Thickness-shear Frequencies of an Infinite Quartz Plate with Material Property Variation Along the Thickness
Ji Wang, Wenliang Zhang, Dejin Huang, Tingfeng Ma, Jianke Du
备注：
This is to be presented and published with the 2014 IEEE International Frequency Control Symposium, May 19-22, 2014, Taipei International Convention Center, Taipei
Properties of the quartz crystal blank of a resonator is assumed homogeneous, uniform, and perfect in design, manufacturing, and applications. As end products, quartz crystal resonators are frequently exposed to gases and liquids which can cause surface damage and internal degradation of blanks under increasingly hostile conditions. The combination of service conditions and manufacturing process including chemical etching and polishing can inevitably modify the surface of quartz crystal blanks with changes of material properties, raising the question of what will happen to vibrations of quartz crystal resonators of thickness-shear type if such modifications to blanks are to be evaluated for sensitive applications. Such questions have been encountered in other materials and structures with property variations either on purpose or as the effect of environmental or natural processes commonly referred to as functionally graded materials, or FGMs. Analyses have been done in applications as part of studies on FGMs in structural as well as in acoustic wave device applications. A procedure based on series solutions has been developed in the evaluation of frequency changes and features in an infinite quartz crystal plate of AT-cut with the symmetric material variation pattern given in a cosine function with the findings that the vibration modes are now closely coupled. These results can be used in the evaluation of surface damage and corrosion of quartz crystal blanks of resonators in sensor applications or development of new structures of resonators.
Intrinsic and extrinsic perturbations on the topological insulator Bi2Se3 surface states
利用密度泛函电子结构方法，研究了本征和非本征扰动对强拓扑绝缘体Bi $_2$ Se $_3$表面态Dirac锥的影响.我们认为原子弛豫，薄膜厚度作为内在和界面薄介电膜作为一个外在的源扰动的表面状态。我们发现原子弛豫对狄拉克锥的简并度没有影响，而薄膜厚度对表面态有相当大的影响，诱导一个间隙，随着薄膜厚度的减小而单调增加。我们认为两个绝缘基板BN和石英作为介电薄膜，并表明，表面终端石英钝化或不钝化起着至关重要的作用，在维护狄拉克锥简并，而BN是更惰性的TI表面状态。用一种简单的算法计算出相对于体原子的相对轨道贡献，并在此基础上证明了自旋-轨道耦合打开时体原子能带的反转.表面态的层投影电荷密度分布表明，这些态并不严格局限于表面.这些态的空间限制扩展到两到三个五重层，一个五重层由Bi和Se的五个原子层组成
