Numerical modeling of Czochralski growth of Li2MoO4 crystals for heat-scintillation cryogenic bolometers

Stelian, Carmen; Velázquez, M.; Veber, Philippe; Ahmine, A.; Sand, Jean-Baptiste; Buşe, Gabriel; Cabane, H.; Duffar, T.

doi:10.1016/j.jcrysgro.2018.04.003

Cited by 11 publications

(11 citation statements)

References 16 publications

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“…The P1 approximation model takes into account an additional heat source term in Equation that describes the radiative heat transfer for an absorbing, emitting, and scattering medium (the scattering effect is not considered in the present simulations). Numerical modeling based on this model has shown that deep convex shapes of the crystal‐melt interface are explained by the internal radiative heat exchanges . Numerical simulations in refs.…”

Section: Resultsmentioning

confidence: 98%

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Numerical Analysis of Thermal Stress in Semi‐Transparent Oxide Crystals Grown by Czochralski and EFG Methods

Stelian

Muzy

Labor³

et al. 2018

Crystal Research and Technology

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Crystal growth of oxides is generally difficult since large curvatures of the growth interface in these systems generate high thermal stress, dislocations and crystal cracking. Three-dimensional numerical modeling is applied to investigate thermal stress distribution in sapphire and langatate La3Ta0.5Ga5.5O14 (LGT) semi-transparent crystals grown by Czochralski (Cz) and Edge-defined Film-fed Growth (EFG) techniques. The analysis of thermal stress distribution in a sapphire ingot grown in a Czochralski furnace shows high von Mises stresses distributed almost symmetrically on large areas in the crystal. Thermal stress computations for piezoelectric langatate crystals grown in a Czochralski configuration show non-symmetrical von Mises distribution with higher stress on one side of the ingot. These numerical results are in agreement with experimental results showing non-symmetrical cracking at the outer surface of the crystal. 3D modeling of multi-die EFG growth of white sapphire ribbons shows that the von Mises stress is almost constant when the number of ribbons is increased from two to ten. Two models are applied to simulate the internal radiative heat transfer in the sapphire crystals: P1 approximation and the Rosseland radiation model. Numerical results show that applying Rosseland formula introduces significant errors in temperature field calculations especially in the case of the EFG configuration.

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Section: Resultsmentioning

confidence: 98%

“…Numerical simulations in refs. [] have been validated by comparing the computed shape of the growth interface to the experimental results.…”

Section: Resultsmentioning

confidence: 99%

Numerical Analysis of Thermal Stress in Semi‐Transparent Oxide Crystals Grown by Czochralski and EFG Methods

Stelian

Muzy

Labor³

et al. 2018

Crystal Research and Technology

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“…The growth direction was considered parallel to the y-axis. More details about modeling Czochralski growth of Li2MoO4 crystals are given in our previous work [6].…”

Section: Model Descriptionmentioning

confidence: 99%

“…A new Czochralski furnace was set up based on the numerical modeling performed in [6]. This configuration was numerically optimized in order to reduce the thermal stress in the crystals and to avoid that fast crystallization starts from the crucible bottom, which was previously observed during the growth of 3 cm diameter ingots in the non-optimized furnace [6]. The first ingot grown by using the automatic control was 5 cm in diameter and 15 cm in length (Fig.…”

Section: Crystals Of 5 CM In Diametermentioning

confidence: 99%

Experimental and numerical investigations of the Czochralski growth of Li2MoO4 crystals for heat-scintillation cryogenic bolometers

Stelian

Velázquez

Veber

et al. 2020

Journal of Crystal Growth

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A new technology for the mass production of lithium molybdate (Li2MoO4) crystals needed for the realization of the cryogenic neutrinoless double-beta decay detectors is under development within the framework of the CLYMENE project. Crystals with 4 and 5 cm in diameter were grown in two different Czochralski configurations. The first configuration, based on inductive heating of a RF coil coupled with a platinum crucible, was used to grow crystals of 4 cm in diameter. Bolometric tests performed with two samples cut from a 230 g crystal have shown less performances of the large sample (158 g), which had a cleavage, as compared to the small non-cracked sample (13.5 g). Numerical 2 modeling was applied to investigate the temperature field in the furnace, the melt convection and thermo-elastic stresses in the crystal. Numerical results reveal 30% higher thermal stress at the bottom part of the ingot in the case of a concave shape of the crystal tail (experimental case) as compared to the case of a convex shaped tail. This could explain why the fracture started at the bottom part of the 230 g crystal boule, and highlights the importance of the crystal shape in the last stage of growth process. The furnace configuration used to grow 5 cm-diameter crystals was numerically optimized in order to reduce the thermal stress in the crystals. The first kg-mass Li2MoO4 ingot grown in the optimized configuration exhibit regular shape and good structural quality.

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“…For instance, for semitransparent oxidic crystals, Stelian et al. [ 12,13,10 ] have applied a 3D numerical modelling to investigate thermal stress distribution in sapphire and langatate semitransparent crystals grown by the Czochralski (CZ) and by the edge‐defined film‐fed growth (EFG) technique. As method for treating the internal radiation in sapphire crystals (optically thick) they applied the P 1 ‐approximation, which was successfully validated by comparing the computed shape of the solid–liquid interface to the experimental results.…”

Section: Crystal Growth Model Computational Procedure and Exemplarymentioning

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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Numerical modeling of Czochralski growth of Li2MoO4 crystals for heat-scintillation cryogenic bolometers

Cited by 11 publications

References 16 publications

Numerical Analysis of Thermal Stress in Semi‐Transparent Oxide Crystals Grown by Czochralski and EFG Methods

Numerical Analysis of Thermal Stress in Semi‐Transparent Oxide Crystals Grown by Czochralski and EFG Methods

Experimental and numerical investigations of the Czochralski growth of Li2MoO4 crystals for heat-scintillation cryogenic bolometers

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

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