We calculate the velocity surface of bulk acoustic waves propagating in the YZ-, XY- and ZX- planes of proton-exchanged LiNbO_3, based on the theory of acoustic wave in anisotropic solid with piezoelectricity. The calculation results show that the velocity change due to proton-exchange when the wave propagating along X-axis is larger than that along Z- axis for Y-cut substrate, in spite of longitudinal or transverse wave. The curve of velocity surface for PE Z-cut substrate is near to a circle, while that for pure Z-cut LiNbO_3 is a hexagonal. The velocity surface for PE X-cut LiNbO_3 seems to be turned an angle from that for pure X-cut LiNbO_3. The detail results, discussions and comparison with the experiment will present in this paper.
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机译：基于具有压电性的各向异性固体中的声波理论，我们计算了在质子交换的LiNbO_3的YZ，XY和ZX平面中传播的体声波的速度表面。计算结果表明，纵切波或横波波，Y切割基片沿X轴传播的速度大于沿Z轴传播的速度时，由于质子交换引起的速度变化。 PE Z切割衬底的速度表面曲线接近圆形，而纯Z切割LiNbO_3的速度表面曲线为六边形。 PE X切割的LiNbO_3的速度表面似乎与纯X切割的LiNbO_3的速度表面成一个角度。本文将提供详细的结果，讨论和与实验的比较。
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