Crystal Growth of the R 2 SiO 5 Compounds ( R = Dy, Ho, and Er) by the Floating Zone Method Using a Laser-Diode-Heated Furnace

: In recent years, rare earth silicate compounds have attracted the extensive attention of researchers owing to their potential for applications in scintillation crystals in gamma ray or X-ray detectors, as well as in thermal or environmental barrier coatings. Large high quality crystals of three members of the rare earth monosilicates family of compounds, R 2 SiO 5 (with R = Dy, Ho, and Er), have been grown by the floating zone method, using a laser-diode-heated floating zone furnace. Crystal growths attempts were carried out using different parameters in order to determine the optimum conditions for the growth of these materials. The phase purity and the crystalline quality of the crystal boules were analysed using powder and Laue X-ray diffraction. Single crystal X-ray diffraction experiments were carried out to determine the crystal structures of the boules. The optimum conditions used for the crystal growth of R 2 SiO 5 materials are reported. The phase purity and high crystalline quality of the crystals produced makes them ideal for detailed investigations of the intrinsic physical and chemical properties of these materials.


Introduction
Rare earth silicates have been thoroughly investigated over the past seven decades owing to their high potential for use in applications.To date, several chemical phases have been identified in the R-Si-O systems , e.g., rare earth monosilicates, R 2 SiO 5 , disilicates, R 2 Si 2 O 7 , apatite-type phases, R 4.67 (SiO 4 ) 3 O or R 4 (SiO 4 ) 3 , and R 4 (Si 3 O 10 )(SiO 4 ).The majority of the studies have been focused on the first two families of compounds, R 2 SiO 5 and R 2 Si 2 O 7 , mainly due to the polymorphism exhibited by these materials and their physical and chemical properties [19].The structural phase diagram of the R 2 Si 2 O 7 shows a relatively high number of structural types possible in these materials [24][25][26][27][28], whereas R 2 SiO 5 compounds exhibit a lower degree of polymorphism [19].
Two types of crystal structures can be found in the literature for the rare earth monosilicates, labelled in the literature as X1 (or A) and X2 (or B) [19].The compounds R 2 SiO 5 containing larger rare earth ions (with R = La → Gd) crystallize in the X1-type structure.Rare earth monosilicate compounds that incorporate smaller rare earth ions (with R = Tb → Lu) are dimorphic with temperature, at low temperature these systems crystallize in the X1-type, and at relatively high temperature (900 ≤ T ≤ 1100 • C), they undergo a structural phase transition to the X2-type structure [29,30].
The X1-R 2 SiO 5 polymorphs have a monoclinic (P2 1 /c) crystal structure that is comprised of three different cation sites, and five anion sites.The larger trivalent rare earth R 3+ ions occupy a nine-fold and a seven-fold oxygen coordinated sites, whereas the smaller tetravalent Si 4+ ion sit at the centre of tetra-fold coordinates sites [31].The X2-R 2 SiO 5 polymrophs crystallize in a monoclinic (given in the literature as the different settings B2/b, C2/c and I2/a) crystal structure, containing the same number of cation and anion sites as the X1-type structure.The main difference to the X1-type is that the rare earth R 3+ ions occupy a six-fold and a seven-fold oxygen coordinated sites, with the latter polyhedron described previously as a capped octahedron [32].
Rare earth monosilicates, R 2 SiO 5 , have been extensively investigated due to their performance as laser host materials [33], scintillation crystals in gamma ray or X-ray detectors [34], as well as environmentally benign thermal barrier coatings (TBC/EBC) [35], and more recently, as quantum memory-storage materials [36].Despite the communities interest for these materials, studies of the intrinsic properties of R 2 SiO 5 have been hindered by the difficulties in preparing bulk phase pure samples [19,37], due to the presence, in the polycrystalline samples, of impurities consisting of other rare earth silicate compounds.The drawback arises from the similar thermal stability ranges of the various chemical and structural phases existing in the temperature-composition phase diagrams of the R-Si-O systems.To overcome this drawback and to study the fundamental properties of the rare earth monosilicates, high quality single crystal samples are required.
Pure and doped R 2 SiO 5 crystals have been previously grown using the Czochralski [33,[38][39][40][41][42][43][44][45][46][47], flux [19,29,41,[48][49][50], micropulling-down [51,52] techniques.Er 2 SiO 5 crystals were also obtained when attempting to synthesize the intermetallic compound ErFeRe [32].Nevertheless, the R 2 SiO 5 crystals previously grown were prepared using solvents, yielding crystals of relatively small size, employing crucibles or relatively slow growth rates (1-6 mm/h).One of the "ideal" methods for the growth of relatively large, high quality single crystals is the floating zone technique.The effectiveness of this method arises from the lack of crucible or solvent during the growth process, preventing thus the contamination of the boules.A Tb doped Gd 2 SiO 5 crystal was obtained using an optical floating zone (FZ) furnace, however, the authors reported limited information regarding the growth process and crystal quality of the grown boule [53].Other related compounds, R 2 Si 2 O 7 , have been previously grown using optical FZ furnaces, however, the boules tended to have a high number of thermally generated cracks, and single grains isolated from the crystal boules were of relatively small sizes [54,55].Previous studies [31,[56][57][58][59][60][61] have demonstrated the feasibility of the FZ technique using a laser floating zone furnace for preparing single crystals of relatively large size of members of the rare earth monosilicate family, Gd 2 SiO 5 , Nd x Gd 2−x SiO 5 and Lu x Gd 2−x SiO 5 (pure and Nd or Yb doped).
In the present work, we report the growth, for the first time, of single crystals of the rare earth monosilicate compounds, R 2 SiO 5 (with R = Dy, Ho, Er), by the FZ method, using a laser-diode-heated floating zone (LDFZ) furnace.This is especially important for the study of the physical and chemical properties intrinsic to these materials, and especially for the optical, thermal, mechanical properties, as well as chemical reactivity, degradation and corrosion, i.e., the key characteristics that would allow the use of the R 2 SiO 5 compounds in applications, such as scintillation crystals in gamma ray or X-ray detectors, as well as in TBC/EBC.Furthermore, the results of our work point to the possibility of producing crystals of other R-Si-O systems by the floating zone method using a laser-diode-heated furnace, opening up the route to detailed investigations of this vast class of materials.

Materials and Methods
R 2 SiO 5 (with R = Dy, Ho, Er) were first synthesized in polycrystalline form by reacting powders of the starting oxides, Dy 2 O 3 , Ho 2 O 3 or Er 2 O 3 (all of 99.99% purity), and silica, SiO 2 (≥99.995%).The results of our efforts to synthesise R 2 SiO 5 in polycrystalline form are described elsewhere in a more detailed paper [62].The polycrystalline material previously synthesised was used to prepare feed rods for the crystal growth experiments.Crystals of the rare earth monosilicate compounds, R 2 SiO 5 (with R = Dy, Ho, Er), were then grown using a LDFZ furnace (Model FZ-LD-5-200W-II-VPO-PC, Crystal Systems Corporation, Hokuto, Japan), using different growth conditions.The quality of the crystal boules was investigated using a Laue X-ray imaging system with a Photonic Science CCD camera.Small quantities of each crystal boule were then ground for phase purity analysis, whilst small pieces were cleaved from the crystals for investigations of the crystal structures of the R 2 SiO 5 crystals.
Room temperature powder X-ray diffraction (PXRD) patterns were collected on a Panalytical X'Pert PRO MPD (Bragg-Brentano geometry) using Cu radiation (λ Kα1 = 1.5406Å and λ Kα2 = 1.5444Å, CuKα 1 to CuKα 2 ratio ∼ 1:0.023), over an angular range of 10-110 • in 2θ, with a step size of 0.00835 • .For the Dy-containing sample, the pulse height distribution (PHD) settings were changed in order to reduce the fluorescence-induced background [63,64].The lower level PHD setting of the X-celerator line (1D) detector was increased to 56%, while the upper level was maintained at 80%.The analysis of the diffractograms was performed using the Fullprof software suite [65].
Single crystal X-ray diffraction (SCXRD) experiments were carried out on small pieces (∼20-40 µm) cleaved from R 2 SiO 5 boules.SCXRD measurements were firstly performed on the as-grown Dy 2 SiO 5 , Ho 2 SiO 5 , and Er 2 SiO 5 crystal fragments, at room temperature, on an Oxford Diffraction Xcalibur diffractometer.Data over large regions of reciprocal space were collected using Mo radiation (λ Kα = 0.71073 Å).SCXRD data were then collected, at room temperature, on annealed crystal fragments isolated from the as-grown R 2 SiO 5 boules.All the SCXRD data were indexed and integrated using CrysAlisPro (Rigaku) [66].An empirical absorption correction was used, with the automatic configuration implemented in the ABSPACK module.The crystal structure was refined using SHELXL [67,68], as implemented in Olex2 [69].

Results and Discussion
Following our efforts in optimizing the synthesis of polycrystalline material of R 2 SiO 5 (with R = Dy, Ho, Er), we have successfully prepared samples with considerably reduced levels of the impurity phases, following the same strategy as in Reference [62].The polycrystalline material contained mainly the desired X2-R 2 SiO 5 phase, and a small amount of impurities, R 2 Si 2 O 7 and R 4.67 (SiO 4 ) 3 O phases (see Figure 1a-d).

Floating Zone Crystal Growth Using a Conventional Floating Zone Furnace
We first tried to grow a crystal boule of Ho 2 SiO 5 in air atmosphere, in a flow of 1 L/min, using a four-mirror halogen lamp optical image furnace (Model FZ-T-10000-H-VI-VP-PC, Crystal Systems Corporation, Hokuto, Japan), equipped with four 1 kW halogen lamps, in similar conditions to the ones used for the crystal growth by the FZ method of similar rare earth silicate compounds [53,55].Despite the fact that the feed rod could be molten, our attempts to form a stable molten zone failed.The feed rod did not appear to melt congruently, and it was not possible to ensure a good viscosity of the liquid that would allows us to maintain a molten zone and proceed further with the crystal growth experiment.Nonetheless, we were able to solidify a very small amount of the liquid on top of the seed rod.Phase purity analysis (not shown) carried out on the ground tip of the seed rod shows the presence of two phases, X2-Ho 2 SiO 5 and Ho 4.67 (SiO 4 ) 3 O.The stabilisation of the Ho 4.67 (SiO 4 ) 3 O impurity is consistent with the observations made as a result of our attempts to synthesise pure, polycrystalline R 2 SiO 5 samples.Annealing at high temperature and/or for an increased amount of time appears to facilitate the formation of the Ho 4.67 (SiO 4 ) 3 O phase.Due to the temperature profile characteristic for the conventional halogen-heated FZ furnace [70], exposure to the high heat generated by the halogen lamps during the warming up phase of the growth process produces a similar effect, thus favoring the stabilisation of the Ho 4.67 (SiO 4 ) 3 O phase to the detriment of the X2-Ho 2 SiO 5 phase.Moreover, this result is in agreement with our hypothesis that the areas of thermal stability of the various chemical and structural phases existing in the R-Si-O systems overlap [19,27,55].

Floating Zone Crystal Growth Using a Laser-Diode-Heated Floating Zone Furnace
Following our failed attempts to grow R 2 SiO 5 crystals by the FZ method, using a conventional, halogen-heated, floating zone furnace, we then tried to prepare crystals of the rare earth monosilicates using a LDFZ furnace equipped with five 200 W InGaAs lasers (λ = 976 nm).
We have successfully grown crystals of the R 2 SiO 5 (with R = Dy, Ho, and Er) by the FZ method, using the LDFZ furnace.A series of experiments were performed to optimize the crystal growth parameters and to obtain crystal boules of high crystalline quality.Several rare earth monosilicate crystal boules were obtained using different growth conditions, and a summary of the parameters used is given in Table 1.In all cases, polycrystalline rods were used as seeds to allow for a systematic study of the effect of the growth conditions on the quality of the crystals.We have first attempted to grow crystal boules of R 2 SiO 5 in air, at ambient pressure, in dynamic conditions (in a flow of air of 1 L/min), applying a similar strategy as for the crystal growth using the FZ technique of related compounds, the rare earth disilicates, R 2 Si 2 O 7 [55].Although the R 2 SiO 5 crystal boules appear to melt congruently, during the growth of the Dy 2 SiO 5 and Er 2 SiO 5 boules, small bubbles appeared in the molten zone (see Figure 2a).Moreover, as the growth progressed, the bubbles grew larger and, after a while, they were able to overcome the surface tension and disappear.The disappearance of a bubble did not lead to the separation of the molten zone owing to a sufficiently high viscosity and surface tension of the liquid.Nevertheless, analysis of the boules grown revealed the incorporation of gas bubbles into some of the crystal boules.Despite the presence of bubbles during the growth process, no signs of evaporation were observed, for any the growths, on the quartz tube surrounding the feed and seed rods.
Almost all the crystal boules tended to have a high number of thermally generated cracks, except in the case of the Ho 2 SiO 5 boules.In all cases, the cracks developed in the first few millimetres of the crystal boules, and as the crystal growth progressed, the cracks propagated into the growing Dy 2 SiO 5 and Er 2 SiO 5 crystals.In the case of Ho 2 SiO 5 , the cracks disappeared almost completely after 5-10 mm from the beginning of the boule.Moreover, the Dy 2 SiO 5 and Er 2 SiO 5 crystal boules were very fragile and they cleaved or broke when removing them from the LDFZ furnace.
To reduce the thermal strain on the crystal boules during the crystal growth process and to prevent the formation of cracks, we have also carried out growth attempts of R 2 SiO 5 in air, at ambient pressure, but in static conditions (without a flow of gas).In all cases, the change from dynamic to static conditions did not appear to have a significant effect in reducing the number of cracks in the crystal boules.Nevertheless, we observed that the formation of bubbles in the liquid seems to occur more often.
Previous studies highlighted the effect of employing higher gas pressure on the occurrence of bubbles in the melt during the growth process [70][71][72].We have thus performed a new series of crystal growth trials, in an argon/oxygen gas mixture (Ar:O 2 = 80:20%), at 5 bars pressure.Our experiments showed that the application of a higher gas pressure suppresses the formation of bubbles in the melt for the growths of the R 2 SiO 5 (with R = Dy, Ho, and Er) crystal boules, thus improving considerably the stability of the molten zone during the growth process (see Figures 2b and 3).During our growth experiments, the temperature of the melt was monitored continuously as a function of time.These data, shown in Figure 3, indicate that the during the crystal growths of the R 2 SiO 5 compounds carried out in an argon/oxygen gas mixture (Ar:O 2 = 80:20%), at 5 bars pressure, the molten zone appeared to be more stable than the during the growth attempts performed in air, at ambient pressure, in static conditions.Furthermore, for almost the entire duration of the growth processes, the temperatures of the molten zones measured using the infrared thermometer were constant for the growth experiments that were stable and determined to be ∼1896 • C for Dy 2 SiO 5 , 1922 • C in the case of Ho 2 SiO 5 , and 1945 • C for Er 2 SiO 5 , respectively.For comparison, the temperature profile recorded during the growth of a Ho 2 SiO 5 crystal boule prepared in air, at ambient pressure, in static conditions, and at a growth rate of 10 mm/h, shows fluctuations in the temperature of the melt associated with the instability of the molten zone due to the formation of bubbles during the growth process.To test the accuracy of the infrared thermometer, we have grown crystal boules of TiO 2 using the LDFZ furnace, in air, at ambient pressure.During these growth experiments, the temperature of the melt (not shown) was found to vary in the temperature range 1835-1845 • C.These values are consistent with the previously reported value for the melting point of TiO 2 [73], suggesting thus that the temperatures of the melt for the R 2 SiO 5 compounds may be well approximated using the infrared thermometer. .Temperature profiles measured in situ, using an infrared thermometer, during the growths of R 2 SiO 5 compounds using the LDFZ furnace, in a mixed argon/oxygen (Ar:O 2 = 80:20%) gas atmosphere, at a pressure of 5 bars and at a growth rate of 12 mm/h.The data corresponding to the crystal growth of Dy 2 SiO 5 is shown in red, Ho 2 SiO 5 in blue and Er 2 SiO 5 in orange, respectively.The temperatures of the melts measured by the infrared thermometer are marked for each compound using horizontal dashed lines.For comparison, the temperature profile recorded during the growth of a Ho 2 SiO 5 crystal boule prepared in air, at ambient pressure, in static conditions, and at a growth rate of 10 mm/h, is shown in light purple colour.
In all cases, applying a gas pressure had a positive effect in reducing the number of cracks in the crystal boules.During the growths of Dy 2 SiO 5 and Ho 2 SiO 5 , the cracks completely disappeared after ∼5 mm from the beginning of the boule.Note that the cracks that can be seen at the end of the Dy 2 SiO 5 crystal boule on Figure 5a appeared after separation, upon cooling and at the moment when the lasers were switched off.Despite our attempts to reduce the occurrence of the thermally induced cracks, either by employing slower growth rates or changing the atmosphere conditions, we were not able to prepare a crack-free Er 2 SiO 5 crystal boule.Nevertheless, our experiments suggest that the number of cracks can be reduced upon applying a high gas pressure, and furthermore, the grown boules are less fragile.A previous study reports on the effect of gas pressure on the temperature profile during the growth process [70].The authors argue that the decrease in temperature observed at higher pressure of oxygen gas at all points along the crystal boule can be explained by a larger heat exchange between the grown crystal and greater number of gas molecules at higher pressure.The same study suggests that increasing the gas pressure could lead to an increased occurrence of cracks in the crystals, due to the a sharper gradient of temperature along the sample.Our results suggest that, in the case of the R 2 SiO 5 compounds, known for their low thermal conductivities [31,[74][75][76][77][78][79], the sharper temperature gradient characteristic of the LDFZ furnace coupled with a higher gas pressure of an argon/oxygen gas mixture help to promote the heat exchange between the crystal boule and the gas molecules and minimise the internal strain responsible for the formation of cracks.These two parameters were found to be crucial for the successful growth of large, high quality crystals of these materials by the FZ method.
Our results suggest that the cracks form to help to relieve the internal thermal strain of the crystal boule.The temperature profile measured using the infrared thermometer (see Figure 4) shows that the temperature along the crystal boule is much lower in the crack-free regions of the crystal boule (temperature profile measured at the surface of the boule at ∼28 mm from the beginning of the crystal boule), while in the regions of the boule with cracks (at ∼15 mm from the beginning of the crystal boule), anomalies can be observed in the data, possibly due to a reduced heat exchange between the boule and the gas atmosphere.The apparent lower temperature at the surface of the the polycrystalline seed (at ∼8 mm) than at the surface of the grown crystal (at ∼28 mm) can be explained by a heat exchange between the polycrystalline seed rod and the alumina holder used for mounting the seed.Vertical temperature profiles measured in situ, using an infrared thermometer, during the growth of a Ho 2 SiO 5 crystal boule in a mixed argon/oxygen (Ar:O 2 = 80:20%) gas atmosphere, at a pressure of 5 bars and at a growth rate of 12 mm/h.The maximum in temperature corresponds to the relative position of the molten zone.The black, red and orange curves are taken at 8, 15 and 28 mm, respectively, from the beginning of the boule.

Characterization of the R 2 SiO 5 Crystal Boules Grown by the Floating Zone Method
Crystal boules of Dy 2 SiO 5 , Ho 2 SiO 5 and Er 2 SiO 5 were thus successfully grown by the FZ method, using the LDFZ furnace.The boules were typically 4-5 mm in diameter and 20-45 mm long.All the boules grown were transparent to light, with a bright yellow (Dy 2 SiO 5 ), a pale yellow/pink (Ho 2 SiO 5 ), and a pink (Er 2 SiO 5 ) colour.Figures 5a-c show the photographs of the R 2 SiO 5 crystal boules grown in optimal conditions, i.e., in a mixed argon/oxygen (Ar:O 2 = 80:20%) gas atmosphere, at a pressure of 5 bars and at a growth rate of 12 mm/h.All R 2 SiO 5 crystal boules developed facets as they grew (at ∼10 mm from the beginning of the crystal boule), and two to four strong facets were present for the remaining of the length of all grown crystals.All the crystal boules separated from the seed at ∼3-4 mm from the beginning of the crystal boule.The quality of the grown boules was investigated by X-ray Laue diffraction and all the crystals showed similar crystalline quality despite the cracks and the different conditions employed during the crystal growth process.Figure 6 shows the Laue photographs taken along the length and on the cross section of the Ho 2 SiO 5 crystal boule grown in air, at ambient pressure, and at a growth rate of 10 mm/h.The Laue patterns were identical along the whole length of the crystal boule, and moreover, the Laue photographs taken on the cross section (the crystal boule cleaved naturally at the position where the horizontal crack formed) were consistent with one another at several points.Structural and phase purity analysis was carried out at room temperature on ground crystal pieces cut from the as-grown R 2 SiO 5 (with R = Dy, Ho, and Er) crystal boules and the PXRD patterns are displayed in Figures 7a-c.Profile matching to the monoclinic (I2/a) structure show no trace of impurities and confirm that the R 2 SiO 5 crystals are belonging to the X2-type.The lattice parameters determined by PXRD are given in Table 2.The lattice parameters of the R 2 SiO 5 crystal boules are in agreement with our results obtained for polycrystalline samples.Figure 7d shows the dependence of the lattice parameters on the effective ionic radii for the R 2 SiO 5 (with R = Dy, Ho, and Er) crystals.All lattice parameters exhibit a monotonic decrease in agreement with the lanthanide contraction.Table 2. Lattice parameters for R 2 SiO 5 (with R = Dy, Ho, and Er), refined from the room temperature PXRD data collected on ground pieces isolated from the as-grown crystal boules.The Bragg peaks were indexed with the monoclinic (I2/a) structure of the X2 polymorphs.

Chemical Composition
Lattice To determine the crystal parameters, small pieces were cleaved from the as-grown R 2 SiO 5 crystal boules and SCXRD measurements were performed at room temperature.The crystal details obtained from the refinement of the SCXRD data measured at room temperature are given in Supplementary Data and Figure 8 shows the crystal structure of X2-R 2 SiO 5 polymorphs.The characteristics of the oxygen polyhedra formed around the rare earth and silicon ions are given in Supplementary Data (data were obtained from VESTA software [81], based on bond valence parameters from Reference [82]).In all R 2 SiO 5 crystals, the average bond R-O lengths are larger in the seven-fold coordinated polyhedron, R 2 O 7 , than in the six-fold oxygen coordinated rare earth sites, R 1 O 6 .It should also be noted that the values of the quadratic elongation and bond angle variance for the R 1 O 6 and SiO 4 polyhedra indicate that these polyhedra are distorted in comparison to the ideal octahedra and tetrahedra, respectively.Attempts to fit SCXRD data using different models for the occupancies of the cationic sites showed that the best model is the one in which the occupancies of the R and Si sites were fixed to the nominal value of 1.The crystal structures were refined using anisotropic thermal displacement parameters for the cationic sites, and isotropic thermal displacement parameters for the anionic sites.Attempts to fit the data using anisotropic displacement parameters for the oxygen sites yielded "pancake"-like ellipsoids due to the smaller weight of the O compared to the heavier R and Si.Further experiments of SCXRD at higher angles and/or using a different X-ray source (e.g., Ag radiation [83]), or alternatively single crystal neutron diffraction measurements, would yield data that would allow us to refine with a higher precision the thermal parameters for the oxygen sites.Previous reports demonstrated that R 2 SiO 5 (with R = Tb → Yb, and Y) can also crystallize in the structural type stable at lower temperature, i.e., X1-structure [29,30].In an attempt to obtain large, high quality crystals of the X1-type of R 2 SiO 5 (with R = Dy, Ho, and Er), crystal fragments isolated from the as-grown boules were annealed, following the post-annealing procedure carried out on crystals of other materials that undergo thermally induced structural phase transitions [84,85].Small R 2 SiO 5 crystal fragments were annealed in air, at 950 • C, a temperature lower than the X1 → X2-type structural phase transition temperature [29,30], for 30 days, and then slowly cooled to room temperature at a rate of 50 • C/h.The results of the long post-annealing experiments are confirmed by SCXRD data collected at room temperature on annealed R 2 SiO 5 crystal fragments (see Supplementary Data; for simplification only the SCXRD data for the annealed Dy 2 SiO 5 crystal fragment is shown).The crystal data of all annealed samples were identical with the parameters obtained for as-grown crystals.These results suggest that the X1 → X2-type structural phase transition is irreversible in the conditions employed for the post-annealing of the R 2 SiO 5 crystals.

Figure 2 .Figure 3
Figure 2. Floating zone growth of a boule of: (a) Dy 2 SiO 5 in a flow of air of 1 L/min, at ambient pressure, at a growth rate of 10 mm/h.(b) Dy 2 SiO 5 in an argon/oxygen gas mixture (Ar:O 2 = 80%:20%), at 5 bars pressure, at a growth rate of 12 mm/h.

Figure 4 .
Figure 4. Vertical temperature profiles measured in situ, using an infrared thermometer, during the growth of a Ho 2 SiO 5 crystal boule in a mixed argon/oxygen (Ar:O 2 = 80:20%) gas atmosphere, at a pressure of 5 bars and at a growth rate of 12 mm/h.The maximum in temperature corresponds to the relative position of the molten zone.The black, red and orange curves are taken at 8, 15 and 28 mm, respectively, from the beginning of the boule.

Figure 6 .
Figure 6.X-ray Laue back reflection photographs taken at different points along the crystal length on the sides of the Ho 2 SiO 5 crystal boule grown in air, at ambient pressure, and at a growth rate of 10 mm/h.Laue patterns taken on a cleaved cross section (where the crack can be seen) are consistent with one another at several points.

Figure 7 .
Figure 7. Room temperature PXRD patterns of ground as-grown 2 SiO 5 crystal pieces, presented in the following order: (a) Dy 2 SiO 5 , (b) Ho 2 SiO 5 , and (c) Er 2 SiO 5 .The experimental profiles (red closed circles) and full profile matching refinements (black solid lines) made using the X2-type with a monoclinic (I2/a) structure are shown, with the differences given by the blue solid lines.(d) Evolution of the lattice parameters, a, b, c and β, as a function of the effective ionic radii reported in Reference [80] for hexacoordinated R 3+ ions.

Figure 8 .
Figure 8. Crystal structure of X2-R 2 SiO 5 obtained from the refinement of the SCXRD data measured at room temperature.Representation of the local coordination around the cationic sites and the connection between the polyhedra (right).

Table 1 .
Summary of the conditions used for the growth using a LDFZ furnace of R 2 SiO 5 (with R = Dy, Ho, and Er) crystal boules.All the boules grown were transparent to light, with a bright yellow (Dy 2 SiO 5 ), a pale yellow/pink (Ho 2 SiO 5 ), and a pink (Er 2 SiO 5 ) colour.
* The sign marks the crystal boules of the best crystalline quality, and thus, the optimal growth conditions that allowed us to obtain these boules.