| Abstract: | A phase transformation in a one component polycrystal starts to grow instantaneously and with a constant rate from the grain boundaries. After the time t there exist regions of the old and of the new phase. The derivation of the statistical quantities characterizing this state at t is unknown yet. Therefore we reduce this complicate three-dimensional problem to a one-dimensional model analogously to the linear chain in lattice dynamics or to the one-dimensional energy band model. A closed analytical treatment of this model is practicable. It is derived in detail for those one-dimensional systems, which transform according to a rate law of n-th order (n ≧ 0). |
