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In this paper, we discuss how quenched strains in phonon and phason variables and/or quenched dislocations can lead to peak broadening and distortion in quasicrystal diffraction patterns. We argue that high-resolution electron micrographs and observations of distortions in electron diffraction patterns indicate the presence of anisotropic strains in the phason variable in the icosahedral phase of Al-Mn and related alloys. Such strains also contribute to the x-ray peak widths and line shapes.

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The temperature dependence of x-ray peak intensities of icosahedral AlCuFe is studied in detail. Above 670 °C, measurements of the Debye-Waller factor suggest the presence of dynamical phasons. Softening of the phason modes drives a structural transition at -670*^0 below which the quasicrystal decomposes into coherent micrograins of a lower-symmetry phase. Implications for quasicrystal stability are discussed.PACS numbers: 61.50.Em, 61.55.Hg, 63.90.-ft A central problem in the study of quasicrystalline materials is to understand why nature should prefer quasiperiodic to periodic long-range order. Experimentally this question has been difficult to address because phason disorder, a persistent feature of quasicrystalline alloys, disrupts the quasiperiodic ordering and renders structural investigations (and structure-related properties) difficult to interpret. * Recently, a new class of icosahedral quasicrystal has been found which is free of phason disorder."^ Single grains of the AlCuFe icosahedral phase U phase) have resolution-limited diffraction peak widths and peak positions that index precisely to an icosahedral reciprocal lattice. The coherence length of the quasiperiodic long-range order ^ exceeds 8000 A. Additionally, x-ray powder scans of the isomorphic AlCuRu / phase show no sign of phason strain broadening of diffraction peaks. ^ The advent of these perfect quasicrystals allows, for the first time, the study of well-ordered icosahedral alloys, free from the ambiguities imposed by phason disorder.This Letter addresses the related issues of quasicrystal stability and phason dynamics and presents a detailed study of the Debye-Waller (DW) factor of single grains of /-AlCuFe. The results are threefold. First, the phason relaxation time, Tph, at high temperature ( > 670 °C), is on the order of minutes, orders of magnitude less than theoretical estimates.^ Second, most samples exhibit an elastic instability at -670 "^C, below which the quasicrystal transforms into a lower-symmetry phase. A single sample which did not exhibit the instability is discussed at the end of the Letter. Third, below the structural transformation icosahedral diffraction persists, indicating a coherent decomposition into microcrystallites which maintain correlations across grain boundaries.AlCuFe samples were prepared from elemental constituents (99.999% pure) in an induction furnace under an atmosphere of high-purity argon. The bulk atomic composition was Al65Cu23Fei2. After alloying, ingots of several centimeters in size were vacuum encapsulated in quartz ampoules and annealed at 825 °C for 10 days. Upon removal from the furnace, the ampoules were rapidly cooled to room temperature. Faceted dodecahedral

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