(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 4.0, MathReader 4.0, or any compatible application. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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", "Text"], Cell[BoxData[ \(\(a = 5.653*^-10;\)\)], "Input"], Cell["\<\ Lattice parameter taken from: Data in Science and Technology : Semiconductors, edited by O. Madelung \ (Springer-Verlag, New York, 1992).\ \>", "Text"], Cell[BoxData[ \(\(b1 = \(\@6\/6\) a;\)\)], "Input"], Cell["\<\ Elastic parameters taken from H. J. McSkimin, A. Jayaraman, and P. A. Jr., Journal of Applied Physics 38, \ 2362 (1967). Below are the Voigt averages of these numbers (units of Pa for \[Mu])\ \>", \ "Text"], Cell[BoxData[{ \(\(\[Mu] = 4.867*^10;\)\), "\[IndentingNewLine]", \(\(\[Nu] = 0.2344;\)\)}], "Input"], Cell[TextData[{ "Surface Energy taken at 77K from:\nMoon, W-J and Umeda, T. and Saka, H. \ Philosophical Magazine Letters Vol 83 No 4 P 233-240 (2003)\n(units of ", Cell[BoxData[ \(TraditionalForm\`J/m\^2\)]], ")" }], "Text"], Cell[BoxData[ \(\(\[Gamma] = 0.015;\)\)], "Input"], Cell[TextData[{ "For a 30 degree partial located ", Cell[BoxData[ \(TraditionalForm\`x\_o\)]], "away from the 90 the force per length felt is given by equation 3-90. " }], "Text"], Cell[BoxData[ \(b2 = {Sin[\[Pi]\/6], 0, Cos[\[Pi]\/6]}*\(\@6\/6\) a; \[Xi] = {0, 0, \(-1\)};\)], "Input"], Cell[BoxData[ \(F[x_] := Cross[\((b2 . \[Sigma][{x, 0, 0}])\), \[Xi]]\)], "Input"], Cell["\<\ The attractive force is from the stacking fault. The stacking \ fault energy is given above and the energy per line length is \[Gamma].x. \ The force in the x direction will be the gradient of the energy taken with \ respect to the x direction so the force per line length is just \[Gamma]. \ \ \>", "Text"], Cell["\<\ So the equilibrium length is just the point at which the force \ equals zero\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Roots[\(F[x]\)[\([1]\)] - \[Gamma] \[Equal] 0, x]\)], "Input"], Cell[BoxData[ \(x == \(-1.796242711486858`*^-8\)\)], "Output"] }, Open ]], Cell["So the equilibrium separation is approximately 17.9 nm", "Text"] }, FrontEndVersion->"4.0 for X", ScreenRectangle->{{0, 1600}, {0, 1200}}, WindowSize->{943, 1060}, WindowMargins->{{Automatic, 51}, {26, Automatic}}, Magnification->1.5 ] (*********************************************************************** Cached data follows. 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