The main application of Ti doped sapphire (Ti:sapphire) lies in the field of lasers, thanks to its outstanding production of ultra-short pulses due to the presence of doping Ti3+ ions. The absorption and emission mechanisms of this crystal are intricate, necessitating consideration of point defects existing in the grown crystal. A plethora of liquid-phase growth methods yield crystals of diverse sizes and quality. This paper gives a comprehensive review of the literature on managing dopants during the growth of Ti doped bulk sapphire crystals.Substantial research has indicated that the presence of detrimental Ti4+ ions diminishes the crystal laser efficiency due to their residual absorption. Although annealing under reducing atmosphere is an efficient way to increase the Ti3+/Ti4+ ratio, this process becomes increasingly time-consuming as the demand for larger optical components increases. Consequently, it would be more practical and convenient to control this ratio directly during the growth processes. However, the conversion mechanisms between the two Ti ions valences during crystal growth and annealing remain largely unexplored.A study of the thermodynamics of the Al2O3/TiO2 and Al2O3/Ti2O3 solid and liquid solutions as a function of the partial pressure (pO2) and oxygen activity is crucial for understanding these mechanisms. This paper presents corrected, reliable phase diagrams that enable quantitative prediction of the effect of pO2 on the melt concentrations of the two ions. Consequently, a novel value of the absorption coefficient constant, pertinent to Ti4+ concentration measurement, is proposed. Equilibrium with the solid solution yields segregation coefficients that appear distinct for the two ions. Given their influence on oxygen activity during growth, the effect of surrounding furnace parts, such as graphite casing or Mo crucible, is also important.Understanding the behavior of Ti3+and Ti4+ ions in the grown crystal as a function of pulling time and considering the pO2 levels in the furnace atmosphere, requires the knowledge of solid-state electrochemistry, including the charge carriers and the Al and O vacancies. This foundation allows the development of a physico-chemical model illustrating the evolution of ion valence during growth. Analysis of experimental results from existing literature gives the necessary diffusion coefficients and reaction rate constants. Investigating crystal-atmosphere interaction provides the required boundary condition for solving the problem. The findings exhibit qualitative agreement with experimental measurements of Ti3+ and Ti4+ concentrations in grown Ti:sapphire crystals.

The solid-liquid interfaces of silicon grains have been observed by an in-situ system. Two silicon seeds having different crystallographic orientations (as ⟨100⟩, ⟨110⟩, and ⟨111⟩) along the growth direction were placed side by side in a silica crucible for the direct comparison of interface behavior during the melt-growth process. Experimental evidence proved the existence of flat {111} surfaces at different grain orientations during crystallization. The difference in the interface positions of the two grains was used to calculate the undercooling of the {111} surfaces. The growth rate-undercooling relationship was linear in all experiments, showing that the observed flat surfaces were planes vicinal to {111} facets, growing through a step flow mode. The terrace length was constant but different from one experiment to another. Therefore, this work indicates that it is crucial to consider the vicinal surface kinetics in the analysis of Si facet planes and grooves during the melt-growth process.

The {100} and {110} solid/liquid interfaces of silicon are considered atomically rough, following the atom-byatom growth mode during crystallization processes. However, observed differences in growth kinetics are not yet well understood. In this study, the growth behavior of {1 0 0} and {1 1 0} crystal/melt interfaces in silicon is studied. The growth velocity at different cooling rates is investigated for both growth orientations. Experimental results show that these growth velocities are similar, irrespective of the cooling rate. An analysis of the ratio of the kinetic coefficients of both orientations shows that they are comparable.

The morphology of the solid–liquid interface and the GB development during directional solidification process of multi-crystalline silicon (mc-Si) has been studied with an in situ observation system. A small angle grain boundary was observed to have a gradually increasing faceted groove, finally reaching a steady state. A geometric model is used to simulate the growth of groove facets with consideration of different facet growth kinetics. It appears that the kinetics of a face vicinal to a {111} plane is most likely to reproduce the observed behavior. Later on, variations of groove size and grain boundary direction occurred. The geometric simulation results show that such perturbations could be produced by the interaction of single dislocations with one of the vicinal facets.

The {100} and {110} solid/liquid interfaces of silicon are considered atomically rough, following the atom-by-atom growth mode during crystallization processes. However, observed differences in growth kinetics are not yet well understood. In this study, the growth behavior of {100} and {110} crystal/melt interfaces in silicon is studied. The growth velocity at different cooling rates is investigated for both growth orientations. Experimental results show that these growth velocities are similar, irrespective of the cooling rate. An analysis of the ratio of the kinetic coefficients of both orientations shows that they are comparable.

The {1 0 0} and {1 1 0} solid/liquid interfaces of silicon are considered atomically rough, following the atom-by-atom growth mode during crystallization processes. However, observed differences in growth kinetics are not yet well understood. In this study, the growth behavior of {1 0 0} and {1 1 0} crystal/melt interfaces in silicon is studied. The growth velocity at different cooling rates is investigated for both growth orientations. Experimental results show that these growth velocities are similar, irrespective of the cooling rate. An analysis of the ratio of the kinetic coefficients of both orientations shows that they are comparable.

Brittleness of sapphire has been studied by four point bending and ball on three ball tests. A significantly larger flexural stress was observed for crystals grown by the Verneuil process compared to EFG (Edge-defined Film-fed Growth) crystals. Crystallographic defects were characterized by X-ray topography and it was shown that sub -grain boundaries found in Verneuil crystals do not impact the fracture behavior. Larger amounts of basal dis-locations in Verneuil boules appeared to account for the differences in brittleness. The dislocation densities have been related to the temperature fields experienced by the crystals during the growth processes. Characterization of point defects by thermo-stimulated luminescence revealed that they are more numerous in Verneuil crystals, especially after annealing, and that they pin dislocations, contributing to the mechanical response of the crystal.

Mechanical properties of lithium molybdate single crystals, Li2MoO4, are studied from room temperature to 650 °C. Density functional theory calculations gave the seven elastic constants of the rhombohedral crystal at 0 K. Brillouin light scattering experiments delivered comparable values at room temperature, and measurements up to 650 °C show a linear decrease in the constants with temperature. Nano-indentation results were typical of a brittle material with a low Young modulus and allowed deriving Young's moduli, for c (63 GPa) and m (48 GPa) faces, in agreement with those computed from measured elastic constants. Compressive rupture tests were performed. At 650 °C, the rupture stress was in the range 2–7.5 MPa. No clear evidence of a plastic regime was observed before cracking, even at temperatures close to the melting point.

and kann obtained from numerical simulations of Ti:sapphire annealing experiments (left) and their applications during crystal growth (right).

The theoretical phase diagrams of the binary Al2O3-Ti2O3 and Al2O3-TiO2, as systems calculated using FactSage software and its thermodynamic databases, are reoptimized. This has been performed on the basis of a literature survey on experimental precipitation limits of Ti2O3 and TiO2 in the Al2O3 solid solution. The appropriate oxygen partial pressure (pO(2)) range for controlling the valence state of Ti ions during Ti:sapphire crystal growth is obtained with respect to the calculated Ellingham type predominance diagram. Factors affecting the pO(2) such as furnace gas, crucible materials, and graphite heating elements are analyzed. The influence of pO(2) on Ti3+ and Ti4+ concentrations in the solid and liquid phases is derived from thermodynamic equilibrium calculations. The equilibrium segregation coefficients of Ti3+ and Ti4+ in sapphire are calculated to be 0.046 and 0.011, respectively. Taking into account the data extrapolated from experiments, a value of 0.06 +/- 0.02 is proposed for the equilibrium segregation coefficient of total Ti under low pO(2).

An original physico-chemical model is proposed that accounts for the conversion mechanism between Ti3+ and Ti4+ during Ti:sapphire crystal growth process. This model involves release of O-2 from the crystal surface, which consumes aluminum vacancies. Consequently, these vacancies diffuse from the bulk crystal toward the surface, leading to the conversion of Ti4+ into Ti3+. A set of mass balance differential equations is established for these chemical species, taking into account diffusion and chemical reaction. The boundary condition for concentration of aluminum vacancies on crystal surface is given as the function of P-O2 and temperature. A preliminary numerical simulation is performed to study the proposed model, using COMSOL Multiphysics (R) software. The obtained radial concentration distribution profiles of Ti3+ and Ti4+ are in qualitative agreement with the experimental results, showing that the proposed model has potential for further studying point defect reactions during crystal growth of ionic crystals.

Lithium molybdate single crystals up to one kilogram have been grown by a conventional Czochralski process. The growth configuration (geometry, coil, crucible, insulation casing) was optimized by numerical simulation of heat and mass transfer. Dislocations are shown to belong to the basal glide system. Their density (<= 104 cm-2) and luminescence properties indicate crystal quality similar to that of previously reported crystals grown by Czochralski technique. Numerical simulation of thermo-elastic stresses suggest that the crack observed in one of these crystals is rather due to a mechanical accident than to internal stresses during growth.

As the requirements in terms of crystal defect/quality and production yield are generally contradictory, it is necessary to develop methods in order to find the best compromise for the growth conditions of a given crystal. Simple growth-rate/temperature-gradient charts are a possible tool in this respect. After the recall of the classical analytical equations useful for describing the process and defect engineering, a simple pedagogic case explains the building and use of such charts. The more complex application to the directional casting of photovoltaic Si necessitated the development of new physical models for twinning and equiaxed growth. This allowed plotting charts that proved useful for industrial applications. The conclusions discuss the drawbacks and advantages of the method. It finally proves to be a pedagogic tool for teaching crystal growth engineering.

Structural features of Al2O3-YAG-ZrO2:Y eutectic plates grown by the EFG process have been studied. X-ray tomography shows that all three phases are continuous along the whole sample, suggesting a fully coupled ternary eutectic growth. However the growth of alumina and YAG is well described by a classical binary coupled growth, in spite of the facetted structure of their growth interface. Colonies are observed at high growth rate and have been related to the chemical rejection of zirconium ions at the solid-liquid interface, possibly due to a slight off-stoechiometry of the raw material.

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 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.

The effect of a submerged heater on the Bridgman crystal growth process under travelling magnetic field is studied. It is known that the magnetic field generates melt flow from crystal center to crucible wall which can suppress morphological instability development, but it also increases the curvature of the crystallization front. The advantage of the submerged heater method is the ability of better control over the temperature distribution in the vicinity of the solid-liquid interface, as well as the constancy of the growth zone geometry, in particular the height of the melt above the phase boundary, which helps reduce the axial heterogeneity of the resulting crystal. Within the steady state approach we perform numerical simulation of Bridgman growth process under simultaneous action of travelling magnetic field and a submerged heater. It is shown that the submerged heater can intensify the flow in the radial direction generated by travelling magnetic field near the growing crystal while the curvature of the crystallization interface remains almost unaffected. On the other hand, it is also possible to decrease significantly the flow close to the crystallization front.

Mechanical properties of Al2O3/Y3Al5O12/ZrO2 ternary eutectic ceramics are strongly affected by structural defects as pores or colonies. Experimental investigation of the microstructure of this ternary composite indicates that the colonies are generally observed when the solidification occurs at high rates. In this work, the influence of the growth rate on the solid-liquid interface shape and formation of colonies in directional solidification of Al2O3/Y3Al5O12/ZrO2 by Bridgman, Edge-defined Film-fed Growth (EFG), and Czochralski (Cz) methods is numerically and experimentally investigated. Numerical modeling of the Bridgman growth process shows large curvatures of the solid-liquid interface when the pulling rate is increased up to 80 mm/h. The ingots solidified at rates between 5 and 80 mm/h exhibit colony type microstructure. The analysis of EFG growth of ceramic ribbons reveals less curved solid-liquid interfaces in this system. Numerical modeling shows significant increase in the interface curvature with increasing pulling rate. The microstructure of ribbons grown at pulling rates between 6 and 12 mm/h exhibits colonies only for the ingots solidified at higher rate. Simulations carried out for Czochralski growth process show that the solidification front is almost plane in this system. These results are in agreement with experimental observations showing good structural quality of Cz grown crystals with a flat solid-liquid interface. Finally it is concluded that formation of colonies in directional solidification of this ternary eutectic composite is linked to large curvatures of the growth interface.

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.

The Kyropoulos growth system is used to grow large high quality sapphire crystals. But since they grow inside a sealed furnace, there is no established monitoring system to allow observing the growth. This makes it difficult to control the growth parameters ensuring a desired geometrical shape. In the present work a melt-height monitoring system is imagined in the growth system, which would allow the acquisition of the evolving melt level along with the pulling distance of seed and the measured weight of the growing crystal submerged in the melt. Based on all these parameters, it is demonstrated that it would be possible to trace the shape of the growing crystal. The needed accuracy for the measurement tools is studied.

Lithium molybdate Li2MoO4 (LMO) crystals of mass ranging between 350 and 500 g are excellent candidates to build heat-scintillation cryogenic bolometers likely to be used for the detection of rare events in astroparticle physics. In this work, numerical modeling is applied in order to investigate the Czochralski growth of Li2MoO4 crystals in an inductive furnace. The numerical model was validated by comparing the numerical predictions of the crystal-melt interface shape to experimental visualization of the growth interface. Modeling was performed for two different Czochralski furnaces that use inductive heating. The simulation of the first furnace, which was used to grow Li2MoO4 crystals of 3-4 cm in diameter, reveals non-optimal heat transfer conditions for obtaining good quality crystals. The second furnace, which will be used to grow crystals of 5 cm in diameter, was numerically optimized in order to reduce the temperature gradients in the crystal and to avoid fast crystallization of the bath at the later stages of the growth process. (C) 2018 Elsevier B.V. All rights reserved.