Order-Disorder Phase Transitions in Quasicrystals

Diffuse scattering around Bragg reflections was observed by anomalous X-ray scattering in a single decagonal quasicrystal of Al₇₂Ni₁₈Fe₁₀. Intensity modulations of the diffuse scattering were measured for four incident X-ray beam energies. Quantitative analysis of the diffuse scattering data shows the presence of atomic short-range order (SRO) in three kinds of pair-correlation functions: Al-Ni, Ni-Fe and Fe-Al. The SRO diffuse scattering is decomposed into each component by self-consistent calculation. Using Metropolis Monte Carlo simulations, the SRO diffuse scattering is calculated qualitatively using the SRO parameters. Asymmetric distributions of the diffuse scattering were seen along a longitudinal direction, even though the Al₇₂Ni₁₈Fe₁₀ quasicrystal has quite small mosaicity.

	Figure 1. \|Df\|² and \|\|² as a function of q (=4p(sinq)/l) for the four energies.
	Figure 2. Diffraction pattern of the decagonal quasicrystal Al₇₂Ni₁₈Fe₁₀ using an imaging plate. Incident beam is perpendicular to the decagonal axis (c*-axis).
	Figure 3. \|\| dependence of FWHM of Bragg reflections. In comparison with that of Al₇₀Ni₁₅Co₁₅ and Al₇₂Ni₂₀Co₈, no “random phason strain” was seen in Al₇₂Ni₁₈Fe₁₀.
	Figure 4. Reciprocal space perpendicular to the periodic direction of the decagonal Al₇₂Ni₁₈Fe₁₀ phase. The area of the spot is proportional to the intensity of the reflection. The diffuse scattering has been measured around the labeled reflections.
	Figure 5. The observed diffuse scattering around (a) , (b), (c) , (d) and (e) Bragg reflections at 8.103 keV. Absolute intensity is given in electron units. The open stars present the ideal positions for the weak Bragg reflections.
	Figure 6. The calculated thermal diffuse scattering around (a), (b), (c), (d) and (e) Bragg reflections.
	Figure 7. Theoretical phasonic diffuse scattering around Bragg reflections using (a) K₁=0.2 and K’=-0.1, (b) K₁=0.1 and K’=-0.1, (c) K₁=0.1 and K’= 0, (d) K₁=0.1 and K’= 0.1 and (e) K₁=0.1 and K’=0.2. K₁ is the phason elastic constant. Anisotropic distributions are enhanced by the coupling constant between phonon and phason, K’.
	Figure 8. The scattered intensities at each incident energies vs. q around Bragg reflection along (a) transverse (T-) and (b) longitudinal (L-) directions. Measurement regions are displayed in figure 5(b). Only along L-direction, the scattered intensity shows q^-4 dependence, which is derived from the strongly distorted regions.
	Figure 9. Three kinds of pair-correlation functions, a_Al-Ni(q), a_Ni-Fe(q) and a_Fe-Al(q), in Laue units per atom. q-region is the longitudinal direction in the center of Bragg reflection.
	Figure 10. Two kinds of 2 nm-diameter columnar cluster. One is (a) a star-type-cluster. The other is (b) a decagon-type-cluster. Two circles exhibit 2 nm-diameter. The closed and open circles reveal atoms at z=1/4 and z=3/4, respectively. The occupation domains are located at (a) (1/5, 1/5, 1/5, 1/5, 1/4) and (b) (2/5, 2/5, 2/5, 2/5, 1/4) in the five-dimensional decagonal lattice, respectively.
	Figure 11. The simulated SRO diffuse scattering around (a) , (b) , (c) , (d) and (e) Bragg reflections by the Metropolis Monte Carlo method. In the simulations, the observed SRO diffuse scattering at 8.103 keV and SRO parameters are used.
	Figure 12. The SRO parameters of an Al-transition metal pair are optimized qualitatively by the Metropolis Monte Carlo method.

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ab@nda.ac.jp

Department of Materials Science and Engineering
National Defense Academy

Last Modified: April 1, 2009