I fundamental equation and its physically acceptable solutions.

(Rodulfo de Gil, Eldrys)

The equation (1/4) (c/a)^{2} = σ2 + 2ασ - 2, which relates all structural parameters for the
ternary ABC_{2} semiconductors with chalcopyrite structure, is analyzed (*c* and a are the tetragonal lattice constants, σ = 4*x* =1, *x* = fractional coordinate of C atom, α = (d^{2}_{AC} +
d^{2}_{BC})/(d^{2}_{AC} - d^{2}_{BC}), d_{AC} and d_{BC} are
the A-C and C-B bond distances respectively). The analysis gives the following results: 1. For 2.236 > (d_{BC}/d_{AC}) >0.447, a chalcopyrite-type structure is not possible. 2. For 0.447 <
(d_{BC}/d_{AC}) < 0.557 or 1.732 < (d_{BC}/d_{AC})< 2.236, (*c/a*) < 2 (tetragonal
compression). 3. For (d_{BC}/d_{AC}) = 0.557 or 1.732 (*c/a*) ≤ 2. 4. For 0.557< (d_{BC}/d_{AC}) < 1.732, (*c/a*) ≥ 2. 5. For a given d_{BC}/d_{AC} the *c/a* values are between 0 and 2 (2|α| - 3)^{½} with |α|>1.5.