Water expands upon freezing. What happens when water is cooled below 0 °C in an undeformable, constant-volume container? This is a fundamental question in materials thermodynamics, and is also relevant in biological, geological, and technological applications in which ice forms under nano-, meso-, or macroscale confinement. Here, we analyze the phase-equilibria and kinetic behaviors of water and ice-1h in an isochoric (constant-volume) system. By making use of the Helmholtz potential F(temperature, volume), in contrast to the Gibbs potential G(temperature, pressure), we demonstrate significant changes in phase behavior when the specific volume of the container is constrained below that of ice-1h. We construct a T–V (temperature–volume) phase diagram for water and ice that features a broad two-phase equilibrium region, and we further derive an isochoric nucleation theory that reveals the existence of a critical confinement volume, on the order of microns, below which ice-1h is kinetically prohibited from forming.

水在冻结时膨胀。当在不可变形的恒定容积容器中将水冷却到0°C以下时，会发生什么情况？这是材料热力学中的一个基本问题，也与在纳米，中观或宏观约束下形成冰的生物，地质和技术应用有关。在这里，我们分析了等静（恒定体积）系统中水和冰-1h的相平衡和动力学行为。与吉布斯电位G（温度，压力）相比，通过利用亥姆霍兹电位F（温度，体积），我们证明了当容器的比容限制在冰-1h以下时，相行为会发生重大变化。我们构造一个电视 具有宽的两相平衡区域的水和冰的（温度-体积）相图，并且我们进一步推导出了等速成核理论，该理论揭示了存在一个以微米为单位的临界限制体积，在该体积以下，冰-1h在动力学上被禁止形成。