The Physics of the Hume-Rothery Electron Concentration Rule
For a long time we have shared the belief that the physics of the Hume-Rothery electron concentration rule can be deepened only through thorough investigation of the interference phenomenon of itinerant electrons with a particular set of lattice planes, regardless of whether d-states are involved ne...
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| Format: | Article |
| Language: | English |
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MDPI AG
2017-01-01
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| Series: | Crystals |
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| Online Access: | http://www.mdpi.com/2073-4352/7/1/9 |
| _version_ | 1811306864912105472 |
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| author | Uichiro Mizutani Hirokazu Sato |
| author_facet | Uichiro Mizutani Hirokazu Sato |
| author_sort | Uichiro Mizutani |
| collection | DOAJ |
| description | For a long time we have shared the belief that the physics of the Hume-Rothery electron concentration rule can be deepened only through thorough investigation of the interference phenomenon of itinerant electrons with a particular set of lattice planes, regardless of whether d-states are involved near the Fermi level or not. For this purpose, we have developed the FLAPW-Fourier theory (Full potential Linearized Augmented Plane Wave), which is capable of determining the square of the Fermi diameter, ( 2 k F ) 2 , and the number of itinerant electrons per atom, e/a, as well as the set of lattice planes participating in the interference phenomenon. By determining these key parameters, we could test the interference condition and clarify how it contributes to the formation of a pseudogap at the Fermi level. Further significant progress has been made to allow us to equally handle transition metal (TM) elements and their compounds. A method of taking the center of gravity energy for energy distribution of electrons with a given electronic state has enabled us to eliminate the d-band anomaly and to determine effective ( 2 k F ) 2 , and e/a, even for systems involving the d-band or an energy gap across the Fermi level. The e/a values for 54 elements covering from Group 1 up to Group 16 in the Periodic Table, including 3d-, 4d- and 5d-elements, were determined in a self-consistent manner. The FLAPW-Fourier theory faces its limit only for elements in Group 17 like insulating solids Cl and their compounds, although the value of e/a can be determined without difficulty when Br becomes metallic under high pressures. The origin of a pseudogap at the Fermi level for a large number of compounds has been successfully interpreted in terms of the interference condition, regardless of the bond-types involved in the van Arkel-Ketelaar triangle map. |
| first_indexed | 2024-04-13T08:54:28Z |
| format | Article |
| id | doaj.art-4d0beb0c6d574b7195c2e3ebb67315c2 |
| institution | Directory Open Access Journal |
| issn | 2073-4352 |
| language | English |
| last_indexed | 2024-04-13T08:54:28Z |
| publishDate | 2017-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Crystals |
| spelling | doaj.art-4d0beb0c6d574b7195c2e3ebb67315c22022-12-22T02:53:22ZengMDPI AGCrystals2073-43522017-01-0171910.3390/cryst7010009cryst7010009The Physics of the Hume-Rothery Electron Concentration RuleUichiro Mizutani0Hirokazu Sato1Nagoya Industrial Science Research Institute, 1-13 Yotsuya-dori, Chikusa-ku, Nagoya 464-0819, JapanDepartment of Physics, Aichi University of Education, Kariya-shi, Aichi 448-8542, JapanFor a long time we have shared the belief that the physics of the Hume-Rothery electron concentration rule can be deepened only through thorough investigation of the interference phenomenon of itinerant electrons with a particular set of lattice planes, regardless of whether d-states are involved near the Fermi level or not. For this purpose, we have developed the FLAPW-Fourier theory (Full potential Linearized Augmented Plane Wave), which is capable of determining the square of the Fermi diameter, ( 2 k F ) 2 , and the number of itinerant electrons per atom, e/a, as well as the set of lattice planes participating in the interference phenomenon. By determining these key parameters, we could test the interference condition and clarify how it contributes to the formation of a pseudogap at the Fermi level. Further significant progress has been made to allow us to equally handle transition metal (TM) elements and their compounds. A method of taking the center of gravity energy for energy distribution of electrons with a given electronic state has enabled us to eliminate the d-band anomaly and to determine effective ( 2 k F ) 2 , and e/a, even for systems involving the d-band or an energy gap across the Fermi level. The e/a values for 54 elements covering from Group 1 up to Group 16 in the Periodic Table, including 3d-, 4d- and 5d-elements, were determined in a self-consistent manner. The FLAPW-Fourier theory faces its limit only for elements in Group 17 like insulating solids Cl and their compounds, although the value of e/a can be determined without difficulty when Br becomes metallic under high pressures. The origin of a pseudogap at the Fermi level for a large number of compounds has been successfully interpreted in terms of the interference condition, regardless of the bond-types involved in the van Arkel-Ketelaar triangle map.http://www.mdpi.com/2073-4352/7/1/9Hume-Rothery electron concentration ruleinterference conditionpseudogap |
| spellingShingle | Uichiro Mizutani Hirokazu Sato The Physics of the Hume-Rothery Electron Concentration Rule Crystals Hume-Rothery electron concentration rule interference condition pseudogap |
| title | The Physics of the Hume-Rothery Electron Concentration Rule |
| title_full | The Physics of the Hume-Rothery Electron Concentration Rule |
| title_fullStr | The Physics of the Hume-Rothery Electron Concentration Rule |
| title_full_unstemmed | The Physics of the Hume-Rothery Electron Concentration Rule |
| title_short | The Physics of the Hume-Rothery Electron Concentration Rule |
| title_sort | physics of the hume rothery electron concentration rule |
| topic | Hume-Rothery electron concentration rule interference condition pseudogap |
| url | http://www.mdpi.com/2073-4352/7/1/9 |
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