Wave Harmonization in Hierarchic Quasicrystals by the Analytic Metric  

作　　者：Antony J. Bourdillon 

机构地区：[1]UHRL, San Jose, CA, USA

出　　处：《Journal of Modern Physics》2019年第11期1364-1373,共10页现代物理（英文）

摘　　要：Thirty seven years after the discovery of quasicrystals, their diffraction is completely described by harmonization between the sine wave probe with hierarchic translational symmetry in a structure that is often called quasiperiodic. The diffraction occurs in geometric series that is a special case of the Fibonacci sequence. Its members are irrational. When substitution is made for the golden section τ by the semi-integral value 1.5, a coherent set of rational numbers maps the sequence. Then the square of corresponding ratios is a metric that harmonizes the sine wave probe with the hierarchic structure, and the quasi-Bragg angle adjusts accordingly. From this fact follows a consistent description of structure, diffraction and measurement.Thirty seven years after the discovery of quasicrystals, their diffraction is completely described by harmonization between the sine wave probe with hierarchic translational symmetry in a structure that is often called quasiperiodic. The diffraction occurs in geometric series that is a special case of the Fibonacci sequence. Its members are irrational. When substitution is made for the golden section τ by the semi-integral value 1.5, a coherent set of rational numbers maps the sequence. Then the square of corresponding ratios is a metric that harmonizes the sine wave probe with the hierarchic structure, and the quasi-Bragg angle adjusts accordingly. From this fact follows a consistent description of structure, diffraction and measurement.

关 键 词：QUASICRYSTAL ICOSAHEDRA Hierarchic HARMONIZATION METRIC Geometric Series 

分 类 号：O17[理学—数学]