The first order phase transition between two nuclear ordered antiferromagnetic solid He-3, namely U2D2-He-3 and CNAF-He-3, was studied. Those two phases exist at the temperature below about 1 mK and have the first order phase transition between them with the critical magnetic field B-Cl. We studied time and spatial evolution of the stable phase during the field-sweep induced phase transition near T = 0. We found that the stable phase developed in two stages. During the first stage, many small seeds appeared throughout a crystal. Those nucleated seeds grew faster than the nucleation process, however terminated growing at some limited size due to a chemical potential loss by the latent heat release. The second stage was understood as the process of latent heat release through solid-liquid interface. (c) 2006 Elsevier B.V. All rights reserved.