Formulas for the Pressure and Bulk Modulus in Uniaxial Strain.

Scheidler, Michael J.

doi:10.21236/ada304036

Cited by 3 publications

(11 citation statements)

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“…Although the actual value of Δ G is high, τ 12 = 1.8 GPa is reasonable for the sample, for which modeled shock pressures P are 2 to 5 GPa in the rock itself (Turtle & Pierazzo, ). To compare τ and P , we use the following approximation from Scheidler ():

P_{u} = P_{h} + K_{0} ([], \frac{2}{3} ((), {(|, \frac{dK}{dP})}_{0} + \frac{μ_{0}}{K_{0}})) {((), \frac{V}{V_{0}} - 1)}^{2}

and the following fundamental relationship in uniaxial strain:

P_{u} = σ_{1} - \frac{4}{3} τ

…”

Section: Resultsmentioning

confidence: 99%

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A Numerical Model for Twin Nucleation in Shocked Zircon and Comparison With Natural Samples

Jones

Moser

Shieh

2018

Geophysical Research Letters

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Twins in zircon are increasingly being used as an indicator of shock metamorphism on Earth and other planetary bodies, yet the conditions of their formation have not been quantified. We modeled the shear stress involved with homogeneous nucleation of the most common zircon twin false(112false)false[true1̄true1̄1false]. This stress is between 1.7 to 2.6 GPa for the range of crystal sizes common to the crust, stresses that are restricted to impact deformation regimes as opposed to tectonism. The twin nucleation stress is largely pressure independent, and it is likely that twins can form over a much larger range of shock pressures than is currently appreciated. This prediction is validated by the occurrence of twins in shocked zircon from distal regions of the 2.02 Ga Vredefort impact structure.

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P_{u} = P_{h} + K_{0} ([], \frac{2}{3} ((), {(|, \frac{dK}{dP})}_{0} + \frac{μ_{0}}{K_{0}})) {((), \frac{V}{V_{0}} - 1)}^{2}

and the following fundamental relationship in uniaxial strain:

P_{u} = σ_{1} - \frac{4}{3} τ

…”

Section: Resultsmentioning

confidence: 99%

“…In uniaxial strain, the stress state is not hydrostatic but more generally triaxial. Therefore, shear stress is introduced and has a definite relationship with the shock pressure (Scheidler, 1996). Shear stresses in impact reconstructions, however, are rarely reported.…”

Section: Introductionmentioning

confidence: 99%

A Numerical Model for Twin Nucleation in Shocked Zircon and Comparison With Natural Samples

Jones

Moser

Shieh

2018

Geophysical Research Letters

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“…Lattice sizes in this study consisted of a cubic lattice, with a side length of 200 sites. The lattice spacing a, between sites was constrained to 1 nm; typical lattice constants or inter-site distances for organic semiconductors range between 0.36 nm and 1.7 nm [41,51,70,71]. Periodic boundary conditions were also enforced in the directions perpendicular to the external field.…”

Section: Kinetic Monte Carlomentioning

confidence: 99%

Introducing correlations into carrier transport simulations of disordered materials through seeded nucleation: impact on density of states, carrier mobility, and carrier statistics

Brown

Shaheen

2018

J. Phys.: Condens. Matter

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Disorder in organic semiconductors has made it challenging to achieve performance gains; this is a result of the many competing and often nuanced mechanisms effecting charge transport. In this article, we attempt to illuminate one of these mechanisms in the hopes of aiding experimentalists in exceeding current performance thresholds. Using a heuristic exponential function, energetic correlation has been added to the Gaussian disorder model (GDM). The new model is grounded in the concept that energetic correlations can arise in materials without strong dipoles or dopants, but may be a result of an incomplete crystal formation process. The proposed correlation has been used to explain the exponential tail states often observed in these materials; it is also better able to capture the carrier mobility field dependence, commonly known as the Poole-Frenkel dependence, when compared to the GDM. Investigation of simulated current transients shows that the exponential tail states do not necessitate Montroll and Scher fits. Montroll and Scher fits occur in the form of two distinct power law curves that share a common constant in their exponent; they are clearly observed as linear lines when the current transient is plotted using a log-log scale. Typically, these fits have been found appropriate for describing amorphous silicon and other disordered materials which display exponential tail states. Furthermore, we observe the proposed correlation function leads to domains of energetically similar sites separated by boundaries where the site energies exhibit stochastic deviation. These boundary sites are found to be the source of the extended exponential tail states, and are responsible for high charge visitation frequency, which may be associated with the molecular turnover number and ultimately the material stability.

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“…These two characteristic distances make up two of the lattice constants (a y = 1.61 nm, a z = 0.39 nm). Since conjugated polymers can be regarded as arrays of chromophores that are identified as fully conjugated segments of the polymer [18,66], the remaining lattice constant is the π -conjugation length along the backbone of the P3HT (a x = 3.9 nm, which is ∼10 repeat units of the polymer) [67]. In order to account for the spatial disorder in the P3HT, each lattice site is shifted by a random vector creating an off-lattice representation that never exceeds 0.4a, where a represents the lattice constant [66].…”

Section: P3ht/swnt Devicementioning

confidence: 99%

“…Since conjugated polymers can be regarded as arrays of chromophores that are identified as fully conjugated segments of the polymer [18,66], the remaining lattice constant is the π -conjugation length along the backbone of the P3HT (a x = 3.9 nm, which is ∼10 repeat units of the polymer) [67]. In order to account for the spatial disorder in the P3HT, each lattice site is shifted by a random vector creating an off-lattice representation that never exceeds 0.4a, where a represents the lattice constant [66]. Periodic boundary conditions in the xand z-directions (where the xz-plane lies parallel to the PHJ interface) are employed to prevent finite-size effects.…”

Section: P3ht/swnt Devicementioning

confidence: 99%

Anomalous thickness-dependence of photocurrent explained for state-of-the-art planar nano-heterojunction organic solar cells

2012

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Due to their simple geometry and design, planar heterojunction (PHJ) solar cells have advantages both as potential photovoltaics with more efficient charge extraction than their bulk heterojunction (BHJ) counterparts, and as idealized interfaces to study basic device operation. The main reason for creating BHJs was the limited exciton diffusion length in the active materials of the PHJ: if an exciton is generated at a distance greater than its diffusion length from the hetero-interface of the PHJ, it would be very unlikely to be able to contribute to the photocurrent. Based on this argument one expects a maximum in the photocurrent of PHJs for a thickness of the active layer equal to the exciton diffusion length (~10 nm). However, in two recently developed PHJs that have appeared in the literature, a maximum photocurrent is observed for 60-65 nm of poly(3-hexylthiophene) (P3HT). In this work, we explore this anomaly by combining both an optical T-matrix and a kinetic Monte Carlo simulation that tracks the exciton behavior in the PHJs. The two systems considered are a P3HT/single walled carbon nanotube (SWNT) device, and a P3HT/phenyl-C61-butyric acid methyl ester (PCBM) device. The model demonstrates how a bulk exciton sink can explain the shifted maximum in the P3HT/SWNT case, whereas in the P3HT/PCBM case the maximum is mainly determined by PCBM molecules interdiffusing in the P3HT upon annealing. Based upon the results of this model it will be possible to more intelligently design nanostructured photovoltaics and optimize them toward higher efficiencies.

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Formulas for the Pressure and Bulk Modulus in Uniaxial Strain.

Cited by 3 publications

References 0 publications

A Numerical Model for Twin Nucleation in Shocked Zircon and Comparison With Natural Samples

A Numerical Model for Twin Nucleation in Shocked Zircon and Comparison With Natural Samples

Introducing correlations into carrier transport simulations of disordered materials through seeded nucleation: impact on density of states, carrier mobility, and carrier statistics

Anomalous thickness-dependence of photocurrent explained for state-of-the-art planar nano-heterojunction organic solar cells

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