Wave Harmonization in Hierarchic Quasicrystals by the Analytic Metric

• 作者: Antony J. Bourdillon
• 来源期刊: 现代物理(英文)
• 学科: 数学
• 关键词: QUASICRYSTAL ICOSAHEDRA Hierarchic HARMONIZATION METRIC Geometric Series
• 年，卷（期）: xdwlyw_2019,（11）
• 页码范围: 1364-1373
• 页数: 10页
• 分类号: O17

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.