Heterogeneous nucleation in a polycrystalline solid occurs (i) at the surface of its container, (ii) at its microstructural sites, namely, grain boundaries, grain junctions, and intergrain-strain regions, and (iii) at the defect sites, namely, dislocations, vacancies, and stacking faults (planar defects) in its single crystal grains. We analyze their thermodynamic and kinetic effects in terms of classical nucleation theory by taking into account (a) the increase in Gibbs free energy, G, due to the lattice misfit of the nuclei forming in the parent phase and (b) the decrease in G due to the angle subtended by the nucleus on the external surface, grain boundaries, and grain junctions. Hence we deduce that several combinations of nucleation sites in different materials and also in different polycrystalline samples of the same material may produce the same energy barrier against nucleation and overall growth. The overall nucleation and growth rates are dependent upon the surface to volume ratio, χ, of a sample in a vessel and the vessel's material. Pressurizing a crystalline solid is known to produce either its polymorphic crystal form or a solid that shows no Bragg peaks and appears amorphous. We argue that when self-diffusion rate becomes slower than the pressurizing rate, (dP/dt)T, a multiplicity of states nucleating at different sites become kinetically frozen on their path to crystal growth. In such a case, the transformed solid would appear amorphous. A solid of high χ would transform to a polymorph when (dP/dt)T is low and to a state that appears amorphous when (dP/dt)T is high. Known studies of 0.08-0.1 cm3 volume samples in diamond-anvil high pressure cells provide qualitative evidence of formation of both crystal polymorphs and apparently amorphous solids. Methods are suggested for observing such an occurrence in large polycrystalline samples.