an style="font-size:16px;font-family:微软雅黑, sans-serif">石英晶体的弹性常数与切型an>
an style="font-size:16px;font-family:微软雅黑, sans-serif">一、英晶体的弹性常数an>
an style="font-family:微软雅黑, sans-serif;font-size:16px">通过上节讨论an>an style="font-size:16px">,an>an style="font-family:微软雅黑, sans-serif;font-size:16px">我们已经知道石英晶体的弹性常数矩阵为:an>an style="font-size:16px">an>
an style="font-family:微软雅黑, sans-serif;font-size:16px">石英晶体的弹性常数反映晶体的弹性性质。从这些弹性常数矩阵看出an>an style="font-size:16px">,an>an style="font-family:微软雅黑, sans-serif;font-size:16px">用双足标表示的弹性常数共有an>an style="font-size:16px">36an>an style="font-family:微软雅黑, sans-serif;font-size:16px">个分量。三斜晶系是完全各向异性体an>an style="font-size:16px">,an>an style="font-family:微软雅黑, sans-serif;font-size:16px">对称性最低an>an style="font-size:16px">,36an>an style="font-family:微软雅黑, sans-serif;font-size:16px">个不等于零的弹性常数分量中an>an style="font-size:16px">,an>an style="font-family:微软雅黑, sans-serif;font-size:16px">独立的分量有an>an style="font-size:16px">21an>an style="font-family:微软雅黑, sans-serif;font-size:16px">个。而石英晶体的独立弹性常数分量为an>an style="font-size:16px">6an>an style="font-family:微软雅黑, sans-serif;font-size:16px">个。an>
an style="font-family:微软雅黑, sans-serif;font-size:16px">当弹性常数an>an style="font-size:16px">san>an style="font-family:微软雅黑, sans-serif;font-size:16px">和an>an style="font-size:16px">can>an style="font-family:微软雅黑, sans-serif;font-size:16px">,的足标an>an style="font-size:16px">ian>an style="font-family:微软雅黑, sans-serif;font-size:16px">,an>an style="font-size:16px">=1an>an style="font-family:微软雅黑, sans-serif;font-size:16px">,an>an style="font-size:16px">2an>an style="font-family:微软雅黑, sans-serif;font-size:16px">,an>an style="font-size:16px">3an>an style="font-family:微软雅黑, sans-serif;font-size:16px">时,它分别表示沿an>an style="font-size:16px">xan>an style="font-family:微软雅黑, sans-serif;font-size:16px">,an>an style="font-size:16px">yan>an style="font-family:微软雅黑, sans-serif;font-size:16px">,an>an style="font-size:16px">zan>an style="font-family:微软雅黑, sans-serif;font-size:16px">方向的弹性伸缩性质;当an>an style="font-size:16px">ian>an style="font-family:微软雅黑, sans-serif;font-size:16px">,an>an style="font-size:16px">j4an>an style="font-family:微软雅黑, sans-serif;font-size:16px">,an>an style="font-size:16px">5an>an style="font-family:微软雅黑, sans-serif;font-size:16px">,an>an style="font-size:16px">6an>an style="font-family:微软雅黑, sans-serif;font-size:16px">时,它分别表示沿an>an style="font-size:16px">xan>an style="font-family:微软雅黑, sans-serif;font-size:16px">,an>an style="font-size:16px">yan>an style="font-family:微软雅黑, sans-serif;font-size:16px">,an>an style="font-size:16px">zan>an style="font-family:微软雅黑, sans-serif;font-size:16px">平面的切变性质;当an>an style="font-size:16px">ian>an style="font-family:微软雅黑, sans-serif;font-size:16px">≠an>an style="font-size:16px">jan>an style="font-family:微软雅黑, sans-serif;font-size:16px">它分别表示两种伸缩之间或两种切变之间,以及伸缩与切变之间的弹性耦合性质。这种弹性常数又称为交叉弹性常数,现在以石英晶振,石英晶体的弹性柔顺常数an>an style="font-family:微软雅黑, sans-serif;font-size:16px">为例,进一步说明如下:an>
an style="font-family:微软雅黑, sans-serif;font-size:16px">(an>an style="font-size:16px">1an>an style="font-family:微软雅黑, sans-serif;font-size:16px">)与石英晶体伸缩性质有关的弹性柔顺常数为an>an style="font-size:16px">s11an>an style="font-family:微软雅黑, sans-serif;font-size:16px">,an>an style="font-size:16px">s22(=s11an>an style="font-family:微软雅黑, sans-serif;font-size:16px">),an>an style="font-size:16px">s33an>an style="font-family:微软雅黑, sans-serif;font-size:16px">。an>
an style="font-family:微软雅黑, sans-serif;font-size:16px">(an>an style="font-size:16px">2an>an style="font-family:微软雅黑, sans-serif;font-size:16px">)与石英晶体伸缩之间耦合性质有关的交叉弹性柔顺常数为:an>an style="font-size:16px">s12an>an style="font-family:微软雅黑, sans-serif;font-size:16px">,an>an style="font-size:16px">s13an>an style="font-family:微软雅黑, sans-serif;font-size:16px">,an>an style="font-size:16px">S2an>an style="font-family:微软雅黑, sans-serif;font-size:16px">(an>an style="font-size:16px">=S13an>an style="font-family:微软雅黑, sans-serif;font-size:16px">)。an>
an style="font-family:微软雅黑, sans-serif;font-size:16px">(an>an style="font-size:16px">3an>an style="font-family:微软雅黑, sans-serif;font-size:16px">)与石英晶体切变性质有关的弹性柔顺常数为an>an style="font-size:16px">s44=s55an>an style="font-family:微软雅黑, sans-serif;font-size:16px">,an>an style="font-size:16px">s55)an>an style="font-family:微软雅黑, sans-serif;font-size:16px">,an>an style="font-size:16px">s66.an>
an style="font-family:微软雅黑, sans-serif;font-size:16px">(an>an style="font-size:16px">4an>an style="font-family:微软雅黑, sans-serif;font-size:16px">)与石英晶体切变之间耦合性质有关的交叉弹性柔顺常数为:an>an style="font-size:16px">s56(=2S14).an>
an style="font-family:微软雅黑, sans-serif;font-size:16px">(an>an style="font-size:16px">5an>an style="font-family:微软雅黑, sans-serif;font-size:16px">)与石英晶体伸缩和切变之间耦合性质有关的交叉弹性柔顺常数为:an>an style="font-size:16px">s14an>an style="font-family:微软雅黑, sans-serif;font-size:16px">,an>an style="font-size:16px">524an>an style="font-family:微软雅黑, sans-serif;font-size:16px">(an>an style="font-size:16px">=-S14)an>an style="font-family:微软雅黑, sans-serif;font-size:16px">。an>
an>an>