Why Do Tuning Fork Crystals Have a Negative Parabolic Temperature Coefficient?

[Troyvm]

I would like to understand the reason that tuning fork crystals have the negative parabolic temperature coefficient shape. Is it the material, the crystal cut or how its mounted. What is the physics behind that.

Thank you

 

[Tom.G]

Crystal cut.
See: http://leapsecond.com/hpan/an200-2.pdf

 

[Tom.G]

Corrected link in previous post (I hope): http://leapsecond.com/hpan/an200-2.pdf