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A2—Nucleation and nuclei growth (Avrami Eq. 1)
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\( 2(1 - \alpha )[ - \ln (1 - \alpha )]^{1/2} \)
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\( [ - \ln (1 - \alpha )]^{1/2} \)
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A3—Nucleation and nuclei growth (Avrami Eq. 2)
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\( 3(1 - \alpha )[ - \ln (1 - \alpha )]^{3/2} \)
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\( [ - \ln (1 - \alpha )]^{1/3} \)
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A4—Nucleation and nuclei growth (Avrami Eq. 3)
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\( 4(1 - \alpha )[ - \ln (1 - \alpha )]^{3/4} \)
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\( [ - \ln (1 - \alpha )]^{1/4} \)
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R2—Phase boundary controlled reaction (contracting area)
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\( 2(1 - \alpha )^{1/2} \)
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\( [1 - (1 - \alpha )]^{1/2} \)
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R3—Phase boundary controlled reaction (contracting volume)
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\( 3(1 - \alpha )^{2/3} \)
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\( [1 - (1 - \alpha )]^{1/3} \)
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D1—One-dimensional diffusion
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\( (1/2)\alpha \)
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\( \alpha^{2} \)
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D2—Two-dimensional diffusion (Valensi equation)
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\( [ - \ln (1 - \alpha )]^{ - 1} \)
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\( (1 - \alpha )\ln (1 - \alpha ) + \alpha \)
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D3—Three-dimensional diffusion (Jander equation)
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\( (3/2)[1 - (1 - \alpha )^{1/3} ]^{ - 1} (1 - \alpha )^{2/3} \)
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\( [1 - (1 - \alpha )^{1/3} ]^{2} \)
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D4—Three-dimensional diffusion (Ginstling–Brounshtein equation)
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\( (3/2)[1 - (1 - \alpha )^{1/3} ]^{ - 1} \)
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\( [1 - (2/3)\alpha )] - (1 - \alpha )^{2/3} \)
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F1—Random nucleation with one nucleus on the individual particle
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\( 1 - \alpha \)
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\( - \ln (1 - \alpha ) \)
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F2—Random nucleation with two nuclei on the individual particle
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\( (1 - \alpha )^{2} \)
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\( 1/(1 - \alpha ) \)
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F3—Random nucleation with three nuclei on the individual particle
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\( (1/2)(1 - \alpha )^{3} \)
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\( 1/(1 - \alpha )^{2} \)
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P1—Mampel power law \( \left( {n \, = \,{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-0pt} \!\lower0.7ex\hbox{$2$}}} \right) \)
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\( 2\alpha^{1/2} \)
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\( \alpha^{1/2} \)
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P2—Mampel power law \( \left( {n \, = \,{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 3}}\right.\kern-0pt} \!\lower0.7ex\hbox{$3$}}} \right) \)
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\( 3\alpha^{2/3} \)
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\( \alpha^{1/3} \)
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P3—Mampel power law \( \left( {n \, = \,{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 4}}\right.\kern-0pt} \!\lower0.7ex\hbox{$4$}}} \right) \)
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\( 4\alpha^{3/4} \)
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\( \alpha^{1/4} \)
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