Fracture and Hardness of Semiconductor Alloys.

Sher, A.; Schilfgaarde, Mark van; Chen, A B; Berding, M. A.

doi:10.21236/ada176800

Cited by 3 publications

(3 citation statements)

References 8 publications

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“…On the other hand polarization in the ferroelectric phase will have a finite value, P[u] and this polarization arises continuously over the transformation temperature from state 2. This is a well known problem with the LDA and GGA which underestimate the band gaps since their exchange correlations do not include the effect of excited states (40)(41)(42)(43).…”

Section: Calculation Detailsmentioning

confidence: 99%

First-principles calculations of Born effective charges and spontaneous polarization of ferroelectric bismuth titanate

Roy

Prasad

Auluck

et al. 2010

J. Phys.: Condens. Matter

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In this study, we present the results of our first-principles calculations of the band structure, density of states and the Born effective charge tensors for the ferroelectric (ground state B1a1) and paraelectric (I4/mmm) phases of bismuth titanate. The calculations are done using the generalized gradient approximation (GGA) as well as the local density approximation (LDA) of the density functional theory. In contrast to the literature, our calculations on B1a1 structure using GGA and LDA yield smaller indirect band gaps as compared to the direct band gaps, in agreement with the experimental data. The density of states shows considerable hybridization among Ti 3d, Bi 6p and O 2p states indicating covalent nature of the bonds leading to the ferroelectric instability. The Born effective charge tensors of the constituent ions for the ground state (B1a1) and paraelectric (I4/mmm) structures were calculated using the Berry phase method. This is followed by the calculation of the spontaneous polarization for the ferroelectric B1a1 phase using the Born effective charge tensors of the individual ions. The calculated value for the spontaneous polarization of ferroelectric bismuth titanate using different Born effective charges was found to be in the range of 55±13 µC/cm 2 in comparison to the reported experimental value of (50±10 μC/cm 2 ) for single crystals. The origin of ferroelectricity is attributed to the relatively large displacements of those oxygen ions in the TiO 6 octahedra that lie along the a-axis of the bismuth titanate crystal. 77.22.Ej, 85.50.Gk, 71.15.Mb 3 PACS Number (s):

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Section: Calculation Detailsmentioning

confidence: 99%

First-principles calculations of Born effective charges and spontaneous polarization of ferroelectric bismuth titanate

Roy

Prasad

Auluck

et al. 2010

J. Phys.: Condens. Matter

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“…Using the Cij single crystal of Ref [31] and Voigt-Reuss-Hill approximation [32], the obtained values of the shear modulus G for different polycrystalline ceramics are summarized in Table 2. There are different relationships frequently employed to predict the hardness H and the fracture toughness KIC of the materials [33][34][35][36][37].…”

Section: Theory and Discussion Of The Resultsmentioning

confidence: 99%

Quasi-linear correlation between shear and young’s moduli in some polycrystalline ceramics

Daoud,

Saini,

Rekab-Djabri

2024

IJPR

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This work aims to investigate the correlation between the shear modulus and the Young’s modulus of some pore-free polycrystalline ceram-ics. Our study shows that the shear modulus correlates quasi-linearly with the Young’s modulus. The best fit was obtained using the linear model. The fit of the shear modulus G as a function of the Young modulus E obeys this linear expression: G = 0.43E - 7.7 (where both G and E are expressed in GPa). The coefficient of the correlation was found at around 0.994. Our expression was used to predict the shear modulus G of some other polycrystalline ceramics, especially: Dy2O3, Er2O3, and Y2O3 materials, which are estimated at around 65.6, 72.4, and 51.8 GPa, respectively. We attempt also to estimate the Vickers hardness of our materials of interest using an empirical expression of the literature. Unfortunately our predicted results are larger than those reported previously in the literature.

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“…The band gap is calculated from the halide composition around a unit cell's central point by using a cluster approximation. The cluster approximation is a means of introducing and studying local disorder in infinite lattices and has widespread use in estimating both electronic 44,45 and ionic 13,30,46 interactions. Clusters of 354 and 642 halide sites are therefore used with equivalent radii of r cluster = 1.91 and 2.33 nm, respectively, based upon the number of halide sites within a given spherical volume.…”

Section: Resultsmentioning

confidence: 99%

Modeling the Photoelectrochemical Evolution of Lead-Based, Mixed-Halide Perovskites Due to Photosegregation

Ruth,

Kuno

2023

ACS Nano

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Lead-based, mixed-halide perovskites such as methylammonium lead iodide-bromide [MAPb(I1–x Br x )3] undergo anion photosegregation under illumination. This is observed as low-band-gap photoluminescence from photogenerated iodine-rich domains due to favorable band offsets that induce carrier funneling into them. Unfortunately, theoretical rationalizations of mixed-halide photosegregation are complicated by biases inherent in photoluminescence-based observations. Recent compositionally weighted X-ray diffraction (XRD) measurements now reveal broad distributions of photosegregated stoichiometries not captured by existing photosegregation models. To better bridge experiment and theory, we perform kinetic Monte Carlo (KMC) simulations of photosegregation within the context of a band-gap-based thermodynamic model, which has previously accounted for numerous experimental observations. Our KMC simulations are modified to consider high carrier density Fermi–Dirac statistics that result from carrier funneling and accumulation within photosegregated I-rich domains. Obtained KMC results reproduce broad terminal halide (x terminal) distributions seen experimentally and illustrate how they are characterized by a central, heavily I-enriched stoichiometry. I-rich domain “drifting” during photosegregation rationalizes the long photosegregation time scales seen experimentally with drifting simultaneously, producing a wake of variable stoichiometry I-rich inclusions that form the lion’s share of stoichiometric heterogeneities seen in compositionally weighted XRD measurements. These simulations and accompanying rationalizations further reveal a general criterion for realizing favorable free energies to induce demixing. Central to the criterion is the statistical occupation of low gap inclusions in the parent alloy by excitations. The resulting model thus provides a general framework for conceptualizing mixed-halide perovskite light and temperature sensitivities mediated by photocarriers.

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Fracture and Hardness of Semiconductor Alloys.

Cited by 3 publications

References 8 publications

First-principles calculations of Born effective charges and spontaneous polarization of ferroelectric bismuth titanate

First-principles calculations of Born effective charges and spontaneous polarization of ferroelectric bismuth titanate

Quasi-linear correlation between shear and young’s moduli in some polycrystalline ceramics

Modeling the Photoelectrochemical Evolution of Lead-Based, Mixed-Halide Perovskites Due to Photosegregation

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