# Key melt properties for controlled synthesis of glass beads by aerodynamic levitation coupled to laser heating

Jan Baborák, Maureen Yembele, Petr Vařák, Sandra Ory, Emmanuel Véron,

Michael J Pitcher, Mathieu Allix, Pavla Nekvindová, Alessio Zandonà

► To cite this version:

Jan Baborák, Maureen Yembele, Petr Vařák, Sandra Ory, Emmanuel Véron, et al. Key melt properties for controlled synthesis of glass beads by aerodynamic levitation coupled to laser heating. International Journal of Applied Glass Science, 2023, 14 (3), pp.455-467. 10.1111/ijag.16627. hal-04235059

HAL Id: hal-04235059

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Submitted on 10 Oct 2023

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# Key melt properties for controlled synthesis of glass beads by aerodynamic levitation coupled to laser heating

Jan Baborák¹,², Maureen Yembele²,³, Petr Vařák¹, Sandra Ory², Emmanuel Véron², Michael J. Pitcher², Mathieu Allix², Pavla Nekvindová¹, Alessio Zandonà²,⁴*

¹ Department of Inorganic Chemistry, University of Chemistry and Technology, Technická 5, 166 28, Prague, Czech Republic

² CNRS, CEMHTI UPR3079, Univ. Orléans, F-45071 Orléans, France

³ Laboratoire commun Canopée, CNRS, Univ. Lorraine, Saint Gobain, France

⁴ Friedrich-Alexander-Universität Erlangen-Nürnberg, Department of Materials Science (Glass and Ceramics), Martensstr. 5, 91058 Erlangen, Germany

## Abstract

Binary alkali silicate glasses were synthesized as beads by aerodynamic levitation coupled to laser heating to test the applicability of the method to this compositional range. While bubble-free lithium disilicate beads could be easily obtained, sodium and potassium silicates proved more challenging to melt without significant alkali evaporation: the final samples contained bubbles and exhibited compositional drifts compared to the starting stoichiometry, especially at high SiO₂ content. The risk of volatilization from the melts was evaluated empirically: the volatility of each oxide component scaled to the ratio between its melting temperature *T*<sub>m</sub> and the *T*<sub>m</sub> of the target composition (*r*<sub>evap</sub>), while the difference between such ratios (*Δ*<sub>evap</sub>) provided a qualitative estimation of the risk of differential evaporation. The formulated approach enables to evaluate the suitability of aerodynamic levitation synthesis for a given target glass composition: while low melting temperature and low liquidus viscosity (*η* < 10⁰ Pa s) represent the primary optimal conditions, more viscous materials can still be prepared without major compositional drifts using a more careful melting procedure, especially if *r*<sub>evap</sub> and *Δ*<sub>evap</sub> are minimized.

**Keywords:** aerodynamic levitation coupled to laser heating (ADL), alkali silicate glass, glass beads, viscosity, high-temperature evaporation

*Corresponding author: Alessio Zandonà, alessio.zandona@fau.de
# 1. Introduction

Thanks to unique properties such as viscous flow, glass-forming melts can be shaped in well-defined and complex geometries with good-quality surface finishes. These features are essential for the widespread cost-effective use of glass for the production of, for instance, hollow containers and flat window panes¹. Depending on the desired final geometry, numerous shaping methods have been developed by the glass industry, from simple casting to glass blowing and float processing². Specifically concerning the manufacturing of spherical glass beads, which have found historical applications in jewelry³ and, more recently, as optical lenses and retro-reflective paint additives⁴, several manufacturing routes have been reported (for instance⁵⁻⁷), which however exhibit only limited compositional versatility and size selectivity.

On the other hand, academic researchers in materials science and solid-state chemistry have been synthesizing glass beads for decades using aerodynamic levitation coupled to laser heating (ADL)⁸,⁹, in order to study the properties of melts at high temperature (e.g. by X-ray or neutron scattering)¹⁰, ¹¹ but also as a response to the evergrowing push towards new materials discovery¹². Indeed, this containerless method facilitates the vitrification of compositions (e.g. aluminates¹³⁻²⁰, gallates¹⁴, ²¹⁻²⁴, titanates²⁵, ²⁶, niobates²⁷, ²⁸, tungstates²⁹) which fall substantially outside the category of classically defined glass formers, due to the possibility of achieving very high melting temperatures (up to 3300 K) and fast cooling rates (~300 K s⁻¹), additionally suppressing heterogeneous crystal nucleation and avoiding potential sample-crucible reactions. These exotic compositions, both in their glassy state and after controlled crystallization, can exhibit interesting features (e.g. high refractive index and transparency, persistent luminescence, advantageous electrical and mechanical properties) which make them promising candidates for future technological applications.

Although numerous studies also reported the ADL synthesis and characterization of silicate or borate glasses and melts (for instance³⁰⁻⁴⁷), the strong volatility of some chemical components⁴⁸⁻⁵⁰ (e.g. B₂O₃ and alkali oxides) under laser irradiation still represents a major drawback of ADL-driven materials discovery, limiting its applicability within these chemical domains. Borate and silicate glasses can be easily prepared by conventional melt-quenching, but ADL was recently shown to provide a superior approach to
elucidate transition metal saturation and homogenous nucleation in aluminosilicate glasses and glass-
ceramics⁵¹⁻⁵³, again taking advantage of the high melting temperatures, fast cooling rates and suppression
of heterogeneous surface nucleation. Furthermore, it can be speculated that the shaping capabilities of ADL
may provide a cost-effective route to manufacture high-added-value optical components, especially
considering the increasing need for miniaturized imaging systems in portable electronic devices⁵⁴.

Consequently, this study aims to assess key melt parameters such as glass-forming ability, melting
point, viscosity and high-temperature evaporation tendency, to identify the optimal conditions for
reproducible glass synthesis by ADL taking binary alkali silicates as model samples. The overall analysis
is meant to facilitate an even unexperienced user in successfully approaching materials discovery and high-
temperature melt characterization by ADL, evaluating beforehand the suitability of the target compositions
and possibly minimizing the risks related to high-temperature volatilization.

2. **Experimental**

2.1 Glass synthesis

Binary silicate glasses were selected for this work to investigate the challenges of synthesizing
glasses by ADL over a broad range of melt viscosities and evaporation tendencies, thereby focusing on
simple compositions. In the following, the synthesis of nine compositions of glass by conventional melt-
quenching and/or ADL is studied: three lithium silicates, i.e. **LS2** (Li₂O·2SiO₂), **LS4** (Li₂O·4SiO₂) and **LS8**
(Li₂O·8SiO₂); three sodium silicates, i.e. **NS2** (Na₂O·2SiO₂), **NS4** (Na₂O·4SiO₂) and **NS8** (Na₂O·8SiO₂);
three potassium silicates, i.e. **KS2** (K₂O·2SiO₂), **KS4** (K₂O·4SiO₂) and **KS8** (K₂O·8SiO₂). Raw materials
for the synthesis included: silicon oxide SiO₂ (Alfa Aesar, 99.5%), lithium carbonate Li₂CO₃ (Aldrich,
99%), sodium carbonate Na₂CO₃ (Strem chemicals, 99.5+%), potassium carbonate K₂CO₃ (Fluka, 99%).
All glasses were stored in a desiccator to avoid reaction with H₂O and CO₂ from the air.

ADL was used to prepare beads of the listed nine compositions. To facilitate the analysis of the
ADL method, 3 g of LS2, NS2 and KS2 were additionally synthesized as reference materials by
conventional melt-quenching. The precursor carbonates and SiO₂ for each glass batch were suspended in
ethanol and mixed in an agate mortar; when the ethanol evaporated, the mixture was loaded into a small Pt
crucible and heated up in an electric furnace with a rate of 10 K min⁻¹ up to 1173 K. This temperature was
held for 1 h to allow for full reaction of the powder precursors. Subsequently, the samples were heated at
the same rate to 1623 K and melted for 1 h. Finally, the samples were extracted from the furnace and
quenched by rapidly immersing the bottom of the Pt crucible in water. To ensure good homogeneity, the
melting at 1623 K for 1 h was repeated after crushing each sample into fine powder. The obtained glass
shards were transparent with no observable bubbles or heterogeneities.

The above-mentioned chemical precursors were used also to prepare samples by ADL on an
experimental setup described in previous works⁵¹,⁵². A novel procedure involving the addition of a binder
(cornstarch) to a water-based slurry was tested and carefully optimized to quickly prepare numerous well-
compacted hemispherical pellets of very reproducible mass (35±5 mg). Their shape enabled stable
levitation and the achievement of containerless conditions from the beginning of the synthesis; the well-
defined starting mass favored a strict control over the synthesis parameters (e.g. cooling rate), while their
improved mechanical stability minimized material loss due to pellet breakage and supported the subsequent
evaluation of mass losses solely due to evaporation. 2 g of precursors were mixed with cornstarch (5% in
mass of the inorganic powders) and water until obtaining a slurry of suitable viscosity. A syringe was then
used to deposit small drops of this slurry on an aluminum foil, where they were left overnight to dry at room
temperature into hemispherical greens; drying was completed in an electric furnace for 2 h at 473 K to
ensure full compaction (note that cornstarch decomposes at approximately 600 K⁵⁵). Pellets prepared this
way were then placed into the ADL copper nozzle, levitated by a stream of oxygen and melted using two
CO₂ (10.6 µm) lasers with a heating protocol of ~45 s in total (Fig. 1). Gas flow rate and gas composition
were previously shown to have a strong impact on volatilization⁵⁶ and were therefore kept constant
throughout the experiments to focus solely on differences arising from the composition of the samples. The
melting process was monitored with the help of a camera, while the temperature was estimated with a
pyrometer (wavelength = 0.9 µm). In the absence of an accurate emissivity calibration for each sample,
temperature readings may vary by as much as ±100 K at the maximum laser power but still allow a consistent approach across different compositions.

The expected increasing temperature sensitivity (i.e. tendency towards high-temperature vaporization⁴⁸⁻⁵⁰) of the samples along the series LSX-NSX-KSX (X = 2, 4 or 8) was tackled using the following synthesis strategy: LSX samples were invariably prepared first, optimizing the melting parameters (temperature reading, time) to minimize their high-temperature dwell while still obtaining good-quality glass beads with (possibly) no bubbles visible to the naked eye. Then, the exact same procedure was applied to the corresponding NSX and KSX samples, as visualized on Fig. 1; note that the same temperature readings as for LSX could be achieved for NSX and KSX samples using an equal or lower laser power, supporting the reliability of the results concerning high-temperature evaporation (see below). More specifically, we performed the syntheses at maximum pyrometer readings of ~1500 °C for *MS2*, ~1700 °C for *MS4* and ~1800 °C for *MS8*. Samples prepared in this way were glassy and transparent, with a variable bubble content.

<figure><img src="image_2.png" /><figcaption>**Figure 1.** Example of time-temperature curves acquired with a 0.9 µm pyrometer during ADL synthesis of LS2, NS2 and KS2 glass beads, schematically separated into four main stages: pre-reaction, melting,</figcaption></figure>
temperature homogenization and fining, quenching. The pyrometer reading (light color shades) is noisy due to instabilities during the levitation. The signal was smoothed (thick curves) using a Savitzky-Golay filter⁵⁷ (second polynomial order). The rate of the free cooling was estimated between the beginning of the quench (1801 K at 47 s) and the end of signal detection (1070 K at 50 s).

In order to test the validity of our approach over a wider compositional range, we melted two additional samples according to the same procedure: a lithium borate LB2 (Li₂O·2B₂O₃) using Li₂CO₃ (Aldrich, 99%) and H₃BO₃ (Alfa Aesar, 99.5%) precursors and a sodium phosphate NP (Na₂O·P₂O₅) using NaH₂PO₄ (Aldrich, 99%) as a precursor. In both cases, glass beads could be easily obtained without any signs of evaporation loss, at maximal pyrometer readings of 1050 °C and 1125 °C respectively. Sample LB2 was subsequently intentionally heated to higher temperatures (up to 1200 °C) to induce high-temperature volatilization and mass loss.

## 2.2 Glass characterization

The three compositions synthesized by conventional melt-quenching (LS2, NS2 and KS2) were characterized by differential scanning calorimetry (DSC) to investigate their glass stability and glass transition temperature $T_g$, using a SETARAM Multi HTC 1600 and loading ~500 mg of powder in the Pt crucibles for each measurement. First, simple upscans were performed up to 1173 K and used to estimate glass stability according to the Hrubý method⁵⁸:

$$K_{gl} = \frac{T_c - T_g}{T_m - T_c} \qquad (\text{Eq. 1})$$

where $T_c$ stands for the crystallization onset, $T_g$ for the glass transition temperature and $T_m$ for the melting temperature. The real $T_g$ of the samples (viscosity $\eta \approx 10^{12}$ Pa s) was obtained by rate-matching measurements at 10 K min⁻¹: the glass samples were heated beyond their glass transition to achieve melt relaxation, subsequently cooled at 10 K min⁻¹ to constraint their thermal history and then measured during a second upscan at 10 K min⁻¹. During this segment, the glass transition onset ($T_{onset}$) was extracted from
the heat flow curve using the double-tangent method. As demonstrated in previous works⁵⁹⁻⁶³, rate-matching DSC measurements can be associated to viscosity η through the relation:

$$log_{10}\eta(T_{onset}) = -log_{10}|q_{c,h}| + K_{onset} \quad (Eq. 2)$$

where $q_{c,h}$ is the heating and cooling rate applied during DSC measurements and $K_{onset}$ is a constant, calibrated at 11.20(±0.15) Pa s. For $q_{c,h} = 10$ K min⁻¹, one obtains $log_{10}\eta(T_{onset}) = 11.98$ Pa s ≈ 12 Pa s.

Based on $T_g$ values obtained from DSC and data from the literature⁶¹,⁶⁴, full viscosity curves were fitted for the three compositions LS2, NS2 and KS2, using the Waterton-Mauro-Yue-Ellison-Gupta-Allan (w-MYEGA) equation⁶⁵,⁶⁶:

$$log_{10}\eta = log_{10}\eta_{\infty} + (12 - log_{10}\eta_{\infty})\frac{T_g}{T} \exp\left[\left(\frac{m}{12 - log_{10}\eta_{\infty}} - 1\right)\left(\frac{T_g}{T} - 1\right)\right] \quad (Eq. 3)$$

in which $log_{10}\eta_{\infty}$ defines viscosity at the limit of infinite temperature and $m$ the melt fragility. For the fits, only these two parameters were varied, while $T_g$ was fixed to the values obtained from DSC.

Concerning ADL synthesis, high-temperature evaporation was monitored by measuring the mass of each dried pellet (still including only the inorganic precursors and the cornstarch, assuming all H₂O was lost during drying at 200 °C) and of the respective resulting glass bead; the mass of the pellets allowed to calculate the expected bead mass (after subtracting the mass of the corn starch and of CO₂ removed during melting) and compare it to the measured one, estimating mass losses due to high-temperature evaporation. For each composition, ten pellets/beads were considered for statistics. One bead of each composition was then analyzed by Laser Ablation Inductively Coupled Plasma Mass Spectrometry (LA-ICP-MS) by adapting the analytical protocol developed at the IRAMAT-CEB for glass matrices⁶⁷. On average, the beads had a diameter of 2 mm and were polished to study a cross section of the core of the bead. The laser ablated circular spots with a diameter of 0.1 mm; 4 acquisitions were performed (1 in the center and 3 near the edges) to confirm sample homogeneity and quantify compositional drifts due to evaporation. Due to their expected higher hygroscopicity, LB2 and NP beads were measured without any polishing step, shortly after the synthesis; two subsequent ablations at the same spot were used to confirm the homogeneity of the beads between surface region and interior.
### 3. Results

To measure some key properties and support the subsequent discussion of ADL processing, glasses LS2, NS2 and KS2 were first synthesized by conventional melt-quenching. Simple DSC upscans performed at 10 K min⁻¹ on these samples revealed clear and expectable differences in glass stability, quantified through the Hrubý parameter $K_{gl}$⁵⁸ (Tab. 1): the temperature difference between glass transition and crystallization (and therefore similarly $K_{gl}$) increased substantially going from LS2 to NS2 and KS2 (Fig. 2- a). Based on the results of previous authors⁶⁸, we assumed that this higher glass stability also corresponds to a higher glass-forming ability of the respective melts.

$T_g$ values (at which viscosity $η = 10^{11.98±0.15}$ Pa s) were obtained using rate-matching DSC measurements⁵⁹⁻⁶³: they enabled to fit full viscosity curves for the three glass-forming melts (Fig. 2- b), using high-temperature viscosity data from literature⁶¹,⁶⁴. While $T_g$ increased going from LS2 to NS2 and KS2, fragility indices $m$ exhibited an opposite trend (Tab. 1), eventually making KS2 the most viscous and LS2 the least viscous liquid among the three samples. At the melting temperature $T_m$, we calculated a viscosity of $10^{1.51}$ Pa s for LS2, $10^{2.94}$ Pa s for NS2 and $10^{2.38}$ Pa s for KS2.

**Table 1.** Parameters obtained from DSC measurements and viscosity fits of the reference samples synthesized by conventional melt-quenching: $T_g$ stands for the glass transition temperature (from rate-matching DSC measurements at 10 K min⁻¹), $T_c$ for the onset of crystallization (on simple DSC upscans at 10 K min⁻¹), $T_m$ for the liquidus temperature (from literature⁶⁹⁻⁷¹), $K_{gl}$ for the glass stability parameter after Hrubý⁵⁸, $m$ for the fragility index and $log_{10}η_∞$ for the logarithmic viscosity at infinite temperature (from viscosity fits using the w-MYEGA model, Eq. 2). $log_{10}η(T_m)$ provides the viscosity at the melting temperature, calculated through the w-MYEGA fits.
<table><thead><tr><th>Sample</th><th>Composition</th><th>T<sub>g</sub><br>(K)</th><th>T<sub>c</sub><br>(K)</th><th>T<sub>m</sub><br>(K)</th><th>K<sub>gl</sub></th><th>m</th><th>log<sub>10</sub>η<sub>∞</sub><br>(η in Pa s)</th><th>log<sub>10</sub>η(T<sub>m</sub>)<br>(η in Pa s)</th></tr></thead><tbody><tr><td>LS2</td><td>Li<sub>2</sub>O·2SiO<sub>2</sub></td><td>726±5</td><td>837±5</td><td>1306</td><td>0.24±0.02</td><td>41.4±0.7</td><td>-1.5±0.1</td><td>1.5</td></tr><tr><td>NS2</td><td>Na<sub>2</sub>O·2SiO<sub>2</sub></td><td>728±5</td><td>916±5</td><td>1148</td><td>0.81±0.03</td><td>37.1±0.9</td><td>-1.8±0.2</td><td>2.9</td></tr><tr><td>KS2</td><td>K<sub>2</sub>O·2SiO<sub>2</sub></td><td>768±5</td><td>1043±5</td><td>1309</td><td>1.03±0.03</td><td>34.6±0.9</td><td>-2.2±0.3</td><td>2.4</td></tr></tbody></table>

<figure><img src="image_3.png" /><figcaption>**Figure 2.** a) Heat flow curves obtained during DSC upscans at 10 K min⁻¹ applied to samples LS2, NS2 and KS2 synthesized by conventional melt-quenching; a shaded area labeled as *T*ᵢ marks the glass transition region, while *T*<sub>c</sub> labels the onset of crystallization. b) w-MYEGA fits (fit parameters in **Table 1**) of the full viscosity curves of LS2, NS2 and KS2, based on the *T*<sub>g</sub> values determined within this work and high-temperature viscosity data from literature<sup>61, 64</sup>. Horizontal arrows signal the viscosity at *T*<sub>m</sub> for each composition.</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>**Figure 3.** (a) $r_{evap}$ (Eq. 4) and (b) $\Delta_{evap}$ (Eq. 5) parameters computed for the compositions analyzed within this work, using data from literature$^{69-71}$. Vertical arrows in the (a) panel correspond to the $\Delta_{evap}$ values plotted in (b).</figcaption></figure>

To obtain a crude prediction of the tendency towards high-temperature volatilization of the nine samples to be synthesized by ADL (LS2, LS4, LS8, NS2, NS4, NS8, KS2, KS4 and KS8), the two parameters $r_{evap}$ (Eq. 4) and $\Delta_{evap}$ (Eq. 5) are here defined as:

$$r_{evap} = \frac{T_{m,\Sigma}}{T_m} \qquad (\text{Eq. 4})$$

$$\Delta_{evap} = r_{evap,max} - r_{evap,min} \qquad (\text{Eq. 5})$$

where $T_m$ is the melting point of a given oxide component and $T_{m,\Sigma}$ the melting point of the target multicomponent glass (both obtainable from phase diagrams, see Table 2); $r_{evap,max}$ and $r_{evap,min}$ respectively stand for the highest and lowest $r_{evap}$ values among all components of the target glass. As demonstrated below, a higher $r_{evap}$ indicates an increasing tendency of a given oxide component to evaporate from the
respective multicomponent melt at high temperature. Especially if one of the melt components exhibits $r_{evap} > 0.8$ (indicative threshold based on the results of this work), $\Delta_{evap}$ can then be used to estimate the risk of evaporation-driven compositional drifts: increasing $\Delta_{evap}$ manifest an increasing risk of uneven high-temperature losses. The values for the melts analyzed within this work are summarized in Fig. 3: $r_{evap}$ was observed to generally increase with a higher $SiO_2$ content in these binary glasses, due to the rising $T_m$ of the mixtures. Alkali oxides invariably exhibited higher values as compared to $SiO_2$, with $Li_2O$ plotting between 0.7 and 1.1, $Na_2O$ between 0.8 and 1.3 and $K_2O$ between 1.0 and 1.3. The observed trends mirrored those expectable based on previous literature sources analyzing the high-temperature vaporization of simple oxides$^{48-50}$. Also, $\Delta_{evap}$ slightly increased proportionally to the $SiO_2$ content of the glasses, reaching the highest values in $K_2O$-containing samples (up to ~0.5) and the lowest in those containing $Li_2O$ (~0.1).

<table><caption>**Table 2.** Melting points $T_m$ from literature$^{69-71}$ and resulting $r_{evap}$ and $\Delta_{evap}$ parameters for the nine samples analyzed within this work.</caption><thead><tr><th rowspan="2">Sample</th><th rowspan="2">T<sub>m</sub><br>(K)</th><th colspan="2"><i>r</i><sub>evap</sub></th><th rowspan="2">Δ<sub>evap</sub></th></tr><tr><th>M<sub>2</sub>O</th><th>SiO<sub>2</sub></th></tr></thead><tbody><tr><td>LS2</td><td>1306</td><td>0.76</td><td>0.66</td><td>0.11</td></tr><tr><td>LS4</td><td>1633</td><td>0.95</td><td>0.82</td><td>0.13</td></tr><tr><td>LS8</td><td>1788</td><td>1.04</td><td>0.90</td><td>0.14</td></tr><tr><td>NS2</td><td>1148</td><td>0.82</td><td>0.58</td><td>0.24</td></tr><tr><td>NS4</td><td>1738</td><td>1.24</td><td>0.88</td><td>0.36</td></tr><tr><td>NS8</td><td>1808</td><td>1.29</td><td>0.91</td><td>0.38</td></tr><tr><td>KS2</td><td>1309</td><td>1.10</td><td>0.66</td><td>0.44</td></tr><tr><td>KS4</td><td>1248</td><td>1.05</td><td>0.63</td><td>0.42</td></tr><tr><td>KS8</td><td>1553</td><td>1.31</td><td>0.78</td><td>0.52</td></tr></tbody></table>
After this preliminary examination, ADL was used to synthesize glass beads of these nine target compositions. Due to the increasing melt viscosity inferred above, obtaining perfect bubble-free beads proved increasingly difficult moving from Li₂O- to Na₂O- and K₂O-bearing melts, as already inferable from a visual inspection of the samples (Fig. 4); a similar effect was noticed in the case of increasing SiO₂ content (e.g. in the series LS2-LS4-LS8). Despite the complexity of these phenomena, previous experiments performed both in a space laboratory and in normal gravity conditions suggest that the rotation of the droplet renders bubble escape even more challenging than in conventional melting, favoring bubble migration towards an axial position, with buoyancy playing a lesser role.⁷²⁻⁷⁴ Bubbles are expected to originate from the decomposition of cornstarch and carbonate precursors, as well as from direct injection of the levitation gas jet during the initial melting stage, when the droplet has not yet achieved a stable spherical shape.

<figure><img src="image_5.png" /><figcaption>**Figure 4.** Pictures of beads synthesized by ADL. Visible influence of silica content and different alkali oxides. The distance between the vertical black bars is 1 mm.</figcaption></figure>

The bead mass expected after decarbonation of the pellets and that of the synthesized glass beads was compared to quantify losses due to evaporation during ADL melting (Fig. 5-a); error bars on the graph are plotted according to the standard deviation of the data over ten measured beads. Note that the samples with lower content of silica were melted at lower temperatures (1800 K), while a higher melting temperature
(up to 2100 K) was required to prepare samples with lower M₂O content. Li₂O-bearing samples invariably plotted closer to the expected mass, while Na₂O- and especially K₂O-containing beads exhibited mass losses up to roughly 20%. In all cases, a lower initial content in alkali oxide (or alternatively a higher SiO₂ content) led to more noticeable mass losses. As demonstrated in Fig. 5-b, the average mass losses determined for the nine target compositions exhibited a clear correlation to the *r*<sub>evap</sub> value of the most volatile components, i.e. the alkali oxides Li₂O, Na₂O or K₂O (as expectable from previous studies on the vaporization behavior of oxides<sup>48-50</sup>).

<figure><img src="image_6.png" /><figcaption>**Figure 5.** a) Comparison between measured and expected masses of glass beads synthesized by ADL, as a function of their nominal *M*₂O (*M* = Li, Na, K) content; error bars correspond to the standard deviation over 10 measured beads. b) correlation between the average mass loss of each target composition and the *r*<sub>evap</sub> value of its most volatile component (alkali oxide *M*₂O).</figcaption></figure>

LA-ICP-MS measurements performed on one representative bead for each composition confirmed these observations (Fig. 6): Li₂O-containing beads plotted very close to the 1:1 diagonal, i.e. their measured composition was very close to the nominal one. On the contrary, those containing Na₂O and K₂O were invariably found to plot lower, signaling a non-negligible alkali loss during melting. SiO₂-rich matrices
such as NS8 and KS8 lost up to 80% of their initial alkali oxide content; these losses exhibited a correlation
to the values of Δ<sub>evap</sub> for the respective composition.

All in all, the samples exhibiting the highest mass losses and chemical drifts corresponded to those
richer in bubbles (Fig. 4): considering that a better fining could have only been achieved at higher
temperatures (i.e. at lower viscosity) or with longer high-temperature dwells (which would have aggravated
high-temperature vaporization), it is easy to see that certain compositions are intrinsically unsuitable for
the synthesis of glass beads by ADL. This concept is developed and specified in the following.

<figure><img src="image_7.png" /><figcaption>**Figure 6.** a) Comparison between nominal M<sub>2</sub>O content (M = Li, Na, K) of the nine samples synthesized by ADL and the values measured by LA-ICP-MS on representative beads; b) correlation between the M<sub>2</sub>O loss in each of the measured beads and the Δ<sub>evap</sub> value of the respective target composition.</figcaption></figure>

4. Discussion

This simple study highlights some critical aspects of the ADL method for the synthesis of oxide
glass beads, with the goal of extending its applicability to broader compositional landscapes, involving for
example highly volatile components. From the point of view of mere glass formation, this technique
exhibits unrivalled versatility: (i) its containerless conditions suppress heterogeneous nucleation of crystal
phases and avoid contamination from crucible and refractory materials; (ii) laser heating can attain up to
~3300 K, above the melting temperature of any stable oxide material; (iii) the setup enables fast cooling rates in the order of several hundreds of K s⁻¹ (depending on levitation gas, bead size and composition), facilitating the quenching of melts prone to devitrification. Considering these advantageous features, it would appear that the ADL method should invariably represent the optimal choice for the obtainment of homogeneous, bubble-free beads of a desired stoichiometry. Nevertheless, the results obtained here signal that other key melt properties contribute to determine the suitability of a given composition for ADL synthesis, which can be evaluated beforehand for a smart compositional design.

As known from conventional glass production<sup>75</sup>, fining and bubble removal can only be accomplished if the melt viscosity allows for bubble escape<sup>76</sup>. More specifically to ADL synthesis, sufficient melt fluidity is also necessary to form a sufficiently spherical droplet and obtain stable levitation on the gas jet. It is therefore apparent that melt viscosity plays a major role in determining successful ADL synthesis of bubble-free glass beads. An evaluation of viscosity at the melting temperature T<sub>m</sub> is thereby particularly revealing, since it represents the lowest temperature at which a liquid droplet can be obtained during heating, minimizing evaporation risks that could affect the sample at higher temperatures. The comparison among some representative glass formers (Fig. 7, melting temperatures<sup>69–71, 77–84</sup> and viscosity estimations<sup>61, 63, 81, 85–87</sup> from previous literature) emphasizes how the lowest viscosity possibly obtainable in a stable melt can vary substantially according to composition: while less polymerized or less strongly bonded aluminate and tellurate liquids are immediately very fluid after melting (log<sub>10</sub>η(T<sub>m</sub>) < 1), (alumino)silicate melts plot at noticeably higher viscosities. In the case of fully polymerized SiO<sub>2</sub> and GeO<sub>2</sub>, log<sub>10</sub>η(T<sub>m</sub>) values exceed 4 and sufficiently low viscosity for bubble removal can only be achieved at very high temperature after substantial mass losses, which could explain the virtually complete absence of literature on the reproducible ADL synthesis of transparent bubble-free beads of these yet very good glass formers.
<figure><img src="image_8.png" /><figcaption>**Figure 7.** Correlation between melting temperatures $T_m$ and viscosity at $T_m \log_{10}\eta(T_m)$ for a range of representative glass-forming melts, based on viscosity data from this work (LS2, NS2 and KS2) and reliable literature sources (see related text for references).</figcaption></figure>

Obviously, high viscosity at $T_m$ will force the ADL operator to increase laser power until sufficient fluidity can be achieved for homogenization and bubble escape. When dealing with viscous melts ($\log_{10}\eta(T_m) > 1$ on Fig. 7), it is therefore necessary to take into account their susceptibility towards differential high-temperature evaporation of their chemical components (i.e. $\Delta_{evap}$), which could cause compositional drifts. As also supported by the results of this work, alkali oxides are for instance more volatile than $SiO_2$ and tend to be lost during high temperature melting$^{88-90}$, leading to an overall $SiO_2$ enrichment. Although quantitative estimations of the tendency of simple oxides towards thermal vaporization are available in the literature$^{48-50}$, they are difficult to apply to multicomponent systems. Moreover, numerous studies analyzed high-temperature evaporation in melts of geological relevance$^{91-93}$, but no overarching understanding of these processes has been offered yet, especially in the case of exotic compositions. Here, the empirical parameters $r_{evap}$ and $\Delta_{evap}$ have been shown to predict with satisfactory
reliability the risk of compositional drifts during ADL synthesis, empirically identifying the most sensitive
component(s) with an alternative method to the consultation of high-temperature vaporization rates of
simple oxides⁴⁸⁻⁵⁰. Particularly when the achievement of low viscosity for bubble removal requires heating
above the *T*<sub>m</sub> of the target glass by hundreds of kelvins, the results of this work suggest that non-negligible
high-temperature evaporation should be expected for *r*<sub>evap</sub> values significantly exceeding ~0.8, although this
threshold may vary according to the chosen composition, ADL setup, levitation gas, desired final bead size
and melting procedure. For instance, a shorter high-temperature dwell may limit vaporization, though
possibly preventing satisfactory homogenization and fining. Similarly, *Δ*<sub>evap</sub> values above ~0.2 signaled a
high risk of compositional drift for the Na<sub>2</sub>O- and K<sub>2</sub>O-bearing samples synthesized within this work,
stressing the general need to minimize this parameter during compositional design. Incidentally, *Δ*<sub>evap</sub>
minimization can be obtained through the choice of (near-)eutectic compositions, which are also typically
known to represent the most favorable regions for glass formation in a phase diagram.

Extending this treatment to other compositions of possible interest for glass scientists (Fig. 8), it is
easy to see that r<sub>evap</sub> values are able to reproduce the comparatively high volatility<sup>48-50</sup> of glass former oxides
such as B<sub>2</sub>O<sub>3</sub> or TeO<sub>2</sub>. As for aluminates such as CaAl<sub>2</sub>O<sub>4</sub> and Y<sub>3</sub>Al<sub>5</sub>O<sub>12</sub>, their high melting temperature
brings the r<sub>evap</sub> of their constituting oxides to relatively high values (0.8-1): indeed, previous authors
reported non-negligible mass loss from SrO-Al<sub>2</sub>O<sub>3</sub> melts during ADL synthesis<sup>94</sup>, although no significant
compositional drifts should be expected due to the low Δ<sub>evap</sub> (vertical arrows). Note that the calculation of
r<sub>evap</sub> is expected to estimate less precisely the evaporation behavior of elements prone to oxyreduction such
as transition metals, since melting or decomposition temperatures of the respective oxides can strongly
depend on the oxidation state.
<figure><img src="image_9.png" /><figcaption>**Figure 8.** *r*<sub>evap</sub> parameters computed for some representative glass-forming substances (LB2: Li<sub>2</sub>O·2B<sub>2</sub>O<sub>3</sub>, LG2: Li<sub>2</sub>O·2GeO<sub>2</sub>, LT2: Li<sub>2</sub>O·2TeO<sub>2</sub>, NB2: Na<sub>2</sub>O·2B<sub>2</sub>O<sub>3</sub>, NG2: Na<sub>2</sub>O·2GeO<sub>2</sub>, NT2: Na<sub>2</sub>O·2TeO<sub>2</sub>, YAG: 3Y<sub>2</sub>O<sub>3</sub>·5Al<sub>2</sub>O<sub>3</sub>); vertical arrows are a graphical representation of Δ<sub>evap</sub>. Melting temperatures were obtained from previous literature<sup>69–71, 80–82, 95–100</sup>. See also Fig. 3-a for a complete symbol legend.</figcaption></figure>

To finally test the outlined approach and demonstrate the applicability of ADL synthesis to compositions including volatile components, two additional samples were prepared: LB2 (Li<sub>2</sub>O·2B<sub>2</sub>O<sub>3</sub>) and NP (Na<sub>2</sub>O·P<sub>2</sub>O<sub>5</sub>), whose key melt properties are summarized in Table 3. Due to their comparatively low melting temperature and low viscosity, both glasses could easily be prepared in the form of bubble-free beads (Fig. 9); their measured composition closely corresponded to the nominal one, ruling out the occurrence of major volatilization during laser heating. Intentional melting of LB2 at higher temperatures (~1200°C on the pyrometer reading) led instead to mass losses up to 45% and to a general enrichment of the melt in B<sub>2</sub>O<sub>3</sub>, which made evident the merely qualitative character of the estimation of volatilization tendencies using r<sub>evap</sub> and Δ<sub>evap</sub>. Although the molar loss in B<sub>2</sub>O<sub>3</sub> from the samples was substantially higher than that in Li<sub>2</sub>O (Fig. 9-b), the difference was clearly not as pronounced as expectable from the values
plotted in Fig. 8. As such, ADL users approaching the synthesis of a new composition should consider these empirical parameters as a valuable indicative tool, though being aware of their inability to quantitatively capture the subtleties of evaporation mechanism and kinetics.

<table><caption>**Table 3.** Key melt parameters for samples LB2 and NP: melting temperatures⁹⁶, ¹⁰¹, ¹⁰² *T*<sub>m</sub>, approximate viscosity¹⁰³, ¹⁰⁴ at the melting temperature *log*<sub>10</sub>*η*(*T*<sub>m</sub>), *r*<sub>evap</sub> for the respective oxide components and Δ<sub>evap</sub>.</caption><thead><tr><th>Sample</th><th>Composition</th><th><i>T</i><sub>m</sub> (K)</th><th>log<sub>10</sub>η(<i>T</i><sub>m</sub>)<br>(η in Pa s)</th><th><i>r</i><sub>evap</sub></th><th><i>r</i><sub>evap</sub></th><th><i>r</i><sub>evap</sub></th><th><i>r</i><sub>evap</sub></th><th>Δ<sub>evap</sub></th></tr></thead><tbody><tr><td>LB2</td><td>Li<sub>2</sub>O·2B<sub>2</sub>O<sub>3</sub></td><td>1190</td><td>&lt; 0</td><td>0.69</td><td>-</td><td>1.61</td><td>-</td><td>0.92</td></tr><tr><td>NP</td><td>Na<sub>2</sub>O·P<sub>2</sub>O<sub>5</sub></td><td>900</td><td>0.3</td><td>-</td><td>0.64</td><td>-</td><td>1.06</td><td>0.42</td></tr></tbody></table>

<figure><img src="image_10.png" /><figcaption>**Figure 9.** (a) Results of LA-ICP-MS measurements performed on glass beads synthesized by the ADL method for Na₂O·P₂O₅ (NP) and Li₂O·2B₂O₃ (LB2) compositions. The data points labelled as “NP, ICP” and “LB2, ICP” correspond to the average of several beads synthesized without evident signs of evaporation (pictures are provided as onsets). In the case of LB2, two beads were intentionally melted at higher</figcaption></figure>
temperatures to induce volatilization, with mass losses (ML) up to 45% of the expected mass. (b) LA-ICP-MS results for the beads that underwent mass losses up to 45%, recalculated in terms of the actual molar Li₂O and B₂O₃ content of the two samples.

## 5. Conclusions

Aerodynamic levitation coupled to laser heating represents a highly prized method for glass synthesis, new materials discovery and high-temperature in-situ melt characterization. Evaporation of volatile components during laser melting has however noticeably limited its applicability over an extended compositional landscape. This study reveals that the viscosity at the melting temperature $log_{10}\eta(T_m)$ should be critically evaluated before the synthesis: for $log_{10}\eta(T_m) < 1$, glass-forming melts will be easily obtained as bubble-free beads without major volatilization concerns. In case of more viscous melts, the empirical parameters $r_{evap}$ and $\Delta_{evap}$ can support a smart compositional design minimizing high-temperature mass loss and chemical drifts.

## Acknowledgements

Jan Baborak wishes to acknowledge the Barrande Fellowship Program coordinated by the French Institute in Prague (IFP) and the Czech Ministry of Education, Youth and Sports (MEYS). This work was supported by the specific UCT university research funding, Grant No. A2_FCHT_2022_075. Alessio Zandonà wishes to acknowledge the Deutsche Forschungsgemeinschaft (DFG), project n. 448961237, ZA 1188/1-1 and ZA 1188/2-1. All authors wish to acknowledge Bernard Gratuze from IRAMAT-CEB (UMR7065) for the LA-ICP-MS measurements.
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