Patent ID: 7051728

Claim:
A method of cutting quartz plate where angles of said cuts are determined according to the following formula: T f = ⁢ 3.9 + 6.5 ⁢ ⁢ cos 2 ⁢ ⁢ θ + ⁢ 1 2 ⁡ [ c 66 ⁢ T c 66 ⁢ sin 2 ⁢ θ + c 44 ⁢ T c 44 ⁢ cos 2 ⁢ θ + T c 14 ⁢ c 14 ⁢ sin ⁢ ⁢ 2 ⁢ ⁢ θ c 66 ⁢ sin 2 ⁢ θ + c 44 ⁢ cos 2 ⁢ θ + c 14 ⁢ sin ⁢ ⁢ 2 ⁢ ⁢ θ ] + ⁢ [ a ′ · ( sin ⁡ ( ω · θ + ϕ ′ ) + sin ⁡ ( ω · θ + ϕ ′ ) 2 ) ] + δ where T ƒ =frequency temperature coefficient, θ=angle of rotation from the Z axis, c xx =is the value of stiffness. The subscripts denote the stiffness of a given rhombohedral axis, ω=the angular velocity of the wave traversing the crystal face, a′=the amplitude of the wave traversing the crystal face, φ′=the phase delay imposed on the wave traversing the crystal face due to resistance by its surroundings, and δ=offset value between the idealized wave and the wave with a damping function.