Abstract
Universal and straight-forward formulas for finding coincidence coefficients of space lattices of two phases and their plane lattices having a coincidence site lattice relationship are derived by means of elementary theory of numbers. The coincidence coefficient of a space lattice is α2(3)=1/|C(1)| and that of their plane lattices are α2(h)= (H(2)C(1)/|C(1)|, C(1) being a basic vector correspondence matrix of CSL, and H(2)= [h1(2)h2(2)h3(2)]. In case C(1) is unknown, coincidence coefficients of a space lattice and their plane lattices can be found through the basic vector correspondence matrix φ of two phases and coincidence coefficient matrix C then α23= k1(2)k2(2)/d3, α2(h)=(CH(2),dk1(2))/d2. To find matrix C is much easier than to find C(1).
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