Elastic constants and their temperature dependence for the intermetallic compound Ti<sub>3</sub>Al

Tanaka, Katsushi; Okamoto, Kyosuke; Inui, Haruyuki; Minonishi, Y.; Yamaguchi, M.; Koiwa, M.

doi:10.1080/01418619608245145

Cited by 119 publications

(51 citation statements)

References 18 publications

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“…Table 6 shows the comparison between prediction and experimental (Tanaka et al 1996b) and DFT-based calculated cohesive energy and elastic constants. The agreement is very satisfactory considering that the titanium aluminide BOPs were developed by fitting to the alloy with the 1 : 1 stoichiometry.…”

Section: à3mentioning

confidence: 99%

“…Table 6. Equilibrium properties of D0 19 -Ti 3 Al, lattice parameters a and c, cohesive energies and elastic constants, calculated using constructed BOPs and compared with experimental data (Tanaka et al 1996b), and DFT-based calculations ; the DFT cohesive energy value is taken from our FP LMTO calculations (see also van Schilfgaarde et al (1991) The first important finding is that the surface is everywhere positive so that shearing along the (111) plane does not lead to any instabilities with respect to the ideal lattice. The three minima seen on this surface correspond to the three stackingfault-type defects described below.…”

Section: à3mentioning

confidence: 99%

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Atomistic modelling of TiAl I. Bond-order potentials with environmental dependence

Znám

Nguyen-Manh

Pettifor

et al. 2003

Philosophical Magazine

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Bond-order potentials (BOPs) for L1 0 TiAl have been developed and constructed within a tight-binding framework. In addition to the usual attractive bond-energy contribution arising from the formation of covalent bonds and pairwise contribution describing the overlap repulsion and electrostatic interaction, we have included an environmentally dependent term to represent the strong repulsion experienced by the valence sp electrons in transition metals and their alloys. The latter contribution is crucial for reproducing the negative Cauchy pressures of TiAl and other transition-metalbased intermetallic compounds. The constructed BOPs have been tested in the following ways: firstly, examination of the mechanical stability of the tetragonal L1 0 lattice with respect to large deformations and other crystal structures with the same stoichiometry; secondly, calculation of the surface for f111g planes and related evaluation of the energies of stacking-fault-type defects; thirdly, calculation of energies of the -interfaces that are present in the lamellar TiAl and energies associated with the formations of point defects in TiAl. The results of all these calculations show very good agreement with various ab-initio calculations. Importantly, we find that this potential is transferable to the different bonding environment in the hexagonal D0 19 Ti 3 Al. Hence these BOPs are suitable for atomistic study of dislocations and other extended defects not only in L1 0 TiAl but also in Ti 3 Al and possibly structures with other titanium-rich stoichiometries.

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Section: à3mentioning

confidence: 99%

Section: à3mentioning

confidence: 99%

Atomistic modelling of TiAl I. Bond-order potentials with environmental dependence

Znám

Nguyen-Manh

Pettifor

et al. 2003

Philosophical Magazine

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“…Here we give only a brief description of the basic principle and experimental setting. Interested readers may refer to Tanaka et al (1996b) for more details.…”

Section: Elastic Constants Measured By Rectangular Parallelepiped Resmentioning

confidence: 99%

Elastic constants of Ti₅₀Ni₃₀Cu₂₀alloy prior to martensitic transformation

Ren

Taniwaki

Otsuka

et al. 1999

Philosophical Magazine A

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Elastic constants of Ti 50 Ni 30 Cu 20 alloy prior to the martensitic transformation B2 B19 was measured for the ® rst time by using the rectangular parallelepiped resonance method. The softening in both shear modulus c and c 44 was found with approaching transformation temperature. As a result of soft c 44 , the anisotropy factor shows a low value of 2.8 in the vicinity of the transformation temperature. c 11 , c 12 , and bulk modulus were found to show little temperature dependence in the vicinity of the transformation temperature. Compared with the binary Ti 50 Ni 50 alloy, Ti 50 Ni 30 Cu 20 alloy exhibits a 40% higher and increasing anisotropy with approaching transformation temperature. Based on the experimental results, we explained why Ti 50 Ni 30 Cu 20 transforms into B19 martensite, while Ti 50 Ni 50 transforms into a strange monoclinic B19 martensite. §1. Introduction Despite the fact that Ti± Ni is the most important shape memory alloy for various technological applications (for example, Otsuka and Shimizu (1986)), its martensitic transformation (MT) mechanism, which governs its properties, has remained poorly understood for many years compared with other shape memory alloys. The central problem is how to explain the abnormal structure of TiNi martensite B19 .In contrast to other martensites of b (B2) phase alloys which are invariably formed by di erent ways of basal plane stacking (see Nishiyama (1978) for a review), B19 martensite exhibits a large and strange non-basal distortion ({001} 110 B2 shear) to the well-known basal plane structure B19 (Heheman and Sandrock 1971, Kudoh et al. 1985). This non-basal shear gives a monoclinic distortion to B19 structure and lowers the orthorhombic symmetry of B19 to monoclinic, thus the distorted martensite is named as B19 . The reason for such a non-basal distortion is unclear. On the other hand, the addition of 20 at.% Cu into Ti 50 Ni 50 alloy changes the transformation product into common B19 martensite for Ti 50 Ni 30 Cu 20 alloy (Nam et al. 1990b), although the parent phase for both alloys has the same B2 (CsCl) structure. Accompanying such a change of transformation product, the

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“…The elastic constants were determined by applying an appropriate set of distortions with the distortion parameter δ varying between −0.02 and +0.02. Calculations of the lattice vibrations were carried out using the density functional perturbation theory (DFPT) 22 Considering that the bulk modulus can be as a measure of the average bond strength and the shear modulus can be as a measure of the resistance to a change in bond angle by an external force, Tanaka et al 44 proposed that G/B represents the relative directionality of the bonding in the material. For those carbon phases, the calculated ratio of G 0 /B 0 in rang from 1.04 to 1.15 is slightly smaller than 1.19 of diamond, which indicates that the directionality of the bonding is strong.…”

Section: Computational Detailsmentioning

confidence: 99%

Strength, hardness, and lattice vibrations ofZ-carbon andW-carbon: First-principles calculations

Gao

2012

Phys. Rev. B

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Elastic constants and their temperature dependence for the intermetallic compound Ti₃Al

Cited by 119 publications

References 18 publications

Atomistic modelling of TiAl I. Bond-order potentials with environmental dependence

Atomistic modelling of TiAl I. Bond-order potentials with environmental dependence

Elastic constants of Ti₅₀Ni₃₀Cu₂₀alloy prior to martensitic transformation

Strength, hardness, and lattice vibrations ofZ-carbon andW-carbon: First-principles calculations

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Elastic constants and their temperature dependence for the intermetallic compound Ti3Al

Cited by 119 publications

References 18 publications

Atomistic modelling of TiAl I. Bond-order potentials with environmental dependence

Atomistic modelling of TiAl I. Bond-order potentials with environmental dependence

Elastic constants of Ti50Ni30Cu20alloy prior to martensitic transformation

Strength, hardness, and lattice vibrations ofZ-carbon andW-carbon: First-principles calculations

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Product

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Elastic constants and their temperature dependence for the intermetallic compound Ti₃Al

Elastic constants of Ti₅₀Ni₃₀Cu₂₀alloy prior to martensitic transformation