The Convolutional Multiple Whole Profile (CMWP) Fitting Method, a Global Optimization Procedure for Microstructure Determination
The analysis of line broadening in X-ray and neutron diffraction patterns using profile functions constructed on the basis of well-established physical principles and TEM observations of lattice defects has proven to be a powerful tool for characterizing microstructures in crystalline materials. The...
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| Format: | Article |
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MDPI AG
2020-07-01
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| Series: | Crystals |
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| Online Access: | https://www.mdpi.com/2073-4352/10/7/623 |
| _version_ | 1797562147180380160 |
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| author | Gábor Ribárik Bertalan Jóni Tamás Ungár |
| author_facet | Gábor Ribárik Bertalan Jóni Tamás Ungár |
| author_sort | Gábor Ribárik |
| collection | DOAJ |
| description | The analysis of line broadening in X-ray and neutron diffraction patterns using profile functions constructed on the basis of well-established physical principles and TEM observations of lattice defects has proven to be a powerful tool for characterizing microstructures in crystalline materials. These principles are applied in the convolutional multiple-whole-profile (CMWP) procedure to determine dislocation densities, crystallite size, stacking fault and twin boundary densities, and intergranular strains. The different lattice defect contributions to line broadening are separated by considering the <i>hkl</i> dependence of strain anisotropy, planar defect broadening and peak shifts, and the defect dependent profile shapes. The Levenberg–Marquardt (LM) peak fitting procedure can be used successfully to determine crystal defect types and densities as long as the diffraction patterns are relatively simple. However, in more complicated cases like hexagonal materials or multiple-phase patterns, using the LM procedure alone may cause uncertainties. Here, we extended the CMWP procedure by including a Monte Carlo statistical method where the LM and a Monte Carlo algorithm were combined in an alternating manner. The updated CMWP procedure eliminated uncertainties and provided global optimized parameters of the microstructure in good correlation with electron microscopy methods. |
| first_indexed | 2024-03-10T18:24:22Z |
| format | Article |
| id | doaj.art-138abf7e509c4fe1aeeef722c00b38ba |
| institution | Directory Open Access Journal |
| issn | 2073-4352 |
| language | English |
| last_indexed | 2024-03-10T18:24:22Z |
| publishDate | 2020-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Crystals |
| spelling | doaj.art-138abf7e509c4fe1aeeef722c00b38ba2023-11-20T07:05:06ZengMDPI AGCrystals2073-43522020-07-0110762310.3390/cryst10070623The Convolutional Multiple Whole Profile (CMWP) Fitting Method, a Global Optimization Procedure for Microstructure DeterminationGábor Ribárik0Bertalan Jóni1Tamás Ungár2Department of Materials Physics, Eötvös Loránd University Budapest, H-1117 Pázmány P. sétány 1/A, HungaryDepartment of Materials Physics, Eötvös Loránd University Budapest, H-1117 Pázmány P. sétány 1/A, HungaryDepartment of Materials Physics, Eötvös Loránd University Budapest, H-1117 Pázmány P. sétány 1/A, HungaryThe analysis of line broadening in X-ray and neutron diffraction patterns using profile functions constructed on the basis of well-established physical principles and TEM observations of lattice defects has proven to be a powerful tool for characterizing microstructures in crystalline materials. These principles are applied in the convolutional multiple-whole-profile (CMWP) procedure to determine dislocation densities, crystallite size, stacking fault and twin boundary densities, and intergranular strains. The different lattice defect contributions to line broadening are separated by considering the <i>hkl</i> dependence of strain anisotropy, planar defect broadening and peak shifts, and the defect dependent profile shapes. The Levenberg–Marquardt (LM) peak fitting procedure can be used successfully to determine crystal defect types and densities as long as the diffraction patterns are relatively simple. However, in more complicated cases like hexagonal materials or multiple-phase patterns, using the LM procedure alone may cause uncertainties. Here, we extended the CMWP procedure by including a Monte Carlo statistical method where the LM and a Monte Carlo algorithm were combined in an alternating manner. The updated CMWP procedure eliminated uncertainties and provided global optimized parameters of the microstructure in good correlation with electron microscopy methods.https://www.mdpi.com/2073-4352/10/7/623X-ray line profile analysisneutron line profile analysisCMWPglobal optimumdislocation densitiesgrain size |
| spellingShingle | Gábor Ribárik Bertalan Jóni Tamás Ungár The Convolutional Multiple Whole Profile (CMWP) Fitting Method, a Global Optimization Procedure for Microstructure Determination Crystals X-ray line profile analysis neutron line profile analysis CMWP global optimum dislocation densities grain size |
| title | The Convolutional Multiple Whole Profile (CMWP) Fitting Method, a Global Optimization Procedure for Microstructure Determination |
| title_full | The Convolutional Multiple Whole Profile (CMWP) Fitting Method, a Global Optimization Procedure for Microstructure Determination |
| title_fullStr | The Convolutional Multiple Whole Profile (CMWP) Fitting Method, a Global Optimization Procedure for Microstructure Determination |
| title_full_unstemmed | The Convolutional Multiple Whole Profile (CMWP) Fitting Method, a Global Optimization Procedure for Microstructure Determination |
| title_short | The Convolutional Multiple Whole Profile (CMWP) Fitting Method, a Global Optimization Procedure for Microstructure Determination |
| title_sort | convolutional multiple whole profile cmwp fitting method a global optimization procedure for microstructure determination |
| topic | X-ray line profile analysis neutron line profile analysis CMWP global optimum dislocation densities grain size |
| url | https://www.mdpi.com/2073-4352/10/7/623 |
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