Long-duration cryopreservation of biological tissue (most often semen, egg cells, or fertilized embryos) is typically done at 77 K, since the samples can be easily kept at that temperature by immersing them in liquid nitrogen. As tissues are cooled down to that temperature, they pass through one of two different phase transitions: either a standard freezing transition into a (locally) crystalline solid, or a glass transition into an amorphous solid (i.e. a glass. For most biological tissues, this glass consists mostly, but not entirely of amorphous ice.) In the context of cryopreservation of biological tissues, this glass transition is usually referred to as vitrification. In practice, the main thing that determines which phase transition the tissues will pass through is the speed at which they are cooled: slow cooling (typically done between 0.1 K/min and 30 K/min) usually leads to a freezing transition, while fast cooling (typically done faster than 2500 K/min) usually leads to a vitrification transition.
The latter transition usually leads to better outcomes (although it is much more complicated to implement). But I've only found sources that say that the reason for the difference is that vitrification "helps to prevent the formation of ice crystals and helps prevent cryopreservation damage", or very similar language.
Why exactly does amorphous ice do less damage to biological tissue than ice crystals? Is it because ice crystals expand more upon freezing than amorphous ice does upon vitrifying, thereby imposing higher structural stresses within the cells?
Just thinking intuitively based on my experiences from everyday life, it isn't obviously to me that turning a biological tissue into glass would be any less damaging than turning it into ice.