液晶近晶C相双轴特性的统计理论

采用格胞模型,定义了分子取向序参量、双轴序参量、质心位置序参量以及取向与质心位置耦合序参量.由自由能极小求得指向矢倾斜角与双轴序参量间的关系.对典型Sc相液晶物质TBBA,TBSA和NOBA的双轴序参量随温度的变化以及取向序参量和倾斜角对双轴序参量的影响作了数值计算,并与实验结果进行比较.表明这种双轴特性主要产生于Sc相的指向矢倾斜结构和分子取向的有序性. 关键词：     

三维动态Ising模型中的非平衡相变:三临界点的存在

用Monte Carlo方法模拟了三维动态Ising模型中的非平衡相变,用统计的观点研究了序参量的大小和分布以描述该相变过程.保持温度和外场频率不变,改变外场大小使之由小到大变化,序参量由非零值变成零值.在低温阶段,序参量呈非连续变化,为典型的非连续相变,在高温阶段,序参量呈连续变化,为典型的连续相变.本文确定了界定非平衡转变的相界,并进一步确定了相界上区分非连续连续相变的三临界点.外场频率ω减小时,三临界点温度T_TCP向高温部分移动,并满足T_TCP=1.33× 关键词： 动态相变 Ising模型 三临界点     

液晶SmC*相螺旋结构的统计理论

采用格胞模型,定义在格胞中心上的分子取向序参量、质心位置序参量和两者耦合序参量。选用双轴性并有横向电偶极矩的分子的作用两体势,求出系统的自由能,对自由能求变分得到指向矢满足的微分方程,由此方程得到SmC^*相指向矢与分子层面法线倾斜,并沿该法线作螺旋式变化,求得倾斜角和螺距的近似表示式,计算了DOBAMBC等三种典型SmC^*相液晶的倾斜角和螺距随温度的变化,结果与实验相符。     

向列型液晶的硬棒理论与分子取向短程关联

在向列型液晶的硬棒理论中引入分子取向短程关联。理论的出发点是Ｓｉｎ－ＤｏｏＬｅｅ的自由能表示，这一表示基于Ｃａｒｎａｈａｎ－Ｓｔａｒｌｉｎｇ状态方程。用包括了分子短程关联的取向熵代替原来平均场形式的取向熵项，得到新的自由能表示。通过自由能对分子取向分布求变分确定平衡态分布。对液晶ＰＡＡ进行了数值计算。给出了相变点序参数、熵变、相变点致密度和相对密度变化的计算值。考虑短程关联后的理论值较通常硬棒理论有显著改进。因此，在某种程度上克服了硬棒理论的困难。     

液晶SmC*相自发极化的统计理论

采用格胞模型，定义在格胞中心上的极化序参量．选用双轴性并具有横向电矩的分子作用势，求得系统的自由能，得到自发极化强度的大小和螺旋变化螺距的表达式．计算了DOBAMBC和3M2CPOOB等4种典型SmC^*相液晶的自发极化强度大小和螺距随温度的变化及其受分子横向电矩的影响，结果与实验相符．表明SmC^*相的自发极化强度主要产生于分子的双轴性和横向电矩． 关键词：     

氢键铁电体相变的格林函数理论(Ⅱ)

在文献[1]的基础上,计算了包括四体相互作用项的氢键铁电系统自由能,给出了确定铁电一级相变时序参数跃变和居里温度的表示式。通过对自由能在相变温度附近行为的详细分析,表明了微观理论结果与朗道热力学理论完全一致,并给出了朗道自由能表示式中各系数与微观相互作用参数之间的关系,使各系数的物理意义更加明确。再通过与PbHPO₄,PbDPO₄和H₂C₄O₄等晶体的实验结果比较,进一步证明本文理论能成功地处理氢键铁电体的一级相变和二级相变问题。 关键词：     

有序-无序型铁电和反铁电相变的格林函数理论

本文在对称截断近似下,对格林函数在研究有序-无序型铁电和反铁电相变中的应用做了初步探讨。还发现,可以直接利用所得的序参数S随温度T变化关系,同时确定相变的二个临界参数S_c和T_c,从而自然得出相交级数(一级相变或二级相变)的结论。本文较详细地讨论了所得结果,并给出了几种晶体的理论结果与实验的比较。 关键词：     

序参量的自洽方程与手征对称性恢复的相变

本文用解析方法研究了有限温度和密度下的手征相变.把零温情形下序参量的自洽方程加以推广,建立了有限温度情形下的相应方程.由此得到了序参量随温度的变化关系,证实了手征对称性恢复的相变的存在,求出了理论的相图.     

元胞自动机交通流模型的相变特性研究

系统地研究 VDR模型和T²模型在不同车流密度时车辆位置的相关性. 通过VDR模型、BJH模型和T²模型的序参量计算，确定在这三个模型中车流从自由流动到阻塞的相变特性，结果发现引入慢启动规则后，在不同的延迟概率和最大速度情况下，将引起交通相变特性的改变. 关键词： 交通流 元胞自动机 相关函数 序参量     

化合物HoMn6Sn6的磁晶各向异性及自旋重取向相变研究

采用交换相互作用的分子场理论模型对金属间化合物HoMn₆Sn₆的自旋重取向相变进行了研究. 从理论上计算了HoMn₆Sn₆的易磁化方向以及Ho和Mn离子磁矩与c轴夹角随温度的变化. 基于单离子模型计算了Ho离子的一阶和二阶磁晶各向异性常数K_1R和K_2R随温度的变化. 研究表明，为了很好描述该化合物的自旋重取向相变，必须考虑Ho离子的四阶晶场项及相应的二阶磁晶各向异性常数K_2R，K_2R与K_1R和Mn离子磁晶各向异性常数K_1t之间的相互竞争是导致HoMn₆Sn₆自旋重取向相变的重要因素. 关键词： 稀土-过渡族金属间化合物 自旋重取向 磁晶各向异性     

Free energy landscape from path-sampling: application to the structural transition in LJ38

We introduce a path-sampling scheme that allows equilibrium state-ensemble averages to be computed by means of a biased distribution of non-equilibrium paths. This non-equilibrium method is applied to the case of the 38-atom Lennard-Jones atomic cluster, which has a double-funnel energy landscape. We calculate the free energy profile along the Q₄ bond orientational order parameter. At high or moderate temperature the results obtained using the non-equilibrium approach are consistent with those obtained using conventional equilibrium methods, including parallel tempering and Wang-Landau Monte Carlo simulations. At lower temperatures, the non-equilibrium approach becomes more efficient in exploring the relevant inherent structures. In particular, the free energy agrees with the predictions of the harmonic superposition approximation.     

Free energy of semiflexible polymers and structure of interfaces

The free energy of semiflexible polymers is calculated as a functional of the compositional scalar order parameter and the orientational order parameter of second-rank tensor S_ij on the basis of a microscopic model of wormlike chains with variable segment lengths. We use a density functional theory and a gradient expansion to evaluate the entropic part of the free energy, which is given in a power series of .The interaction term of the free energy is derived with a random phase approximation. For the rigid rod limit, the nematic-isotropic transition point is given by , N and w being the degree of polymerization and the anisotropic interaction parameter, respectively, and the degree of ordering at the transition point is 0.33448. We also find that the contour length of polymer chains becomes larger in a nematic phase than in an isotropic phase. Interface profiles are obtained numerically for some typical cases. In the neighborhood of isotropic-isotropic interfaces, polymer chains tend to align parallel to the interface on the polymer-rich side and perpendicular on the poor side. When an isotropic region and a nematic region coexist, orientational order parallel to the interface is preferred in the nematic region. Received: 28 May 1998 / Revised: 12 August 1998 / Accepted: 8 September 1998     

Internal energy and parameters of the order-disorder phase transition in titanium monoxide TiO y

Quantum-mechanical ab initio calculations are used to simulate the free energy functions for titanium monoxide TiO _y . The effect of the long-range order of the Ti₅O₅ type superstructure on the internal energy of the compound is studied by the supercell method. The dependences of the configuration entropy and free energy on the long-range order parameter are determined. It is found that the order-disorder phase transition in titanium monoxide must occur in accordance with the mechanism of the first-order phase transition with a critical value of the long-range order parameter of 0.971. The calculated parameters of the phase transition are compared with the experimental data and the results obtained using the model of point charges and by calculating the Madelung energy. It is concluded that the short-range order and the phonon entropy must be taken into account in calculating the equilibrium phase diagrams for strongly nonstoichiometric compounds.     

Experimental determination of magnetic landau parameters in ErRh4B4

From d.c. magnetization data obtained between 0.45 and 13 K we derive the bare Curie temperature, the temperature dependence of the paramagnetic susceptibility, and the coefficients of the higher order terms in the Landau expansion of the magnetic free energy for ErRh₄B₄. We find the unexpected result that the fourth order term is small or zero. Consequently the sixth order term plays the dominant role in stabilizing the magnetic phase.     

Structural stability in the spinel compound CdIn2S4

Summary Experimental as well as theoretical investigations have been made about the detailed nature of the cation distribution in the spinel compound CdIn₂S₄. A microwave passive radiometry technique has been adopted to search for phase transitions in the temperature range 300 to 500 K. The experimental results are consistent with the specific-heat data obtained by Czaja and give further evidence for a second-order transition at 403 K. A recently developed semi-classical approximation has been used in order to obtain reliable structuraa energy values without introducing any adjustable parameter. Our theoretical result for the equilibrium lattice constant is very close to the experimental value. As for the cation distribution it appears that the distribution corresponding to the inverse phase is favoured in energy, atT=0 K, with respect to the normal one. Supported in part by M.P.I., Italia.     

Spontaneous polarization and repolarization in crystals of the perovskite type

Based on molecular kinetic concepts, we have theoretically studied the processes of polarization and repolarization in ABO₃ crystals with a perovskite structure. We have calculated the free energy taking into account the possible displacements of the A atoms of the transition element from the equilibrium positions and the ordering of the dipole moments; we have found the dependence of the free energy for different phases of the crystal on temperature, the dipole order parameter, and the energy constants. We have obtained the thermodynamic equilibrium equation determining the temperature dependence of the degree of dipole order; we have found the Curie-Weiss transition temperature from the paraelectric to the ferroelectric state. Analysis of the equations obtained allowed us to provide a basis for the polarization and repolarization processes observed experimentally in BaTiO₃ and KNbO₃ crystals and to estimate the phase transition temperatures.Dnepropetrovsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 8–14, May, 1995.     

A generalized Ginzburg-Landau approach to second harmonic generation

We develop a generalized Ginzburg-Landau theory for second harmonic generation (SHG) in magnets by expanding the free energy in terms of the order parameter in the magnetic phase and the susceptibility tensor in the corresponding high-temperature phase. The non-zero components of the SHG susceptibility in the ordered phase are derived from the symmetries of the susceptibility tensor in the high-temperature phase and the symmetry of the order parameter. In this derivation, the dependence of the SHG susceptibility on the order parameter follows naturally, and therefore its nonreciprocal optical properties. We examine this phenomenology for the magnetoelectric compound Cr₂O₃ as well as for the ferroelectromagnet YMnO₃. Received 27 August 1999     

Elastic properties of the RIV-RIII rotator phases of alkanes

A model free energy has been constructed to describe the R_IV-R_III rotator phase transition in alkanes in terms of the elastic strains and order parameter. The conditions for the R_IV-R_III phase transition are discussed. From the free energy, the order parameter and the elastic strains are determined. The model free energy describes the first or second order character of the R_IV-R_III transition depending on the strength of the coupling. The elastic properties in the vicinity of the R_IV-R_III transition are discussed on the basis of a free energy expansion. The temperature dependence of the elastic constants is calculated on both sides of the transition. The coupling between the order parameter and elastic stains is shown to have a crucial influence on the phase behavior and the order of the transition.