Bishambhar Dayal Saksena

The structure and morphology of α-quartz

Some features of the quartz morphology such as the well-developed nature of the faces of the primary rhombo-hedron, their position to the left of electric axes in left quartz, and the plane and the nature of the cleavage in quartz have been explained on the basis of the crystal structure.

Variation of the piezo-electric constants of α-quartz with temperature

The method of finding the piezo-electric constants with the help of the variations of bond distances and bond angles on strain has been utilised in finding the variations of the piezo-electric constants ε11 and ε41 of α-quartz with temperature. It is found that the variations of ε11 with temperature can be explained on the basis of the change of co-ordinates with temperature. At 558° C. the silicon atoms are found to occupy the same positions as they do in β-quartz. As the transition temperature is reached, the longitudinal coefficient ε11 drops to zero, while the transverse coefficient ε41 decreases by only 15%. The piezo-electric constant of β-quartz has been similarly determined and its value comes out to be 1·05×104 for a non-ionic crystal (k=·724) and 1·45×104 for an ionic crystal (k=1).

A new method of calculating the piezo-electric constants of α-quartz

A method of calculating the piezo-electric constants of α-quartz is described which consists in determining the electric moment developed by changes of bond-lengths and bond-angles on strain. Considering three atoms P, Q, R, of which P and R are silicon atoms and Q an oxygen atom orvice-versa, the electric moment developed on strain may be resolved into moments in the plane PQR and moments perpendicular to this plane. Resolving these moments along the axes of the crystal and summing up for all the forty-two planes in the unit cell, we get the piezoelectric equations and constants of the crystal. The electric moment in the plane is equivalent to the moment produced by the change of bondlength along the direction of the bonds before strain, while for the moment normal to the plane we take the average value,i.e., half the value of the moment normal to the plane when the displacements of the atoms are wholly normal to the plane. The method gives good agreement with the observed values.