Calculation of debye temperature for crystalline structures—a case study on Ti, Zr, and Hf

Chen, Qing; Sundman, Bo

doi:10.1016/s1359-6454(01)00002-7

Cited by 149 publications

(71 citation statements)

References 42 publications

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“…The Debye temperature for pure Ti was estimated to be 403 K which was comparable to the published value of 385 K for α-Ti. 32) Similarly, the Debye temperature for pure Zr was estimated to be 280 K which was in good agreement with the reported value of 275.9 K for α-Zr. 20) These good agreements of our estimated Debye temperatures for pure metals (Ti, Zr) with the previously published values support the validity of the current estimation of the Debye temperatures for the experimental Ti-Zr alloys.…”

Section: Discussionsupporting

confidence: 87%

Elastic Properties of As-Solidified Ti-Zr Binary Alloys for Biomedical Applications

2016

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Young s modulus (E), shear modulus (G), bulk modulus (K) and Poisson s ratio (ν) of Ti-Zr binary alloys containing 20, 40, 50, 60, 70 and 80 at% Zr and component pure metals (Ti, Zr) prepared by arc-melting followed by solidi cation process were determined precisely by ultrasonic sound velocity measurements. X-ray diffraction analysis showed that all the as-solidi ed alloys and pure metals were with a single-phase structure of the hexagonal close-packed lattice (martensitically formed α

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Section: Discussionsupporting

confidence: 87%

Elastic Properties of As-Solidified Ti-Zr Binary Alloys for Biomedical Applications

2016

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“…The results obtained agree well with previous studies [8,51,52]. The Debye temperatures of the three compounds are larger than that of tantalum.…”

Section: Debye Temperaturesupporting

confidence: 91%

The Effects of Al and Ti Additions on the Structural Stability, Mechanical and Electronic Properties of D8m-Structured Ta5Si3

Liu

Cheng

et al. 2016

Metals

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Abstract:In the present study, the influence of substitutional elements (Ti and Al) on the structural stability, mechanical properties, electronic properties and Debye temperature of Ta 5 Si 3 with a D8 m structure were investigated by first principle calculations. The Ta 5 Si 3 alloyed with Ti and Al shows negative values of formation enthalpies, indicating that these compounds are energetically stable. Based on the values of formation enthalpies, Ti exhibits a preferential occupying the Ta 4b site and Al has a strong site preference for the Si 8h site. From the values of the bulk modulus (B), shear modulus (G) and Young's modulus (E), we determined that both Ti and Al additions decrease both the shear deformation resistance and the elastic stiffness of D8 m structured Ta 5 Si 3 . Using the shear modulus/bulk modulus ratio (G/B), Poisson's ratio (υ) and Cauchy's pressure, the effect of Ti and Al additions on the ductility of D8 m -structured Ta 5 Si 3 are explored. The results show that Ti and Al additions reduce the hardness, resulting in solid solution softening, but improve the ductility of D8 m -structured Ta 5 Si 3 . The electronic calculations reveal that Ti and Al additions change hybridization between Ta-Si and Si-Si atoms for the binary D8 m -structured Ta 5 Si 3 . The new Ta-Al bond is weaker than the Ta-Si covalent bonds, reducing the covalent property of bonding in D8 m -structured Ta 5 Si 3 , while the new strong Ti 4b -Ti 4b anti-bonding enhances the metallic behavior of the binary D8 m -structured Ta 5 Si 3 . The change in the nature of bonding can well explain the improved ductility of D8 m -structured Ta 5 Si 3 doped by Ti and Al. Moreover, the Debye temperatures, Θ D , of D8 m -structured Ta 5 Si 3 alloying with Ti and Al are decreased as compared to the binary Ta 5 Si 3 .

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“…In HfOs, the elastic constants derived from GGA method has agreed well with theoretical values from Arıkan's [13] and Liu's work [14]. Meanwhile, the elastic constants for pure Hf metal are calculated and presented with the published experimental values [37] for comparison, where the GGA computed elastic constants are in better agreement with experimental values [37].…”

Section: Elastic Propertiessupporting

confidence: 72%

First-Principles Investigation of Structural, Electronic and Elastic Properties of HfX (X = Os, Ir and Pt) Compounds

Xia

Wang

et al. 2017

Metals

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Abstract:The structural, electronic and elastic properties of B2 structure Hafnium compounds were investigated by means of first-principles calculations based on the density functional theory within generalized gradient approximation (GGA) and local density approximation (LDA) methods. Both GGA and LDA methods can make acceptable optimized lattice parameters in comparison with experimental parameters. Therefore, both GGA and LDA methods are used to predict the electronic and elastic properties of B2 HfX (X = Os, Ir and Pt) compounds. Initially, the calculated formation enthalpies have confirmed the order of thermodynamic stability as HfPt > HfIr > HfOs. Secondly, the electronic structures are analyzed to explain the bonding characters and stabilities in these compounds. Furthermore, the calculated elastic properties and elastic anisotropic behaviors are ordered and analyzed in these compounds. The calculated bulk moduli are in the reduced order of HfOs > HfIr > HfPt, which has exhibited the linear relationship with electron densities. Finally, the anisotropy of acoustic velocities, Debye temperatures and thermal conductivities are obtained and discussed.

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Calculation of debye temperature for crystalline structures—a case study on Ti, Zr, and Hf

Cited by 149 publications

References 42 publications

Elastic Properties of As-Solidified Ti-Zr Binary Alloys for Biomedical Applications

Elastic Properties of As-Solidified Ti-Zr Binary Alloys for Biomedical Applications

The Effects of Al and Ti Additions on the Structural Stability, Mechanical and Electronic Properties of D8m-Structured Ta5Si3

First-Principles Investigation of Structural, Electronic and Elastic Properties of HfX (X = Os, Ir and Pt) Compounds

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