Kaptay George
Institute of Physical Metallurgy, Metal Forming and Nanotechnology, University of Miskolc, 3515 Miskolc, Hungary.
HUN-REN-ME Materials Science Research Group, University of Miskolc, 3515 Miskolc, Hungary.
Materials (Basel). 2024 Dec 10;17(24):6048. doi: 10.3390/ma17246048.
The phase rule of Gibbs is one of the basic equations in phase equilibria. Although it has been with us for 150 years, discussions, interpretations and extensions have been published. Here, the following new content is provided: (i). the choice of independent components is discussed, and the component rule is introduced, (ii). independent state variables are divided into compositional and non-compositional ones, (iii). the generalized phase rule is derived replacing number two in the original phase rule by the number of independent non-compositional state variables introduced above, (iv). the degree of freedom is decreased by the number of compositional constraints in special points (azeotrope and congruent melting) of phase diagrams, (v). a rule is derived connecting the maximum number of coexisting phases with the dimensions of the phase diagram, (vi). examples show how to apply the phase rule to unary, binary and ternary phase diagrams and their sections, (vii). the same is extended with the discussion of calculable and not calculable phase fractions, (viii). it is shown that the current definition of the degree of freedom is not sufficient in the number of cases, (ix). the current definition of the degree of freedom is extended, (x). the application of the generalized phase rule is demonstrated when other non-compositional state variables are applied for nano-phase diagrams, and/or for phase diagrams under the influence of electric potential difference, external magnetic field, mechanical strain or the gravitational field.
吉布斯相律是相平衡中的基本方程之一。尽管它已问世150年，但相关的讨论、解释和扩展仍不断涌现。本文提供了以下新内容：(i). 讨论了独立组分的选择，并引入了组分规则；(ii). 将独立状态变量分为组成型和非组成型；(iii). 推导了广义相律，即将原始相律中的数字2替换为上述引入的独立非组成型状态变量的数量；(iv). 在相图的特殊点（共沸物和一致熔融）处，自由度因组成约束的数量而降低；(v). 推导了一条将共存相的最大数量与相图维度联系起来的规则；(vi). 通过示例展示了如何将相律应用于一元、二元和三元相图及其截面；(vii). 对可计算和不可计算的相分数的讨论进行了扩展；(viii). 表明在许多情况下，当前自由度的定义并不充分；(ix). 扩展了当前自由度的定义；(x). 展示了在纳米相图和/或受电势差、外部磁场、机械应变或引力场影响的相图中应用其他非组成型状态变量时广义相律的应用。
