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Study of ideal strengths of metals and alloys by statistical moment method: Temperature dependence

Published online by Cambridge University Press:  31 January 2011

Vu Van Hung ,
K. Masuda-Jindo  and
Nguyen Thi Hoa
Vu Van Hung
Affiliation:
Hanoi National Pedagogic University, Hanoi, Vietnam
K. Masuda-Jindo*
Affiliation:
Department of Material Science and Engineering, Tokyo Institute of Technology, Nagasuta, Midori-ku, Yokohama 226-8503, Japan
Nguyen Thi Hoa
Affiliation:
Hanoi National Pedagogic University, Hanoi, Vietnam
*
a)Address all correspondence to this author. e-mail: [email protected]
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Abstract

The ideal strengths of metals and alloys at finite temperatures have been studied using the statistical moment method. The tensile and shear strengths of the body-centered cubic (bcc) transition metals like Mo and W (refractory metals), and ordered FeAl (B2) and Fe3Al (DO3) alloys are calculated as a function of the temperature. The orthogonal tight-binding method is used for bcc transition elements, while the universal binding-energy relation (UBER)-type of pairwise potentials, derived from ab initio density-functional theory, is used for the FeAl and Fe3Al alloys. We discuss the temperature dependence of the tensile and shear strengths of the metals and alloys in conjunction with those of the second-order elastic constants.

Keywords

Debye temperatureElastic propertiesStrength
Type
Articles
Information
Journal of Materials Research , Volume 22 , Issue 8 , August 2007 , pp. 2230 - 2240
Copyright
Copyright © Materials Research Society 2007

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References

REFERENCES

1Hirth, J.P.Lothe, L.: Theory of Dislocations McGraw-Hill New York 1968Google Scholar
2Haasen, P., Suzuki, H.Gerola, H.: Dislocations in Solids, edited by F.R.N. Nabarro, Vol. 1–110, North-Holland Publishing Company Amsterdam, NY, Oxford 1979–1996Google Scholar
3Sih, G.C.: Mechanics of Fracture Initiation and Propagation Kluwer Academic Publishers Boston 1991CrossRefGoogle Scholar
4Šob, M., Wang, L.G.Vitek, V.: Theoretical tensile stress in tungsten single crystals by full-potential first-principles calculations. Mater. Sci. Eng., A 264–236, 1075 1997CrossRefGoogle Scholar
5Sob, M., Wang, L.G.Vitek, V.: The role of higher-symmetry phases in anisotropy of theoretical tensile strength of metals and intermetallics. Philos. Mag. B 78, 653 1998CrossRefGoogle Scholar
6Morris, J.W. Jr., Krenn, C.R.: The internal stability of an elastic solid. Philos. Mag. A 80(12), 2827 2000CrossRefGoogle Scholar
7Roundy, D., Krenn, C.R.Cohen, M.L.: The ideal strength of tungsten. Philos. Mag. A 81(7), 1725 2001CrossRefGoogle Scholar
8Krenn, C.R., Roundy, D., Morris, J.W. Jr.Cohen, M.L.: Ideal strength of bcc metals. Mater. Sci. Eng., A 319–321, 111 2001CrossRefGoogle Scholar
9Clatterbuck, D.M., Krenn, C.R., Cohen, M.L., Morris, J.W. Jr.Phonon instabilities and the ideal strength of aluminum. Phys. Rev. Lett. 91, 135501 2003CrossRefGoogle ScholarPubMed
10Friák, M., Šob, M.Vitek, V.: Ab initio study of the ideal tensile strength and mechanical stability of transition-metal disilicides. Phys. Rev. B 68, 184101 2003CrossRefGoogle Scholar
11Friak, M., Šob, M.Vitek, V.: Ab initio calculation of tensile strength in iron. Philos. Mag. 83, 3529 2003CrossRefGoogle Scholar
12Ogata, S., Hirosaki, N., Kocer, C.Shibutani, Y.: An ab initio study of the ideal tensile and shear strength of single-crystal β-Si3N4. J. Mater. Res. 18, 1168 2003CrossRefGoogle Scholar
13Vinci, R.P.Vlassak, J.J.: Mechanical behavior of thin films. Ann. Rev. Mater. Sci. 26, 431 1996CrossRefGoogle Scholar
14Bahr, D.F., Kramer, D.E.Gerberich, W.W.: Non-linear deformation mechanisms during nanoindentation. Acta Mater. 46(10), PP3605 1998CrossRefGoogle Scholar
15Gouldstone, A., Koh, H.J., Zeng, K.Y., Giannakopoulos, A.E.Suresh, S.: Discrete and continuous deformation during nanoindentation of thin films. Acta Mater. 48, 2277 2000CrossRefGoogle Scholar
16Woodcock, C.L.Bahr, D.F.: Plastic zone evolution around small scale indentations. Scripta Mater. 43, 783 2000CrossRefGoogle Scholar
17de la Fuente, O.R., Zimmeman, J.A., Gonzalez, M.A., de la Figuera, J., Hamilton, J.C., Pai, W.W.Rojo, J.M.: Dislocation emission around nanoindentations on a (001) fcc metal surface studied by scanning tunneling microscopy and atomistic simulations. Phys. Rev. Lett. 88, 036101 2002CrossRefGoogle Scholar
18Tang, N.Hung, V.V.: Investigation of the thermodynamic properties of anharmonic crystals by the momentum method. I. General results for face-centered cubic crystals. Phys. Status Solidi B 149, 511 1988CrossRefGoogle Scholar
19Tang, N.Hung, V.V.: Investigation of the thermodynamic properties of anharmonic crystals by the momentum method. II. Comparison of calculations with experiments for inert gas crystals. Phys. Status Solidi B 161, 165 1990CrossRefGoogle Scholar
20Tang, N., Hung, V.V.: Investigation of the thermodynamic properties of anharmonic crystals by the momentum method. III. Thermodynamic properties of the crystals at various pressures. Phys. Status Solidi B 162, 371 1990CrossRefGoogle Scholar
21Hung, V.V.Masuda-Jindo, K.: Application of statistical moment method to thermodynamic properties of metals at high pressures. J. Phys. Soc. Jpn. 69, 2067 2000CrossRefGoogle Scholar
22Hung, V.V., Tich, H.V.Masuda-Jindo, K.: Study of self-diffusion in metals by statistical moment method: Anharmonic effects. J. Phys. Soc. Jpn. 69, 2691 2000CrossRefGoogle Scholar
23Masuda-Jindo, K.Hung, V.V.: Atomistic study of fracture of crystalline materials by lattice Green’s function method. Effects of anharmonicity of lattice vibration. J. Phys. Soc. Jpn. 73, 1205 2004CrossRefGoogle Scholar
24Masuda-Jindo, K., Hung, V.V.Tam, P.D.: Thermodynamic quantities of metals investigated by an analytic statistical moment method. Phys. Rev. B 67, 094301 2003CrossRefGoogle Scholar
25Masuda-Jindo, K., Nishitani, S.R.Hung, V.V.: hcp–bcc structural phase transformation of titanium: Analytic model calculations. Phys. Rev. B 70, 184122 2004CrossRefGoogle Scholar
26Masuda-Jindo, K., Hung, V.V.Menon, M.: Study of dislocations in nanoscale semiconductors by ab initio molecular dynamics and lattice Green’s function methods. Phys. Status Solidi C 2, 1781 2005CrossRefGoogle Scholar
27Hung, V.V., Masuda-Jindo, K.Hanh, P.H.M.: Application of the statistical moment method to thermodynamic quantities of silicon. J. Phys.: Condens. Matter 18, 283 2006Google Scholar
28Hung, V.V., Lee, J.Masuda-Jindo, K.: Investigation of thermodynamic properties of cerium dioxide by statistical moment method. J. Phys. Chem. Solids 67, 682 2006CrossRefGoogle Scholar
29Leamy, H.J.: The elastic stiffness coefficients of iron-aluminum alloys—II. The effect of long-range order. Acta Metall. 15, 1839 1967CrossRefGoogle Scholar
30Leamy, H.J., Gibson, E.D.Kayser, F.X.: The elastic stiffness coefficients of iron-aluminum alloys—I. Experimental results and thermodynamic analysis. Acta Metall. 15, 1827 1967CrossRefGoogle Scholar
31Robertson, I.M.: Phonon dispersion curves in ordered and disordered Fe3Al. Solid State Commun. 53, 901 1985CrossRefGoogle Scholar
32Robertson, I.M.: Phonon dispersion curves for ordered, partially-ordered and disordered iron–aluminium alloys. J. Phys.: Condens. Matter 3, 8181 1991Google Scholar
33Anthony, L., Okamoto, J.K.Fultz, B.: Vibrational entropy of ordered and disordered Ni3Al. Phys. Rev. Lett. 70, 1128 1993CrossRefGoogle ScholarPubMed
34Nagel, L.J., Anthony, L., Okamoto, J.K.Fultz, B.: An experimental study of the difference in vibrational entropy between ordered and disordered Fe3Al. J. Phase Equilib. 18, 551 1997CrossRefGoogle Scholar
35Besson, R.Morillo, J.: Development of a semiempirical n-body noncentral potential for Fe-Al alloys. Phys. Rev. B 55, 193 1997CrossRefGoogle Scholar
36Ducastelle, F.: Order and Phase Stability in Alloys North-Holland Amsterdam 1999Google Scholar
37Tight-Binding Approach to Computational Materials Science,, edited by P.E.A. Turchi, A. Gonis, and L. Colombo (Mater. Res. Soc. Symp. Proc. 491, 1998)Google Scholar
38Cohen, R.E., Mehl, M.J.Papaconstantopaulos, D.A.: Tight-binding total-energy method for transition and noble metals. Phys. Rev. B 50, 14694 1994CrossRefGoogle ScholarPubMed
39Mehl, M.J.Papaconstantopaulos, D.A.: Applications of a tight-binding total-energy method for transition and noble metals: Elastic constants, vacancies, and surfaces of monatomic metals. Phys. Rev. B 54, 4519 1996CrossRefGoogle ScholarPubMed
40Masuda, K., Hamada, N.Terakura, K.: Calculation of elastic constants of BCC transition metals: Tight-binding recursion method. J. Phys. F: Met. Phys. 14, 47 1984CrossRefGoogle Scholar
41Haas, H., Wang, C.Z., Fähnle, M., Elsasser, C.Ho, K.M.: Environment-dependent tight-binding model for molybdenum. Phys. Rev. B 57, 1461 1998CrossRefGoogle Scholar
42Mrovec, M., Nguyen-Manh, D., Pettifor, D.G.Vitek, V.: Bond order potential for molybdenum: Application to dislocation behavior. Phys. Rev. B 69, 094115 2004CrossRefGoogle Scholar
43Chen, N.X.: Modified Möbius inverse formula and its applications in physics. Phys. Rev. Lett. 64, 1193 1990CrossRefGoogle ScholarPubMed
44Chen, N.X., Chen, Y.Li, G.Y.: Theoretical investigation on inversion for the phonon density of states. Phys. Lett. A 149, 357 1990CrossRefGoogle Scholar
45Liu, S-J., Li, M.Chen, N-X.: Mobius transform and inversion from cohesion to elastic constants. J. Phys.: Condens. Matter 5, 4381 1993Google Scholar
46Chen, N.X., Li, M.Liu, S.J.: Phonon dispersions and elastic constants of Ni3Al and Möbius inversion. Phys. Lett. A 195, 135 1994CrossRefGoogle Scholar
47Chen, X., Dou, C.H.Chuan, W.Y.: Multidimensional inverse lattice problem and a uniformly sampled arithmetic Fourier transform. Phys. Rev. E 55, R5 1997Google Scholar
48Shaojun, L., Suqing, D.Benken, M.: First-principles calculation of vibrational entropy for Fe–Al compounds. Phys. Rev. B 58, 9705 1998CrossRefGoogle Scholar
49Rose, J.H., Smith, J.R.Ferrante, J.: Universal features of bonding in metals. Phys. Rev. B 28, 1835 1983CrossRefGoogle Scholar
50Cagin, T.Ray, J.R.: Elastic constants of sodium from molecular dynamics. Phys. Rev. B 37, 699 1988CrossRefGoogle ScholarPubMed
51Frenkel, J.: On the theory of elasticity and stiffness of crystalline solids. Z. Phys. 37, 572 1926CrossRefGoogle Scholar
52Orowan, E.: Fracture and strength of solids. Rep. Prog. Phys. 12, 185 1949CrossRefGoogle Scholar
53Featherston, F.H.Neighbours, J.R.: Elastic constants of tantalum, tungsten, and molybdenum. Phys. Rev. 130, 1324 1963CrossRefGoogle Scholar
54Kim, S.C.Kwon, T.H.: Temperature variation of elastic constants of NaCl. Phys. Rev. B 45, 2105 1992CrossRefGoogle ScholarPubMed
55Zener, C.: Contributions to the theory of beta-phase alloys. Phys. Rev. 71, 846 1980CrossRefGoogle Scholar
56Mikhailovskii, I.M., Poltinin, P.Y.Fedorova, L.I.: The tensile fracture of microcrystalline tungsten. Sov. Phys. Solid State 23, 757 1981Google Scholar
57Simmons, G.Wang, H.: Single Crystal Elastic Constants and Calculated Aggregated Properties, MIT Press Cambridge 1971Google Scholar
58Romero, R.: Martensitic transformation and negative Poisson ratios in β Cu-based alloys. Phys. Status Solidi B. 213, R7 19993.0.CO;2-S>CrossRefGoogle Scholar
59Li, T., Morris, J.W. Jr., Chrzan, D.C.: Ideal tensile strength of B2 transition-metal aluminides. Phys. Rev. B 70, 054107 2004CrossRefGoogle Scholar
60Li, T., Morris, J.W. Jr., Chrzan, D.C.: Ab initio study of the ideal shear strength and elastic deformation behaviors of B2 FeAl and NiAl. Phys. Rev. B 73, 024105 2006.CrossRefGoogle Scholar