4.8.1 Piezoelectric effect The polarization intensity Pxx is proportional to the stress o that is (482) Where F, pressure applied in the direction of X-X axis piezoelectric constant, d,=2.3×10-12CN-1 for quartz crystal length of the cut width of the cut
The polarization intensity Pxx is proportional to the stress xx , that is , lb F P d d x xx = 1 1 xx = 1 1 (4.82) Where Fx = pressure applied in the direction of X-X axis, d1 = piezoelectric constant, 1 2 1 1 2.3 10 − − d = CN for quartz crystal, l = length of the cut, b = width of the cut. 4.8.1 Piezoelectric effect
4.8.1 Piezoelectric effect The polarization intensity P is also equal to the electrical charge density produced on cut surface 16 (483) Where qrr= the charges produced on th e surface perpendicular to the X-X axis From eqs. (4.82)and(4.83)we get II (484)
The polarization intensity Pxx is also equal to the electrical charge density produced on cut surface: lb q P xx xx = (4.83) Where qxx = the charges produced on the surface perpendicular to the X-X axis. From Eqs. (4.82) and (4.83) we get qxx = d1 1Fx (4.84) 4.8.1 Piezoelectric effect
4.8. 1 Piezoelectric effect Eq(4.84 shows that the produced charge qxx, when a quartz crystal cut is applied with a pressure in the X-X direction, is proportional to the applied forceR, but is independent of cut's geometrical size. Contrary to this, when the forcex is applied in the y-y direction
Eq. (4.84) shows that the produced charge xx q , when a quartz crystal cut is applied with a pressure in the X-X direction, is proportional to the applied force Fx , but is independent of cut’s geometrical size. Contrary to this, when the force Fx is applied in the Y-Y direction 4.8.1 Piezoelectric effect
4.8.1 Piezoelectric effect The produced charge still appears on the surface perpendicular to the X-X axis, with the magnitude (485) Where 12 piezoelectric constant for the stress applied in the y-Y direction Ly, l-- length and the width of the quartz cut, respectively According to the symmetrical property of the quartz crystal axes, there is hus eq. (4.85)changes to (486)
The produced charge still appears on the surface perpendicular to the X-X axis, with the magnitude y x y y x y xy F l l F d bl l b q = d1 2 = 1 2 (4.85) Where d1 2 = piezoelectric constant for the stress applied in the Y-Y direction l y ,l x = length and the width of the quartz cut, respectively According to the symmetrical property of the quartz crystal axes, there is 1 2 1 1 d = −d Thus Eq. (4.85) changes to y x y xy F l l q d = − 1 1 (4.86) 4.8.1 Piezoelectric effect
4.8. 1 Piezoelectric effect O The produced charge of a quartz crystal cut, when it is applied with a compressive force in the mechanical axis Y-y, is proportional to the geometrical size of the cut, the polarity of the charge is then opposite(negative sign in Eq (4.86)) to the polarity of the charge produced when it is applied with a compressive force in the electrical axisⅩ-Ⅹ
❑The produced charge of a quartz crystal cut, when it is applied with a compressive force in the mechanical axis Y-Y, is proportional to the geometrical size of the cut, the polarity of the charge is then opposite (negative sign in Eq. (4.86)) to the polarity of the charge produced when it is applied with a compressive force in the electrical axis X-X. 4.8.1 Piezoelectric effect