Potential thermal barrier coating material: High entropy ceramic (Ca0.5Sr0.5)(5RE)2O4 with enhanced thermophysical properties
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Thermal Stability
Phonon scattering
The anharmonicity resulted from the intrinsic phonon interaction is neglected by quasiharmonic approximation. Although the intensive researches about anharmonicity have been done, up to now the free energy contributed by the anharmonicity is still difficult to calculate. Here we put forward a new method that can well include the anharmonicity. We introduce the implicit temperature dependence of effective frequency by volume modification. The quasiharmonic approximation becomes a special case in our method corresponding to non volume modification. Although our method is simple and only a constant need to determine, the anharmonicity is well included. Thermodynamic properties of MgO predicted with our method are excellent consistent with the experiment results at very wide temperature range. We also believe that our method will be helpful to reveal the characteristic of anharmonicity and intrinsic phonon interaction.
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Abstract The thermal diffuse scattering (TDS) of X‐rays in the anharmonic one‐phonon and harmonic two‐phonon approximations is considered. The complete expression for the one‐phonon intensity of X‐rays is derived by perturbation theory and presented for a polyatomic crystal in the high‐temperature limit. The method of evaluating the corrections of the X‐rays intensities for the thermal diffuse scattering is given and the importance taking into account the anharmonic effects in the one‐phonon scattering for KZnF 3 , CsCl, and YBa 2 Cu 3 O 7−δ crystals at room temperature is discussed. Anharmonic TDS‐effects achieve considerable magnitudes for soft (acoustic) anharmonic crystals as CsCl.
Phonon scattering
Crystal (programming language)
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According to the existing combustion mechanisms, the main reactions related to NO2 have been investigated in this research. Based on the transition state theory, the YL method proposed by Yao and Lin is utilized to obtain both the anharmonic and harmonic rate constants in a canonical system, respectively. The anharmonic effect of these reactions is also examined by comparing the anharmonic rate constant with the harmonic rate constant. The calculations indicate that there is a junction between the anharmonic and harmonic rate constants, and the anharmonic rate is lower than the harmonic one at high temperature. The results show that the anharmonic effect is significant and cannot be ignored, especially at high temperature. Finally, inspired by the least square idea, the kinetics and thermodynamic parameters of reaction mechanism involving NO2 are also given in fuel combustion processes.
Harmonic
Constant (computer programming)
Transition state theory
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Abstract We report a computational study, using the “moments method” [Y. Gao and M. Daw, Modell. Simul. Mater. Sci. Eng. 23 045002 (2015)], of the anharmonicity of the vibrational modes of single‐walled carbon nanotubes. We find that modes with displacements largely within the wall are more anharmonic than modes with dominantly radial character, except for a set of modes that are related to the radial breathing mode that are the most anharmonic of all. We also find that periodicity of the calculation along the tube length does not strongly affect the anharmonicity of the modes but that the tubes with larger diameter show more anharmonicity. Comparison is made with available experiments and other calculations.
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The theoretical and experimental studies of anharmonic temperature factor in X-ray and neutron diffraction are reviewed since early works in 1963. These studies are in the framework of effective one body particle potential in which atoms are treated as independent oscillators.The experimental works are classified into two major groups : investigations of anti-centrosymmetric anharmonicity and centrosymmetric anharmonicity. It is pointed out that anti-centrosymmetric anharmonicity is well determined from the accurate Bragg intensity data at a certain temperature but centrosymmetric anharmonicity, because of the correlation of harmonic and anharmonic potential parameters, both of which are centrosymmetric. It is more reliable to determine the centrosymmetric anharmoni-city using the temperature dependence of integrated Bragg intensities unless extremely high Q data are collected.It is suggested that the degree of anharmonicity is much betterdescribed by a ratio of anharmonic term to harmonic term in one body particle potential than the magnitude of anharmonic potential parameter itself. The anharmonic effect is more significant for those substances which have smaller anharmonic potential coefficients.The relationships between anharmonicity of temperature factor and structural phase transition is discussed in the case of several perovskite substances.
Harmonic potential
Harmonic
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The spinel growth induces undulation of the thermal growth oxide layer and decreases the service life of plasma-sprayed thermal barrier coatings. An analytical model is introduced to investigate the effect of spinel growth on the delamination of thermal barrier coating. The analytical results show that the number per unit area and the growth rate of spinel have significant influence on the delamination of thermal barrier coating. The stiffer and thicker thermal barrier coating is more easily to delaminate from the bond coat due to the existence of spinels. The effect of spinel on the delamination cannot be neglected. How to reduce the growth rate and the number of spinel is a key problem to prolong the service life of thermal barrier coatings.
Delamination
Barrier layer
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A general method is formulated for the calculation of the phonon spectrum of anharmonic metals by applying the pseudopotential method. On the basis of the recently developed theory of anharmonic crystals, the frequencies of selfconsistent phonons and their damping in the adiabatic approximation are obtained, taking into account the effective cubic anharmonic interactions. The importance of indirect many body forces in anharmonic metals is stressed. The three body interactions are explicitly taken into consideration.
Pseudopotential
Basis (linear algebra)
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<sec>Anharmonic effect is often one of the physical root causes of some special material properties, such as soft mode phase transition, negative thermal expansion, multiferroicity, and ultra-low thermal conductivity. However, the existing methods of quantifying the anharmonicity of material do not give a clear and accurate anharmonicity descriptor. The calculation of the anharmonic effect requires extremely time-consuming molecular dynamics simulation, the calculation process is complex and costly. Therefore, a quantitative descriptor is urgently needed, which can be used to implement quick calculation so as to understand, evaluate, design, and screen functional materials with strong anharmonicity.</sec><sec>In this paper, we propose a method to quantify the anharmonicity of materials by only phonon spectrum and static self-consistent calculation through calculating and analyzing the material composed of germanium and its surrounding elements. In this method, the lattice anharmonicity is decomposed into the anharmonic contribution of independent phonon vibration modes, and the quantitative anharmonicity descriptor <inline-formula><tex-math id="M3">\begin{document}$ {\sigma }_{\boldsymbol{q},j}^{A} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231428_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231428_M3.png"/></alternatives></inline-formula> of phonons is proposed. Combining it with the Bose-Einstein distribution, the quantitative descriptor <inline-formula><tex-math id="M4">\begin{document}$ {A}_{{\mathrm{p}}{\mathrm{h}}}\left(T\right) $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231428_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231428_M4.png"/></alternatives></inline-formula> of temperature-dependent material anharmonicity is proposed. We calculate the bulk moduli and lattice thermal conductivities at 300 K of nine widely representative materials. There is a clear linear trend between them and our proposed quantitative descriptor <inline-formula><tex-math id="M5">\begin{document}$ {A}_{{\mathrm{p}}{\mathrm{h}}}\left(T\right) $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231428_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231428_M5.png"/></alternatives></inline-formula>, which verifies the accuracy of our proposed descriptor. The results show that the descriptor has the following functions. i) It can systematically and quantitatively classify materials as the strength of anharmonicity; ii) it intuitively shows the distribution of the anharmonic effect of the material on the phonon spectrum, and realizes the separate analysis of the phonon anharmonicity that affects the specific properties of the material; iii) it is cost-effective in first-principles molecular dynamics calculations and lays a foundation for screening and designing materials based on anharmonicity.</sec><sec>This study provides an example for the high-throughput study of functional materials driven by anharmonic effect in the future, and opens up new possibilities for material design and application. In addition, for strongly anharmonic materials such as CsPbI<sub>3</sub>, the equilibrium position of the atoms is not fixed at high temperatures, resulting in a decrease in the accuracy of quantifying anharmonicity using our proposed descriptor. In order to get rid of this limitation, our future research will focus on the distribution of atomic equilibrium positions in strongly anharmonic materials at high temperatures, so as to propose a more accurate theoretical method to quantify the anharmonicity in strongly anharmonic materials.</sec>
Lattice (music)
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We report a computational study, using the "moments method" [Y. Gao and M. Daw, Modelling Simul. Mater. Sci. Eng. 23 045002 (2015)], of the anharmonicity of the vibrational modes of single-walled carbon nanotubes. We find that modes with displacements largely within the wall are more anharmonic than modes with dominantly radial character, except for a set of modes that are related to the radial breathing mode which are the most anharmonic of all. We also find that periodicity of the calculation along the tube length does not strongly affect the anharmonicity of the modes, but that the tubes with larger diameter show more anharmonicity. Comparison is made with available experiments and other calculations.
Mode (computer interface)
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Proper consideration of anharmonicity is important for the calculation of thermal conductivity. However, how the anharmonicity influences the thermal conduction in amorphous materials is still an open question. In this work, we uncover the role of anharmonicity on the thermal conductivity of amorphous silica ($a\text{\ensuremath{-}}{\mathrm{SiO}}_{2}$) by comparing the thermal conductivity predicted from the harmonic theory and the anharmonic theory. Moreover, we explore the effect of anharmonicity-induced frequency shift on the prediction of thermal conductivity. It is found that the thermal conductivity calculated by the recently developed anharmonic theory (quasi-harmonic Green-Kubo approximation) is higher than that calculated by the harmonic theory developed by Allen and Feldman. The use of anharmonic vibrational frequencies also leads to a higher thermal conductivity compared with that calculated using harmonic vibrational frequencies. The anharmonicity-induced frequency shift is a mechanism for the positive temperature dependence of the thermal conductivity of $a\text{\ensuremath{-}}{\mathrm{SiO}}_{2}$ at higher temperatures. Further investigation on the mode diffusivity suggests that although anharmonicity has a larger influence on locons than diffusons, the increase in thermal conductivity due to anharmonicity is mainly contributed by the anharmonicity-induced increase of the diffusivity of diffusons. Finally, it is found that the cross-correlations between diffusons and diffusons contribute most to the thermal conductivity of $a\text{\ensuremath{-}}{\mathrm{SiO}}_{2}$, and the locons contribute to the thermal conductivity mainly through collaboration with diffusons. These results offer new insights into the nature of the thermal conduction in $a\text{\ensuremath{-}}{\mathrm{SiO}}_{2}$.
Amorphous silica
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