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In the classical
Peierls--Nabarro (P-N) theory of dislocation,
there is a long-standing contradiction that the stable configuration
of dislocation has maximum energy rather than minimum energy. In
this paper, the dislocation energy is calculated rigorously in the
context of the full lattice theory. It is found that besides the
misfit energy considered in the classical P-N theory, there is an
extra elastic strain energy that is also associated with the
discreteness of lattice. The contradiction can be automatically
removed provided that the elastic strain energy associated with the
discreteness is taken into account. This elastic strain energy is
very important because its magnitude is larger than the misfit
energy, its sign is opposite to the misfit energy. Since the elastic
strain energy and misfit energy associated with discreteness cancel
each other, and the width of dislocation becomes wide in the lattice
theory, the Peierls energy, which measures the height of the
effective potential barrier, becomes much smaller than that given in
the classical P-N theory. The results calculated here agree with
experimental data. Furthermore, based on the results obtained, a
useful formula of the Peierls stress is proposed to fully include
the discreteness effects. 相似文献
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锯齿型单壁碳纳米管的广义层错能计算 总被引:1,自引:0,他引:1
基于密度泛函理论的第一性原理方法,计算了两种不同半径的锯齿型单壁碳纳米管以及单层石墨的广义层错能曲线。对小位移处广义层错能曲线进行斜率拟合所得切变模量与其它文献值一致。对三条广义层错能曲线的对比可知,锯齿型碳纳米管与单层石墨的广义层错能曲线相近,锯齿型单壁碳纳米管的曲率效应不明显。 相似文献
5.
On the core structure and mobility of the 〈100〉{010} and 〈100〉{01^-1} dislocations in B2 structure YAg and YCu 下载免费PDF全文
Dislocations are thought to be the principal mechanism of high ductility of the novel B2 structure intermetallic compounds YAg and YCu.In this paper,the edge dislocation core structures of two primary slip systems 〈100 〉{010} and 〈100 〉 {011} for YAg and YCu are presented theoretically within the lattice theory of dislocation.The governing dislocation equation is a nonlinear integro-differential equation and the variational method is applied to solve the equation.Peierls stresses for 〈100 〉 {010} and 〈100 〉 {011} slip systems are calculated taking into consideration the contribution of the elastic strain energy.The core width and Peierls stress of a typical transition-metal aluminide NiAl is also reported for the purpose of verification and comparison.The Peierls stress of NiAl obtained here is in agreement with numerical results,which verifies the correctness of the results obtained for YAg and YCu.Peierls stresses of the 〈100 〉 {011} slip system are smaller than those of〈100 〉 {010} for the same intermetallic compounds originating from the smaller unstable stacking fault energy.The obvious high unstable stacking fault energy of NiAl results in a larger Peierls stress than those of YAg and YCu although they have the same B2 structure.The results show that the core structure and Peierls stress depend monotonically on the unstable stacking fault energy. 相似文献
6.
From Discreteness to Continuity: Dislocation Equation for Two-Dimensional Triangular Lattice 下载免费PDF全文
A systematic method from the discreteness to the continuity is presented for the dislocation equation of the triangular lattice. A modification of the Peierls equation has been derived strictly. The modified equation includes the higher order corrections of the discrete effect which are important for the core structure of dislocation. It is observed that the modified equation possesses a universal form which is model-independent except the factors. The factors, which depend on the detail of the model, are related to the derivatives of the kernel at its zero point in the wave-vector space. The results open a way to deal with the complicated models because what one needs to do is to investigate the behaviour near the zero point of the kernel in the wave-vector space instead of calculating the kernel completely. 相似文献
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An improvement of the lattice theory of dislocation for a two-dimensional triangular crystal 下载免费PDF全文
The structure of dislocation in a two-dimensional triangular crystal has been studied theoretically on the basis of atomic interaction and lattice statics. The theory presented in this paper is an improvement to that published previously.Within a reasonable interaction approximation, a new dislocation equation is obtained, which remedies a fault existing in the lattice theory of dislocation. A better simplification of non-diagonal terms of the kernel is given. The solution of the new dislocation equation asymptotically becomes the same as that obtained in the elastic theory, and agrees with experimental data. It is found that the solution is formally identical with that proposed phenomenologically by Foreman et al, where the parameter can be chosen freely, but cannot uniquely determined from theory. Indeed, if the parameter in the expression of the solution is selected suitably, the expression can be well applied to describe the fine structure of the dislocation. 相似文献
10.
Core structure and Peierls stress of the 90° dislocation and the 60° dislocation in aluminum investigated by the fully discrete Peierls model 下载免费PDF全文
The core structure, Peierls stress and core energy, etc. are comprehensively investigated for the $90^\circ$ dislocation and the $60^\circ$ dislocation in metal aluminum using the fully discrete Peierls model, and in particular thermal effects are included for temperature range $0\leq T \leq 900$ K. For the $90^\circ$ dislocation, the core clearly dissociates into two partial dislocations with the separating distance $D\sim 12$ Å, and the Peierls stress is very small $\sigma_{\rm p}<1$ kPa. The nearly vanishing Peierls stress results from the large characteristic width and a small step length of the $90^\circ$ dislocation. The $60^\circ$ dislocation dissociates into $30^\circ$ and $90^\circ$ partial dislocations with the separating distance $D\sim 11$ Å. The Peierls stress of the $60^\circ$ dislocation grows up from $1$ MPa to $2$ MPa as the temperature increases from $0$ K to $900$ K. Temperature influence on the core structures is weak for both the $90^\circ$ dislocation and the $60^\circ$ dislocation. The core structures theoretically predicted at $T=0$ K are also confirmed by the first principle simulations. 相似文献