Modelling diffusion in crystals under high internal stress gradients

Olmsted, David L.; Phillips, Rob

doi:10.1088/0965-0393/12/5/003

Cited by 28 publications

(14 citation statements)

References 16 publications

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“…The accuracy of the linear approximations for the formation and migration barriers has been demonstrated previously [12].…”

Section: Diffusion In Zones 0-3mentioning

confidence: 84%

“…Zone 4 is then identified as the set of atoms not in the bulk crystal (e.g. fcc) environment plus extra shells of atoms surrounding these non-crystalline atoms where the stress gradients are too large to be handled by discrete diffusion [12]. Zone 3 consists of the shell of near-crystalline atoms surrounding Zone 4.…”

Section: Initialization For Each New Defect Structurementioning

confidence: 99%

“…The diffusion of point defects through the strained crystalline lattice of Zones 0-3 can be efficiently modeled by considering discrete (site-by-site) diffusion (DD) using transition state theory along with the formation and migration enthalpies appropriate to each site or transition [12]. In most problems, the size of Zones 0-3 is hugely larger than that of Zone 4 and the point defect transition rates in Zones 0-3 are much slower than those in Zone 4, so that this efficient diffusion model captures the large length and time scales of the problem.…”

Section: Diffusion In Zones 0-3mentioning

confidence: 99%

“…The Ercolessi and Adams embedded atom potential for Aluminum is used [26]. For this potential, the vacancy formation enthalpy at zero pressure and temperature is ∆H f = 0.69 eV and the vacancy misfit volume is ∆V f = 9.75Å 3 [12]. At T = 600K, the vacancy concentration in bulk Al is then c = 1.6 × 10 −6 .…”

Section: Geometry and Materials Propertiesmentioning

confidence: 99%

“…At T = 600K, the vacancy concentration in bulk Al is then c = 1.6 × 10 −6 . The vacancy migration enthalpy at zero temperature and pressure is ∆H m = 0.61 eV and the principal values of the vacancy misfit volume tensor at the transition state for site-tosite hopping are (11.15, −1.97, −5.74)Å 3 , where the first value corresponds to the 100 direction perpendicular to jump direction, the second value corresponds to the 110 jump direction, and the third value corresponds to the 110 direction perpendicular to jump direction [12].…”

Section: Geometry and Materials Propertiesmentioning

confidence: 99%

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Multiscale diffusion method for simulations of long-time defect evolution with application to dislocation climb

Baker

Curtin

2016

Journal of the Mechanics and Physics of Solids

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In many problems of interest to materials scientists and engineers, the evolution of crystalline extended defects (dislocations, cracks, grain boundaries, interfaces, voids, precipitates) is controlled by the flow of point defects (interstitial/substitutional atoms and/or vacancies) through the crystal into the defect. Precise modeling of this behavior requires fully atomistic methods in and around the extended defect, but the flow of point defects entering the extended defect region can be treated by coarse-grained methods. Here, a multiscale algorithm is presented to provide this coupling. Specifically, direct accelerated molecular dynamics (AMD) of extended defect evolution is coupled to a diffusing point defect concentration field that captures the long spatial and temporal scales of point defect motion in the presence of the internal stress fields generated by the evolving defect. The algorithm is applied to study vacancy absorption into an edge dislocation in aluminum where, under a sufficient driving stress and vacancy supersaturation, vacancy accumulation in the core leads to nucleation of a double-jog that then operates as a sink for additional vacancies; this corresponds to the initial stages of dislocation climb modeled with explicit atomistic resolution. The method is general and so can be applied to many other problems associated with nucleation, growth, and reaction due to accumulation of point defects in crystalline materials.

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“…The accuracy of the linear approximations for the formation and migration barriers has been demonstrated previously [12].…”

Section: Diffusion In Zones 0-3mentioning

confidence: 84%

Section: Initialization For Each New Defect Structurementioning

confidence: 99%

Section: Diffusion In Zones 0-3mentioning

confidence: 99%

Section: Geometry and Materials Propertiesmentioning

confidence: 99%

Section: Geometry and Materials Propertiesmentioning

confidence: 99%

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Multiscale diffusion method for simulations of long-time defect evolution with application to dislocation climb

Baker

Curtin

2016

Journal of the Mechanics and Physics of Solids

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Impact of the Mechanical Stress on Switching Characteristics of Electrochemical Resistive Memory

et al. 2014

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with electrode size as small as 5 nm. [ 26 ] Whereas low-power operation [ 3 ] and fast switching [ 15 ] were demonstrated in ECMs, recent experiments on ECM devices [ 25,27 ] have questioned the long-term stability of the CF, which is necessary to enable nonvolatile storage of data. To assess the switching behavior and CF stability in ECMs, the detailed evolution of electrical, chemical and mechanical forces in the CF must be understood. Figure 2 a shows the measured current-voltage ( I -V ) curve for an ECM with Ag top electrode, GeS 2 electrolyte and W bottom electrode during set and reset transition. Details about the preparation of the ECM devices can be found elsewhere. [ 15 ] The set transition from high to low resistance takes place at V set ≈ 0.3 V, while the reset transition to high resistance occurs at V reset . In the set process, the CF is fi rst formed by nucleation [ 28,29 ] followed by CF growth, [ 6,24 ] which is activated by positive ion migration as shown in Figure 2 b: metallic ions from the reactive-metal electrode (Ag) hop among localized states separated by energy barriers E A0 in amorphous GeS 2 . The electric fi eld lowers the ion-migration barrier to the value:where α = 0.3 is a barrier-lowering coeffi cient (see Figure S1 in the Supporting Information for a complete list of all model parameters used in the simulation) and V is the voltage across the electrolyte. [ 6,24,30 ] Barrier lowering enhances the hopping rate in the fi eld direction, thus increasing the growth rate of the CF diameter φ according to:where A is a pre-exponential constant proportional to cation mobility, T is the local temperature at the CF and E A was obtained from Equation 1 . In Equation 2 , E A controls ion migration in the vertical direction from top to bottom electrode, while the accumulation of defects along the CF causes growth in the radial direction, which is captured by the parameter φ (e.g., see Figure 1 c). Note that the parameter φ represents an effective CF diameter, to properly describe non-cylindrical (e.g., conical) CF shapes and the case of multiple fi laments contributing to the resistive switching. [ 12,26 ] For instance, in the case of multiple fi laments the effective diameter in Equation 2 obeys φ 2 = Σ φ i 2 , where φ i represents the diameter of the individual i -th fi lament and φ properly describes the resistance R ∝ φ −2 of the set state.To control the size of the growing CF during the set transition, the current was kept equal to a compliance value I C = 1 mA in Figure 2 a, thus resulting in a resistance of about 0.3 kΩ in the set state. The current-controlled CF growth was Resistive switching in oxides and other insulating materials provides a promising approach to nanoscale memory devices, where the stored logic state can be changed by activating/deactivating a conductive fi lament (CF). [ 1,2 ] Among resistive switching devices, the electrochemical memory (ECM) attracts strong interest because of outstanding properties such as extremely small programming current, [ 3 ] fast switching...

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Failure modes and mechanisms for rechargeable Lithium-based batteries: a state-of-the-art review

Lyu

Ren

2018

Acta Mech

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Modelling diffusion in crystals under high internal stress gradients

Cited by 28 publications

References 16 publications

Multiscale diffusion method for simulations of long-time defect evolution with application to dislocation climb

Multiscale diffusion method for simulations of long-time defect evolution with application to dislocation climb

Impact of the Mechanical Stress on Switching Characteristics of Electrochemical Resistive Memory

Failure modes and mechanisms for rechargeable Lithium-based batteries: a state-of-the-art review

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