Cryogenic fractures can be achieved in the samples if it is submerged in liquid nitrogen or anything similar to it and some sort of mechanical stress or vibrations stronger than the material's tensile strength is allowed to be exerted on it.

In absence of any such mechanical perturbation also, cracks can form, if a high thermal gradient is generated. It depends on the sample properties like thermal conductivity, tensile strength, elasticity, dimension of the sample (nanometer or micrometer scale) and thereby surface to volume ratio. But, in brief, if the cooling process is very prompt, then the chance of generating high thermal gradient and therefore cryogenic fracture is higher.

Foram Dave

3 - 4 mm is a relatively thick sample in terms of 'heat' transfer and you may stress it even with 'instant' cooling in liquid nitrogen. I'd look to thin the sample in some way as the heat/cold transfer will be much quicker. Cryo-EM is a well-known technique and preferable to freeze-fracture.

You just have to keep it in the nitrogen until no more bubbles are formed. When there is no more evaporation the two materials are more or less at thermal equilibrium and you can break your sample.

For some tests PEEK samples with thickness 3-4 mm are prefarable. The method proposed by Rémi Rafael, is enough universal for differenf form and sizes of the polymer samples.