Owing to emergence of piezoelectric polarization at deformation also electric removal of D in a crystal changes. In this case in the general definition of shift under P it is necessary to understand Pe+Pu sum where Pe is caused by electric field, and Pu — deformation. Generally a E, Pe and Pu do not coincide also expression for D turns out difficult. However for some directions coinciding with axes of high symmetry, the direction of the specified vectors are identical. Then for the size of shift it is possible to write
The size of a vector of polarization P (and area density of piezoelectric charges proportional to it about') in a certain interval of changes is proportional to the size of mechanical deformations. Let's designate through and a of unilateral stretching along axis X:
Let's estimate the size of a piezoelectric field now. Let's put that to sides of a quartz plate, perpendicular to axis X, the mechanical of 1 1055 N/m Then is enclosed, agrees (deformation will be equal u=1,3 10-Substituting this value in a formula (we receive |E | == 5900 V / =59 In/cm. At a plate thickness, say, of d == 0,5 cm tension between facings will be equal to U=Ed ~ 30 Century. We see that piezoelectric fields and tension can be very considerable. Applying stronger piezoelectric materials instead of quartz and using properly the chosen deformation types, it is possible to the piezoelectric tension measured by many thousands of volts.
The piezoelectric effect (direct and the return) widely for the device of various electromechanical. For this purpose sometimes use the compound piezoelements intended for implementation of deformations of different type.
The square root from this size (To) is called as a constant of communication Using the , S and values given above, we find that for K2 quartz ~ 01 For all other known piezoelectric crystals of K2 renders also small in comparison with unit and does not exceed 0,
Piezoelectric properties are observed, except quartz, at a large number of other crystals. Is much stronger, than at, they are expressed at segnetovy salt. Strong piezoelectric materials are crystals of connections of elements of the 2nd and 6th groups of system (SDS, ZnS), and also many other chemical compounds.
where E - intensity of electric field in a crystal, and - permeability at continuous deformation. A ratio , for example, at deformation of unilateral stretching (compression) along one of electric axes X. It is one of two main in the theory of piezoelectricity (the second ratio is given).
The size is called as the piezoelectric module. The sign can be both, and negative. As also the dimensionless size, in the same units, as P, i.e. in C/m the Size of a superficial of piezoelectric charges on sides, perpendicular to axis X, ' = is equal
Along with longitudinal piezoelectric effect there is also cross piezoelectric effect. It is that at compression or stretching along axis Y there is a along axis X and on the same sides of ABCD and EFGH there are polarizing charges. Thus it appears that signs of charges on each side at compression along Y (in cross effect, as at stretching along X (in longitudinal effect.
If the plate is fixed and cannot be deformed, at creation of electric field in it there will be additional mechanical tension its size s is proportional to intensity of electric field in a crystal:
Along with piezoelectric effect there is also the return to it the phenomenon: in piezoelectric crystals emergence of a is followed by mechanical deformations. Therefore if on the facings strengthened on the to give voltage, the crystal under the influence of a field and deformed.
Let's review an example of application of the main ratios now (and (We will put that the quartz plate which is cut out as is stated above, along axis X, and the facings concerning sides are opened. As the charge of facings before deformation was equal to zero, and quartz is dielectric, and after deformation of a facing will be not loaded. According to definition of shift it means that D = Then from a ratio (follows that at deformation in a plate there will be an electric field of c intensity
which more S. Uvelicheniye of elastic rigidity it is caused by emergence of the tension at the return pyezoeffekt interfering deformation. Influence of piezoelectric properties of a crystal on its mechanical properties is characterized by size