First‐principles study on the structural, phonon, and thermodynamic properties of the ternary carbides in Ti–Al–C system
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Abstract The structural, phonon, and thermodynamic properties of the ternary carbides Ti 2 AlC, Ti 3 AlC, and Ti 3 AlC 2 in the Ti–Al–C system are investigated by using first‐principles calculations in this paper. Phonon dispersion curves and partial density of states have been investigated and revealed the different Ti–C bond characteristics between Ti 3 AlC and the two other compounds. The Gibbs energy, entropy, heat capacity, and thermal expansion coefficient of the three compounds are predicted by means of the quasi‐harmonic approximation. Furthermore, the thermal electronic contribution has been included in the thermodynamic properties. The obtained results of this study are in good agreement with the available experimental data.Keywords:
MAX phases
Density of states
Volumetric heat capacity
Debye model
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Solid-state physics
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A theoretical study of the Mo2TiAlC2 compound belonging to the MAX phases has been performed by using the first-principles pseudopotential plane-wave method within the generalized gradient approximation (GGA). We have calculated the structural, elastic, electronic and optical properties of Mo2TiAlC2. To confirm mechanical stability, the elastic constants Cij are calculated. Other elastic parameters such as bulk modulus, shear modulus, compressibility, Young modulus, anisotropic factor, Pugh ratio, Poissons ratio are also calculated. The energy band structure and density of states are calculated and analyzed. The results show that the electrical conductivity is metallic with a high density of states at the Fermi level in which Mo 4d states dominate. Furthermore, the optical properties such as dielectric function, refractive index, photoconductivity, absorption coefficients, loss function and reflectivity are also calculated. Its reflectance spectrum shows that it has the potential to be used as a promising shielding material to avoid solar heating.
Pseudopotential
MAX phases
Shear modulus
Density of states
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Negative Thermal Expansion
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The thermal expansion properties of crystalline organic compounds are investigated by data mining of the Cambridge Structural Database (CSD). The mean volumetric thermal expansion coefficient is 168.8 × 10-6 K-1 and the mean uniaxial thermal expansion coefficient is 71.4 × 10-6 K-1, based on 745 and 1129 different observations, respectively. Normal and anomalous coefficients can be identified using these values and the associated standard deviations. The anisotropy of the thermal expansion is also evaluated and found to have a very broad distribution. 4719 different structures, comprising 4093 different molecular compounds and 626 additional polymorphs have been analyzed on their thermal expansion properties. Approximately 34% of these structures may have at least one orthogonal axis with negative thermal expansion, much more than generally believed. Moreover 127 structures have been identified which could have negative volumetric thermal expansion. Experimental validation using a robust protocol with data collected at more than 2 different temperatures is required to validate these cases.
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Thermal expansion of MAX phases along different directions tended to be different because of the anisotropy of hexagonal crystals. Herein, a new Hf2SeC phase was synthesized and confirmed to be relatively isotropic, whose coefficients of thermal expansion (CTEs) were determined to be 9.73 {\mu}K-1 and 10.18 {\mu}K-1 along a and c directions. The strong M-S bond endowed Hf2SC and Zr2SC lower CTEs than Hf2SeC and Zr2SeC. A good relationship between the thermal expansion anisotropy and the ratio of elastic stiffness constant c11 and c33 was established. This straightforward approximation could be used to roughly predict the thermal expansion anisotropy of MAX phases.
MAX phases
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Atmospheric temperature range
Standard molar entropy
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MAX phases
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Rietveld Refinement
Powder Diffraction
Hot isostatic pressing
MAX phases
Atmospheric temperature range
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