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MathGroup Archive 1992

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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





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