GaAs(110) crystal structure package.

*To*: mathgroup at yoda.physics.unc.edu*Subject*: GaAs(110) crystal structure package.*From*: mclean at mnbsun.phy.queensu.ca (Alastar McLean (rm 377))*Date*: Thu, 13 Feb 92 09:54:52 EST

[The files described in this email have been placed on the MathGroup anonymous ftp archive in pub/Packages/GALLIUM_ARSENIDE. The .Hqx file has been tested on a Mac under Mathematica 2.0 after extraction with BinHex 4.0 and works fine. Please report any problems with the archive files to the mathgroup address. -smc] README file for GaAs(110) crystal structure package. ___________________________________________________________________ Alastair McLean Dpt Physics, Queen's University, Kingston, Ontario, K7L 3N6. mclean at mnbsun.phy.queensu.ca 13 February 1992 Copyright 1992 Permission is granted to modify and/or make copies of the files listed below for any purpose other than direct profit, or as part of a commercial product, provided this copyright notice is left intact and incorporated in the modified version. OVERVIEW The Mathematica source code that I have included in this package allows the GaAs(110) surface to be rendered within Mathematica. It is similar to the CrystalStructure.m package that was distributed with the first version of Mathematica. CrystalStructure.m is a representation of the diamond lattice and my packages were partly inspired by the clarity with which CrystalStructure.m renders the diamond lattice, when the final output is generated Postscript, and the fact that I wanted to be able to rotate the crytal structure and view it from different angles to look for symmetry planes etc. Basically these models are alternatives to ball and stick type models. My own research involves studying the electronic structure of semi- conductor surfaces and interfaces and I wanted to generate some models of epitaxial Sb and Bi overalyers on GaAs(110). To do this I had to first generate a model of the zinc blende (110) surface. Some of the packages I have included are therefore applicable to any zinc blende material (GaAs1.m, GaAs2.m, GaAs3.m & GaAs5.m). The other packages (GaAs4.m, GaAs6.m & GaAs7.m) are models of Bi or Sb overlayers on GaAs(110) and I have used the results of electron diffraction studies to position the atoms. The models true to life in the respect that they are scale models. In addition to the packages I have included a detailed Mathematica notebook which shows how to view the packages and describes the packages in considerably more detail than I do here. The notebook is in Macintosh format and it has been run through BinHex 4.0. If you are interested in these packages I strongly suggest you examine the notebook. If you use these packages are a basis for more elaborate packages I would be interested to see the results. If would be nice to have a library of crystal structures available. They are quite painstaking to construct and I'm sure they could be generated in a more elegant fashion. I used brute force ! If you have any comments I can be contacted at mclean at mnbsun.phy.queensu.ca CONTENTS GaAsNotebook.Hqx, GaAs1.m. GaAs2.m, GaAs3.m, GaAs4.m, GaAs5.m, GaAs6.m, GaAs7.m PACKAGE DESCRIPTION GaAsNotebook.Hqx A Macintosh Mathematica notebook which demonstrates how to view the GaAs packages and contains a lot of background information about the structures, including references to the diffraction studies and lots of zinc blende crystal structure jokes (although I refrained from sharing the joke about the bravais lattice). The notebook has been run through BinHex 4.0 to merge the resource and data forks of the Macintosh original. GaAs1.m A section through a zinc blende lattice parallel to (110). Part of a - how to build a zinc blende lattice - tutorial (see the notabook). Sections through the zinc blende lattice parallel to the (110) plane contain zigzag chains of anions (black) and cations (gray). GaAs2.m Tutorial part 2. Building a zince blende lattice in a layer-by-layerfashion. Two (110) planes. No interplane bonds. GaAs3.m Tutorial part 3. Two (110) planes with interplanar bonds GaAs4.m Two GaAs(110) planes, illustrating the surface relaxation of the first and second layers. Relaxation atomic positions taken from LEED studies (Phys Rev B, 42, 8592 (1990)) GaAs5.m Three layer unrelaxed (110) surface model. This is applicable to any zinc blende lattice as I use bulk terminated atomic positions. GaAs6.m Two layers of GaAs(110) plus one layer of either Bi or Sb, unrelaxed atomic geometry GaAs7.m Two layers GaAs(110) plus one layer of Bi in relaxed geometry. Atomic positions are specific to Bi on GaAs(110) and taken from Phys Rev B, 42, 8592 (1990). DISPLAYING THE PACKAGES If you cannot examine the Macintosh notebook, you can display the packages using e.g. << GaAs1.m Show[Picture, ViewPoint->{-1.643, -2.718, 1.168}, BoxRatios->{1, 1, 0.5}] Good Luck ! Alastair McLean