夹杂理论及其在断裂研究中的应用

利用无限介质中的格林函数,本文首先导出一般形状的夹杂所产生的拘束应力场,夹杂中的无应力应变ε_ij^*可以是位置的函数,在此基础上,给出了平面问题的全部计算公式,文中把裂纹或空腔看做是其弹性常数为零的一种特殊的异性夹杂,在物体受到外加应力场的作用时,计算了与椭圆空腔等效的夹杂的无应力应变,对于扁平形状的夹杂,在其端点附近显示出与裂纹完全类似的r^-1/2式应力奇点,算出了相应的应力强度因子,对于本文结果的一些应用做了讨论,例如椭圆空腔与外加应力场的交互作用,马氏体转变和形变孪晶所伴随形成的微观裂纹等。 关键词：     

利用超声脉冲回波重合法测定铌酸锂单晶弹性常数CijE和CijD

本文从基本的压电Christoffel方程出发导出三角晶系3m点群压电晶体弹性常数的表示式。并采用10MHz射频超声脉冲回波重合法测量了沿LiNbO₃不同对称方向传播的声速,结合e_ij和ε_ij⁵给出了LiNbO₃全部弹性常数C_ij^E和C_ij^D。它们是C₁₁^E=19.8 关键词：     

陶瓷材料中圆形夹杂的本征应变导致的微开裂

由夹杂转变引起的微开裂与陶瓷材料的断裂和增韧机制密切相关。本文采用位错连续分布的方法,导出圆形夹杂发生本征应变时在母体材料中形成的微裂纹的位错密度函数、张开位移及应力强度因子的解析表达式,并据本文得到的结果进行了分析和讨论。 关键词：     

NiTi合金中应力诱导的I/C相变及其界面动力学的研究

在改装了的拉力试验机上,以不同的拉伸速率ε(0.79—18×10^-5s^-1)进行加、卸载试验,并用中间扭摆和四端电位法同时测量了Ni-49at％Ti合金丝在应力诱导I/C相变过程的内耗Q^-1、模量M/M₀、电阻率ρ/ρ₀和应力-应变曲线。研究了应力循环和应变速率的影响。在Q^-1-ε曲线上出现Q^-1峰,而在f²-ε曲线上出现与之相对应的模量极小。内耗峰的高度Q_p^-1和模量亏损值均随ε增大而增大。根据界面动力学模型和内耗的实验数据,计算得应力诱导I/C相变过程界面的动力学关系为V=V^*(△G—△G_R)^m,V^*和m为动力学参数,△G_R为相变过程中运动相界面所受的阻力,计算得△G_R≈1cal/mol。讨论了内耗和模量亏损、软模效应之间的关系。 关键词：     

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：     

弹性连续介质中氢致裂纹传播理论

弹性连续介质中的氢原子,在裂纹应力场的诱导下发生聚集,形成氢气团,本文计算了气团分布区平均氢浓度,并将该区看作沿裂纹尖端分布的弹性夹杂,确定了夹杂的本征应变,研究了夹杂的应力场P_ij对裂纹位错密度的影响,求得了裂纹尖端总的应力强度因子,认为氢脆机理是氢气团增大了裂纹尖端应力强度因子,最后还讨论了氢致开裂的物理过程及氢致裂纹扩展速率,所得结果与实验符合很好。 关键词：     

样品表面层有微观应变梯度时Warren-Averbach方法的修正

本文讨论了样品表面层有微观应变梯度时X射线衍射线形分析的方法.设样品表面层微观应变随深度t的变化满足关系式<ε_L²>=∑a_m(L)t^m,从而改进了Warren-Averbacb方法,使之可以应用到表面层存在微观应变梯度的情形.若<ε_L²>=a₀(L)+a₁(L)t,则分析二种波长不同的X射线同一衍射方向的衍射线形,可以得到微观应变随深度的变化规律. 关键词：     

As+注入硅的紫外-可见椭圆偏振光谱

本文采用椭圆偏振光谱法研究了剂量为1×10¹⁶—3×10¹²cm^-2的As⁺注入硅,及其在700℃退火后的光学性质。得出:当As⁺注入剂量增大到某一程度后,便呈非晶特性。低于临界剂量的样品,其n-λ,ε₂-λ关系曲线随剂量的增大而往下方移动,呈有规律变化;退火后,在大于4000?波段,n-λ与ε₂-λ曲线基本恢复到单晶硅状态。但在小于4000?的紫外区却未完全恢复,注入剂量越大,偏离单晶硅就越大。并指出,紫外光区是离子注入硅的信息敏感区;用有效质量模型计算出注入剂量与损伤度的关系。计算结果与实验符合得较好。 关键词：     

一维六方准晶非周期平面内的平面应变理论

针对一维六方准晶中一种新平面弹性问题, 即非周期平面内的平面弹性问题, 通过引入应力势函数, 建立了一维六方准晶中非周期平面内的平面应变理论. 作为应用, 求解了一维六方准晶中垂直于准周期方向的椭圆孔口问题, 得到了其弹性应力场的解析解. 在极限情形下, 可给出裂纹问题的解. 关键词： 一维六方准晶 椭圆孔口 广义解析函数     

存在异性夹杂的位错塞积

本文采用位错连续分布方法,导出了在外应力作用下异性夹杂和障碍之间相对障碍的单螺位错塞积和双螺位错塞积的分布函数的解析表达式D₁(η),D₂(η)。在靠近障碍一端,D₁(η)和D₂(η)具有-1/2次幂的奇异性,在靠近夹杂一端,D₂(η)具有-ω次幂的奇异性。并用双位错塞积的情况表示了与异性夹杂相接触的反平面剪切裂纹问题,导出了应力强度因子。这些表达式对于02/G₁<∞完全适用。对所得的结果进行了讨论。 关键词：     

Dielectric relaxation phenomena of rigid polar liquid molecules under giga hertz electric field

The dielectric relaxation phenomena of rigid polar liquid molecules chloral and ethyltrichloroacetate (j) in benzene, n-hexane and n-heptane (i) under 4.2, 9.8 and 24.6 GHz electric fields at 30°C are studied to show the possible existence of double relaxation times τ ₂ and τ ₁ for rotations of the whole and the flexible parts of molecules. The probability of showing double relaxation is more in aliphatic solvents indicating their nonrigidity. The symmetric and asymmetric distribution parameters γ and δ are obtained from X _ij ^′ /X _0ij and X _ij ^″ /X _0ij and w _j →0 where X _ij ^′ and X _ij ^″ are real and imaginary parts of the complex orientational susceptibility X _i ^* and X _0ij is the low frequency susceptibility which is real. X _ij ’s are involved with the measured dielectric relative permittivities ε _ij ^′ , ε _in ^″ , ε _0ij and ε _∞ij of solutions. The theoretical weighted contributions c ₁ and c ₂ towards dielectric dispersions by Fröhlich’s method are compared with the experimental ones obtained from the graphical variation of X _ij ^′ /X _0ij and X _ij ^″ /X _0ij with weight fractions w _j ’s at w _j → 0. The measured dipole moments μ ₂ and μ ₁ of the whole and the flexible part of a polar molecule in terms of the linear coefficients β’s of X _ij ^′ ’s with w _j ’s and the estimated τ ₂ and τ ₁ reveal their associations with aliphatic solvents. The theoretical dipole moments μ _theo’s from the available bond angles and bond moments of the substituent polar groups of the molecules with the estimated μ’s suggest the mesomeric, inductive and electromeric effects in them under GHz electric field.     

Two-Channel Effective Range Expansion and Bound-State Properties

The S matrix and the f matrix amplitudes are considered for the case of two coupled elastic scattering channels, which differ in values of orbital angular momenta. Matrix elements of S and f matrices are parametrized in terms of scattering phases ?? _i (i?=?1, 2) and a mixing parameter ${\epsilon}$ and are expressed in terms of matrix elements c _ij = (K ^?1) _ij where K is the reaction K matrix. Quantities ${g_{ij}(k)=k^{l_i+l_j+1}c_{ij}(k)}$ are expanded in powers of k ², k being the relative momentum of colliding particles B and C. Then functions g _ij (k) and c _ij (k) are continued analytically to the pole of amplitudes f _ij corresponding to the bound state A of colliding particles. This procedure allows to get the position of the pole as well as the residues of amplitudes f _ij at that pole which are related directly to vertex constants and asymptotic normalization coefficients corresponding to the vertex A ?? B?+?C.     

Invariance of the Massless Field Equations under Changes of the Metric

It is shown that the Maxwell equations with sources, expressed in terms of the covariant tensor field F_ijand the current density four-vector Jⁱ, are invariant under the change of the metric g_ijby g_ij = g_ij+ l_il_jif l_iis a principal null direction of F_ijand that an analogous result holds in the case of the massless Klein-Gordon equation if l_iis null and orthogonal to the gradient of the field and in the case of the null dust equations if l_iis parallel to the dust four-velocity. An elementary proof of the following generalization of the Xanthopoulos theorem is also given: Let (g_ij, F_ij) be an exact solution of the Einstein-Maxwell equations and let l_ibe a principal null direction of F_ij, then (g_ij+ l_il_j, F_ij) is also an exact solution of the Einstein-Maxwell equations if and only if (l_il_j, 0) satisfies the Einstein-Maxwell equations linearized about the background solution (g_ij, F_ij). Furthermore, analogous theorems, where the source of the gravitational field is a massless Klein-Gordon field or null dust, are presented.     

Perturbation calculation of the distribution functions of mixtures of hard spheres

The distribution functions for a mixture of additive hard spheres of diameter σ_ii are calculated by means of an expansion in powers of σ _ij ⁿ - dⁿ , using an unperturbed single-component hard-sphere fluid of diameter d. Although the expansion converges only when the hard spheres in the mixture are nearly equal in size, it is useful because it is the only practical scheme available for obtaining the distribution functions of multicomponent hard-sphere mixtures.     

Renormalization problem in nonrenormalizable massless Φ4 theory

Nonrenormalizable massless Φ⁴ theory is made finite by regularization via higher derivatives in the kinetic part of the Lagrangean. The theory is shown to remain finite in the infinite cutoff limit if certain integrals over functions of one variable, with computable Taylor expansion at the origin, are finite. The values of these integrals are the only unknowns in the double series in powers ofg andg ^2/ε obtained for the Green's functions in massless (Φ⁴)_4+ε with generic ε. For ε=1 and ε=2, these series reduce to double series in powers ofg and lng. The problems of extension to (Φ⁴)_4+ε with mass, of causality and unitarity, of the relation to the BPHZ formalism, and of the indeterminacy of the result are discussed.     

Extension to velocity dependent gauge transformations

In previous papers it was shown that in phase space a generator of gauge transformations for a singular Lagrangian \(L(q,\dot q)\) is given byG[ε^α]=ε _k ^α φ _α ^k (q,p,t) where φ _α ^k are first class constraints andG is subjected to a stationarity condition. A non-trivial extension from velocity (or momentum) independent gauge transformations to velocity dependent ones is realized, by replacing gauge functions ε^α(t) with momentum dependent functions ε^α(q,p,t), as long asG satisfies the stationarity condition. Inversely, it is proved in a classical framework that, within velocity dependent gauge transformations, all generators of gauge transformations can be expressed in terms of the linear combinations of φ _α ^k .     

直流偏置电场下BaTiO３基陶瓷介电常数非线性机理的研究

采用传统固相法制备了Ba_0.6Sr_0.4TiO_３(BST)和BaZr< sub>xTi_１-xO_３(x=0.25，0.3，0.35，0.4)（ＢＺＴ）陶瓷 ，并对其在直流偏置电场下的介电常数非线性行为进行了系统、详细的研究.结果表明，基 于Devonshire的宏观相变理论(phenomenological theory)提出的公式ε_r(app) ε_r(0)=1［1+αε^{３_{r(0)E２ ］1/3和ε(E)=ε1－ε2E2+ε3E4，均可定量地解释BST体系顺电相的介电常数非线性行为，其中εr (app)表示材料在电场下的介电常数，εr(0)表示不加电场即静态下材料 的介电常数，α是非谐性因子，E表示电场强度，ε(E)表示材料在电场下的介电常数，ε１，ε２，ε３分别表示线性、非线性和高阶介电常数. 而对于处于铁电相和居里温度附近的BST体系，则需要考虑铁电畴对介电常数非线性的贡献 ，这种贡献随着外加直流偏置电场强度的增大逐步减小.对于弛豫铁电体BZT体系，即使处于 顺电相，也必须考虑由极性微区的冻结与合并引起的介电常数的下降，极性微区对介电常数 非线性的贡献随着电场强度和温度的上升而有所下降. 关键词： BST x}Ti_１-xO_３')" href="#">BaZr_xTi_１-xO_３ 可调性 介电 常数非线性 直流偏置电场}     

Effects of the overlap between wave functions of impurity centers on the activation energy of hopping conduction

The hopping conductivity σ₃ has been studied in samples of slightly counterdoped crystalline Si: B with a boron concentration of 2×10¹⁶ cm^?3<N<10¹⁷ cm^?3 and a compensation of 10^?4≤K≤10^?2. It is found that at K≤10^?3 the activation energy ε₃ is not lower (as it must be according to classical notions at finite K) but larger than the value ε_N=e ² N ^1/3/κ, where e is the electronic charge and κ is the dielectric constant. With decreasing N, the energy ε₃ drops slower and, with decreasing K, grows faster than follows from the standard theory. At K≤10^?4, ε₃ is higher than ε _N by a factor of 1.5–2. The result is explained by the effect of the overlap between wave functions of neighboring impurity centers on the structure of the impurity band.     

Renner parameters of isotopic polyatomic molecules

From a consideration of the form of the bending potential in internal coordinates for a ¹Π electronic state of a linear molecule, the equations for calculating the bending vibrational frequencies and Renner parameters of different isotopic molecules are obtained, and relations connecting the Renner parameters of different isotopes are derived. The recent results for the [Gtilde] ¹Π _u and [Htilde] ¹Π _u states of acetylene isotopes [5] are consistent with the theory, but it is not possible at present to determine the sign of ε₅₅ for the [Htilde] ¹Π _u state from the C₂HD isotope effect on ε₄₄.