空孔クラスターの温度依存性

抄録

The rates of numbers of hole-clusters in crystal lattice are given by statistical mechanics using the methode of the theory of high-nolymer solution which had been published by R. J. Flory.
From the theory proposed here, the well known relation exp[-ε_v/_kT] which expresses the rate of number of point vacancies in a crystal lattice, is shown to be poper only at low temperature. It is generally, from the theory, expressed by the formula [Z+1+exp(ε_v/_kT)]^-1 at given temperature instead of the relation above, where Z is the number of adjacent lattice points.
Still more, the rate of number of given i-hole clusters, which comproses a vacancy with i pieces of holes, is also generally expressed by ni/N=(1/2)Z(Z-1)^i-2 exp[-ε_i/_kT]{1-iZ[Z+1+exp(ε_l/_kT)]^-1} for i≠1, where ε_i is the formation energy of i-hole cluster.
The estimations for some moleculas crystals show that the rates of numbers of i-hole clusters are order of 10^-4, 10^-7 and 10^-8 for i=1, 2 and 3 at melting points The difference owing to Z with respect to point vocancy is nearly 0.3% at melting point.
Furthermore we can say that the number of holes of the largest hole cluster at melting point for molecular crystal is about 300-400.