Temperature sensitivity of plate modes in ST quartz

On considering 13 modes with shear horizontal (SH) polarization, propagating perpendicular to the x-axis in a ST quartz plate, it is experimentally shown and theoretically verified how the temperature coefficient of delay (TCD) and its behavior vs. temperature depend monotonically on the order n of the mode. This property is attributed to the different sensitivities of the modes towards temperature variations in c₁₂, c₁₄ and c₄₄ elastic moduli. The modes sensitivities towards density ρ, elastic moduli c₁₁, c₁₃, c₃₃ and plate thickness h are either temperature independent or negligibly small. The best thermal stability (TCD≈0) over the widest temperature range (2-92°C) has been detected for the 6^th mode, while the largest one (350 ppm/°C) has been measured for the 13^th mode, at 47°C. For comparison, five Lamb modes, propagating along the x-direction in the same quartz plate, show a non monotonic dependence of the thermal coefficient on the mode number, a temperature independent TCD in the range 2-92°C, a minimum and maximum value of the TCD (≈0.7 ppm/°C and ≈100 ppm/°C) for the 0^th symmetric mode and for the 1^st anti-symmetric mode, respectively