I've read in a book that a crystal set to work in its odd overtone is more efficiently operated compared to that of its even overtone. If anyone can explain it to me in detail, or provide a link that provides a detailed explanation, it would really be helpful. I've already searched everywhere in the net and in the local library and it's all the same, they only say that it IS efficient but doesn't explain why.
In thickness shear oscillation mode, that is exclusively used for standard high frequency crystals, only odd orders involve a differential voltage at the surface electrodes.
A transistor or amplifier that is biased correctly clips symetrically when it is over-driven. The symmetrical clipping produces only odd harmonics.
Therefore an oscillator with an odd-overtone crystal will oscillate at the odd harmonic correctly and easily.
You can assume, that the fundamental isn't present in the crystal oscillator at all. It's typically supressed by a LC circuit, so the oscillation condition is only met for the overtone.