Study On Pure Mode Axes Of Orthorhombic System Crystals

Elasticity is an inherent property of all crystal.When mechanical disturbance occurs in a part of a crystal,an elastic wave will be formed due to the spread of the disturbance inside the crystal.Because of the anisotropy of crystal,there are three elastic waves along a certain direction of the wave vector.If the direction of energy velocity is the same as the wave vector,then the direction is called a pure mode axis.When the elastic wave propagates along the pure mode axis,the direction of particle vibration must meet the requirement of pure shear wave or pure longitudinal wave.It is obvious that pure mode axis is of important guiding significance for the design and development of transducer.In this paper,pure mode axes of orthorhombic system crystalsare studied by the method of slowness surface,and the question of the influence of piezoelectric effect on the pure mode axis is discussed.Specifically,the slowness surface equation of orthorhombic system crystals is solved by using MATLAB software,and the three dimensional slowness surface of a crystal can also be simulated.The direction of a radius vector of a slowness surface is the same as the direction of the phase velocity.The direction of a normal direction on a slowness surface is the direction of the energy velocity.A pure mode axis can be got by judging the direction which meets the requirement of a radius vector being consistent with the normal direction point by point on a three dimensional slowness surface.The results are as follows.Orthorhombic system is divided into three crystal classes.The crystal whose symmetry belongs to mmm point group does not have the piezoelectric effect.Crystal of 222 or mm2 point group symmetry possesses the piezoelectric effect.When the piezoelectric effect is neglected,pure mode axes of the crystal of orthorhombic system are(1,0,0)?(?)?(0,1,0)?(?)?(0,0,1) and (?).Taking the piezoelectric effect into consideration,the number of independent components of the elastic stiffness coefficient significantly increased for crystal which belongs to 222 or mm2 point group.In this case,for Rochelle salt crystal of 222 point group symmetry and barium sodium niobate crystal of mm2 crystal class,the slowness surfaces have some changes.But the pure mode axes of these two crystals are not affected by the piezoelectric effect.