Measuring Dislocation Density in Aluminum With Resonant Ultrasound Spectroscopy

Barra, Felipe; Caru, Andres; Cerda, Maria Teresa; Espinoza, Rodrigo; Jara, Alejandro; Lund, Fernando; Mujica, Nicolás

doi:10.1142/s0218127409025006

Cited by 17 publications

(16 citation statements)

References 23 publications

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“…As briefly reported in [51], attempts to fit resonant frequencies assuming homogeneity and isotropy fail considerably. In fact, under the assumption of isotropy, measurements of matrix has five independent values.…”

Section: B Resonant Ultrasound Spectroscopymentioning

confidence: 99%

Ultrasound as a probe of dislocation density in aluminum

et al. 2012

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Dislocations are at the heart of the plastic behavior of crystalline materials yet it is notoriously difficult to perform quantitative, non-intrusive, measurements of their single or collective properties. Dislocation density is a critical variable that determines dislocation mobility, strength and ductility. On the one hand, individual dislocations can be probed in detail with transmission electron microscopy. On the other hand, their collective properties must be simulated numerically. Here we show that ultrasound technology can be used to measure dislocation density. This development rests on theory---a generalization of the Granato-L\"ucke theory for the interaction of elastic waves with dislocations---and Resonant Ultrasound Spectroscopy (RUS) measurements. The chosen material is aluminum, to which different dislocation contents were induced through annealing and cold rolling processes. The dislocation densities obtained with RUS compare favorably with those inferred from X-ray diffraction, using the modified Williamson-Hall method

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Section: B Resonant Ultrasound Spectroscopymentioning

confidence: 99%

Ultrasound as a probe of dislocation density in aluminum

et al. 2012

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“…In this respect, some researchers [5,15,16] have investigated density of dislocations by ultrasound waves and have proposed some relationships between dislocation density and changes in the speed of elastic waves propagation. Sablik and Landgraf [17,18], Kobayashi et al [19], and Yaegashi [20] reported some relationships between dislocation density and magnetic properties.…”

Section: Introductionmentioning

confidence: 99%

An Investigation on Dislocation Density in Cold-Rolled Copper Using Electrochemical Impedance Spectroscopy

et al. 2013

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Variation of electrochemical impedance with dislocation density was investigated using electrochemical impedance spectroscopy (EIS). For this purpose, EIS measurements were carried out on 10, 20, 30, 40, and 50% cold-rolled commercially pure copper in 0.1 M NaCl (pH = 2) solution. Nyquist plots illustrated that the electrochemical reactions are controlled by both charge transfer and diffusion process. Increasing dislocation density, the magnitude of electrochemical impedance of samples was decreased. Decreasing magnitude of impedance at intermediate frequencies indicated increasing double-layer capacitance. Charge transfer resistance decreased from value 329.6 Ωcm 2 for annealed sample to 186.3 Ωcm 2 for sample with maximum dislocation density (1.72 × 10 15 m −2 ). Phase angles were lower for samples that contained more dislocation density, indicating more tendencies to loss of electrons and releasing atoms into electrolyte.

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“…The velocity of acoustic waves has a negative dispersion at low frequencies and then increases as a function of frequency around ω BP . Notice that the defects have an effect even at low frequencies, suggesting the model can be tested, say, using Resonant Ultrasound Sectroscopy (RUS), a tool that has been used to measure dislocation densities in polycrystalline materials [59,60], or hyper sound damping in the subteraherz range, as measured in vitreous silica [61,62]. Additional possible topics for further research include a numerical, atomistic, study of the hypothesized linear defects; the effect they would have on thermal and electrical conductivity properties, particularly at very low temperatures where quantum effects would be dominant; and the role they may or may not have in plasticity properties and in the glass transition.…”

Section: Figmentioning

confidence: 99%

Normal modes and acoustic properties of an elastic solid with line defects

Lund¹

2015

Phys. Rev. B

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The normal modes of a continuum solid endowed with a random distribution of line defects that behave like elastic strings are described. These strings interact with elastic waves in the bulk, generating wave dispersion and attenuation. As in amorphous materials, the attenuation as a function of frequency ω behaves as ω 4 for low frequencies, and, as frequency increases, crosses over to ω 2 and then to linear in ω. Dispersion is negative in the frequency range where attenuation is quartic and quadratic in frequency. Explicit formulae are provided that relate these properties to the density of string states. Continuum mechanics can thus be applied both to crystalline materials and their amorphous counterparts at similar length scales. The possibility of linking this model with the microstructure of amorphous materials is discussed.Introduction. The normal modes of a continuum elastic solid can be easily counted using the classical theory of elasticity. However, since there is no intrinsic length scale, an artificial short distance cut-off must be introduced in order to obtain a finite result for the total number of modes of a given material. The Debye model does that, imposing a high frequency cut-off, the Debye frequency ω D , so that the resulting total number of degrees of freedom equals the number of degrees of freedom inferred from the number of atoms in the solid. This provides a firm underpinning, at wavelengths long compared to interatomic spacing, for all properties of solids that depend on the counting on such modes. If the solid is crystalline, a similar counting can also be performed, exploiting the invariance of the system under discrete translations. This counting reduces to that provided by the Debye model at long wavelengths, and provides, as well, a firm underpinning for properties at shorter wavelengths, down to the size of the unit cell.The situation for amorphous solids, without a discrete translation invariance, has long been unsatisfactory. While at long wavelengths the situation is well described, as expected, by the Debye model, at wavelengths on the order of tens of mean interatomic distances, abundant evidence, from specific heat [1], thermal conductivity [2], Raman scattering [3], neutron scattering [4], and inelastic X-ray scattering measurements [5], points to the existence of normal modes with a frequency distribution that is peaked around 0.1-0.2 ω D . This distribution is qualitatively similar for many such materials, and the details, but not the broad features, depend on external parameters such as temperature, density, pressure, as well as chemical and thermal history [6][7][8][9][10][11][12][13][14][15]. This distribution, dubbed the "Boson Peak" (BP), cannot be blamed on a (non-existent) crystalline structure, and deviates without ambiguity from the distribution for a continuum, at frequencies where the continuum approximation works reasonably well in the case of crystals. Much research has been performed in order to provide some rationale for this state of affairs [16][17][18][...

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Measuring Dislocation Density in Aluminum With Resonant Ultrasound Spectroscopy

Cited by 17 publications

References 23 publications

Ultrasound as a probe of dislocation density in aluminum

Ultrasound as a probe of dislocation density in aluminum

An Investigation on Dislocation Density in Cold-Rolled Copper Using Electrochemical Impedance Spectroscopy

Normal modes and acoustic properties of an elastic solid with line defects

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