非晶Ni-P合金晶化过程中生成的六角亚稳相(Ⅲ)——六角多型体

利用电子显微镜旋转晶体法发现了非晶Ni-P合金晶化过程中生成的另外两个新的六角亚稳相(α₂相与α₃相)。它们与文献[3]报道的六角亚稳相(α₁)具有相同的α值(6.73?),但c值分别为α₁的3/2倍与4倍,表明这些相属于长周期多型体结构,α₂相具有六角密堆结构的消光规律。此外,还证实了α₁中的面心立方亚点阵(α=5.50?)实际上是一个单独的面心立方亚稳相,这些六角亚稳相就 关键词：     

非晶Ni-P合金晶化过程中生成的六角亚稳相(Ⅱ)——孪晶生长关系

非晶Ni-P合金晶化过程中生成的六角亚稳相晶体有四种不同取向,用选区电子衍射证明它们之间存在孪晶生长关系。四种晶体共有一个面心立方亚点阵,孪晶关系可用绕此立方亚点阵的<100>轴旋转90o得出。 关键词：     

有简单取向关系的两晶体间电子衍射图相重的规律

有简单取向关系的两个晶体在倒易空间中有部分倒易点相重。仅由相重倒易点构成的倒易面所对应的电子衍射图必定被基体的衍射斑点所覆盖。给出判定第二相相重电子衍射图晶带轴指数的方法,用此方法考察了立方晶体与孪晶、六角密堆相和ω相等衍射图相重的情况。 关键词：     

非晶Ni-P合金晶化过程中生成的六角亚稳相(Ⅱ) 孪晶生长关系

非晶Ni-P合金晶化过程中生成的六角亚稳相晶体有四种不同取向,用选区电子衍射证明它们之间存在孪晶生长关系。四种晶体共有一个面心立方亚点阵,孪晶关系可用绕此立方亚点阵的<100>轴旋转90℃得出。     

非晶Ni-P合金晶化过程中生成的六角亚稳相(Ⅲ) 六角多型体

利用电子显微镜旋转晶体法发现了非晶Ni-P合金晶化过程中生成的另外两个新的六角亚稳相(α_2相与α_3相)。它们与文献[3]报道的六角亚稳相(α_1)具有相同的α值(6.73),但c值分别为α_1的3/2倍与4倍,表明这些相属于长周期多型体结构,α_2相具有六角密堆结构的消光规律。此外,还证实了α_1中的面心立方亚点阵(α=5.50)实际上是一个单独的面心立方亚稳相,这些六角亚稳相就是在它的{111}面上生成的。     

单晶铁沿[101]晶向冲击过程中面心立方相的形成机制

铁的冲击相变过程是科研工作者们关注的热点领域之一.铁沿[100]晶向冲击时会发生体心立方相到密排六方相的转变;而沿[101]晶向冲击时,相变产物除了密排六方相之外还出现一定量的面心立方相.人们已经明确了体心立方到密排六方相的转变机制,然而对于面心立方相的形成机制问题至今还在探索.本文通过分子动力学方法模拟了体心立方单晶铁沿[101]晶向的冲击过程,模拟结果显示体心立方相将转变为高压密排结构(密排六方相和面心立方相);并分析了面心立方相的形成机制:在冲击过程中,单晶铁沿[101]和101]晶向突然收缩,同时沿[010]晶向突然扩张,从而导致体心立方到面心立方相的转变.此外,本文进一步研究了不同应力状态下单晶铁的相变机制,发现沿[101]晶向单轴压缩以及沿[101]和[101]晶向双轴压缩时铁将发生体心立方到面心立方相的转变;而沿[101]和[010]晶向双轴以及三轴压缩时将会发生体心立方到密排六方相的转变.最后进一步计算了三个相的吉布斯自由能随压力的变化,并对冲击模拟结果进行了能量分析,给出了沿[101]晶向冲击条件下高压密排相产生的原因.     

KdVB方程行波解的渐近分析

本文利用奇异摄动的理论和方法,研究v²?4μ时KdVB方程的行波解,得到行波解的三阶渐近展开式的显式,同时得到行波解的一般渐近展开式的表达式:u≈u⁽⁰⁾+εu⁽¹⁾+ε¹u⁽²⁾+…+εⁿu⁽ⁿ⁾+…;并且证明u^(j)(j=1,2,…,n,…)都是有界函数。 关键词：     

面心立方晶体高次孪晶化为一次旋转对称关系

根据孪生几何与旋转矩阵对应关系以及旋转操作归并定理,总可以将高次孪晶的多次孪生操作化为一次旋转操作。本文计算了面心立方晶体一至五次孪晶化为一次旋转操作的旋转轴[uvw]和旋转角φ,并给出适用于计算机自动分析高次孪晶电子衍射图的计算步骤。 关键词：     

KCdF3晶体中Cr3+-Li+中心局域结构研究

利用零场分裂参量与晶体结构之间的定量关系,研究了双掺杂晶体KCdF₃:Cr³⁺,Li⁺的局域结构。指出,对于KCdF₃:Cr³⁺,Li⁺晶体,四角晶场的形成包含两个方面:(1)由于电荷补偿而产生的等效电荷形成的四角对称晶场;(2)Cr³⁺的局域结构发生晶格畸变而产生的四角对称晶场。事实上,当Cr³⁺和Li⁺掺入KCdF₃晶体时,Cr³⁺代替了Cd²⁺离子;由于Cr³⁺离子与Cd²⁺离子的半径不同、电荷不同、质量不同,导致Cr³⁺的局域结构发生晶格畸变,由此而产生四角对称晶场;由于电荷补偿,Li⁺离子取代了[001]方向与Cr³⁺离子邻近的Cd²⁺离子,由此产生的等效电荷而形成的四角晶场。这样,Cr³⁺的局域结构由O_h对称变为C_4v点对称。文中建立了ZFS参量和晶体结构之间的定量关系。在考虑晶格畸变和等效电荷的基础上,研究了KCdF₃:Cr³⁺,Li⁺晶体的ZFS参量,理论结果和实验符合很好。得到了F^-离子向中心离子分别移动为ΔR₁=0.00268nm,ΔR₂=0.001nm,ΔR₃=0.00165nm。     

锰基高温反铁磁形状记忆合金中马氏体逆相变的表面浮突研究

本文利用原子力显微镜原位研究Mn_79.5Fe_15.6Cu_4.9反铁磁高温形状记忆合金在升降温过程中与马氏体相变相关的表面起伏特征, 同时采用X射线衍射、动态热机械分析等实验检测手段辅助分析其微观组织结构演化, 从纳米尺度分析面心立方–面心四方结构相变及表面浮突产生的物理机理. 实验结果表明: 在升降温过程中观察到帐篷型表面浮突, 由面心立方–面心四方马氏体逆相变产生的, 即母相浮突, 这与通常观测到的马氏体浮突不同; 实验证实面心立方–面心四方马氏体逆相变具有切变特征, 马氏体孪晶的逆向切变是产生帐篷型表面浮突的主要机理; 测得逆孪晶切变的浮突角小于1°, 远小于传统形状记忆合金的表面浮突角值, 这是由于面心立方母相与面心四方马氏体相结构差异较小造成的; 表面浮突随温度变化具有极好的可逆性, 这是马氏体相变晶体学可逆性决定的, 表明该合金具有优良的表面形貌记忆效应.     

Uniform boundedness of the solutions for a one-dimensional isentropic model system of compressible viscous gas

This paper studies an initial boundary value problem for a one-dimensional isentropic model system of compressible viscous gas with large external forces, represented by v _t –u _x =0,u _t +(av ^–) _x =(u _x /v) _x +f( ₀ ^x vdx,t), with (v(x, 0),u(x, 0))= (v ₀(x),u ₀(x)),u(0,t)=u(1,t)=0. Especially, the uniform boundedness of the solution in time is investigated. It is proved that for arbitrary large initial data and external forces, the problem uniquely has an uniformly bounded, global-in-time solution with also uniformly positive mass density, provided the adiabatic constant (>1) is suitably close to 1. The proof is based on L ²-energy estimates and a technique used in [9].     

Extension of the module of invertible transformations. Classification of integrable systems

We demonstrate that for the systems of equations, which are invariant under a point group or possess conservation laws of the zeroth or first order, a nontrivial extension of the module of invertible transformations is possible. That simplifies greatly a classification of the integrable systems of equations. Here we present an exhaustive list and a classification of the second order systems of the formu _t =u _xx +f(u, v, u _x v _x ), –v _t=v _xx +g(u, v, u _x ,v _x ), which possess the conservation laws of higher order. The reduction group approach allows us to define the Lax type representations for some new equations of our list.     

Dissociation energies of the I(3/2g) and I(1/2g) states of Ar+ 2

Rotationally resolved pulsed-field-ionization zero-kinetic-energy (PFI-ZEKE) photoelectron spectra of ⁴⁰Ar₂ and ³⁶Ar₂ have been recorded between 124650cm^?1 and 127 150cm^?1 following resonant two-photon excitation via the 0⁺ _u (v¹= 0) Rydberg state located below the Ar (¹S₀) + Ar?((3p)⁵4s′ [1/2]₁) dissociation limit. Four overlapping vibrational progressions were observed and attributed to transitions to the I(1/2u) u⁺ = 35–50, I(3/2g) u⁺ = 0–10, I(1/2g) v⁺ = 0–6 and I(3/2u) v⁺ = 0–2 vibronic states of Ar⁺ ₂. The vibrational quantum numbers of the ionic states were derived from an analysis of the isotopic shifts, and the dissociation energies of the I(3/2g) (D⁺ ₀(⁴⁰Ar⁺ ₂:) = 1509.4 ± 1.2cm^?1) and the I(1/2g) (D⁺ ₀(⁴⁰Ar⁺ ₂) = 616.3 ± 1.2cm^?1) states were determined.     

Long-Time tails in a random diffusion model

Letw = {w(x)xZ^d} be a positive random field with i.i.d. distribution. Given its realization, letX _t be the position at timet of a particle starting at the origin and performing a simple random walk with jump rate w^–1(X_t). The processX={X _t:t0} combined withw on a common probability space is an example of random walk in random environment. We consider the quantities _t =(d/dt) E (X _t ² –M ^–1 t and _t(w) = (d/dt)E_w(X _t ² – M^– 1t). Here E_w. is expectation overX at fixedw and E = E_w (dw) is the expectation over bothX andw. We prove the following long-time tail results: (1) lim_t t^d/2_t= V²M^d/2–3(d/2)^d/2 and (2) lim_t t^d/4 _st(w)= Z_s weakly in path space, with {Z_s:s>0} the Gaussian process with EZ_s=0 and EZ_rZ_s= V²M^d/2–4(d)^d/2 (r + s)^–d/2. HereM and V² are the mean and variance of w(0) under . The main surprise is that fixingw changes the power of the long-time tail fromd/2 tod/4. Since , with ₀ the stationary measure for the environment process, our result (1) exhibits a long-time tail in an equilibrium autocorrelation function.     

Magnetic circularly polarized emission and magnetic circular dichroism of resolved vibronic lines in Cs2GeF6: Mn4+

Magnetic circularly polarized emission (M.C.P.E.) and magnetic circular dichroism (M.C.D.) techniques have been used to study at low temperatures resolved vibronic lines of the ⁴ A _2g ?² E_g transition in octahedral Mn⁴⁺(3d³) in the cubic host Cs₂GeF₆. Measurements have been made with applied magnetic field (and light propagation) along the [001] (F-Mn-F bond) and [111] directions. Though the Zeeman energy patterns are isotropic, the intensity patterns are not, and U′(Γ₈) eigenvectors for arbitrary field orientation have been derived. These have been used to calculate Zeeman intensity patterns for the [001] and [111] crystallographic directions, and the observed intensity variations with orientation are found to provide useful information about intensity mechanisms. In the case of the magnetic dipole origin, the intensity patterns as a function of orientation can be well accounted for by a first-order mechanism which, however, does not predict the small positive M.C.D. observed at the zero-field energy in the [111] orientation. A detailed analysis of this feature and previously measured energy spacings suggest that ζ_3d(Mn⁴⁺) should have a value of ～360 cm^-1 rather than the value 240 cm^-1 usually assumed. Electric dipole vibronic sidebands have been observed corresponding to v ₆(t _2u ), v ₄(t _1u ), v ₃(t _1u ), v ₄(t _1u ) + v ₅(t _2g ) and v ₂(e_g ) + v ₆(t _2u ). Using a U′→U′ vibronic intensity mechanism with spin-orbit mixing (Appendix A), the M.C.P.E. and total emission patterns for the first two of these regions can be quite well accounted for quantitatively. The corresponding M.C.D. in both cases, while in qualitative agreement with the M.C.P.E., shows much more complicated splitting patterns which are not explicable in terms of a simple k = 0 model. The other three vibronic regions can be accounted for qualitatively. In Appendix B a formula is derived which explicitly relates the M.C.P.E. of a vibronic emission line to its M.C.D. absorption counterpart.     

An invariant measure for the equationu tt −u xx +u 3=0

Numerical studies of the initial boundary-value problem of the semilinear wave equationu _tt –u _xx +u ³=0 subject to periodic boundary conditionsu(t, 0)=u(t, 2),u _t (t, 0)=u _t (t, 2) and initial conditionsu(0,x)=u ₀(x),u _t(0,x)=v ₀(x), whereu ₀(x) andv ₀(x) satisfy the same periodic conditions, suggest that solutions ultimately return to a neighborhood of the initial stateu ₀(x),v ₀(x) after undergoing a possibly chaotic evolution. In this paper an appropriate abstract space is considered. In this space a finite measure is constructed. This measure is invariant under the flow generated by the Hamiltonian system which corresponds to the original equation. This enables one to verify the above returning property.     

Spherically symmetric static solutions of the Einstein-Maxwell equations

We report a new formalism to obtain solutions of Einstein-Maxwell’s equations for static spheres assuming the matter content to be a charged perfect fluid of null-conductivity. Defining three new variablesu=4πεr ²,ν=4πpr ^{2 2} andw=(4π/3)(ρ+ε)r ² whereε, ρ andε denote respectively energy densities of the electric, matter and free gravitational fields whereasp is the fluid pressure, Einstein’s field equations are rewritten in an elegant form. The solutions given by Bonnor [1], Nduka [2], Cooperstock and De la Cruz [3], Mehra [4], Tikekar [5,6], Xingxiang [7], Patino and Rago [8] are all shown to possess simple relations betweenu, v, andw whereas Pant and Sah’s [9] solution for which all the three functions,u, v, andw are constants is a trivial case of the present formalism, We have presented six new solutions with ε = 2ρ. For the first three solutionsw andu are constants withv as a variable whereas the remaining three solutions satisfy the equation of state for isothermal gas;v =kw =-ku where (i)k is an arbitrary constant but not equal to 1 or 1/3 (ii)k = 1 and (iii)k = 1/3. We also obtained a generalization of Cooperstock and De la Cruz’s [3] solution which is regular for 2ρ > ε but singular for 2ρ ≤ ε.     

A Construction of Blow up Solutions for Co-rotational Wave Maps

The existence of co-rotational finite time blow up solutions to the wave map problem from ${\mathbb{R}^{2+1} \to N}The existence of co-rotational finite time blow up solutions to the wave map problem from \mathbbR²⁺¹ ? N{\mathbb{R}^{2+1} \to N} , where N is a surface of revolution with metric d ρ ² + g(ρ)² dθ², g an entire function, is proven. These are of the form u(t,r)=Q(l(t)t)+R(t,r){u(t,r)=Q(\lambda(t)t)+\mathcal{R}(t,r)} , where Q is a time independent solution of the co-rotational wave map equation −u _tt  + u _rr  + r ⁻¹ u _r  = r ⁻² g(u)g′(u), λ(t) = t ^−1-ν, ν > 1/2 is arbitrary, and R{\mathcal{R}} is a term whose local energy goes to zero as t → 0.     

4 Ag ↔2 Eg Transition of Mn4+ in Cs2TiF6: MnF6 2-

We report and interpret the ⁴ A_2g ?² E_g absorption, emission, linear dichroism, MCD and MCE of the MnF₆ ^2- octahedra at sites of D_3d symmetry in single crystals of Cs₂TiF₆. The spectra show many sharp features but a simplified calculation using cubic basis functions successfully accounts for all of the major features and much of the detailed structure. The electronic levels are not split by the trigonal field in first order but trigonal distortion splits the three-fold degenerate v ₆(t_2u ) vibration of the octahedron into a two-fold degenerate v ₆(e_u ) and a non-degenerate v ₆(a_1u ) vibration and these two vibrational modes give rise to the features 213 cm^-1 and 246 cm^-1 from the zero-phonon line respectively. Similarly the v ₄(t_1u ) vibration is split into a v ₄(a_2u ) and v ₄(e_u ) vibration and give the features at 313 cm^-1 and 340 cm^-1 respectively.

Several transitions involving two or more quanta of vibration are clearly seen in the emission and MCE spectrum. At an energy shift of greater than 700 cm^-1 from the zero-phonon transition these features are found to consist of progressions in the v ₁(a_1g ) breathing mode and the v ₂(e_g ) two-fold degenerate Jahn-Teller active mode. This structure can again be explained, with one exception, in terms of a calculation which assumes cubic basis functions. The exception is the reversal in sign of the MCE at a frequency v ₆(e_u ) + v ₂(e_g ) compared with that at v ₆(e_u ) which is not fully understood.