If these conditions are met then a transformation of α {\displaystyle \alpha \,\!} into β {\displaystyle \beta \,\!} will proceed by the nucleation of new particles at a rate N ˙ {\displaystyle {\dot {N}}\,\!} per unit volume which grow at a rate G ˙ {\displaystyle {\dot {G}}\,\!} into spherical particles and only stop growing when they impinge upon each other. During a time interval, 0 < τ < t {\displaystyle 0<\tau <t\,\!} , nucleation and growth can only take place in untransformed material. However, the problem is more easily solved by applying the concept of an extended volume – the volume of the new phase that would form if the entire sample was still untransformed.