高阶电光和电致伸缩张量的旋转不变性

根据群论原理,用Matlab语言编制了用于计算具有SO(2)群对称性的任意阶电光和电致伸缩系数张量的通用软件.利用该软件得到了具有SO(2)群对称性的三次和四次电光系数张量以及二阶和三阶电致伸缩系数张量的一般形式,并经坐标变换验证,这些张量形式确实具有围绕物理坐标系中z轴的任意旋转不变性.     

晶体物理性质的空间轴转动对称性

用群论方法导出具有SO(2)群对称性的一般三阶、四阶张量形式;进而给出具有这种对称性的压电、线性电光、二阶非线性极化、弹光、二次电光、电致伸缩、弹性及三阶非线性极化系数矩阵的一般形式.指出含有4度或6度转轴的非中心对称晶类的压电、线性电光及二阶非线性极化性质,以及所有六方晶类的弹光、二次电光、电致伸缩、弹性及三阶非线性极化性质具有关于晶体中唯一高次轴的任意旋转对称性.对所得结果作了讨论.     

二阶非线性弹光张量的旋转不变性

基于群论原理,用Matlab语言编制了用于计算具有SO(2)群对称性的任意阶弹光系数张量的通用软件.在编程中,采用由非对称化的恒等表示基函数构造出具有弹光系数张量本征对称性的对称化恒等表示基函数的方法,以便于编制通用软件.利用该软件得到了具有SO(2)群对称性的二阶非线性应变和应力弹光系数张量的形式,并经坐标变换验证,该张量形式确实具有围绕物理坐标系中Z轴的任意旋转不变性.     

光折变晶体Bi2TeO5的生长及光学性能研究

采用坩埚下降法生长了新型光折变晶体Bi2TeO5,通过优化生长工艺,获得了直径25mm、长度50mm的Bi2TeO5晶体.研究了晶体开裂和变色等缺陷,测试了晶体的光学性能.测得Bi2TeO5晶体的三阶非线性光学响应时间为8.5ps,三阶非线性光学系数为7.4×10-10.     

一种利用实验测量和数值计算确定3m点群晶体弹性系数的方法

将实验测量与数值计算相结合确定低对称性晶体弹性系数的方法可以弥补常规方法测量时造成的弹性系数非对角元误差大的不足.本文将该方法由正交系晶体推广到了三方系3m点群晶体,在数值计算中选取了目前公认的无约束最优化方法中最稳定的两种算法-单纯形法和BFGS法,并增加了弹性系数的约束条件,提高了方法的适应性和正确性.在此基础上,本文利用3m点群晶体LiNbO3和LiTaO3的弹性劲度系数[cij]和顺服系数[sij]的实验数据对该方法进行了讨论及验证.结果表明这种方法对3m点群晶体弹性系数非对角元的计算是可行的.另外,本文还对数值计算时,初值的选取和检验结果合理性等关键性问题进行了详细的讨论.     

PZT陶瓷材料θ相变的序参量

PbZr1-xTixO3(PZT)的θ相变是氧八面体绕[111]轴转过一微小角度θ引起的,由于前人对相变中晶体学原胞的选取不合适,所以不能正确说明晶体结构对称性的变化.本文根据居里原理,分析了相变前后对称性的变化,得出其序参量是一个三阶全对称的极张量,并给出具体的数学形式.     

SrTiO3铁电体反铁畸变序参量的研究

钛酸锶(SrTiO3)的反铁畸变是氧八面体绕[001]轴转过一微小角度θ引起的,由于前人对相变中晶体学原胞的选取不合适,所以不能正确说明晶体结构对称性的变化.本文提出一种晶体学原胞的选取方法,能很好地反映相变前后对称性的变化.由居里原理,分析其序参量是一个三阶全对称的极张量,并给出具体的数学形式.     

晶体和准晶旋声性质的旋转不变性

依据群论原理对计算张量的群论方法作了改进,采用非对称化基函数取代对称化基函数,以便于编程.用MATLAB编制了用于计算属于SO(2)群各阶张量的软件.借助于该软件得到了具有SO(2)群对称性的旋声张量的形式.指出晶体中属于六角系的6、6 mm和622晶类和准晶中属于五角系的5、52、5 m晶类的旋声性质具有围绕晶体或准晶中唯一高次轴的任意旋转不变性.该结果对于旋声性的应用有重要意义.     

新型可实用化红外非线性光学晶体研究进展

红外非线性光学晶体可以变频输出中远红外激光,在国防和民用方面都有重要应用.本文综述了近十年来发现的具有实用前景的新型红外非线性光学材料的研究进展,主要讨论已经获得较大尺寸单晶的新材料.这些晶体具有优秀的综合性能,包括足够大的非线性光学系数,宽的红外透过范围,合适的双折射,较好的单晶生长习性和稳定的物化性质.本文将从晶体结构、晶体生长、物化性能、红外激光输出等方面进行综述,并对红外非线性光学晶体未来的发展方向做出一定的讨论.     

LED大型圆形阵列的光斑照度均匀性

应用LED芯片的照度公式以及LED大型圆形阵列照度分布的对称性,建立了研究LED大型圆形阵列照度均匀度的物理模型,推导出计算LED大型圆形阵列照度均匀度的公式.利用该公式研究了LED大型圆形阵列照度均匀度随阵列半径、随m值以及随目标距离的变化规律.得出:照度均匀度随阵列半径的增加而非线性地增大;照度均匀度随m值的增加而非线性地增大;照度均匀度随目标距离的增加而非线性地减小.这些规律为提高LED大型圆形阵列的照度均匀性提供了理论依据,也为LED大型圆形阵列的照度均匀性设计提供了研究方向和计算方法.弥补了之前研究LED阵列照度均匀性其研究方法上的不足.     

Three‐dimensional thermoelastic stresses in off‐axis oriented single crystals with hexagonal symmetry

A three‐dimensional (3D) thermoelastic stress analysis is carried out on a single crystal with axisymmetric geometry but with a hexagonal crystallographic symmetry. The crystallographic orientation is off‐axis with respect to the cylindrical coordinate system. By applying a Fourier series expansion with respect to the rotational angle ϕ of the cylindrical coordinates, the 3D boundary value problem is reduced to a sequence of 2D ones on the meridian plane, which are solved by the finite‐element method. In our example, the off‐axis orientation is towards a direction of high symmetry, and therefore only four of the six stress tensor components are non‐zero. In the end, the stress tensor is projected onto the slip system of the crystal. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Improper ferromagnetic phase transitions in crystals

A complete set of possible improper phase transitions leading to polarization and magnetization of crystals is found from tensor bases of representations of the black-and-white point group of crystal symmetry by using the multiplication table of irreducible representations. The dependences of the secondary order parameter on the primary order parameter are presented for different classes of the symmetry group.     

Properties of nonlinear elastic waves propagating along acoustic axes

Amplitudes and polarization of nonlinear elastic harmonics exited along an arbitrary acoustic axis of the conic type have been studied as functions of the rotation angle of the polarization vector of the degenerate reference wave. When the reference polarization is rotated by an angle of π, the resulting rotation angle for the polarization vector of the second harmonic turns out to be equal to either zero or 2π or ?2π. The actual type of the behavior of the second harmonic propagating along the given acoustic axis is determined by an algebraical criterion for elastic moduli of the second and the third order for the medium. For polarization of the reference wave, we determined the orientations corresponding to the maximum and minimum for the amplitude of the second harmonic. Similar results were obtained for different cases of collinear interactions between degenerate waves, in particular, for the excitation of longitudinal harmonics. The possible control of nonlinear interactions with the use of degenerate-wave polarization in optics and acoustooptics is also discussed.     

Propagation of elastic waves near acoustic axes in crystals under the action of extreme external forces: I. Piezoelectric crystal in an electric field

The directions of an external electric field at which extreme changes occur in the difference in the velocities of elastic waves propagating along the initial acoustic axis in a piezoelectric medium of arbitrary symmetry are theoretically determined. The problem of degeneracy in an external electric field is considered for elastic waves propagating in a given direction from the vicinity of an initial acoustic axis. The extreme electric fields and corresponding changes in the characteristics of transverse waves are calculated by the example of the behavior of acoustic axes in Bi₁₂GeO₂₀, Bi₁₂SiO₂₀, La₃Ga₅SiO₁₄, and LiNbO₃ crystals.     

Orientational Order of Spin Probe Molecules in Liquid Crystals

We report here measurements of hyperfine splittings and g values of two nitroxide spin probes 4',4'-dimethyl-spiro-(5α-cholestane-3,2'-oxazolidin)-3'-yloxyl and 2-(10-carboxydecyl)-2-hexyl-4,4-dimethyl-3-oxazolidinyloxyl methyl ester dissolved in p-azoxyanisole. Using the principal axes values of g and A tensors available, we have determined all three diagonal components of the orientational order parameter tensor S for these spin probe molecules. We find that for neither of the spin probes used here has this tensor S the cylindrical symmetry that is normally assumed to determine the orientational order parameter tensor S^(p) defined by the long molecular axis from such measurements. We show further that this conclusion about S is independent of any uncertainty in the principal axes values of the g and A tensors, and hence the relations between S and S^(p) normally used do not seem to be well justified. Probable relations are also suggested.     

Elastic Properties of the Triclinic Pseudo-Trigonal Room-Temperature Phase of KIO3

Weakly twinned triclinic crystals of the room temperature γ-phase of KIO₃, grown from aqueous solutions, exhibit a quasi-trigonal behaviour of point symmetry group 3m in respect to thermal expansion, piezoelectric effects, and elastic properties. The elastic tensor and its temperature derivative were determined from ultrasonic resonance frequencies of thick plane-parallel plates and their shift upon variation of temperature, respectively. The static piezoelectric constants d₂₂₂ and d₂₁₁ are about fifty times larger than d₁₁₁ of α-quartz resulting in strong piezoelectric coupling coefficients of elastic waves (k₁ = 0.42; k₆₆ = 0.60). Approaching the γ-β transition at 345.6 K from lower temperatures, the shear stiffness c^E₆₆ shows a drastic softening. The transition appears to be of second-order ferroelastic.     

Orientation of optical axes in absorptive crystals with arbitrary permittivity tensors

The direct relation has been established between the orientations of the optical axes and the components of the inverse complex permittivity tensor of an absorptive crystal possessing an arbitrary symmetry. The particular forms of the general relationships for triclinic crystals, characterized by an arbitrary degree of absorption, are obtained for crystals of all the other symmetry systems. The relationships obtained acquire a substantially simplified form for weakly absorptive crystals. The consideration is based on the relationship established for the components of the inverse permittivity tensor in the Cartesian coordinates and the diadic form of this tensor, which is related to the directions of the optical axes.