Quasicrystals (QCs) have a peculiar structural order characterized by quasiperiodicity and non-crystallographical point group symmetry. To reveal their characteristic physical property reflecting the peculiar structural order, specific heat measurements were performed for Al–Pd–Mn icosahedral QCs (i-QCs) and a series of crystal approximants (CAs) of 2/1- 1/1- and 1/0-cubic types at 400–1200 K. The measured specific heat per atom at constant pressure cP was converted to that at constant volume cV by using data of the thermal expansion coefficient and bulk modulus. Below ∼700 K, the cV values of all the specimens of i-QCs and CAs were close to 3kB ( kB: Boltzman’s constant), i.e., they obeyed Dulong–Petit’s law. With further increase in temperature, the i-QCs showed a dramatic increase in cV with increasing temperature, and reached 5kB at 1100 K. In contrast, the 2/1 CAs showed a similar but slightly smaller increase in cV, whereas the 1/1 and 1/0 CAs showed a negligible increase. The systematic behavior of cV in the order of CAs and QC demonstrates that a large excessive specific heat is a characteristic feature of QCs, reflecting the peculiarity of their structural order. Its possible physical mechanism was discussed in terms of anharmonic atomic vibrations, electronic excitations, and phasonic excitations.

Comparative study of high-temperature specific heat for Al–Pd–Mn icosahedral quasicrystals and crystal approximants

ABSTRACT Due to their unique structural order, quasicrystals have special elastic degrees of freedom called the phason degrees of freedom, in addition to the conventional phonon degrees of freedom. In this study, we demonstrate the presence of phonon–phason coupling, expected from the generalized elastic theory of quasicrystals, in an Al-Pd-Mn icosahedral quasicrystal by a new experimental method that probes directly the elastic free energy function of the QC. Conventional phonon strain was applied to the quasicrystal at a high temperature where phasons are active. In response to the applied phonon strain, phason strain was observed to be induced by X-ray diffraction measurements, which demonstrated clearly the presence of phonon–phason coupling. Then, the coupling strength was quantitatively evaluated by comparing the magnitude of the induced phason strain with the theoretical values. In view of the evaluated coupling strength, the origin of an internal friction peak observed previously for an Al-Pd-Mn icosahedral quasicystal and the possible effects of the coupling on the onset of phasonic elastic instability are discussed.

https://www.tandfonline.com/doi/pdf/10.1080/14786435.2022.2052376?needAccess=true

Direct experimental evidence of phonon–phason coupling in an Al-Pd-Mn icosahedral quasicrystal

The practical application of quasicrystals (QCs) as thermoelectric materials makes icosahedral (i-) Al–Pd–Re QC attractive because of its moderate electrical conductivity (~280 Ω−1 cm−1), relatively high Seebeck coefficient (~100 μV K−1), and low thermal conductivity (~1.3 W m−1 K−1) at room temperature. To develop a thermoelectric Π-shaped power generation module, we need both p- and n-type thermoelectric materials. In this work, we aimed to develop an n-type i-Al–Pd–Re-based QC and investigated the effect of Co substitution for Re on the thermoelectric properties, i.e., the electron-doping effect. We synthesized dense bulk samples with nominal compositions of Al71Pd20(Re1−xCox)9 (x = 0, 0.1, 0.2, 0.3, 0.4, 0.5) via arc-melting, annealing, and sintering methods. We found that Co can produce n-type carriers in dilute substitution amounts of x = 0.1 and 0.2; however, the Seebeck coefficient at 300 K showed an n- to p-type transition with increasing x. This indicates that a simple rigid-band approximation is not applicable for i-Al–Pd–Re QC, which makes it difficult to synthesize an n-type i-Al–Pd–Re-based QC. Although the thermal conductivity was reduced from 1.28 (x = 0) to 1.08 W m−1 K−1 (x = 0.3) at 373 K by lowering of the electron thermal conductivity (electrical conductivity) and the alloying effect via Co substitution, the dimensionless figure of merit was not enhanced because of lowering of the power factor for all samples. The elastic moduli of i-Al–Pd–Re QC decreased by Co substitution, indicating that i-Al–Pd–Re-Co QC had a more ionic and brittle character.

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Thermoelectric Properties of Co-Substituted Al–Pd–Re Icosahedral Quasicrystals

Owing to the quasiperiodic order, one independent term in the elasticity of quasicrystals (phonon–phason coupling) is characteristic of quasicrystals. It is not seen in conventional crystals and has continued to be a significant subject in the research field of quasicrystals. Recently, a novel method was applied to a Mackay-type Al–Pd–Mn icosahedral quasicrystal to prove the existence of phonon–phason coupling and to evaluate its strength based on the elasticity of quasicrystals. This study applied the method to a Tsai-type Ag–In–Yb icosahedral system to evaluate its phonon–phason coupling strength. We applied phonon strain to the quasicrystal at a temperature with active phason, and the induction of phason strain was successfully detected and evaluated using powder X-ray diffraction. We evaluated the phonon–phason coupling elastic constant of the Ag–In–Yb icosahedral quasicrystal to be 0.17 ± 0.04 GPa by quantitatively comparing the measured induced phason strain with our calculation results. 

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Phonon–Phason Coupling Strength in a Tsai-Type Ag–In–Yb Icosahedral Quasicrystal

Icosahedral Al-Cu-Fe quasicrystal (QC) shows moderate electrical conductivity and low thermal conductivity, and both p- and n-type conduction can be controlled by tuning the sample composition, making it potentially suited for thermoelectric materials. In this work, we investigated the effect of introducing chemical disorder through heavy element substitution on the thermal conductivity of Al-Cu-Fe QC. We substituted Au and Pt elements for Cu up to 3 at% in a composition of Al63Cu25Fe12, i.e., Al63Cu25−x(Au,Pt)xFe12 (x = 0, 1, 2, 3). The substitutions of Au and Pt for Cu reduced the phonon thermal conductivity at 300 K (κph,300K) by up to 17%. The reduction of κph,300K is attributed to a decrease in the specific heat and phonon relaxation time through heavy element substitution. We found that increasing the Pt content reduced the specific heat at high temperatures, which may be caused by the locked state of phasons. The observed glass-like low values of κph,300K (0.9–1.1 W m−1 K−1 at 300 K) for Al63Cu25−x(Au,Pt)xFe12 are close to the lower limit calculated using the Cahill model.

Kento Fukushima

Papers

High-Temperature Specific Heat of Al–Cu–Ru Icosahedral Quasicrystals and 1/1 Crystal Approximants

Comparative study of high-temperature specific heat for Al–Pd–Mn icosahedral quasicrystals and crystal approximants

Prediction Model of Hot-Rolled Coil Temperature and Phase Transformation Applied Local Heat Flux Considering Coil Shape