# Bubble distribution in shaped sapphire grown from molybdenum crucibles using the micro-pulling down technique

Laura Wollesen, Abdeldjelil Nehari, Serge Labor, Guillaume Alombert-Goget, Denis Guignier, Kheirreddine Lebbou

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Laura Wollesen, Abdeldjelil Nehari, Serge Labor, Guillaume Alombert-Goget, Denis Guignier, et al. Bubble distribution in shaped sapphire grown from molybdenum crucibles using the micro-pulling down technique. CrystEngComm, 2025, 27 (4), pp.497-506. 10.1039/D4CE01077A. hal-04872582

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# Bubble distribution in shaped sapphire grown from molybdenum crucibles using the micro-pulling down technique

Laura Wollesen<fnref n="1" />, Abdeldjelil Nehari<fnref n="1" />, Serge Labor<fnref n="2" />, Guillaume Alombert-Goget<fnref n="2" />, Denis Guignier<fnref n="2" />, Kheirreddine Lebbou<fnref n="1" />

## Abstract

As a function of the capillary die geometry for fibers ($\phi=1$mm) and rods ($\phi=3$mm), the bubble distribution and size have been studied. It is discussed how the pulling rate and the capillary die design impact the bubble propagation during sapphire crystallization from molybdenum crucibles using the micro-pulling down (μ-PD) technique. At a low pulling rate ($v=0.25$ mm/min), for both fibers and rods, the crystallization interface is flat, the bubble concentration is low, and they are regularly distributed in the periphery of the crystals.

## 1. Introduction

Single crystals obtained artificially by different growth methods (i.e. from the liquid state or a solution) always contain defects. These defects generally depend on the growth conditions. The treatment after the growth process also plays an important role in reducing defects and their distribution. A typical defect for crystals are inclusions bigger than 100 µm. For optical crystals, these defects cause dispersion and absorption of light and thereby reduce the crystal quality. The absorption of light caused by inclusions leads to local heating, which cause mechanical stress and can potentially break the crystal [1] [2]. Sapphire single crystals, whatever the growth technology, have a particular defect, namely bubbles also referred to as micro-voids. Nevertheless, bubbles are also observed in other crystal types [3] [4]. Bubbles in sapphire have diameters varying from 1-100 µm. They have a negative impact on the mechanical [5] and optical properties that ultimately affect the final application of the material. The bubbles degrade the optical properties by reducing transparency [6] [7] as well as laser performance in doped sapphire [8]. Undoped sapphire is often applied as substrate for microelectronics and the presence of bubbles induce surface imperfections during the polishing of the substrate. Therefore, whatever the crystal and especially in the case of white (undoped) and colored sapphire, bubbles are non-desirable for most applications. It has been found for various growth techniques that the bubble distribution in the

<footnote n="1">¹Institut Lumière Matière, Université Lyon 1 - UMR 5306 CNRS, 69622 Villeurbanne, France</footnote>

<footnote n="2">²RSA le rubis SA, BP 16, 38560 Jarrie/Grenoble, France</footnote>
crystal is influenced by the growth rate. For Edge-defined Film-fed Growth (EFG), it has been reported that when using a pulling rate $≤1.5$ mm/min, the bubbles are present mainly close the periphery [7] and can therefore be removed by polishing. Using the Czochralski (CZ) method, the bubbles are often not only present in the bottom and the top of the ingot [9], and is located mainly near the periphery when using a pulling rate $≤2.0$ mm/h [6]. In previous work, we evaluated the bubble distribution in sapphire rods ($\phi=3$ mm) grown from iridium crucibles using the micro-pulling down (μ-PD) technique. It was found that a pulling rate of 0.25 mm/min resulted in bubble-free sapphire rods [10].

The growth from Ir crucibles generally works well for various crystals and methods. However, the abundance of Ir is low [11], and the price is very high. A known crucible alternative is molybdenum. It is more abundant [11] and is considerably cheaper than Ir, making it a favorable crucible material. Unfortunately, a thermodynamic calculation carried out by Satunkin et al. [12] predicts that Mo affects the bubble formation in sapphire. This should be caused by chemical reactions between compounds resulting from the thermal dissociation of $Al_2O_3$ and Mo. It is also possible that impurities coming from the raw $Al_2O_3$ material reacts with the Mo crucible, resulting in a low purity $Al_2O_3$ melt reacting more actively with the Mo [13]. In addition, when using Mo crucibles, it is very important to introduce a vacuum procedure before heating to reduce the oxygen presence in the chamber as Mo oxidizes at elevated temperatures.

In the current paper, we present the growth of cylinder-shaped sapphire crystals with two different diameters, namely fibers ($\phi$: 1 mm) and rods ($\phi$: 3 mm) using the μ-PD method. Mo crucibles were applied as an alternative to the commonly applied Ir crucible. The pulling rate was varied between 0.25 and 2.5 mm/min and the bubble distribution was studied and compared to previous reports on shaped undoped sapphire crystals grown from Ir crucibles.

## 2. Experimental Section

### 2.1 Crystal growth

Shaped undoped sapphire crystals were grown using the μ-PD growth technique. The raw material is α-Al$_2$O$_3$ product by RSA Le Rubis company. It was melted in Mo crucibles with a die including a capillary channel at the bottom. The size and shape of this die, depends on the desired shape of the crystal. For this study, cylinders of two sizes have grown referred to as fibers ($\phi$: 1 mm) and rods ($\phi$: 3 mm). A photograph of the two applied crucibles is presented in Figure 1a and 1b, respectively, and the relevant dimensions of the dies are listed in Table 1. The crucible rests on a Mo after heater (Figure 1c) that affects the thermal gradient around the liquid-solid interface and the crystallization kinetics. The assembled crucible and after heater is positioned inside graphite thermal isolation surrounded by a radio-frequency (RF) coil (Figure 1d). By adjusting the power, the temperature is controlled. A camera visualizes the bottom of the die owing to a window in the growth chamber, small openings/windows
through the thermal isolation and the after heater (indicated by red squares in Figure 1c and 1d). This enables observation of the meniscus and the growing crystal (Figure 1e and 1f). As metallic Mo oxidizes above 400°C [1], vacuum (<5*10⁻⁴ mbar) is obtained in the growth chamber before an argon atmosphere is introduced.

<figure><img src="image_2.png" /><figcaption>Figure 1: Mo crucibles for growth of: a) fibers (φ: 1 mm) and b) Rods (φ: 3 mm). c) Assembled after heater (red square: window) and crucible. d) Inside the µ-PD growth chamber with the graphite thermal isolation and radio frequency (RF) coil visible (red square: window). The screen monitor showing the liquid-solid interface during growth of a e) fiber and f) rod.</figcaption></figure>

<table><caption>Table 1: Relevant dimensions of the Mo crucible capillary dies applied to shape the sapphire crystals during growth.</caption><thead><tr><th rowspan="2">Shape</th><th colspan="2">Die diameter [mm]</th><th rowspan="2">Die length [mm]</th></tr><tr><th>Outer</th><th>Hole</th></tr></thead><tbody><tr><td>Fiber</td><td>1.0</td><td>0.5</td><td>2</td></tr><tr><td>Rod</td><td>3.0</td><td>1.0</td><td>2</td></tr></tbody></table>

The growth is initiated by touching the capillary die from underneath with a single crystal sapphire seed. If the temperature is slightly above the melting point of the raw material, the seed is connected to the melt. The seed is then pulled down with a certain pulling rate (growth rate) and a crystal is growing according to the shape of the die and seed orientation. The seeding procedure for µ-PD is documented step by step with images in an earlier paper [14]. The growing crystal detach from the die once 100% crystallization is reached, meaning the crucible is empty. The seed applied in this study was provided by R.S.A le rubis SA [15].

For all presented sapphire crystals, the experimental conditions are similar (set-up, power-input/temperature, amount of raw material, etc.) except for the pulling rate that was varied from 0.25 to 2.5 mm/min.
## 2.2 Characterization

To investigate the sample surfaces and transversal cross sections, the bubble distribution and bubble size, an optical microscope with transmission and reflection lighting sources was used with various objectives (x5, x10 and x20). The observation system is composed of an optical microscope, a video camera connected to a computer and image acquisition and processing software.

Before investigating the transversal cross sections of the rods and fibers, the surface roughness was reduced by polishing. The obtained surface quality is sufficient to analyze the bubbles by the optical microscope.

SEM and SEM-EDX was performed using a Phenom G2 pro. The samples were beforehand partly covered with a graphite paste to reduce the charging of the surface.

## 3. Results and discussion

Shaped single crystalline sapphire fibers and rods were successfully grown by μ-PD. Photographs of the grown sapphire fibers and rods are presented in Figure 2a and 2b, respectively. The diameter of the fibers and rods fits approximately with the applied die diameters, 1 and 3 mm, respectively. Their lengths are between 200 and 240 mm depending on the quantity of the starting raw material. The crucibles were always empty after growth. All samples are transparent without any coloration and free of visible macroscopic defects such as inclusions and grains boundaries. Some samples have slight diameter oscillations, which was observed especially on the fiber grown with the lowest pulling rate (v=0.25 mm/min). This most likely reflects that the applied power, and thereby temperature, was slightly too low during the growth process, meaning the input power not high enough to maintain a steady state growth. This underlines the importance of a well-controlled temperature to obtain high quality sapphire crystals with the μ-PD technique in good agreement with our previous work [16] [17] [18].

The presence of bubbles in sapphire is well known to reduce the transparency [6] [7]. This can often be concluded visually when the bubble density is high. In this study, the fiber transparency looks visibly comparable whatever the pulling rate (Figure 2a). However, for the rods the transparency is visually reduced at high pulling rates (Figure 2b), which is in a good agreement with our previous work growing sapphire rods from an Ir crucible with μ-PD [10]. This is especially visible for the rod grown using pulling rate 2.5 mm/min, where it even appears dark. In addition, there can be contamination from the graphite isolation in the bulk of the rod as well along the bubbles.
<figure><img src="image_3.png" /><figcaption>Figure 2: Photographs of sapphire grown by μ-PD from Mo crucibles using various pulling rates (v) a) fibers (φ: 1 mm) and b) rods (φ: 3 mm). v is indicated in the figure.</figcaption></figure>

It can be challenging to differentiate between bubble and particle inclusions when studying samples with a microscope, but some general examples and characteristics are here presented. Bubbles are often close to spherical (Figure 3a), except when being elongated along the growth direction and thereby having long “tails” (Figure 3b). Particle inclusions typically have edges or a more distinct shape than the bubbles (Figure 3c).

<figure><img src="image_4.png" /><figcaption>Figure 3: Micrographs of sapphire crystals showing a) typical spherical bubbles, b) a long tailed bubble and c) particles at the surface. The optical microscope was operated in transmission configuration in a) and b) and reflection in c).</figcaption></figure>

Using an optical microscope, the bubble distribution in the sapphire fibers and the rods has been studied transversally (Figure 4) and longitudinally (Figure 5). For clarity schematics of the bubble distribution in the cross sections are presented in Figure 4q. The general main observations are summarized in Table 2 and is discussed in the following sections.

Using a low pulling rate ($v=0.25$ mm/min), for both fibers and rods, very few bubbles are observed (Figure 4a, 4e, 4i, 4m and Figure 5a, 5e). The overall bubble density in sapphire rods increases drastically with increasing pulling rate. For the fibers, the bubble density is increasing as well (Figure
6a) but is low whatever the pulling rate and the bubbles are distributed only at the periphery, 50-80 µm under the surface. Even in fibers grown with the fastest pulling rate ($v=2.5$ mm/min) the bubbles are located at the periphery as a ring/curtain with of width around 100 µm. For fibers grown with pulling rates $\ge 1$ mm/min, the bubble curtains are a periodic network in planes parallel to the growth direction (Figure 4 and Figure 5). For pulling rates $\ge 1.5$ mm/min, there are regions where some of the bubbles are less periodical and more chaotically distributed (Figure 5c, 5d). However, these bubbles are still located

<figure><img src="image_5.png" /><figcaption>**Figure 4:** a-p) Transversal cross sections of sapphire fibers and rods grown with varying pulling rates (indicated in figure). The optical microscope was operated in transmission configuration. Note that the scale bar is not the same for the fibers and the rods. q) Schematic of the bubble distribution in the cross section fibers and rods from this study.</figcaption></figure>
close to the periodically distributed bubbles. When bubbles (or other defects) are located only at the periphery, they can be removed by polishing. It is, therefore, crucial to know the width of the bubble curtain or the diameter of the bubble-free core. The diameter of the bubble-free core is around 0.85 mm for pulling rates ≥1.0 mm/min (Table 2) and the average bubble diameter is between 2 and 8 µm depending on the pulling rate (Figure 6a). The bubble-free core diameter has been estimated for each sample from the micrographs in Figure 4, the value being the largest diameter of a circle without any bubbles.

The rods (φ: 3 mm) grown with pulling rate 1 mm/min present a deformed bubble ring/curtain with a complex hexagonal-like shape (Figure 4f), located 300-700 µm under the surface. The width of this bubble curtain is up to around 300 µm (an arrow in Figure 4n indicate curtain width) and the bubble-free core have a diameter of around 1.5 mm. The center of the rod grown with pulling rate 1.5 mm/min is almost bubble free, with a bundle of bubbles inside the core. The bubble curtain at the periphery is 50-130 µm under the surface and around 350-600 µm wide (Figure 4g and 4p). When the pulling rate was 2.5 mm/min, the bubbles are located 400-500 µm under the surface and are covering the center with a square-like shape (Figure 4h) leaving no usable bubble-free core. Nevertheless, we cannot exclude that certain observed features are not bubbles and instead inclusions related to impurities or the Mo crucible, or is connected to roughness caused by the polishing quality.

There is a difference in the bubble distribution along the length of the rods (longitudinally). There are several types of bubble distributions and they are not necessarily linked to any region of the crystal (beginning, middle or end). There is a periodicity of the bubble arrangement along the growth direction (Figure 5e-h), and similar to the fibers, there are areas with more chaotic distribution, especially when using higher pulling rates. It has earlier been described that at the moment when the bubble is incorporated into the growing crystal, the liquid-solid interface is temporarily and locally deformed [19]. This most likely increase the possibility for incorporating the next bubble arriving at the interface at the approximate same position. This is then a reoccurring process enforcing a periodicity of the bubble

<figure><img src="image_6.png" /><figcaption>Figure 5: Longitudinal study of fibers and rods grown with various pulling rates (indicated in figure). The optical microscope was operated in transmission configuration. The magnification applied was the same for all these micrographs. Note the bubble size and shape in f) and h) is distorted because they are located at least 300 µm inside the crystal. They therefore appear larger.</figcaption></figure>
**incorporation.** The bubbles in Figure 5f and 5h appear distorted and larger compared to the two other pulling rates. It is important to underline this is an artifact caused by the bubbles are located at least 300 µm under the surface. When adjusting the focus of the optical microscope to observe the bubbles, the focus is being made through 300 µm of sapphire or more and cannot be well in focus. Therefore, the bubble diameters are also not estimated for these two rods as they would be highly overestimated. For the two other pulling rates a decreasing diameter tendency with increasing pulling rate is found similar to the fibers (Figure 6a).

<table><caption>Table 2: Overview of bubble distribution for the samples considering the pulling rate (v) and the diameter. *the core of this sample is not completely bubble free.</caption><thead><tr><th rowspan="2">v<br>[mm/min]</th><th colspan="3">Fibers (φ: 1 mm)</th><th colspan="3">Rods (φ: 3 mm)</th></tr><tr><th>Longitudinal<br>bubble<br>distribution</th><th>Transversal<br>bubble<br>distribution</th><th>Bubble-free<br>core diameter<br>[mm]</th><th>Longitudinal<br>bubble distribution</th><th>Transversal<br>bubble<br>distribution</th><th>Bubble-free<br>core diameter<br>[mm]</th></tr></thead><tbody><tr><td>0.25</td><td>Very few<br>bubbles</td><td>Very few<br>bubbles at<br>periphery</td><td>~1.0</td><td>Few</td><td>Few bubbles<br>at periphery</td><td>~3.0</td></tr><tr><td>1.00</td><td>Periodic</td><td>Few at<br>periphery</td><td>~0.85</td><td>Periodic and<br>chaotic</td><td>Hexagonal-<br>like shape</td><td>~1.5</td></tr><tr><td>1.5</td><td>Periodic and<br>chaotic</td><td>Ring at<br>periphery</td><td>~0.85</td><td>Periodic and<br>chaotic</td><td>Broad ring at<br>periphery</td><td>~1.8*</td></tr><tr><td>2.5</td><td>Periodic and<br>chaotic</td><td>Ring at<br>periphery</td><td>~0.85</td><td>Periodic and<br>chaotic</td><td>Core</td><td>-</td></tr></tbody></table>

The bubble density have been estimated from several micrographs (Figure 6b). This is reflecting the bubble density in those micrographs and not the whole fiber/rod. As is seen in Figure 4 the overall bubble density of the rods are higher than the fibers. From the bubble density estimation an increase with increasing pulling rate is found as well.

<figure><img src="image_7.png" /><figcaption>Figure 6: a) Bubble diameter as a function of pulling rate and b) bubble density as a function of pulling rate. The data is extracted from micrographs. Error bars depict the range found in a single micrograph and the point is the average value of these. Note that for some of the data points the error bars are smaller than the symbol.</figcaption></figure>

It is observed now that the bubble distribution depends on the size and shape of the capillary die. The fibers (φ: 1 mm) contain bubbles that are located close to the crystal surface (periphery). They form a
crown that faithfully follows the transversal section (Figure 4b-d). For the rods (φ: 3 mm), it is more complicated as we also find a bubble crown close to the crystal surface for v=1.0 and 1.5 mm/min and a bubble core for v=2.5 mm/min. Comparing these results on the bubble distribution and density in the rods with those of an earlier study on sapphire using Ir crucibles, the trend is comparable [10]. Here wider bubble curtains were also observed in rods grown with 1.5 mm/min. This is an important result as it indicates that sapphire crystals can be grown from Mo crucibles instead of Ir crucibles without compromising on the bubble distribution and density. This also contradicts the prediction that the Mo crucible affects the bubble formation in sapphire [12], or the impact is so small we cannot conclude it for the applied pulling rates.

The distribution of the bubbles shown in Figure 5f-h is characteristic for when the solidification interface has a cellular structure due to the destabilization caused by accumulations of bubbles at the interface [19]. The transversal bubble distribution is affected by the shape of the crystallization front and depends on whether or not the conditions determining stability or instability of a flat liquid-solid interface are satisfied. As a function of pulling rate, Figure 7a-h expose images of the meniscus and interface shape for the fibers and rods. The section size of shaped single crystal fiber or rod pulled by micro-pulling down technique is likely retained during the crystallization process, therefore, the capillary die shape at the bottom of the crucible limits the chemical bonding-induced phase transition in specific region at the level of the crystallization interface and the capillary die size can be considered as thermodynamic parameter during µPD melt shaped crystal pulling (Use these two references https://doi.org/10.1007/s11431-018-9337-1, https://doi.org/10.1016/j.jre.2019.12.014).

It has been shown for µ-PD that with increasing pulling rate the meniscus height is increasing [20] [10], which is in good agreement with our results as well (Figure 7i). From these meniscus shapes (Figure 7a-h) it can be deduced that the diameter and the hole of the capillary die affects the curvature of the liquid-solid interface.

The bubbles are located close the periphery (at lower pulling rates) due to the convection streams (Marangoni flow) within the melt. A parallel can be drawn to the segregation behavior of dopants in sapphire. This has been modeled for Ti-doped sapphire fibers grown by µ-PD using a pulling rate of 0.5 mm/min, where a transversal segregation is predicted for fibers (φ: ≥1.6 mm) [21]. At low pulling rate

<figure><img src="image_8.png" /><figcaption>Figure 7: a-h) Images of the meniscus of the fibers and rods as a function of the pulling rates (indicated in figure). i) Estimated meniscus height as a function of the pulling rate.</figcaption></figure>
(v=0.25 mm/min), the interface is flat (Figure 7a,e) and close to no bubbles are trapped in the fiber and only a few bubbles are trapped in some areas in the rods. When increasing the pulling rate (v≥1 mm/min) the crystallization interface becomes locally instable. The increasing melted region size (meniscus height), allows for convective currents in the melt to stimulate bubble trapping by the crystallization front and thereby into the crystal. Macroscopic deformation of the crystallization front can arise up to 1 mm long, which is accompanied by enhanced bubble trapping. These observations support the assumption of the die shape and size (fiber, rod) and pulling rate strongly affect the crystallization interface stability and the convective flows in the melt. These in combination leads to the bubble distributions observed in Figure 4 and Figure 5.

If the capillary die is wetted by the melt, bubbles inside the melt cannot escape the crystallization front and is trapped. In this situation, the bubble distribution is determined by the hydrodynamic flow of the melt in the neighborhood of the crystallization front and thus the capillary die design plays an important role. It is clear that the fundamental parameters involved in the crystallization by μ-PD are the crucible diameter capillary die, the crystal diameter and the meniscus height of the molten zone. These parameters determine the stationary stable state growth conditions.

In general, for various crystal growth techniques and crystal types, the crucible is often made from Mo [22] [23]. Sapphire has been grown in Mo crucibles before [24] [2] [25] even with the u-PD method [26] [27]. This is due to the relatively easy machining of Mo and its reasonable cost compared to for example metallic Ir or Pt. However, it is therefore important to discuss the possible degradation of Mo when applying it as crucible material to grow high melting point crystals, such as sapphire. The main Mo vaporization reactions are:

$$ \begin{aligned} \mathrm{Mo(s)} + \mathrm{Al_2O_3(l)} & \rightarrow \mathrm{MoO(g)} + \mathrm{Al_2O(g)} + \mathrm{O(g)} \\ \mathrm{Mo(s)} + \mathrm{O(g)} & \rightarrow \mathrm{MoO(g)} \\ \mathrm{Mo(s)} + \mathrm{Al_2O(g)} & \rightarrow \mathrm{MoO(g)} + 2\mathrm{Al(g)} \end{aligned} $$

The main gaseous species are therefore: MoO, Al₂O, MoO₂, Al, O [12]. Those containing Mo such as MoO and MoO₂ are important. It shows a strong influence of the crucible material on the main gaseous species in equilibrium. Therefore, it is possible that bubbles can be gas pockets belonging to the abovementioned gas species. As the thermal insulation around the crucible in this study is graphite, it is also possible that the carbon passes into the liquid in the Mo crucible through the gaseous phase. Yalovets et al. [28] observed by mass spectroscopy N₂, C₂H₄,CO, CO₂, O, O₂, Ar, water vapors and carbon.

To study the sample surfaces closer SEM-EDX was applied. A SEM image revealing particles with various shapes and elemental composition is shown in Figure 8. SEM-EDX line scans was performed (lines indicated at SEM image) and the relevant relative contents are plotted as a function of these lines. The first particle is an elongated pillar appearing bright compared to the bulk fiber surface in the SEM
image, and the line scan reveals it is Cr-rich. It cannot be concluded if it is a Cr₂O₃ from these
measurements or (Al,Cr)₂O₃ as the electron beam is most likely reaching into the bulk at least at some
positions, and thereby giving a signal mixed of the bulk and the particle. The other particles appearing

<figure><img src="image_9.png" /><figcaption>Figure 8: SEM image of sapphire fiber (v=0.25 mm/min) surface with two arrows indicating the position for SEM-EDX line scans. The two line scans are shown on the left with line 1: showing the relative chromium and aluminum content and line 2: the relative carbon and aluminum contents along those lines.</figcaption></figure>

bright in the SEM image are also Cr-rich. This is a contamination that can origin from the raw material,
or more likely the thermal isolation, as this is also applied to grow Cr-containing crystals. The second
studied particle appear darker than the bulk fiber in the SEM image, and is from the SEM-EDX line
scan found to be carbon-rich. This is most likely coming from the graphite thermal isolation as there is
a flow of argon in the chamber that can carry small particles from the graphite and by coincidence lead
some of it to the growing crystal, potentially even the liquid zone that is thereby capturing these particles.
The surface contamination is higher when using a slow pulling rate, which is most likely caused by the
additional time it takes to grow the crystal, leading to a higher risk of having particles depositing on or
near the liquid meniscus. It is important to note that the crystals were carefully cleaned after growth to
remove any non-sticking contaminations such as graphite dust after the growth. For the sample studied
with SEM-EDX for this study, no Mo contamination was identified revealing a good stability of the
crucible after several growths.

These results show the importance of optimizing the set-up carefully to reduce contamination from the
various components inside the growth chamber. The set-up and growth procedure applied in this study
works well in terms of the crucible is stable and no Mo is contaminating the samples at this stage and
the crucible is not strongly degrading. There are no indications that the Mo is oxidizing during the
growth procedures, which can be attributed to the vacuum procedure, high purity Ar flow and the (most
likely) reducing atmosphere. A reducing atmosphere can be created by the graphite thermal isolation
reacting with any oxygen in the atmosphere, for example created by vaporization of molten Al₂O₃,
resulting in CO gas (reducing atmosphere) [29].

**4. Conclusions**
Undoped sapphire grown by micro-pulling down technique using Mo crucibles is characterized by the presence of a particular defect, namely bubbles, that seriously affect the properties of the sapphire crystal. The capillary die design is very important for obtaining high quality sapphire crystals. It is not only responsible for the shape of the crystal, but also for its structural perfection such as defect presence. The formation of bubbles can occur on the surface of the die. The distribution and concentration of the bubbles then depend on the size of the capillary die. The axial, and radial components of the flow velocity affect the bubbles distribution in the meniscus. The velocity field of the melt flow in the meniscus, between the lower part of the die and the crystallization interface, in the shaped sapphire crystal grown by µ-PD method, depends on the size of the capillary die. Control of the bubble distribution can thereby be obtained by choosing the capillary design carefully. With increasing pulling rate there are a decreasing bubble diameter tendency. The bubbles are almost uniformly distributed along the growth direction independently of the growth rate, even when it was high (v=2.5 mm/min). Our previous study on bubble distribution in sapphire grown by µ-PD from iridium crucibles is in good agreement with these results. Through this work, clarification have been gained on the origin, size and distribution of bubbles in shaped sapphire grown by the µ-PD technique from Mo crucibles using graphite thermal isolation. From these results, improvements can be made to the technological processes for growing sapphire without bubbles.

## Acknowledgements

The work was financially supported by ANR Labcom "SaphirLab" research program. The authors thanks CNRS (IRP CNRS "ScintLab" project) for their financial support.

## Author contributions

L.W.: Crystal growth, characterization and writing paper.

A. N.: Experimental participation, crystal growth advices and results discussion.

K.L.: Crystal growth advices, writing paper and results discussion.

G.A.: Participation in paper reading and characterization.

S.L.: Reading paper, provided sapphire raw materials and characterization.

D.G.: Reading paper, provided sapphire raw materials and characterization.

## Conflicts of interest

There are no conflicts to declare.

## Data availability

All the data supporting this work have been included within the article and is available on request.

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