COMPOSITE MATERIALS
Copyright © Thin Film Center Inc, 2006. All rights reserved.
Introduction
This script chooses two material files and constructs a composite material from them. The
models include the linear Kinosita and Nishibori, an arra of parallel plates (ordinary and
extraordinary rays), Maxwell-Garnett, Bruggeman (spherical inclusions) and Bragg and Pippard
(cylindrical inclusions with axis normal to E-field). Input parameters are the material for the
matrix, the material for the inclusions, the volume fraction of the inclusions (zero implies no
inclusions) and the wavelength values for the calculation. The output is in the form of a new
material document. This can have its values plotted in the usual way and it can also be saved to
the current materials database for further calculations.
Dialogs
An explanatory dialog is shown first, Figure 1.
Figure 1. The explanatory dialog. Cancel will terminate the operation of the script.
Figure 2. Dialog for entry of the details of the model.
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If OK is selected then the Model Details dialog will be presented, Figure 2. The composite
material is considered to consist of a matrix and inclusions (even though in some models they are
considered equivalent). The materials, including Air, can be chosen from the current materials
database. The relative quantities of the two materials is entered as the parameter Inclusion
Fraction. This is the fraction of the total volume of the composite material occupied by the
inclusion. It can be considered to be (1.0-Packing Density). A parameter of 0.1 implies that 10%
of the volume of the composite material is occupied by the inclusions.
There are six different two-component models. Kinosita and Nishibori, a simple linear
interpolation that is the technique used in the packing density model built into the design and
materials documents, two models involving stacks of parallel plates using the expressions from
Born and Wolf, Maxwell-Garnett, Bruggeman, and Bragg and Pippard. In all cases the extinction
coefficients of the two components are included (unlike the built-in linear model). The
Bruggeman and Bragg and Pippard models need depolarizing factors. These have been set for
spherical matrix and inclusions in Bruggeman and cylinders in Bragg and Pippard. These can be
changed manually by editing the script, see later.
Calculations
Should the range of data for either of the two materials be less than that required by the script,
a warning message similar to that in Figure 3 will be shown. The calculations will then continue
and the material values corresponding to the final point of its data will be used in the deficient
region.
Figure 3. Warning when the range of a material is less than that reauired by the
script.
The output is in the form of a new material file, Figure 4 including notes on the derivation of
the optical constants, Figure 5.
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Figure 4. The calculated results are inserted in a new material document that can be
saved in the current materials database.
Figure 5. Notes are added that briefly describe the calculations carried out to derive
the results.
Depolarizing Factor
A depolarizing factor that depends on the structure of the inclusions must be included in the
Bruggeman and the Bragg and Pippard models. The default values assigned to the factor are
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0.3333 in Bruggeman, implying spherical inclusions, and 0.5 in Bragg and Pippard, representing
a cylindrical form of inclusion with axis of revolution normal to the electric field. This
arrangement of the Bragg and Pippard model is intended to besimilar to the columnar structure
seen in vapor-deposited thin films. Other values of the depolarizing factor can, however, be used.
A list taken from Bragg and Pippard (and originally from Stoner) follows.
Values of depolarizing factor L
a/b Lparallel Lperpendicular
Plane 0 1 0
0.7 0.432 0.284
Oblate spheroids 0.8 0.394 0.303
0.9 0.362 0.319
Sphere 1 0.333 0.333
1.1 0.308 0.346
1.2 0.286 0.357
Prolate spheroids
1.3 0.266 0.367
1.4 0.249 0.376
Cylinder Infinite 0 0.5
Bragg, W L and A B Pippard, The form birefringence of macromolecules. Acta
Crystallographica, 1953. 6: p. 865-867.
The depolarizing factors can readily be altered. A section of the script code is shown below.
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The two variables that are concerned are LBruggeman and LBragg. The two statements that
set them are:
LBruggeman=1/3 ' spherical particles
and
LBragg=1/2 ' cylinders
(the part of the statement beyond the apostrophe is a comment and will be shown as green in the
script editor.) These two statements should be changed accordingly. We recommend that the
changes be implemented by copying the two statements, commenting the originals by prefixing
them with an apostrophe (there is an automatic command for this in the editor) and changing the
copies. Then the original configuration can be readily restored.
Date: 4 May 2011
Version: 1.10
Version History:
Version 1.00 - 21 Jan 2006: Original version
Version 1.00.01 – 2 April 2006: Minor alterations to explanatory dialog. Description pdf written.
Version 1.10 – 4 May 2011 Reformatted descriptive dialog for Windows 7
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