  Phase diagrams are integral to the application and interpretation of
materials thermodynamics, and none is more ubiquitous than the common
Temperature-Pressure diagram of water and its many icy phases. Inspired by
recent advances in isochoric thermodynamics, we here employ a simple convex
hull approach to efficiently calculate an updated Temperature-Volume phase
diagram for water and five of its solid polymorphs from existing Helmholtz free
energy data. We proceed to highlight fundamental similarities between this T-V
diagram and conventional binary temperature-concentration (T-x) diagrams,
provide the volume coordinates of a variety of three-phase invariant reactions
(e.g. 'confined' or 'volumetric' eutectics, peritectics, etc.) that occur
amongst the phases of pure water under isochoric or confined conditions, and
calculate the phase fraction evolution of Ice Ih with temperature along
multiple isochores of interest to experimental isochoric freezing. This work
provides a requisite baseline upon which to extend the study of isochoric
freezing to cryogenic temperatures, with potential applications in
thermodynamic metrology, cryovolcanism, and cryopreservation.
