The main reason for the longevity of the Classical Nucleation Theory (CNT) is its firm thermodynamic basis; reviewing the discussion about the molecular-scale mechanism of crystal nucleation from solutions, and especially the mechanism of protein crystal nucleation, we note that the diverse nucleation pathways across the metastable phase cannot contradict the thermodynamic conclusions of the CNT. In this review paper, revisiting the basic postulates of CNT, we argue that not only the energy barrier for crystal nucleation but the entire dependence of Gibbs’ thermodynamic potential on the crystal size is worth interpreting. In doing so, two supplementations to CNT have been elaborated. The first one concerns the theoretical method employing Equilibration between the Bond energy (i.e., the intra-crystalline cohesive energy which maintains the integrity of a crystalline cluster), and the surface Destructive Energy (tending to tear-up the crystal) - abbreviated EBDE. Second, we show that the dependence of the Gibbs’ thermodynamic potential on the crystal size determines not only the birth, but also the initial growth (or dissolution during Ostwald ripening) of the just born nuclei of the new phase; this is predicted in the negative branch of the said dependence. Initially, EBDE was used for explaining crystal nucleation from solutions, but most recently, this method was redefined for considering crystal nucleation in melts. The purposively redefined EBDE was applied for considering ice nucleation, which is an important case of spontaneous melt crystallization in nature - the quantitative consideration of the ice crystal nucleation is needed for better understanding of atmospheric processes, such as snowfall, white frost, sleet, hail, and ice fog. By focusing on the action of ice nucleating particles (INPs), which engender heterogeneous nucleation of ice, the snowfall is elucidated in a new way - ice nucleation in the atmosphere is considered as a two-step process, the first one being vapor condensation in liquid droplets, and the second one - water freezing. Also, ice nucleation in frozen foods is re-considered applying EBDE. (It is known that freezing ensures a high-quality product and long shelf life of a wide range of food products, such as fish, meat, vegetables, tropical fruits, coffee, flavor essence, etc.) And because numbers and sizes of ice crystals are decisive for the degree of deterioration of food quality due to freezing, the mean sizes of the ice crystals (which depend on their number) are considered in a quantitative manner. Also, another consideration concerns ice crystal nucleation and growth occurring by freeze concentration of liquid foods. Although aimed at reviewing fundamental aspects of crystal nucleation, it is to be hoped that some results of the considerations in this paper may also be beneficial for practical applications; suggestions in this respect are mentioned throughout the paper. For instance, the direct comparison between ice crystal nucleation in pure water and in frozen foods suggests how the dynamic food freezing step may be optimized, etc. The review ends with a short paragraph presenting the advantages and disadvantages of CNT.

经典成核理论 (CNT) 得以长久存在的主要原因是其坚实的热力学基础；回顾关于溶液中晶体成核的分子尺度机制的讨论，特别是蛋白质晶体成核的机制，我们注意到跨亚稳相的不同成核途径与 CNT 的热力学结论不矛盾。在这篇综述文章中，重新审视了 CNT 的基本假设，我们认为不仅晶体成核的能垒，而且吉布斯热力学势对晶体尺寸的整个依赖性都值得解释。在此过程中，已详细阐述了对 CNT 的两个补充。第一个涉及采用键能之间平衡的理论方法（即，保持晶体簇完整性的晶体内聚能）和表面破坏能（倾向于撕裂晶体） - 缩写为 EBDE。其次，我们表明吉布斯热力学势对晶体尺寸的依赖性不仅决定了新相刚出生的核的诞生，还决定了其初始生长（或奥斯特瓦尔德成熟期间的溶解）；这是在所述依赖的负分支中预测的。最初，EBDE 用于解释溶液中的晶体成核，但最近，这种方法被重新定义为考虑熔体中的晶体成核。有目的地重新定义的 EBDE 用于考虑冰核，这是自然界中自发熔融结晶的一个重要案例——为了更好地理解降雪、白霜、雨夹雪、冰雹和冰雾等大气过程，需要对冰晶成核进行定量考虑。通过关注引起冰异质成核的冰成核粒子 (INP) 的作用，以一种新的方式解释降雪 - 大气中的冰成核被认为是一个两步过程，第一个过程是水汽凝结液滴，第二个——水结冰。此外，冷冻食品中的冰核也被重新考虑应用 EBDE。（众所周知，冷冻可确保鱼、肉、蔬菜、热带水果、咖啡、香精等多种食品的高品质产品和较长的保质期。) 并且由于冰晶的数量和大小对于冷冻导致的食品质量恶化程度具有决定性意义，因此以定量的方式考虑冰晶的平均大小（取决于它们的数量）。此外，另一个考虑因素涉及由液态食品的冷冻浓缩引起的冰晶成核和生长。尽管旨在回顾晶体成核的基本方面，但希望本文考虑的一些结果也可能对实际应用有益；整篇论文都提到了这方面的建议。例如，纯水和冷冻食品中冰晶成核的直接比较表明如何优化动态食品冷冻步骤等。