Fundamentals and engineering of defects

Rudolph, P.

doi:10.1016/j.pcrysgrow.2016.04.004

Cited by 30 publications

(15 citation statements)

References 81 publications

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“…This decay in maximum von Mises stress is due to the decrease of the interface convexity and more accurately to the linearity of temperature field in this region. Rudolph provides more details on the relationship between thermal stress and the linearity of temperature. In order to thoroughly highlight this relationship, von Mises stress and temperature distribution along the outer surface of the crystal without and with resistive heating are presented together in Figure .…”

Section: Resultsmentioning

confidence: 99%

3D Anisotropic Stress Analysis during Kyropoulos Growth of Sapphire Single Crystal

Zermout

Mokhtari

Nehari

et al. 2019

Crystal Research and Technology

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By using 3D finite element calculations, numerical simulations are performed to predict the thermal field as well as the thermal stress in a c-axis sapphire single crystal grown by Kyropoulos technique. The effects of additional resistive heating (placed under the crucible bottom) and crystal rotation are investigated and a comparison is made between the isotropic and anisotropic analysis. The anisotropy of the elastic constants and thermal expansion coefficients as well as their temperature dependence are considered in the anisotropy calculations while Young's modulus and the Poisson ratio are used in the isotropic analysis. Thermal stress is found to be smaller in the anisotropy analysis than that in the isotropic analysis and significant differences are found in their respective distribution patterns. Additional resistive heating acts to decrease both of the crystal-melt interface convexity and the von Mises stress. In addition, crystal rotation combined with additional resistive heating decreases significantly the thermal stress inside the sapphire crystal and along the melt-crystal interface. Therefore, optimizing the heating conditions and using a suitable crystal rotation rate seem to be favorable to control the growth interface shape and to reduce thermal-stress-related defects during the growth process.

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Section: Resultsmentioning

confidence: 99%

3D Anisotropic Stress Analysis during Kyropoulos Growth of Sapphire Single Crystal

Zermout

Mokhtari

Nehari

et al. 2019

Crystal Research and Technology

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“…However, because of the high temperature in this region the stress can be mainly relaxed by plastic deformations such as sliding or multiplication of existing dislocations (the critical shear stress is low). [ 6 ] At later growth stages, the formerly newly grown crystal area moves away from the hot region. Toward lower temperatures the critical shear stress for plastic deformations strongly increases and eventually exceeds the local thermal stress.…”

Section: Introductionmentioning

confidence: 99%

“…What we do not cover by these calculations is the effect of time: the longer a crystal region remains at high temperatures, the smaller will be the remaining level of thermally induced strain and stress, which finally enters the stage of freezing. [ 6 ] A temporal analysis is also the prerequisite to perform computations including the dislocation dynamics, as, e.g., by the Alexander–Haasen model. [ 8 ]…”

Section: Introductionmentioning

confidence: 99%

Numerical Modeling of Heat Transfer and Thermal Stress at the Czochralski Growth of Neodymium Scandate Single Crystals

Böttcher

Miller

Ganschow

2020

Crystal Research and Technology

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The Czochralski growth of NdScO3 single crystals along the [110]‐direction is numerically analyzed with the focus on the influence of the optical thickness on the shape of the crystal–melt interface and on the generation of thermal stresses. Due to lack of data, the optical thickness (i.e., the absorption coefficient) is varied over the entire interval between optically thin and thick. While the thermal calculation in the entire furnace is treated as axisymmetric, the stress calculation of the crystal is done three‐dimensionally in order to meet the spatial anisotropy of thermal expansion and elastic coefficients. The numerically obtained values of the deflection of the crystal/melt interface meet the experimental ones for absorption coefficients in the range between 40 and 200 m−1. The maximum values of the von Mises stress appear for the case of absorption coefficient between 20 and 40 m−1. Applying absorption coefficients in the range between 3 and 100 m−1 leads to local peaks of high temperature in the shoulder region and the tail region near the end of the cylindrical part.

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“…In turn, the performance of photonic crystal devices depends strongly on their geometry, mechanical stress and defects inside (Hart et al, 2012). An interesting literature review on the important defect types, their origins as well as interactions during the bulk crystal growth from the melt and selected epitaxial processes is given in one of the recent review papers (Rudolph, 2016). Some aspects of the effect of anisotropy on defect mode features in CLCs was investigated by Gevorgyan (Gevorgyan, 2018).…”

Section: Introductionmentioning

confidence: 99%

Calculation of reflectance and transmittance of optical birefringent networks based on cholesteric liquid crystals

Grzelczyk

Awrejcewicz

2019

Lat. Am. j. solids struct.

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In this paper we calculated reflectance and transmittance of different optical birefringent networks sandwiched between two isotropic media. To model optical phenomena in the considered systems, we applied the 4×4 matrix method. Some interesting reflectance and transmittance spectra and polar plots for different system parameters and arbitrary incident monochromatic light were reported. The illustrated and discussed results can be useful for understanding optical phenomena in numerous birefringent media. Especially, the reflectance and transmittance spectra computed in this article can be suitable for analysis of more advanced contemporary optical systems, i.e. photonic band gap materials based on cholesteric liquid crystals.

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Fundamentals and engineering of defects

Cited by 30 publications

References 81 publications

3D Anisotropic Stress Analysis during Kyropoulos Growth of Sapphire Single Crystal

3D Anisotropic Stress Analysis during Kyropoulos Growth of Sapphire Single Crystal

Numerical Modeling of Heat Transfer and Thermal Stress at the Czochralski Growth of Neodymium Scandate Single Crystals

Calculation of reflectance and transmittance of optical birefringent networks based on cholesteric liquid crystals

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