0.000000005344130
0.3 1100 1300000000 100 0.000000005076923
0.3 1100 1300000000 105 0.000000004835165
0.3 1100 1300000000 110 0.000000004615385
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