# ideal hcp lattice, ratio c/a = 1.633 proof

by skyav
Tags: c or a, ideal, lattice, proof, ratio
 P: 2 1. The problem statement, all variables and given/known data q: show that for an ideal hcp structure the c/a ratio is equal to (8/3)^(1/2) = 1.633 this question has come up before in the forum but still it has not fully answered: Kouros Khamoushi Dec30-05, 12:27 AM This is the mathematical calculation ^ means to the power of c/2 = a/2 Then a^2 /2 = c^2/2 a^2 + a^2 ----- = (4R)^2 2 2a^2+a^2 -------------- = 16 R^2 2 3a^2 = 2 *16 R^2 a^2 = 2*16 R^2 ----- 3 a = 2* square root of 16 divided by square root of 3 a = 8 / 3 = 1.6329 R Kouros Khamoushi Jan26-06, 06:48 PM The assumptions above are roughly correct, but we have to take into the considerations the Pythagorean Theorem. The Pythagorean Theorem states: b^2=a^2+c^2. as well as c/2 or half of hexagonal crystal structure as well as the cosine for 30 degree triangles generated by the hole in Hexagonal closed packed. So we write: c/a half of this c/2. Cos 30 degree skyav Feb9-09, 03:49 PM Dear all, i have tried. the last post by Kouros Khamoushi almost worked... how ever i do not understand where some of the steps.... 1. c/2 = a/2??? how? 2. 3a^2 = 2 *16 R^2???? where in the world did the factor of 3 come from on the LHS of this eqn. You are prob correct... however please clarify the steps as i am totally baffled. ps. inha: what shape of slice do u mean? also i hope it is from hexagonal lattice? Kind regards.

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