Lattice vibrations in copper at elevated temperatures studied by neutron scattering

Larose, André; Brockhouse, B. N.

doi:10.1139/p76-237

Cited by 44 publications

(12 citation statements)

References 4 publications

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“…Elastic properties are sensitive to temperature 35 , where the best fit to the experimental data gives μ = μ 0 (1−0.437 T / T m ) and B = B 0 (1−0.286 T / T m ). Also, we make a correction for the adiabatic heating.…”

Section: Methodsmentioning

confidence: 99%

Metal behavior in the extremes of dynamics

Zubelewicz

2018

Sci Rep

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When the rate of loading is faster than the rate at which material absorbs and converts energy to plastic work and damages, then there is an excess of energy that is partly stored in the material's microstructure and the rest of it triggers micro-dynamic excitations. The additional storage necessitates the development of plastic flow constraints and is directly responsible for the observed dynamic strengthening. At extreme conditions, we find that the micro-excitations contribute to the dynamic behavior. The phenomena are universally observed in metals, frictional materials and polymers. In essence, strong dynamics creates conditions at which materials are pushed from equilibrium and temporarily reside in an excited state of behavior. This study is focused on the behavior of metals. The concept is incorporated into a mechanisms-based constitutive model and is examined for annealed OFHC copper.When energy is delivered to a material with rates that are faster than the rate at which the material converts the excess energy to plastic work, then the uncompensated energy is partly stored in the material, while the rest of it is converted to micro-dynamic excitations. In metals, the observed strengthening mechanism 1 is linked to kinetics of the drag-controlled dislocation glide under applied stress 2,3 . Often, it is assumed 4 that the thermally activated dislocation mechanism operates at all strain rates, while others 5 have argued that both thermal activation and drag-controlled mechanisms coexist at high strain rates. A comprehensive review of the theoretical concepts and models is presented in refs 6,7 . In various constitutive descriptions, the effort is focused on connecting the material responses at high strain rates with the rapid increase of dislocation density and the development of fine dislocation structures. Subsequently, the microstructural evolution is coupled with external stimuli such as strain rate and temperature.Experimental observations presented in ref. 8 suggest that the dynamic behaviors arise due to the intrinsic resistance of lattice to motion of dislocations. This mechanism competes with an extrinsic resistance exerted by defects such as vacancies, interstitials and dislocations. The phenomena are studied with the use of standard split-Hopkinson pressure bar and Taylor cylinder tests 9 , where the achievable strain rates are in the range of 10 4 /s. The experiments have been further modified for a combined pressure-shear loading 8 , and then, the strain rates can reach a range of 10 5 /s to nearly 10 7 /s. As reported, the strain rates produce thermal instabilities and the fraction of plastic work converted to heat is much lower from the common ratio of β = 0.9. Even stronger loading is achieved in gas gun experiments, where energy is delivered in much shorter times 10 . The micro-dynamic excitations are consistently detected in acoustic emission (AE) measurements. In metals and rocks, the rate of AE counts is proportional to the rate of plastic strain 11,12 , where in metals bursts of acous...

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Section: Methodsmentioning

confidence: 99%

Metal behavior in the extremes of dynamics

Zubelewicz

2018

Sci Rep

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“…The linear temperature dependence is suggested by available P = 0 experimental data on G over the temperature range 0 ≤ T ≤ T m [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. This straight-line representation turns out to be quite accurate: the maximum deviation of the data from the corresponding fitted lines is ∼ 5 % for 21 of the 22 metals analyzed in [30].…”

Section: Experimental Verificationmentioning

confidence: 97%

“…[54] and G(ρ(T ), 0) and T m (ρ(T )) described by Eqs. (13) and (14) with the parameters from Tables 2 and 4 vs. the experimental data on Cu [10] (smaller points) and Au [2] (larger points).…”

Section: Experimental Verificationmentioning

confidence: 99%

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Analytic model of the shear modulus at all temperatures and densities

2003

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An analytic model of the shear modulus applicable at temperatures up to melt and at all densities is presented. It is based in part on a relation between the melting temperature and the shear modulus at melt. Experimental data on argon are shown to agree with this relation to within 1%. The model of the shear modulus involves seven parameters, all of which can be determined from zero-pressure experimental data. We obtain the values of these parameters for 11 elemental solids. Both the experimental data on the room-temperature shear modulus of argon to compressions of ∼ 2.5, and theoretical calculations of the zero-temperature shear modulus of aluminum to compressions of ∼ 3.5 are in good agreement with the model. Electronic structure calculations of the shear moduli of copper and gold to compressions of 2, performed by us, agree with the model to within uncertainties.

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“…Phonon lifetimes are a measure of these scattering processes, but there have been few systematic studies of phonon lifetimes besides optical measurements. For noble metals, work on phonon damping includes only one experimental study on copper 3 and one theoretical calculation using an empirical method that relates the anharmonic force constants to experimental third-order elastic moduli 4 . The mathematical form of the interatomic potential in the latter study contains numerous fitting parameters, and its final form is somewhat uncertain.…”

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confidence: 99%

First-principles study of phonon linewidths in noble metals

Tang

Fultz

2011

Phys. Rev. B

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Phonon lifetimes in Cu, Ag and Au at low and high temperatures were calculated along high symmetry directions using density functional theory combined with second-order perturbation theory. Both harmonic and third-order anharmonic force constants were computed using a supercell small displacement method, and the two-phonon densities of states were calculated for all three-phonon processes consistent with the kinematics of energy and momentum conservation. A non-rigorous Grüneisen model with no q-dependence of the anharmonic coupling constants offers a simple separation of the potential and the kinematics, and proved semi-quantitative for Cu, Ag and Au. A rule is reported for finding the most anharmonic phonon mode in fcc metals.2

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Lattice vibrations in copper at elevated temperatures studied by neutron scattering

Cited by 44 publications

References 4 publications

Metal behavior in the extremes of dynamics

Metal behavior in the extremes of dynamics

Analytic model of the shear modulus at all temperatures and densities

First-principles study of phonon linewidths in noble metals

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