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The electronic structures of hexagonal beta-Al9Mn3Si and phi-Al10Mn3 areinvestigated through self-consistent calculations carried out using the LMTOmethod. This ab-initio approach is combined with an analysis of a simplifiedhamiltonian model for Al based alloys containing transition metal atoms.Results show a strong effect on an atomic structure stabilisation by anindirect Mn-Mn interaction mediated by conduction electrons over medium rangedistances (5 Angstrom and more). Both the role and position of Si atoms areexplained as well as the origin of large vacancies which characterises theseatomic structures. As beta and phi phases are related to Al based quasicrystalsand related approximant structures, it yields arguments on the stabilisation ofsuch complex phases.Comment: revised version with more details and new result

physical review. b, condensed matter

Interplay between electronic structure and medium-range atomic order in hexagonal<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>β</mml:mi><mml:mo>−</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Al</mml:mi></mml:mrow><mml:mrow><mml:mn>9</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Mn</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mi mathvariant="…

Interplay between electronic structure and medium-range atomic order in hexagonalβ−Al9Mn3