# Materials Algorithms ProjectProgram Library

## Program MAP_CRYSTAL_XRDCALC

### Provenance of Source Code

Murugananth Marimuthu,
Phase Transformations Group,
Department of Materials Science and Metallurgy,
University of Cambridge,
Cambridge CB2 3QZ, U.K.

E-mail: Ananth

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### Purpose

Calculation of the retained austenite content in steels using X-ray diffracted intensities from austenite and ferrite.

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### Specification

 Language: C Product form: Source code. Platform: Any Unix and Linux systems.

Complete program.

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### Description

The program uses inputs from your X-ray diffraction results and calculates the retained austenite content of the steel. The code has been developed based on the following equation that relates the integrated intensities with volume fraction of austenite and ferrite:

The R constants for austenite and alpha iron are given by the following expression for each peak respectively:

Where

 v = Atomic volume of unit cell F = Structure Factor Proportional to the ratio of the amplitude of wave scattered by an atom to the amplitude of the wave scattered by one electron. p = Multiplicity factor Takes into account the number of equivalent planes that contribute for a reflection. e-2m = Temperature factor Incorporates the effect of temperature which is known to decrease the intensity of diffracted beam. Lp = Lorentz-polarisation factor Combination of the Lorentz factor and the polarisation factor;      Polarisation factor includes the effect of the electron acceleration in different directions (depending on the electric component of the beam) on the intensity of the scattered beam at any point of consideration;     Lotrentz factor includes the geometric factors that affect the intensity of the beam
The error estimates in the calculations are made either from the intensity or from Integrated intensity depending on the users choice. But in general integrated intensity is of much more interest than the maximum intensity, since the former is characteristic of the specimen while the later is influenced by slight adjustment of the experimental apparatus.

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### References

1. Cullity., B. D, Elements of X-ray diffraction, 1959, pp 105-137

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### Parameters

#### Input parameters

1. 2-Theta
Unit: degrees, The angle between the incident beam and the scattered beam

2. Integrated Intensity
For ferrite and austenite peaks. As obtained from X-ray diffraction experiment

3. Miller Indices of the planes
For austenite and ferrite separately as the program asks you

#### Output parameters

1. Percentage of austenite with error values

2. Result file with identification name as its start
example: test_XRD_result

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### Error Indicators

None.

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### Accuracy

No information supplied.

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none.

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### Example

After you untar the file using command tar -xvf xrdcalc.tar, just type run or ./run to use "xrdcalc"

 Type the Identification name of the material : test Enter the wavelength of the X-radiation used: 1.5418 How many austenite peaks have you got : 3 How many ferrite peaks have you got : 3 Which error estimate fo you prefer 1.  Based on intensities 2.  Based on Integrated Intensities (recommended) Enter option: 2 --------------THETA VALUES-------------------- Enter the TWO THETA value for peak 1 of AUSTENITE: 50.738689 Enter the TWO THETA value for peak 2 of AUSTENITE: 74.999107 Enter the TWO THETA value for peak 3 of AUSTENITE: 91.171608 Enter the TWO THETA value for peak 1 of FERRITE: 65.046341 Enter the TWO THETA value for peak 2 of FERRITE: 82.280563 Enter the TWO THETA value for peak 3 of FERRITE: 98.766502 --------------INTENSITIES-------------------- Integrated Intensity 1 for 2-Theta 50.738689 of Austenite: 3089.500000 Integrated Intensity 2 for 2-Theta 74.999107 of Austenite: 4394.600098 Integrated Intensity 3 for 2-Theta 91.171608 of Austenite: 1998.599976 Integrated Intensity 1 for 2-Theta 65.046341 of ferrite: 106221.796875 Integrated Intensity 2 for 2-Theta 82.280563 of ferrite: 130751.898438 Integrated Intensity 3 for 2-Theta 98.766502 of ferrite: 52179.500000 -------------- INDICES {hkl} -------------------- Enter the {hkl} for 2-theta value 50.738689 of AUSTENITE (enter each number with a space): 0 0 2 Enter the {hkl} for 2-theta value 74.999107 of AUSTENITE (enter each number with a space): 0 2 2 Enter the {hkl} for 2-theta value 91.171608 of AUSTENITE (enter each number with a space): 1 1 3 Enter the {hkl} for 2-theta value 65.046341 of FERRITE (enter each number with a space): 0 0 2 Enter the {hkl} for 2-theta value 82.280563 of FERRITE (enter each number with a space): 1 1 2 Enter the {hkl} for 2-theta value 98.766502 of FERRITE (enter each number with a space): 0 2 2 LATTICE PARAMETER RESULTS ---------------------- AUSTENITE [ 2-Theta=50.738689 ]: 3.598538 AUSTENITE [ 2-Theta=74.999107 ]: 3.581792 AUSTENITE [ 2-Theta=91.171608 ]: 3.579432 FERRITE [ 2-Theta=65.046341 ] : 2.867715 FERRITE [ 2-Theta=82.280563 ] : 2.870189 FERRITE [ 2-Theta=98.766502 ] : 2.872466 Which system are you using 1. CUBIC 2. HEXAGONAL and RHOMBHOHEDRAL 3. TETRAGONAL 4. ORTHORHOMBIC 5. MONOCLINIC 6. TRICLINIC Enter option: 1 -------------- STRUCTURE FACTOR -------------------- The major alloying elements in your steel are : 1. Fe only 2. Fe and Ni 3. Fe and Cr 4. Fe, Ni and Cr Choose option: 2

#### 2. Program results

 -------------- RESULT -------------------- preT:0.000566 Aus:0.055444 fer:0.010212 Percentage of austenite : 2.287 % Error : 0.0566 % Percentage of ferrite : 97.713 % Error : 0.0566 % --------------------- END ------------------

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### Auxiliary Routines

No auxilary routines.

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### Keywords

Retained austenite, X-ray diffraction, Steels.

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