Materials Algorithms Project
Program Library

Program MAP_CRYSTAL_CEMSTRUCT

1. Provenance of code.
2. Purpose of code.
3. Specification.
4. Description of subroutine's operation.
5. References.
6. Parameter descriptions.
7. Error indicators.
8. Accuracy estimate.
9. Any additional information.
10. Example of code
11. Auxiliary subroutines required.
12. Keywords.
13. Download source code.
14. Links.

Provenance of Source Code

M.Lord and H.K.D.H. Bhadeshia,
Phase Transformations Group,
Department of Materials Science and Metallurgy,
University of Cambridge,
Cambridge, U.K.

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Purpose

Calculates the RELATIVE intensities of electron diffraction spots when forming an electron diffraction pattern from a region of cementite (Fe₃C) in a transmission electron microscope.

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Specification

Complete program

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Description

MAP_CRYSTAL_CEMSTRUCT calculates the relative intensities of electron diffraction spots for lattice spots up to those where h = k = l = 3.

Its most important use is in the identification of the cementite phase using electron diffraction, as some spots have extremely weak diffracted intensities. The calculated 'absence' of such spots aids in the identification of zone axes and thus speeds the identification of the cementite phase.

Calculations are performed to double precision. The accuracy of the results is dependent upon the accuracy of the measured atomic positions within the unit cell (taken from the literature) and upon the simplifying assumption that the atomic scattering factors of Fe and C are constant in relation to each other as a function of diffracted angle. Hence the results provide a guide but should not be considered as exact. The evaluation of scattering angles was performed for a 2 Angstrom plane spacing where Fe=2.91, C=1.15 (Angstroms). All other contributions to diffracted intensity are ignored.

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References

1. H. Lipson and N.J.Petch, JISI, 142 95 (1940)
   (Data for cementite atomic co-ordinates).
2. Z.G. Pinsker, Electron Diffraction, Ch. 7, Butterworths Scientific Publications, (1953).
   (Data for atomic scattering factors for electrons)
3. P. Hirsch, A. Howie, R.B. Nicholson, D.W. Pashley and M.J. Whelan, Electron Microscopy of Thin Crystals, 503-508, R.E.Kreiger Publishing Inc, (1977).
   (Discussion of electron diffraction theory)
4. H.P.Klug and L.E.Alexander, X-Ray Diffraction Procedures for Polycrystalline and Amorphous Materials, 135-171, 2nd Ed., John Wiley and Sons, (1974).
   (General overview of Structure Factors)

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Parameters

Input parameters

None

All parameters are defined internally and were taken from the literature.

Output parameters

None

All output is to STDOUT

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Error Indicators

None.

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Accuracy

Program accuracy is constrained by measurement accuracy and by simplifying assumptions. See comments in the Description.

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Further Comments

None.

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Example

1. Program text

       Complete program.

2. Program data

None.

3. Program results

    H K L      INTENSITY(%)
    - - -      ------------
 
    0 0 1         0.0000
    0 0 2         0.0121
    0 0 3         0.0000
    0 1 0         0.0139
    0 1 1         0.0139
    0 1 2         0.0139
    0 1 3         0.0139
    0 2 0         5.0404
    0 2 1         7.2831
    0 2 2        52.3986
    0 2 3        32.8115
    0 3 0         1.0879
    0 3 1         1.0879
    0 3 2         1.0880
    0 3 3         1.0879
    1 0 0         2.8018
    1 0 1         1.5216
    1 0 2         2.8017
    1 0 3        73.3030
    1 1 0         1.1364
    1 1 1         1.0842
    1 1 2         5.3135
    1 1 3        38.1656
    1 2 0        11.5978
    1 2 1        23.8227
    1 2 2        33.8435
    1 2 3         2.6991
    1 3 0        48.8124
    1 3 1         9.5597
    1 3 2         0.1778
    1 3 3         1.9222
    2 0 0        27.8393
    2 0 1         4.5394
    2 0 2         9.9956
    2 0 3         4.5394
    2 1 0        58.2569
    2 1 1         5.2158
    2 1 2        24.9770
    2 1 3         2.9052
    2 2 0         8.3805
    2 2 1         0.9864
    2 2 2        24.6676
    2 2 3        10.5676
    2 3 0         4.6722
    2 3 1         7.8497
    2 3 2        18.4645
    2 3 3        42.2373
    3 0 0         0.2118
    3 0 1         0.1928
    3 0 2         0.2118
    3 0 3         0.2603
    3 1 0         2.4603
    3 1 1         7.7300
    3 1 2        54.0989
    3 1 3        56.7027
    3 2 0         0.9767
    3 2 1         0.0713
    3 2 2         0.8603
    3 2 3         0.0482
    3 3 0       100.0000
    3 3 1         3.0264
    3 3 2        15.6439
    3 3 3         2.8346

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Auxiliary Routines

None.

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Keywords

electron diffraction patterns, electron microscopy, cementite

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Download

Download source code

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