Abstract
Due to the detrimental effects of boron (B) on the efficiency of silicon (Si) photovoltaic cells, complete boron removal from Si is necessary to produce solar grade Si (SoG–Si, with a maximum limit of 0.1 ppmw boron). Gas refining is a promising technique for boron removal from Si, in which the thermodynamic equilibrium never establishes. Hence, by starting from any B concentration in the melt, the required limit for SoG–Si will be achieved. This research is devoted to studying the refractory interactions’ effect with melt and the chamber atmosphere on boron removal. For this purpose, gas refining experiments were carried out in alumina and graphite crucibles with H2 and H2–3% H2O refining gases. Gas refining in Ar, He, and continuous vacuuming conditions were also carried out to study the effect of chamber atmosphere. The gas refining results are supported by the characterization of the evaporated species by molecular beam mass spectroscopy (MBMS) technique. The MBMS measurements indicated that the boron evaporation occurs by the formation of the volatile species BH x , BO y , and B z H x O y compounds. Most of these compounds are already known in the literature. However, HBO, HBOH, and AlBO (in the case of alumina refractories) were measured experimentally in this work. Results indicate that the evaporation of B in the form of AlBO x compounds leads to higher mass transfer coefficients for boron removal in alumina crucibles. Density-functional theory (DFT) and coupled cluster calculations are carried out to provide a thermodynamic database for the gaseous compounds in the H–B–O–Al system, including enthalpy, entropy, and C P values for 21 compounds.
1 Introduction
Power production by photovoltaic (PV) panels has increased almost ten times over the past decade and will continue rising in the future [1,2,3]. More than 90% of the PV panels are produced from silicon (Si) [4]. The Si for PV applications must have a purity degree of 6N (99.9999%), known as solar grade Si (SoG–Si). Among all the impurities that should be removed from Si to reach the SoG–Si, boron (B) is one of the most harmful elements to exist, which will reduce the efficiency of the PV modules. Boron exists in the metallurgical grade Si (MG–Si) in tens of ppmw, while a maximum limit of only 0.1 ppmw is acceptable for SoG–Si. Most metallic impurities can be removed from MG–Si through the directional solidification technique – the last key step in ingot production for solar cells. However, B has a high segregation coefficient (0.8), making it impossible to be separated from Si by the directional solidification technique. Therefore, reliable methods are required for B removal from Si.
The most important metallurgical methods investigated for B removal from Si applied till now are slag refining [5,6,7], plasma refining [8,9,10,11,12], and gas refining techniques [13,14,15,16]. Slag refining is a well-established process for B removal from Si, and is industrialized by Elkem®. In slag refining, the Si melts are equilibrated with slags which absorb B from the liquid Si. Teixeira and Morita [17] reported a boron removal degree as high as almost 85% applying SiO2 and CaO slag system (where slag over Si weight ratio was 2.23). However, Jakobsson and Tangstad [18] and Jakobsson [19] reported lower degrees of boron removal by the same slag system (almost 73% for slag over Si weight ratio of unity could be achieved in this technique). This means reaching to the SoG–Si limit depends on the initial B content of the melt. However, in the gas refining process, the refining gases are blown over the melt surface to remove B from liquid Si in the form of the volatile B species such as: boron oxides (B x O y ), boron hydrides (BH x ), and boron oxyhydroxides (B x O y H z ). In the gas refining process, the thermodynamic equilibrium never establishes, and B can be continuously removed from the liquid Si. This can be regarded as an advantage of gas refining process over the slag refining. In addition, the slag leftover from the slag refining process is a solid waste which then imposes costs for being disposed, especially if the environmental issues must be met in the production site. At the same time, the only by-product of the gas refining is silica fumes (SiO2), which have applications in cement and concrete production [20,21,22]. Plasma refining of Si is also a method resembling gas refining in terms of removing the B species by oxidizing and removing in the form of volatile species, but totally different in physics and power consumption is high in the process.
Boron removal by plasma technique was studied by Baba et al. [23] by applying water vapor and then was further investigated by Nakamura et al. [11] and Alemany et al. [12]. Wu et al. [24] reported the gas refining without plasma torch in an electric arc furnace with Ar–H2O–O2 gas mixtures. From 2012 the gas refining of Si by humidified hydrogen was initiated in NTNU [25,26], by applying an induction furnace and top gas blowing technique. The gas mixture of interest for the NTNU researchers has always been a combination of H2–x% H2O, which leads to high mass transfer coefficient values for B removal and then higher rates of the process. When applying oxidative gases like O2 and H2O, the surface of Si melt oxidizes, and if the surface oxide layer becomes thick, then the evaporation kinetics slow down. The surface passivation of liquid Si is studied in the oxidative plasma refining technique by Vadon et al. [27]. A right selection of the H2/H2O can prevent surface oxidation, and previous studies showed that the maximum process rate could be achieved when x = 3–4%. Safarian et al. [28] compared the effect of addition of Ar and He to the H2–4% H2O and showed that Ar addition reduces the rate of B removal while showing a better result. The mechanism of B removal from Si is mainly known by the formation of B x O y H z compounds and among them, the HBO is known to contribute to B removal from Si more than any other compound, due to its higher vapor pressure [27–29]. The following reaction is suggested for the formation of HBO:
where
The effect of gas flow rate (for H2–H2O gas mixtures) and the gas stream pattern was studied by Sortland and Tangstad [31], and Safarian et al. [30], and they showed that there is a linear relationship between the gas flow rate (Q, NL·min−1) and the mass transfer of the B removal (k B, m·s−1) process. When carrying out the gas refining process by the top blowing technique, many parameters can act on the process rate such as: gas flow rate, type of gas mixture, the distance of the nozzle from the melt surface, diameter of the nozzle compared to the melt surface diameters, and the melt interaction with the refractory holding liquid Si, all these parameters have been studied to some extent in the previous works. Among all the variables in the gas refining of Si, we study the effect of the interaction of refractory – melt and the chamber bulk gas on the kinetics of B removal. In addition to that, the gaseous species evaporating from the melt were characterized experimentally, to expand our knowledge about the Si refining process.
2 Theoretical thermodynamics of H–Al–B–O system
In order to study the thermodynamics of the system, density-functional theory (DFT) calculations were employed by using the M06-2X density functional [32] and a maug-cc-pV(T+d)Z basis set [33] employing the NWChem code [34], and the thermodynamics data for the following gaseous compounds were generated:
HBO, three isomers of HBOH (H2BO, cis-HBOH, and trans-HBOH), H2BOH, two isomers of AlBO (AlOB and AlBO), AlBO2, BO, BO2, B2O2 BH, BH2, BH3, B2O, B2O3, HOBO, HB(OH)2, B(OH)2, B(OH)3, and B2H6.
For a majority of these species high-level quantum chemistry calculations using the coupled cluster with single and double excitations and a perturbative treatment of triple excitations (CCSD(T)) method were also performed [35]. For calculating the heat of formation of some key molecular species, we followed a procedure where first the molecular geometry was optimized using CCSD(T) with the basis set aug-cc-pVQZ [36] for H, B, and O and aug-cc-pV(Q+d)Z [37] for Al using the commonly employed frozen-core approximation. For open-shell species unrestricted Hartree-Fock wavefunctions were used as reference states for the CCSD(T) calculations. Subsequently, harmonic vibrational frequencies were calculated using the same method. Using the optimized geometries, frozen-core calculations with CCSD(T) and the larger aug-cc-pV5Z, aug-cc-pV6Z [38], aug-cc-pV(5+d)Z, and aug-cc-pV(6+d)Z [37] basis sets were carried out in order to approach the complete basis set (CBS) limit. The calculated energy was further corrected for core-valence (CV) electron correlation, where not only valence but also outer core electrons (1s for H and O, 2s and 2p for Si) were correlated in the CCSD(T) calculations (using the cc-pwCVTZ, cc-pwCVQZ, and cc-pwCV5Z basis sets) [39]. Both the frozen-core and CV calculations were extrapolated to the CBS limit using the extrapolation formula E(CBS) = E(ℓ max ) + A/(ℓ max + 1/2)4 [40,41]. Finally, a first-order relativistic correction was added by employing all-electron CCSD(T) with an uncontracted cc-pVTZ [42,43] basis set and the direct perturbation theory (DPT2) method [44,45]. All coupled cluster calculations were performed using the CFOUR software package [46].
The enthalpy of formation, standard entropy, and heat capacity were calculated by standard statistical thermodynamics equations employing calculated vibrational frequencies, rigid-rotor rotational constants calculated from the optimized geometries, and experimental data on electronic fine-structure states [47]. The standard states of B and Al at 298 K are the solid state, but for practical reasons the B and Al atoms were used as reference species in the CCSD(T) calculations. We therefore employed the most accurate estimate of the heat of formation of the B and Al atoms available, to adjust the heat of formation to the correct reference value [48].
In Table 1, the enthalpies of formation, standard entropies, and heat capacities calculated with M06-2X and CCSD(T) are given together with literature data. For H2BO, cis-HBOH, trans-HBOH, AlOB, and AlBO there are no literature values of the thermodynamic quantities. In addition, the uncertainties of the literature data are very large for BH2 and B2O and fairly large for HBO, AlBO2, BO, BO2, and BH3. In these cases, it is recommended to use the calculated CCSD(T) data wherever available and otherwise the M06-2X data. However, BO2 has a specific electronic structure in which the electronic wave function has a multireference character, for which both standard DFT and coupled cluster calculations are less well-suited. This, at the very least, increases the uncertainty of the results and in certain cases makes the results non-trustworthy. Since it is possible to estimate the uncertainty in the calculated enthalpy of formation of the CCSD(T) calculations for “well-behaved” systems, the CCSD(T) results for BO2 are not included here exactly because it is not possible to make valid estimates of the uncertainty. The calculated parameters based on M06-2X and CCSD(T) are presented in the appendix section (Tables A2 and A3). By using the calculated results, the Gibbs free energy for the aforementioned gaseous compounds are calculated and presented in Figure 1. This figure indicates that the boron-oxyhydroxides have a negative value of Gibbs energy for formation over all the temperature ranges, while the boron hydrides get negative values of Gibbs energy only at elevated temperatures (for BH2 and BH3). Figure 2 compares the results generated by M06-2X and CCSD(T) for some selected species.
Thermodynamic data calculated by M06-2X, CCSD(T) [bold in brackets], and literature values (in parentheses: JANAF (italic) ([49]) and others)
Molecule |
|
S 0 (298 K)/J·kmol−1 | C p (298 K)/J·kmol−1 |
---|---|---|---|
HBO | −240.18 [−238.18 ± 5.0] (−198.32 ± 3, −210.63 ± 25a) | 202.40 [202.85] (202.62, 202.69a) | 34.64 [35.29] (35.26, 35.31a) |
H2BO | −84.08 [−69.13 ± 5.0] | 228.20 [228.49] | 41.58 [41.86] |
Cis-HBOH | −75.82 [−51.78 ± 5.0] | 231.82 [231.93] | 40.36 [40.37] |
Trans-HBOH | −80.72 [−58.68 ± 5.0] | 231.36 [231.44] | 40.18 [40.14] |
H2BOH | −291.64 [−276.79 ± 5.0] (−292.88 ± 4.2b) | 230.45 [230.47] | 41.90 [41.82] |
AlOB | −45.19 [−27.55 ± 6.7] | 256.37 [261.83] | 49.95 [50.14] |
AlBO | 3.99 [9.09 ± 6.7] | 251.53 [251.29] | 51.14 [51.06] |
AlBO2 | −547.69 [−525.22 ± 6.7] (−541.41 ± 17) | 276.92 [281.54] (269.56) | 60.81 [61.50] (66.86) |
BO | −0.02 [9.55 ± 5.0] (0 ± 8, 9.81 ± 11a, 25c) | 203.39 [203.54] (203.48, 203.47a, 203.5c) | 29.16 [29.18] (29.20, 29.20a, 29.2c) |
BO2 | −284.54 (−284.51 ± 8; −309.13 ± 20a, −300.4c) | 230.53 (229.81, 230.13a, 229.6c) | 45.21 (43.28, 43.28a, 43.0c) |
BH | 442.42 [443.23 ± 5.0] (442.67 ± 8.4; 442.7c) | 171.69 [171.76] (171.85, 171.8c) | 29.11 [29.11] (29.18, 29.2c) |
BH2 | 304.83 [324.25 ± 5.0] (200.83 ± 63; 318.29 ± 11a) | 194.02 [194.02] (180.19, 193.55a) | 34.70 [34.79] (34.03, 34.72a) |
BH3 | 86.00 [102.10 ± 5.0] (106.69 ± 10; 88 ± 10a, 89.2c) | 188.13 [188.22] (187.88, 187.69a, 188.2c) | 35.84 [35.87] (36.22, 34.78a, 36.0c) |
B2O | 155.90 [175.77 ± 5.9] (96.23 ± 105) | 241.48 [256.91] (227.75) | 47.15 [47.32] (38.41) |
B2O2 | −457.07 [−450.53 ± 5.9] (−456.81 ± 8.4; −457.73 ± 10a; −454.8c) | 247.34 [248.47] (242.60, 249.66a, 242.5c) | 59.08 [59.65] (57.30, 60.27a, 57.3c) |
B2O3 | −860.46 [−836.51 ± 5.9] (−835.96 ± 4.2; −843.8c) | 284.82 [285.87] (283.77, 279.8c) | 65.89 [66.73] (66.86, 66.9c) |
HOBO | −562.00 [−550.98 ± 5.0] (−560.66 ± 4.2; −561.9c) | 242.34 [243.01] (239.73, 240.1c) | 47.03 [47.43] (42.23, 42.2c) |
HB(OH)2 | −666.45 (−643.50 ± 8.4b) | 255.63 | 55.03 |
B(OH)2 | −446.03 (−470 ± 15) | 259.57 (249.02) | 53.71 (52.02) |
B(OH)3 | −1,026.81 (−992.28 ± 2.5; −994.1c) | 269.84 (295.237) | 71.34 (65.34) |
B2H6 | 10.35 (41.0 ± 16.7; 36.6 ± 2.0a; 36.4c) | 231.73 (233.17, 232.49a, 232.1c) | 55.44 (58.10, 57.57a, 56.7c) |

The Gibbs energy for formation of the gaseous compounds in H–Al–B–O system calculated by M06-2X.

Gibbs free energy for selected gaseous compounds calculated by M06-2X and CCSD(T).
3 Experimental procedure
3.1 Refining experiments
In this research, all the refining experiments were carried out in a vacuum induction furnace with the setup configuration presented in Figure 3. As shown in the figure, Si was melted in graphite (high density, with the properties presented by Hoseinpur and Safarian [53]) or alumina sintered (ALSINT) crucibles. The crucible used for holding material was put in a bigger graphite crucible and a thermocouple type C (W – 6% Re, W – 26% Re, protected by an alumina sheath) was placed in-between the crucibles to measure the temperature of the process. The preliminary experiments with two thermocouples, one in the inner crucible and the second one in-between the two crucibles, indicated that there is only a 2–4°C temperature difference, and hence the gas refining experiments were carried out with the thermocouple placed in-between the two crucibles. The inner crucible was charged by 213 g of Si, with a mixture of 50 wt% of polysilicon (FBR®, 8N purity) and 50% Silgrain® (HQ – micron cut; 0.04 wt% Fe, 0.09 wt% Al, 0.013 wt% Ca, 0.001 wt% Ti, 0.085 wt% C, 25 ppmw P, and 30 ppmw B). This mixture provides about 15–20 ppmw B impurity in the initial melt. Before the experiments, the chamber was vacuumed down to 5–7 Pa and flushed by Argon (6N) or Helium (6N) for 3 times. Subsequently, the power was switched on and after the material was melted, a sample was taken from the melt to record the initial composition of the melt. Then, the refining process was started by blowing the refining gas over the Si melt surface, as shown in Figure 3. Table 2 presents the experimental conditions applied for various experiments in this research. The refining gas flow was adjusted by mass flow controller during the experiment and the gas was blown over the melt surface through a quartz lance with a 2 mm nozzle and the nozzle distance to melt surface was kept as 30 mm in all the experiments. In those experiments that humidified hydrogen, which was used as the refining gas, the hydrogen flow was redirected to a gas humidifier unit and then was humidified with 3% H2O. In order to study the effect of bulk atmosphere in the furnace, in one experiment the chamber was filled with He to compare the results with the experiments where Ar was used to fill the chamber. In addition, in another experiment, the gas refining in vacuum conditions was also studied by blowing the refining gas over the melt surface while the chamber was being vacuumed continuously. In this special experiment, the pressure in the chamber was almost 5 mbar while carrying out the gas refining. Then, the gas blowing was started and several samples were taken from the melt during the refining process to track the B concertation change over time. These samples were taken by quartz tubes and later were digested in a mixture of HF and HNO3 acids, subsequently characterized by inductively coupled plasma mass spectrometry (ICP-MS; Agilent 8800 Triple Quad). When the experiments were done, we shut down the power and let the crucible to cool down by itself. Then, some samples were taken from the fumes settled on the chamber’s wall to be characterized by scanning electron microscopy (SEM).

The schematic of the furnace and gas refining set up.
The experimental conditions of the gas refining experiments
Crucibles | Alumina, graphite |
Refining Gas | H2–3% H2O/H2 |
Gas flow rate (NL·min−1) | 3 |
Chamber bulk gas atmosphere | Ar/He/vacuum |
Gas nozzle diameter (mm) | 2 |
Nozzle distance from melt surface (mm) | 30 |
Crucible inner diameter (mm) | 50 ± 1 |
Refining temperature (°C) | 1,450, 1,500, and 1,600 |
3.2 Molecular beam mass spectrometry (MBMS) characterizations
Hot gas analysis in this study was conducted using MBMS. A detailed description of the system used in this study is given by Wolf et al. [54]. For all the MBMS measurements in this study, the MBMS system has been coupled to a high-temperature reactor shown schematically in Figure 4. A sample boat made of graphite, alumina, or silica containing 2 g of a Si–B (350 ppmw) was attached to the end of an alumina rod and inserted into a tubular alumina reactor with an inner diameter of 21 mm, which was housed in a high-temperature furnace. Before running the experiment, the reactor chamber was flushed with Helium gas for 10 min to reduce the oxygen potential in the chamber, and then the furnace was switched on. The He flow to the chamber was maintained during the experiment. The furnace was maintained at a constant temperature of 1,500°C. The reactor was coupled to the sampling orifice of the MBMS device, to sample the high-temperature gases. The orifice was protruded into the furnace to maintain an elevated temperature to prevent condensation of gas phase species on the tip of the orifice. At the beginning of each experiment, the sample boat was held in the cooled zone of the reactor and a background spectrum was acquired for about 1 min. While the MBMS was kept in a constant scanning mode, the sample boat was inserted into the heated region of the reactor and the evaporated species were monitored over time. During experiments, 5% H2 in He flowed through the reactor at a flow rate of 4 NL·min−1. The residence time of released vapors in the reactor before sampling was about 0.1 s. Water steam was added after a few minutes via a vaporizer achieving humidity concentrations of 3–5% in the gas stream flowing to the reactor.
![Figure 4
Setup used for vaporization experiments, from Wolf et al. [54].](/document/doi/10.1515/htmp-2022-0011/asset/graphic/j_htmp-2022-0011_fig_004.jpg)
Setup used for vaporization experiments, from Wolf et al. [54].
Due to the relatively high gas flow necessary to minimize ambient air leaking into the reactor at the connection between furnace and MBMS, vaporization is unlikely to reach equilibrium. Therefore, the gas flow was stopped for about 20 s in some measurements to locally increase the concentration of vapor species above the sample boat. After switching on the gas again, high intensity peaks for qualitative analysis could be recorded. Because of this procedure, the present results are of a rather qualitative nature and therefore, released species were not quantified.
The mass-to-charge ratio (m/z) range of 5–100 was subjected to a preliminary scan via MBMS to determine the major compounds. The ions of interest and their corresponding m/z ratio are all mentioned in Table 3. It should be mentioned that either ions originate from gas molecules or fragmentation within the ionization region of the MS. For example, B+ can originate from any B containing gas molecule. Unfortunately, not all masses could be properly recorded due to superimposing of species with the same m/z originating from background or small amounts of ambient air. For example,
The ions of interest studied in the MBMS and their corresponding m/z ratio
Ion | m/z |
---|---|
|
10, 11 |
|
11, 12 |
|
12, 13 |
|
43, 44 |
|
13, 14 |
|
26, 27 |
|
27, 28 |
H11B18O+ | 30 |
HBOH+ | 29 |
|
36, 38 |
|
42, 43 |
|
52, 54 |
|
53, 54 |
|
68, 70 |
|
69, 70 |
4 Results and discussions
4.1 Rate of B removal in gas refining experiments
The B concertation in liquid Si was measured by ICP-MS and all the results are presented in Table A1 (in appendix section). To study the rate of B removal under experimental conditions, the first-order kinetic model was applied, presented here as follows:
where
The results from gas refining in various crucibles
Experiment code | Crucible | Temperature (°C) | Chamber atmosphere | Blowing gas |
|
---|---|---|---|---|---|
1 | Graphite | 1,500 | Ar | H2 | 0.9 |
2 | Graphite | 1,500 | Ar | H2–3% H2O | 13 |
3 | Graphite | 1,500 | He | H2–3% H2O | 17.3 |
4 | Graphite | 1,500 | Vacuuming (5 mbar) | H2–3% H2O | Apparent = 2.56 and effective = 23.3 |
5 | Alumina | 1,450 | Ar | H2 | 1.64 |
6 | Alumina | 1,500 | Ar | H2 | 4.15 |
7 | Alumina | 1,600 | Ar | H2 | 4.96 |
8 | Alumina | 1,600 | Ar | H2–3% H2O | 15.3 |
Apparent: the k B is calculated by assuming the surface of melt without impinging as the gas – melt contact area. Effective: the k B is calculated by assuming the surface of impinged point as the gas – melt contact area.
4.2 MBMS measurements
The results from the MBMS measurements are all presented in Figure 5. This figure represents the gaseous species that were detected in the gas phase when having liquid Si in quartz, graphite, and alumina boats. In Figure 5, the intensity of the detected species in each sample is normalized based on the sharpest peak. Figure 5(a) shows the B species in He – 5% H2 gas stream without any humidity added to the gas. As mentioned before, the sample was inserted into the chamber after 10 min of He – 5% H2 flushing and hence, it is expected to have oxygen partially present in the chamber. From Figure 5(a) it is clear that the major B species detected in all the samples are BH
x
compounds. However, when comparing the graphite and quartz boats, it is clear that there are more B
x
O
y
compounds with higher intensities in the case of quartz boat. As can be seen in Figure 5(a), in the case of quartz boat, the BO+
2 compound had the second highest intensity after BH2. From Figure 5(a) it is obvious that when alumina boat is applied, the new AlBO+ compound is detected by MBMS, which indicates the positive role of Si melt interaction with alumina leading to the formation of new volatile B compounds. In addition to all the B
x
H
z
, B
x
H
y
O
z
, and B
x
O
y
compounds, the B+ ion is obvious in Figure 5(a). It is worth mentioning that B has a very low vapor pressure [31] and the direct evaporation of B from Si is not assumable. The authors have already studied the vacuum evaporation for Si having P and B concertation of about 10–15 ppmw in the initial melt, and they never detected any B evaporation even in vacuum conditions. Figure 5 shows that the BH
x
compounds have the highest intensities, while the thermodynamic calculations indicated that these compounds have higher Gibbs free energy than the other B containing species. Hence, we believe that the B+ and BH
x
+ ions detected in all cases are mainly the results of fragmentation of bigger molecules in the ionization chamber of MBMS. In addition, Figure 5(b) depicts the detected gaseous species in the gas phase when humidity (3–5%) was added to the gas stream. As it is obvious from this figure that many of the B
x
O
y
peaks (in case of quartz boat) and the AlBO+ peak (in case of the alumina boat) have vanished or have lost their intensities. In the experiment with the graphite and quartz boats, it can be seen that when the humidity was added, the intensity of the compound HBOH+ was increased in both cases, but the HBOH+ compound was detected with higher intensities in the alumina case. HBOH+ is detected as a new compound in this study and previously was proved only to exist by theoretical calculations [55]. It is previously discussed and shown that the concertation of

The measured species in MBMS results: (a) He – 5% H2, (b) He – 5% H2 humidified with 3–5% H2O. (Detected oxide compounds in (a) is due to partial pressures of oxygen remaining in the chamber).
The B removal from Si melt takes place by formation of HBO compound. We can assume the formation of HBOH in gas refining through the following reaction:
However, the thermodynamics calculations presented in Figure 1 indicated that there are other molecules than HBO and HBOH having considerable negative values of Gibbs energy, such as B(OH)3, HB(OH)2, and B2O3, but none of these compounds were detected in the MBMS measurements. This could be due to the need for several elements to reach together at the melt surface and form the aforementioned molecules, which reduces the formation chance of these molecules.
Considering the discussions presented in Section 1 and here, the mechanisms of B removal from liquid Si with H2–H2O gases is schematically summarized in Figure 6. This figure shows that an important step in the process is the dissolution of the

An illustration of the gas refining process in the quartz/alumina (left) and graphite crucibles (right), summarizing the B removal mechanisms.
4.3 Effect of crucible interactions with melt on B removal
A comparison between the experiments (1) with (2) shows that when dry hydrogen was used as the refining gas, almost, no B removal happened from the liquid Si. However, with the addition of humidity to hydrogen (H2–3% H2O), the rate of B removal increased from 0.9 to 13 µm·s−1 which indicates the important role of oxidation reactions on B removal from liquid Si. This indicates that the B removal mainly takes place through the formation of B x H z O y species and not through the BH z compounds, and these results are in good agreement with the findings of Nordstrand and Tangstad [25] and Sortland and Tangstad [13].
From Table 4, it is obvious that the k B in the experiment (5) is greater than the experiment (1). Both experiments were carried out at 1,500°C and with dry H2(g), but in alumina and graphite crucibles, respectively. These results are in good agreement with the MBMS measurements where we showed that in the case of applying alumina crucibles new volatile compounds of B like AlBO+ evaporate from the melt surface, and hence the kinetics of the refining process could be accelerated in the alumina crucibles. When refining in graphite crucibles and with hydrogen gas, we can assume the B removal with BH z compounds, and when doing the refining process in the alumina crucibles, we can assume the removal in the form of B x O z , B x O z H y , and AlBO x compounds.
The effect of the temperature on B removal in the alumina crucibles could also be studied by comparing the results obtained from the experiments (5–7). It is obvious that an increase in temperature leads to an increased rate of the B removal and the value of k
B increases from 1.64 to 4.15 µm·s−1 when the temperature is increased from 1,450 to 1,500°C, which is 2.5 times. However, when the temperature is increased to 1,600°C, the k
B equals 4.96 µm·s−1. Then, beyond 1,500°C the temperature rise is no more effective for B removal. The effect of temperature is already discussed by Safarian et al. [30] indicating that when temperature increases beyond 1,500°C, silicon oxidation becomes more favorable than B oxidation reactions, leading to consumption of all the dissolved oxygen in the melt to form SiO(g). In experiment (7), the humidified hydrogen (H2–3% H2O) was applied as the refining gas and the k
B value increased to 15.3 µm·s−1. A comparison of the experiment (7) with experiment (8) makes it clear that when humidity is added to the refining gas, the rate of B removal has increased almost three times. This indicates that although the alumina crucibles can supply the dissolved
In addition, the Al dissolved from alumina crucibles was also measured and is shown in Figure 7. The following reaction can be suggested for the dissolution of Al from alumina crucible:
Figure 7 indicates that the rate of Al dissolution in the liquid Si increases with temperature and proves that when melting Si in alumina boats and crucibles, there is enough

Aluminum concertation in liquid Si over time of gas refining.
4.4 Effect of chamber gas atmosphere
By comparing the results of experiments (2–4), we can study the chamber bulk gas’ effect on B removal kinetics. From Table 4 it is evident that when the chamber bulk gas is changed to He, the kinetics of B removal has accelerated and the value of k B has increased from 13 to 17.3 µm·s−1, at the same temperature accounting for 33% increase in the process rate. The positive effect of He was already reported by Safarian et al. [28] and they showed that when H2 – 4% H2O is mixed with He, the mass transfer coefficient of the B removal process is higher than that when mixed with Ar. He has smaller molecules compared to Ar, with He and Ar having atomic radius of 0.49 and 0.88 Å, respectively. Then, assuming the same velocity for Ar and He, the momentum of Ar molecules will go higher. The Ar and He molecules will collide with the evaporated B species from the melt surface and the higher the momentum of the foreign molecule (Ar or He), the higher the chance for bouncing the B species molecules back to the melt surface. In addition, even when the B species are successfully evaporated, they should diffuse in the gas phase to take distance from melt surface and find their way out of the crucible, unless they may return to melt through a back reaction, and this slows down the overall process kinetics for B removal. Obtaining the diffusion coefficient of the gaseous B species in the gas phase is beyond the scope of this study, but by considering the diffusion coefficient relation for gas molecules presented by Chapman and Cowling [57], we can obtain a general view about the differences between He and Ar on the diffusion of the B species in the gas phase.
where D denotes the diffusion coefficient, suffixes 1 and 2 indicate gas molecule 1 and gas molecule 2, m is the mass of the molecules, and σ is the average radii of the species, σ 12 = 0.5(σ 1 + σ 2). By assuming Ar and He as the molecule 1, and any gaseous B compound as molecule 2, then from equation (6) it is obvious that the higher the mass and diameter of the gas molecules, the lower the diffusion of the B species in the gas phase. Therefore, it is completely expectable for the same B species under study to have a higher diffusion in He than Ar. In order to accelerate the diffusion of the B species in the gas phase we carried out experiment (4); however, Table 4 indicates that when carrying out the gas refining in vacuum condition, the mass transfer coefficient for B removal has reduced to 2.56 µm·s−1, which was totally opposite to our expectations. In this experiment, the chamber bulk gas was continuously vacuumed during the gas refining experiment. Figure 8 compares the melt surface in experiments (3 and 5). It is obvious from Figure 8(b) and (d) that the surface of the melt has fully impinged in the case of gas blowing in vacuum condition; however, when the chamber was in atmospheric pressure, there was no significant impinging effect on the melt surface (Figure 8[a] and [c]). Figure 8(b) and (d) also indicates that when doing the gas refining in vacuum condition there are less amounts of condensates settled on the lance and crucible compared to Ar atmosphere, and this will further be discussed in the next section.

Photographs of the crucible during the (vacuum) refining experiments. (a) and (c) Gas refining in Ar atmosphere. (b) and (d) Gas refining in vacuum.
It is worth mentioning that when carrying out the gas refining in vacuum conditions, there is almost no condensate on the lance and crucible edge. The formation of the condensates on the cold parts of the crucibles and gas lance provides practical challenges in the gas refining of Si. For example, as shown in Figure 8(a), after 60 min of the refining process, the condensates are grown from the crucible edge toward the center of the crucible, which leads to clogging the gas path toward out of the crucible, affecting the rate of the process. The fluid dynamics for melt impinging by gas blowing is already discussed and numerically simulated in refs. [58–60] and Figure 8(c) and (d) illustrates the gas fluid pattern when blowing in in gas and vacuum conditions, respectively. As shown in Figure 8(c), when the gas lance is blowing in atmospheric pressure conditions, the gas stream spreads over the melt surface. The exact fluid dynamic of the gas blowing under the experimental condition of experiment (3) is already simulated by Safarian et al. [30], and the Figure 8(c) and (d) is regenerated after their simulation results. Figure 8(d) shows the fluid pattern of gas blowing in the vacuum condition and indicates that the gas jet makes a fully impinged point on the melt surface. In the case of vacuum condition, there is less resistance due to the low pressure of the bulk gas in the chamber and this makes the velocity of the gas jet increase, leading to impinging the melt surface. As shown in Figure 8(d), when the gas jet impinges the melt surface, it splits and bounces back and then there is no further contact with the melt surface. As it is obvious in Figure 8(b), the surface area of the impinged region seems to be considerably smaller than the whole melt surface area and this means that under the conditions of experiment (5), the contact area of gas and melt is smaller than that in the other experiments. From the melt surface photograph presented in Figure 8(b), the radius of impinged point (cavity) is determined as r cav = 0.00658 m. The impinging of melt surface with gas jets is already modeled in refs. [61,62] and here we can apply the following equations to calculate the depth of the cavity formed on the melt surface.
where

The calculated geometry of the impinged point on melt surface in vacuum condition, the dimensions are presented in a right scale.
4.5 Silica fume formation in gas refining
During the gas refining experiments with humidified hydrogen, SiO(g) forms as a product of the silicon oxidation process. The SiO(g) can then react with the humidity to produce small solid particles of SiO2 and create white dust on the furnace chamber, known as silica fumes. The formation of silica fumes from the SiO gas is well discussed in the literature [26], and it could be described through the overall reaction:
The morphology of the silica fumes settled on the chamber and lance surfaces in various experiments with chamber atmosphere of Ar, He, and vacuum conditions were studied by SEM and are presented in Figures 10 and 11. Figure 10 indicates a huge difference between the sizes of the fume particles in three different experimental conditions. When He and Ar were used as the chamber bulk gas, the fume particles, settled on the chamber wall, had spherical morphology, consisting of separate spheres or several spheres attached. In addition, it is obvious from Figure 10 that the fume particles are much bigger when the chamber was filled with He gas compared to Ar and vacuum condition. The fumes settled on the chamber wall in Ar and vacuum conditions have relatively smaller sizes than in the case of He. In the case of vacuum conditions, it can be seen that some of the fume particles have grown like a comet tail. Silica fume has applications in concrete production, and the change in the morphology and size of the particles could be of interest for further study.

The SEM micrographs of the fume settled on the chamber wall: (a) He gas in the chamber, (b) Ar gas in the chamber, and (c) chamber vacuumed during the gas refining process.

The SEM micrographs of the condensates settled on the gas lance: (a) and (b) He gas in the chamber, (c) and (d) Ar gas in the chamber, and (e) and (f) vacuum condition.
Figure 11(a and b) shows that the morphology of the fumes settled on the gas lance in case of the He gas is spherical but compared to the fume settled on chamber walls (Figure 10a) have considerably smaller particle sizes. However, in the case of Ar gas, some tubular morphologies could be seen among the other spheres. In the case of the vacuum condition, however, the morphology of the fumes settled on the lance is totally different, and the fume is grown in the form of whiskers and columnar morphologies. We did not find any spherical particle in the sample collected from the lance of the experiment with vacuum condition, while the fume settled on the chamber wall was spherical.
Figure 12 represents the various mechanisms for the formation of silica fumes. As it is obvious from this figure, silica fumes could form in the gas phase without any preferential nucleation site or on the body of the lance, with a preferential growth direction. When forming in gas phase, small seeds could be formed in the gas and then growing equiaxially leading to the formation of spheres. However, if the silica fume forms by initiation on a preferential nucleation site, like the lance body, then a directional growth will form the columnar morphologies and the whisker.

The schematic illustration of the silica fume formation in gas refining of Si. (a) The equiaxed growth and (b) nucleation on surface.
Considering the nucleation and growth mechanisms shown in Figure 12, the differences in the morphologies detected in the fumes could be explained. The larger sizes of the spherical particles detected in the case of He gas (in the sample collected from the chamber wall) are in good agreement with the previous discussion about the higher diffusivities of gaseous species in He compared to Ar. Having higher diffusivity, the gaseous species (SiO and H2O) will reach the surface of the seeds faster. This leads the formation of SiO2 seeds shown in Figure 10(a) to grow larger, before settling on the chamber wall. In the vacuum condition, however, there is lower gas density above the melt, since the chamber is being vacuumed continuously and the pressure is in the range of 5–25 mbar. Then, the seeds formed in the gas phase on top of the melt will immediately reach the chamber wall, where they settle down. Then, similar to the case of Ar atmosphere, the silica fumes in vacuum condition will have smaller sizes. In this case, further growth on the spherical particles settled on the chamber can take place, leading to the comet tail morphologies detected in Figure 10, and schematically shown in Figure 12. In addition, when doing the vacuum refining in the vacuum condition, the velocity of the gas jet flowing out of the nozzle increases intensively (Figure 8(d)). When the gas jet impinges the melt surface and bounces back, it still has high velocity and hence will carry all the silica seeds away from the melt surface toward the chamber wall. However, the continuous gas stream over the outer surface of the gas lance provides the required gaseous reactants (SiO and H2O) for the formation of the silica whiskers and the columns on the gas lance. The photograph of the fumes settled on the chamber wall in the two conditions, vacuum and Ar atmosphere, are shown Figure 13. As shown on this figure, the fumes collected from the experiment carried out in vacuum condition are fluffy, while in the case of Ar the fume is a fine powder.

The photograph of the fumes collected from the chamber after gas refining. (a) In vacuum condition and (b) chamber filled with Ar gas.
5 Conclusion
Boron removal from Si for solar applications was studied in this research. Gas refining experiments were carried out with H2 and H2–3% H2O refining gas in graphite and alumina crucibles. The MBMS was applied to characterize the off-gas of the samples in graphite, alumina, and quartz boats leading to the following remarks:
Refining experiments indicated higher rates of the B removal process in the alumina crucibles compared to graphite.
Boron removal has 33% higher process rate in He atmosphere compared to Ar and 79% higher process rate when carrying out the process in vacuum condition.
MBMS measurements indicated the formation of the AlBO compound, providing higher process rates.
HBO, HBOH (in case of graphite and quartz boats) and AlBO (in case of alumina boats) were measured experimentally by the MBMS technique.
The enthalpy, entropy, and C P values for possible gaseous compounds in the H–B–Al–O system have been studied by DFT and CCSD(T) calculations.
The results show that the shape and size of the Silica fumes will change due to the chamber gas and atmospheric conditions. Silica fume is spherical in the case of Ar and He, and the particle size is larger in the case of Ar. In vacuum conditions, they change to the comet tail morphology.
Acknowledgements
The support from Elkem® Bremanger for Si material is highly acknowledged. The gas refining experiments done by the vacuum induction furnace were all carried out in NTNU and the hot gas characterizations by MBMS were carried out in Forschungszentrum Jülich. The authors appreciations go to Dr Lars Klemet Jakobsson from Elkem® in Kristiansand for his kind comments on the manuscript. UNINETT Sigma2 – the National Infrastructure for High Performance Computing and Data Storage in Norway is acknowledged for a generous grant of computer time (project NN9353K).
-
Funding information: This research was financed by the Norwegian University of Science and Technology (NTNU) and was done in cooperation with the Research Center for Sustainable Solar Cell Technology (FME SuSolTech) in Norway and the institute for energy and climate research (IEK-2), Forschungszentrum Jülich in Germany.
-
Author contributions: Arman Hoseinpur performed the experiments of gas refining and wrote the manuscript, Stefan Andersson carried out the theoretical calculations and drafted section two and corrected manuscript, Michael Müller performed the MBMS measurements, analyzed the MBMS data and corrected the manuscript, Kai Tang contributed significantly to ICP-MS measurements and revised the manuscript, Jafar Safarian supervised the research and revised the manuscript.
-
Conflict of interest: Authors state there is no conflict of interest.
Appendix
Table A1 shows the concentration of B measured by ICP-MS at various times during the gas refining process. In Tables A2 and A3, fits to the calculated thermodynamic quantities are presented, based on the M06-2X and CCSD(T) calculations, respectively. The parameters (a 1, a 2, …, a 7) are for the NASA polynomial functional form as:
The parameters are given for fits in two temperature ranges: 298–1,000 K and 1,000–3,500 K.
The concentration of boron measured by ICP–MS at various times during the gas refining
Experiment number and conditions | Refining time (t, minutes) and B concentration (CB, ppmw) | ||||
---|---|---|---|---|---|
1 (graphite, H2 in Ar, 1,500°C) | t = 0 | t = 10 | t = 33 | t = 50 | |
CB = 15.70 | CB = 15.64 | CB = 14.59 | CB = 14.62 | ||
2 (graphite, H2–3% H2O in Ar, 1,500°C) | t = 0 | t = 40 | t = 78 | t = 98 | |
CB = 9.21 | CB = 3.82 | CB = 2.32 | CB = 1.32 | ||
3 (graphite, H2–3% H2O in He, 1,500°C) | t = 0 | t = 30 | t = 65 | t = 100 | |
CB = 11.77 | CB = 6.65 | CB = 2.1 | CB = 0.9 | ||
4 (graphite, H2–3% H2O in vacuum, 1,500°C) | t = 0 | t = 30 | t = 55 | ||
CB = 11.85 | CB = 10.95 | CB = 9.44 | |||
5 (alumina, H2 in Ar, 1,450°C) | t = 0 | t = 30 | t = 60 | ||
CB = 17.18 | CB = 15.38 | CB = 14.70 | |||
6 (alumina, H2 in Ar, 1,500°C) | t = 0 | t = 10 | t = 30 | t = 52 | t = 62 |
CB = 17.07 | CB = 16.00 | CB = 13.14 | CB = 12.10 | CB = 10.33 | |
7 (alumina, H2 in Ar, 1,600°C) | t = 0 | t = 30 | t = 60 | t = 90 | t = 120 |
CB = 14.70 | CB = 10.07 | CB = 9.26 | CB = 7.75 | CB = 6.3 | |
8 (alumina, H2–3% H2O, in Ar, 1,500°C) | t = 0 | t = 20 | t = 60 | ||
CB = 17.44 | CB = 10.62 | CB = 3.59 |
Thermodynamic data (based on M06-2X calculations) as parameters for NASA polynomials
a 1 | a 2 | a 3 | a 4 | a 5 | a 6 | a 7 | |
---|---|---|---|---|---|---|---|
HBO | |||||||
298–1,000 K | 2.192686 × 1000 | 9.051491 × 10−03 | −1.007469 × 10−05 | 7.108782 × 10−09 | −2.160175 × 10−12 | −2.986665 × 1004 | 9.540324 × 1000 |
1,000–3,500 K | 3.214183 × 1000 | 4.641432 × 10−03 | −2.175393 × 10−06 | 4.850579 × 10−10 | −4.192093 × 10−14 | −3.008395 × 1004 | 4.622818 × 1000 |
H 2 BO | |||||||
298–1,000 K | 2.338867 × 1000 | 1.080959 × 10−02 | −6.917617 × 10−06 | 2.005208 × 10−09 | −1.285423 × 10−13 | −1.123348 × 1004 | 1.118782 × 1001 |
1,000–3,500 K | 3.741728 × 1000 | 7.102868 × 10−03 | −3.447383 × 10−06 | 7.891389 × 10−10 | −6.958257 × 10−14 | −1.164750 × 1004 | 3.859177 × 1000 |
Cis -HBOH | |||||||
298–1,000 K | 2.032732 × 1000 | 1.168748 × 10−02 | −8.077930 × 10−06 | 1.819725 × 10−09 | 3.526881 × 10−13 | −1.017678 × 1004 | 1.315776 × 1001 |
1,000–3,500 K | 3.962777 × 1000 | 5.961031 × 10−03 | −2.616845 × 10−06 | 5.570540 × 10−10 | −4.657031 × 10−14 | −1.066841 × 1004 | 3.341731 × 1000 |
Trans -HBOH | |||||||
298–1,000 K | 2.034096 × 1000 | 1.148565 × 10−02 | −7.475187 × 10−06 | 1.115573 × 10−09 | 6.298503 × 10−13 | −1.076126 × 1004 | 1.313388 × 1001 |
1,000–3,500 K | 3.989144 × 1000 | 5.854720 × 10−03 | −2.544610 × 10−06 | 5.377842 × 10−10 | −4.472614 × 10−14 | −1.126497 × 1004 | 3.155367 × 1000 |
H 2 BOH | |||||||
298–1,000 K | 1.551882 × 1000 | 1.228854 × 10−02 | 3.693286 × 10−08 | −8.297778 × 10−09 | 4.112447 × 10−12 | −3.607081 × 1004 | 1.527393 × 1001 |
1,000–3,500 K | 3.407264 × 1000 | 9.881576 × 10−03 | −4.487463 × 10−06 | 9.807335 × 10−10 | −8.366881 × 10−14 | −3.669478 × 1004 | 5.082490 × 1000 |
AlOB | |||||||
298–1,000 K | 4.888103 × 1000 | 4.581050 × 10−03 | −2.877943 × 10−06 | 2.602405 × 10−10 | 2.611103 × 10−13 | −7.071663 × 1003 | 1.742569 × 1000 |
1,000–3,500 K | 5.970225 × 1000 | 1.941380 × 10−03 | −1.017948 × 10−06 | 2.462068 × 10−10 | −2.260333 × 10−14 | −7.393681 × 1003 | −3.947136 × 1000 |
AlBO | |||||||
298–1,000 K | 5.307458 × 1000 | 4.067187 × 10−03 | −5.387294 × 10−06 | 4.707208 × 10−09 | −1.701416 × 10−12 | −1.243850 × 1003 | −9.993693 × 10−01 |
1,000–3,500 K | 5.715965 × 1000 | 2.113971 × 10−03 | −1.056673 × 10−06 | 2.469242 × 10−10 | −2.209826 × 10−14 | −1.339847 × 1003 | −2.965471 × 1000 |
AlBO 2 | |||||||
298–1,000 K | 3.791587 × 1000 | 1.754482 × 10−02 | −2.389140 × 10−05 | 1.727192 × 10−08 | −5.096931 × 10−12 | −6.760326 × 1004 | 7.391040 × 1000 |
1,000–3,500 K | 7.239279 × 1000 | 3.995178 × 10−03 | −2.046909 × 10−06 | 4.872488 × 10−10 | −4.422530 × 10−14 | −6.837202 × 1004 | −9.465359 × 1000 |
BO | |||||||
298–1,000 K | 3.871990 × 1000 | −2.985725 × 10−03 | 7.619758 × 10−06 | −6.277562 × 10−09 | 1.804076 × 10−12 | −1.079853 × 1003 | 3.004375 × 1000 |
1,000–3,500 K | 2.878687 × 1000 | 1.897566 × 10−03 | −9.394715 × 10−07 | 2.179074 × 10−10 | −1.938733 × 10−14 | −9.342059 × 1002 | 7.553180 × 1000 |
BO 2 | |||||||
298–1,000 K | 1.889568 × 1000 | 1.825942 × 10−02 | −2.642680 × 10−05 | 1.861302 × 10−08 | −5.177116 × 10−12 | −3.539771 × 1004 | 1.253626 × 1001 |
1,000–3,500 K | 6.059342 × 1000 | 1.902560 × 10−03 | −1.023704 × 10−06 | 2.520001 × 10−10 | −2.342658 × 10−14 | −3.630803 × 1004 | −7.752557 × 1000 |
BH | |||||||
298–1,000 K | 3.692089 × 1000 | −1.295861 × 10−03 | 2.470678 × 10−06 | −8.474909 × 10−10 | −1.187262 × 10−13 | 5.214727 × 1004 | −1.020868 × 10−01 |
1,000–3,500 K | 2.681248 × 1000 | 1.926903 × 10−03 | −8.820968 × 10−07 | 1.923252 × 10−10 | −1.628899 × 10−14 | 5.238393 × 1004 | 4.962222 × 1000 |
BH 2 | |||||||
298–1,000 K | 3.573760 × 1000 | 2.255645 × 10−03 | −1.291981 × 10−06 | 1.869105 × 10−09 | −9.248958 × 10−13 | 3.550450 × 1004 | 2.343090 × 1000 |
1,000–3,500 K | 2.617657 × 1000 | 4.453314 × 10−03 | −1.972256 × 10−06 | 4.188262 × 10−10 | −3.473053 × 10−14 | 3.577305 × 1004 | 7.350889 × 1000 |
BH 3 | |||||||
298–1,000 K | 3.507845 × 1000 | −4.731541 × 10−05 | 1.267547 × 10−05 | −1.315187 × 10−08 | 4.349392 × 10−12 | 9.211329 × 1003 | 2.199403 × 1000 |
1,000–3,500 K | 1.813296 × 1000 | 8.772426 × 10−03 | −4.069795 × 10−06 | 8.992461 × 10−10 | −7.711064 × 10−14 | 9.450423 × 1003 | 9.880622 × 1000 |
B 2 O | |||||||
298–1,000 K | 5.125271 × 1000 | 9.296838 × 10−05 | 8.772230 × 10−06 | −1.124201 × 10−08 | 4.265168 × 10−12 | 1.716147 × 1004 | −4.846355 × 10−01 |
1,000–3,500 K | 5.549808 × 1000 | 2.490519 × 10−03 | −1.311315 × 10−06 | 3.180760 × 10−10 | −2.926215 × 10−14 | 1.686821 × 1004 | −3.553158 × 1000 |
B 2 O 2 | |||||||
298–1,000 K | 3.792476 × 1000 | 1.740691 × 10−02 | −2.721236 × 10−05 | 2.297527 × 10−08 | −7.645158 × 10−12 | −5.667889 × 1004 | 3.971579 × 1000 |
1,000–3,500 K | 6.390474 × 1000 | 4.833182 × 10−03 | −2.404358 × 10−06 | 5.600885 × 10−10 | −5.001756 × 10−14 | −5.717459 × 1004 | −8.231215 × 1000 |
B 2 O 3 | |||||||
298–1,000 K | 2.814090 × 1000 | 2.561257 × 10−02 | −3.565608 × 10−05 | 2.698822 × 10−08 | −8.319591 × 10−12 | −1.052014 × 1005 | 1.194845 × 1001 |
1,000–3,500 K | 7.395180 × 1000 | 6.734240 × 10−03 | −3.403456 × 10−06 | 8.022708 × 10−10 | −7.229531 × 10−14 | −1.061972 × 1005 | −1.027722 × 1001 |
HOBO | |||||||
298–1,000 K | 2.152567 × 1000 | 1.703298 × 10−02 | −2.179824 × 10−05 | 1.496985 × 10−08 | −4.150940 × 10−12 | −3.630995 × 1004 | 1.264842 × 1001 |
1,000–3,500 K | 5.244871 × 1000 | 4.536541 × 10−03 | −1.944264 × 10−06 | 4.071948 × 10−10 | −3.367186 × 10−14 | −3.695483 × 1004 | −2.318121 × 1000 |
HB(OH) 2 | |||||||
298–1,000 K | 1.734973 × 10−02 | 2.932618 × 10−02 | −2.767929 × 10−05 | 1.226846 × 10−08 | −1.688567 × 10−12 | −8.124362 × 1004 | 2.302803 × 1001 |
1,000–3,500 K | 5.945754 × 1000 | 9.676424 × 10−03 | −4.180178 × 10−06 | 8.814966 × 10−10 | −7.331603 × 10−14 | −8.265630 × 1004 | −6.632140 × 1000 |
B(OH) 2 | |||||||
298–1,000 K | 1.287905 × 1000 | 2.410929 × 10−02 | −2.689617 × 10−05 | 1.493284 × 10−08 | −3.129964 × 10−12 | −5.489053 × 1004 | 1.776234 × 1001 |
1,000–3,500 K | 6.322698 × 1000 | 5.936437 × 10−03 | −2.390473 × 10−06 | 4.752730 × 10−10 | −3.768453 × 10−14 | −5.601149 × 1004 | −7.050924 × 1000 |
B(OH) 3 | |||||||
298–1,000 K | −8.567872 × 10−01 | 4.568938 × 10−02 | −5.703717 × 10−05 | 3.594749 × 10−08 | −8.891439 × 10−12 | −1.248345 × 1005 | 2.594829 × 1001 |
1,000–3,500 K | 8.739200 × 1000 | 9.130390 × 10−03 | −3.690762 × 10−06 | 7.378861 × 10−10 | −5.887490 × 10−14 | −1.268972 × 1005 | −2.092446 × 1001 |
B 2 H 6 | |||||||
298–1,000 K | 3.771767 × 10−01 | 2.192913 × 10−02 | 7.654154 × 10−08 | −1.131216 × 10−08 | 4.939286 × 10−12 | 1.770757 × 1002 | 1.926986 × 1001 |
1,000–3,500 K | 2.200759 × 1000 | 2.246729 × 10−02 | −1.090734 × 10−05 | 2.497568 × 10−09 | −2.202619 × 10−13 | −6.746032 × 1002 | 8.313307 × 1000 |
Thermodynamic data (based on CCSD(T) calculations) as parameters for NASA polynomials
a 1 | a 2 | a 3 | a 4 | a 5 | a 6 | a 7 | |
---|---|---|---|---|---|---|---|
HBO | |||||||
298–1,000 K | 2.204674 × 1000 | 9.511337 × 10−03 | −1.111546 × 10−05 | 8.031437 × 10−09 | −2.461458 × 10−12 | −2.973189 × 1004 | 9.427524 × 1000 |
1,000–3,500 K | 3.350674 × 1000 | 4.516351 × 10−03 | −2.125080 × 10−06 | 4.752700 × 10−10 | −4.117008 × 10−14 | −2.997224 × 1004 | 3.924689 × 1000 |
H 2 BO | |||||||
298–1,000 K | 2.398786 × 1000 | 1.068061 × 10−02 | −6.758193 × 10−06 | 1.971156 × 10−09 | −1.555221 × 10−13 | −9.448668 × 1003 | 1.091219 × 1001 |
1,000–3,500 K | 3.781941 × 1000 | 7.102937 × 10−03 | −3.463388 × 10−06 | 7.954741 × 10−10 | −7.031671 × 10−14 | −9.864376 × 1003 | 3.658347 × 1000 |
Cis -HBOH | |||||||
298–1,000 K | 2.010623 × 1000 | 1.177298 × 10−02 | −8.074977 × 10−06 | 1.730109 × 10−09 | 3.970424 × 10−13 | −7.282468 × 1003 | 1.327190 × 1001 |
1,000–3,500 K | 3.979889 × 1000 | 5.981595 × 10−03 | −2.639650 × 10−06 | 5.642779 × 10−10 | −4.733128 × 10−14 | −7.787455 × 1003 | 3.241731 × 1000 |
Trans -HBOH | |||||||
298–1,000 K | 2.013771 × 1000 | 1.151420 × 10−02 | −7.339242 × 10−06 | 9.032882 × 10−10 | 7.158498 × 10−13 | −8.107052 × 1003 | 1.324632 × 1001 |
1,000–3,500 K | 3.991013 × 1000 | 5.895086 × 10−03 | −2.577275 × 10−06 | 5.472420 × 10−10 | −4.568047 × 10−14 | −8.620708 × 1003 | 3.134805 × 1000 |
H 2 BOH | |||||||
298–1,000 K | 1.547553 × 1000 | 1.216517 × 10−02 | 5.124492 × 10−07 | −8.789351 × 10−09 | 4.278505 × 10−12 | −3.428123 × 1004 | 1.532063 × 1001 |
1,000–3,500 K | 3.390419 × 1000 | 9.968311 × 10−03 | −4.550637 × 10−06 | 9.984243 × 10−10 | −8.542722 × 10−14 | −3.491191 × 1004 | 5.147095 × 1000 |
AlOB | |||||||
298–1,000 K | 4.920185 × 1000 | 4.483624 × 10−03 | −2.540733 × 10−06 | −1.751085 × 10−10 | 4.411304 × 10−13 | −4.957617 × 1003 | 2.234465 × 1000 |
1,000–3,500 K | 6.023645 × 1000 | 1.881659 × 10−03 | −9.894724 × 10−07 | 2.398008 × 10−10 | −2.204734 × 10−14 | −5.288261 × 1003 | −3.584142 × 1000 |
AlBO | |||||||
298–1,000 K | 5.278695 × 1000 | 4.016536 × 10−03 | −4.785272 × 10−06 | 3.875755 × 10−09 | −1.366362 × 10−12 | −6.237499 × 1002 | −8.694788 × 10−01 |
1,000–3,500 K | 5.769408 × 1000 | 2.080851 × 10−03 | −1.051079 × 10−06 | 2.475126 × 10−10 | −2.227909 × 10−14 | −7.528781 × 1002 | −3.316339 × 1000 |
AlBO 2 | |||||||
298–1,000 K | 3.945705 × 1000 | 1.717656 × 10−02 | −2.332997 × 10−05 | 1.681781 × 10−08 | −4.954623 × 10−12 | −6.493380 × 1004 | 7.157441 × 1000 |
1,000–3,500 K | 7.347670 × 1000 | 3.879522 × 10−03 | −1.993551 × 10−06 | 4.755260 × 10−10 | −4.322536 × 10−14 | −6.569610 × 1004 | −9.493774 × 1000 |
BO | |||||||
298–1,000 K | 3.884928 × 1000 | −3.201944 × 10−03 | 8.507345 × 10−06 | −7.339146 × 10−09 | 2.209619 × 10−12 | 7.045289 × 1001 | 2.982897 × 1000 |
1,000–3,500 K | 2.940350 × 1000 | 1.854292 × 10−03 | −9.287805 × 10−07 | 2.173253 × 10−10 | −1.946645 × 10−14 | 1.890463 × 1002 | 7.208263 × 1000 |
BH | |||||||
298–1,000 K | 3.713848 × 1000 | −1.477944 × 10−03 | 2.971175 × 10−06 | −1.338830 × 10−09 | 4.552086 × 10−14 | 5.224325 × 1004 | −1.822718 × 10−01 |
1,000–3,500 K | 2.693290 × 1000 | 1.938478 × 10−03 | −8.967747 × 10−07 | 1.972295 × 10−10 | −1.682423 × 10−14 | 5.247342 × 1004 | 4.888887 × 1000 |
BH 2 | |||||||
298–1,000 K | 3.558525 × 1000 | 2.406046 × 10−03 | −1.587764 × 10−06 | 2.155872 × 10−09 | −1.032333 × 10−12 | 3.784084 × 1004 | 2.396170 × 1000 |
1,000–3,500 K | 2.637682 × 1000 | 4.463811 × 10−03 | −1.988762 × 10−06 | 4.244878 × 10−10 | −3.535214 × 10−14 | 3.809991 × 1004 | 7.227696 × 1000 |
BH 3 | |||||||
298–1,000 K | 3.529327 × 1000 | −2.150277 × 10−04 | 1.314701 × 10−05 | −1.356482 × 10−08 | 4.465672 × 10−12 | 1.114532 × 1004 | 2.119366 × 1000 |
1,000–3,500 K | 1.821523 × 1000 | 8.831680 × 10−03 | −4.122229 × 10−06 | 9.151737 × 10−10 | −7.877142 × 10−14 | 1.137521 × 1004 | 9.813695 × 1000 |
B 2 O | |||||||
298–1,000 K | 5.210220 × 1000 | −2.958266 × 10−04 | 9.518793 × 10−06 | −1.189647 × 10−08 | 4.480348 × 10−12 | 1.953675 × 1004 | 9.747341 × 10−01 |
1,000–3,500 K | 5.562765 × 1000 | 2.474265 × 10−03 | −1.302851 × 10−06 | 3.160382 × 10−10 | −2.907563 × 10−14 | 1.925514 × 1004 | −1.763733 × 1000 |
B 2 O 2 | |||||||
298–1,000 K | 4.042288 × 1000 | 1.610861 × 10−02 | −2.408586 × 10−05 | 1.990104 × 10−08 | −6.582318 × 10−12 | −5.593133 × 1004 | 2.957229 × 1000 |
1,000–3,500 K | 6.536833 × 1000 | 4.727580 × 10−03 | −2.375651 × 10−06 | 5.574733 × 10−10 | −5.005675 × 10−14 | −5.644265 × 1004 | −8.932933 × 1000 |
B 2 O 3 | |||||||
298–1,000 K | 2.973091 × 1000 | 2.521099 × 10−02 | −3.470911 × 10−05 | 2.599687 × 10−08 | −7.963295 × 10−12 | −1.023566 × 1005 | 1.125446 × 1001 |
1,000–3,500 K | 7.579366 × 1000 | 6.562628 × 10−03 | −3.334145 × 10−06 | 7.888628 × 10−10 | −7.128083 × 10−14 | −1.033735 × 1005 | −1.117347 × 1001 |
HOBO | |||||||
298–1,000 K | 2.295688 × 1000 | 1.643733 × 10−02 | −2.058085 × 10−05 | 1.387339 × 10−08 | −3.790272 × 10−12 | −6.752667 × 1004 | 1.204597 × 1001 |
1,000–3,500 K | 5.297016 × 1000 | 4.509779 × 10−03 | −1.941185 × 10−06 | 4.079875 × 10−10 | −3.383282 × 10−14 | −6.816239 × 1004 | −2.529394 × 1000 |
References
[1] Wilson, G. M., M. Al-Jassim, W. K. Metzger, S. W. Glunz, P. Verlinden, G. Xiong, et al. The 2020 photovoltaic technologies roadmap. Journal of Physics D: Applied Physics, Vol. 53, No. 49, 2020, id. 493001. 10.1088/1361-6463/ab9c6a.Search in Google Scholar
[2] IRENA. Future of Solar Photovoltaic: Deployment, Investment, Technology, Grid Integration and Socio-Economic Aspects, 2019.Search in Google Scholar
[3] Yang, D. Handbook of photovoltaic silicon, handbook of photovoltaic silicon, Springer Berlin Heidelberg, Berlin, Heidelberg, 2019, pp. 1–841.10.1007/978-3-662-56472-1_1Search in Google Scholar
[4] Philips, D. S. and W. Warmuth. Photovoltaics report. PSE Conferences and Consulting Gmbh, Freiburg, 2019.Search in Google Scholar
[5] Thomas, S., M. Barati, and K. Morita. A review of slag refining of silicon alloys. Jom, Vol. 73, No. 1, 2021, pp. 282–292. 10.1007/s11837-020-04474-0.Search in Google Scholar
[6] Safarian, J. Thermochemical aspects of boron and phosphorus distribution between silicon and BaO-SiO2 and CaO-BaO-SiO2 slags. Silicon, Vol. 11, No. 1, 2019, pp. 437–451. 10.1007/s12633-018-9919-8.Search in Google Scholar
[7] Hosseinpour, A. and L. Tafaghodi Khajavi. Phosphorus removal from Si-Fe alloy using SiO2-Al2O3-CaO slag. Metallurgical and Materials Transactions B, Vol. 50, No. 4, 2019, pp. 1773–1781. 10.1007/s11663-019-01586-0.Search in Google Scholar
[8] Baek, S. H., H. Lee, D. J. Min, S. J. Choi, B. M. Moon, and H. D. Jung. Novel recycling method for boron removal from silicon by thermal plasma treatment coupled with steam and hydrogen gases. Metals, Vol. 7, No. 10, 2017, id. 401. 10.3390/met7100401.Search in Google Scholar
[9] Yvon, A., E. Fourmond, C. Ndzogha, Y. Delannoy, C. Trassy, A. Yvon, et al. Inductive plasma process for refining of solar grade silicon. EPM 2003 4th International Conference on Electromag- Netic Processing of Materials, 2011, 125–130.Search in Google Scholar
[10] Imler, W. R., R. E. Haun, R. A. Lampson, M. Charles, and P. Meese. Efficacy of plasma arc treatment for the reduction of boron in the refining of solar-grade silicon. Conference Record of the IEEE Photovoltaic Specialists Conference, Vol. 9718, No. 1, 2011, pp. 003435–003439. 10.1109/PVSC.2011.6186685.Search in Google Scholar
[11] Nakamura, N., H. Baba, Y. Sakaguchi, S. Hiwasa, and Y. Kato. Boron removal in molten silicon with steam added plasma melting method. Journal of the Japan Institute of Metals, Vol. 67, No. 10, 2003, pp. 583–589. 10.2320/jinstmet1952.67.10_583.Search in Google Scholar
[12] Alemany, C., C. Trassy, B. Pateyron, K.-I. Li, and Y. Delannoy. Refining of metallurgical-grade silicon by inductive plasma. Solar Energy Materials and Solar Cells, Vol. 72, No. 1–4, 2002, pp. 41–48. 10.1016/S0927-0248(01)00148-9.Search in Google Scholar
[13] Sortland, Ø. S. and M. Tangstad. Boron removal from silicon melts by H2O/H2 gas blowing: Mass transfer in gas and melt. Metallurgical and Materials Transactions E, Vol. 1, No. 3, 2014, pp. 211–225. 10.1007/s40553-014-0021-x.Search in Google Scholar
[14] Chen, H., X. Yuan, K. Morita, Y. Zhong, X. Ma, Z. Chen, et al. Reaction mechanism and kinetics of boron removal from molten silicon via CaO-SiO2-CaCl2 slag treatment and ammonia injection. Metallurgical and Materials Transactions B: Process Metallurgy and Materials Processing Science, Vol. 50, No. 5, 2019, pp. 2088–2094. 10.1007/s11663-019-01639-4.Search in Google Scholar
[15] Jiang, W., W. Yu, H. Qin, Y. Xue, C. Li, and X. Lv. Boron removal from silicon by hydrogen assistant during the electromagnetic directional solidification of Al–Si alloys. International Journal of Hydrogen Energy, Vol. 44, No. 26, 2019, pp. 13502–13508. 10.1016/j.ijhydene.2019.03.248.Search in Google Scholar
[16] Chen, Z., Y. You, and K. Morita. Exploration of boron removal from molten silicon by introducing oxygen resources into ammonia blowing treatment. Canadian Metallurgical Quarterly, Vol. 58, No. 1, 2019, pp. 82–88. 10.1080/00084433.2018.1507781.Search in Google Scholar
[17] Teixeira, L. A. V. and K. Morita. Removal of boron from molten silicon using CaO–SiO2 based slags. ISIJ International, Vol. 49, No. 6, 2009, pp. 783–787. 10.2355/isijinternational.49.783.Search in Google Scholar
[18] Jakobsson, L. K. and M. Tangstad. Thermodynamics of boron removal from silicon using CaO-MgO-Al2O3-SiO2 slags. Metallurgical and Materials Transactions B, Vol. 49, No. 4, 2018, pp. 1699–1708. 10.1007/s11663-018-1250-7.Search in Google Scholar
[19] Jakobsson, L. K. Distribution of boron between silicon and CaO–SiO2, MgO–SiO2, CaO–MgO–SiO2 and CaO–Al2O3–SiO2 slags at 1,600°C. [PhD thesis]. Norwegian University of Science and Technology (NTNU), 2013. http://hdl.handle.net/11250/249460.Search in Google Scholar
[20] Bayraktar, O. Y. Possibilities of disposing silica fume and waste glass powder, which are environmental wastes, by using as a substitute for portland cement. Environmental Science and Pollution Research, Vol. 28, 2021, pp. 16843–16854. 10.1007/s11356-020-12195-9.Search in Google Scholar
[21] Golewski, G. L. and D. M. Gil. Studies of fracture toughness in concretes containing fly ash and silica fume in the first 28 days of curing. Materials, Vol. 14, No. 2, 2021, pp. 1–21. 10.3390/ma14020319.Search in Google Scholar
[22] Vikan, H. and H. Justnes. Rheology of cementitious paste with silica fume or limestone. Cement and Concrete Research, Vol. 37, No. 11, 2007, pp. 1512–1517. 10.1016/j.cemconres.2007.08.012.Search in Google Scholar
[23] Baba, H., N. Yuge, Y. Sakaguchi, M. Fukai, F. Aratani, and Y. Habu. Removal of boron from molten silicon by argon-plasma mixed with water vapor. Tenth E.C. Photovoltaic Solar Energy Conference, Springer Netherlands, Dordrecht, 1991, pp. 286–289.10.1007/978-94-011-3622-8_72Search in Google Scholar
[24] Wu, J.-J., W.-H. Ma, B. Yang, Y.-N. Dai, and K. Morita. Boron removal from metallurgical grade silicon by oxidizing refining. Transactions of Nonferrous Metals Society of China (English Edition), Vol. 19, No. 2, 2009, pp. 463–467. 10.1016/S1003-6326(08)60296-4.Search in Google Scholar
[25] Nordstrand, E. F. and M. Tangstad. Removal of boron from silicon by moist hydrogen gas. Metallurgical and Materials Transactions B, Vol. 43, No. 4, 2012, pp. 814–822. 10.1007/s11663-012-9671-1.Search in Google Scholar
[26] Næss, M. K., G. Tranell, J. E. Olsen, N. E. Kamfjord, and K. Tang. Mechanisms and kinetics of liquid silicon oxidation during industrial refining. Oxidation of Metals, Vol. 78, No. 3–4, 2012, pp. 239–251. 10.1007/s11085-012-9303-9.Search in Google Scholar
[27] Vadon, M., Ø. Sortland, M. Tangstad, G. Chichignoud, and Y. Delannoy. Passivation threshold for the oxidation of liquid silicon and thermodynamic non-equilibrium in the gas phase. Metallurgical and Materials Transactions B, Vol. 49, No. 6, 2018, pp. 3330–3342. 10.1007/s11663-018-1381-x.Search in Google Scholar
[28] Safarian, J., C. Sanna, and G. Tranell. Boron removal from silicon by moisturized gases. 33rd European Photovoltaic Solar Energy Conference and Exhibition BORON, Vol. 2, No. 7491, 2016, pp. 476–479.Search in Google Scholar
[29] Altenberend, J., G. Chichignoud, and Y. Delannoy. Study of mass transfer in gas blowing processes for silicon purification. Metallurgical and Materials Transactions E, Vol. 4, No. 1, 2017, pp. 41–50. 10.1007/s40553-016-0105-x.Search in Google Scholar
[30] Safarian, J., K. Tang, J. E. Olsen, S. Andersson, G. Tranell, and K. Hildal. Mechanisms and kinetics of boron removal from silicon by humidified hydrogen. Metallurgical and Materials Transactions B, Vol. 47, No. 2, 2016, pp. 1063–1079. 10.1007/s11663-015-0566-9.Search in Google Scholar
[31] Safarian, J. and M. Tangstad. Vacuum refining of molten silicon. Metallurgical and Materials Transactions B, Vol. 43, No. 6, 2012, pp. 1427–1445. 10.1007/s11663-012-9728-1.Search in Google Scholar
[32] Zhao, Y. and D. G. Truhlar. The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other function. Theoretical Chemistry Accounts, Vol. 120, No. 1–3, 2008, pp. 215–241. 10.1007/s00214-007-0310-x.Search in Google Scholar
[33] Papajak, E. and D. G. Truhlar. Efficient diffuse basis sets for density functional theory. Journal of Chemical Theory and Computation, Vol. 6, No. 3, 2010, pp. 597–601. 10.1021/CT900566X.Search in Google Scholar PubMed
[34] Valiev, M., E. J. Bylaska, N. Govind, K. Kowalski, T. P. Straatsma, H. J. J. van Dam, et al. NWChem: A comprehensive and scalable open-source solution for large scale molecular simulations. Computer Physics Communications, Vol. 181, No. 9, 2010, pp. 1477–14789. 10.1016/J.CPC.2010.04.018.Search in Google Scholar
[35] Bartlett, R. J. and M. Musiał. Coupled-cluster theory in quantum chemistry. Reviews of Modern Physics, Vol. 79, No. 1, 2007, pp. 291–352. 10.1103/RevModPhys.79.291.Search in Google Scholar
[36] Kendall, R. A., T. H. Dunning, and R. J. Harrison. Electron affinities of the first-row atoms revisited. Systematic basis sets and wave functions. The Journal of Chemical Physics, Vol. 96, No. 9, 1992, pp. 6796–6806. 10.1063/1.462569.Search in Google Scholar
[37] Dunning, T. H., K. A. Peterson, and A. K. Wilson. Gaussian basis sets for use in correlated molecular calculations. X. The atoms aluminum through argon revisited. The Journal of Chemical Physics, Vol. 114, No. 21, 2001, pp. 9244–9253. 10.1063/1.1367373.Search in Google Scholar
[38] van Mourik, T. and T. H. Dunning. Gaussian basis sets for use in correlated molecular calculations. VIII. Standard and augmented sextuple zeta correlation consistent basis sets for aluminum through argon. International Journal of Quantum Chemistry, Vol. 76, No. 2, 2000, pp. 205–221. 10.1002/(SICI)1097-461X(2000)76:2##205:AID-QUA10$$3.0.CO;2-C.Search in Google Scholar
[39] Peterson, K. A. and T. H. Dunning. Accurate correlation consistent basis sets for molecular core–valence correlation effects: the second row atoms Al–Ar, and the first row atoms B–Ne revisited. The Journal of Chemical Physics, Vol. 117, No. 23, 2002, pp. 10548–10560. 10.1063/1.1520138.Search in Google Scholar
[40] Feller, D., K. A. Peterson, and J. Grant Hill. On the effectiveness of CCSD(T) complete basis set extrapolations for atomization energies. The Journal of Chemical Physics, Vol. 135, No. 4, 2011, id. 044102. 10.1063/1.3613639.Search in Google Scholar
[41] Martin, J. M. L. Ab initio total atomization energies of small molecules - towards the basis set limit. Chemical Physics Letters, Vol. 259, No. 5–6, 1996, pp. 669–678. 10.1016/0009-2614(96)00898-6.Search in Google Scholar
[42] Dunning, T. H. Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen. The Journal of Chemical Physics, Vol. 90, No. 2, 1989, pp. 1007–1023. 10.1063/1.456153.Search in Google Scholar
[43] Woon, D. E. and T. H. Dunning. Gaussian basis sets for use in correlated molecular calculations. III. The atoms aluminum through argon. The Journal of Chemical Physics, Vol. 98, No. 2, 1993, pp. 1358–1371. 10.1063/1.464303.Search in Google Scholar
[44] Klopper, W. Simple recipe for implementing computation of first-order relativistic corrections to electron correlation energies in framework of direct perturbation theory. Journal of Computational Chemistry, Vol. 18, No. 1, 1997, pp. 20–27. 10.1002/(SICI)1096-987X(19970115)18:1##20:AID-JCC3$$3.0.CO;2-1.Search in Google Scholar
[45] Stopkowicz, S. and J. Gauss. Relativistic corrections to electrical first-order properties using direct perturbation theory. The Journal of Chemical Physics, Vol. 129, No. 16, 2008, id. 164119. 10.1063/1.2998300.Search in Google Scholar
[46] Matthews, D. A., L. Cheng, M. E. Harding, F. Lipparini, S. Stopkowicz, T.-C. Jagau, et al. Coupled-cluster techniques for computational chemistry: the CFOUR program package. The Journal of Chemical Physics, Vol. 152, No. 21, 2020, id. 214108. 10.1063/5.0004837.Search in Google Scholar
[47] McQuarrie, D. A. and J. D. Simon. Molecular thermodynamics, University Science Books, Sausalito (California), 1999.Search in Google Scholar
[48] Karton, A. and J. M. L. Martin. Heats of formation of beryllium, boron, aluminum, and silicon re-examined by means of W4 theory. The Journal of Physical Chemistry A, Vol. 111, No. 26, 2007, pp. 5936–5944. 10.1021/jp071690x.Search in Google Scholar
[49] Chase, M. W. NIST-JANAF termochemical tables. Journal of Physical and Chemical Reference Data. Monograph, Vol. 9, 1998, id. 1.Search in Google Scholar
[50] Gurvich, L. V. and I. V. Veyts. Thermodynamic Properties of Individual Substances, Hemisphere Publication, New York, 1989.Search in Google Scholar
[51] Porter, R. F. and S. K. Gupta. Heats of formation of gaseous H2BOH and HB(OH)2. The Journal of Physical Chemistry, Vol. 68, No. 9, 1964, pp. 2732–2733. 10.1021/j100791a511.Search in Google Scholar
[52] Cox, J., D. D. Wagman, and V. Medvedev. CODATA Key Values for Thermodynamics, Hemisphere Publication, New York, 1989.Search in Google Scholar
[53] Hoseinpur, A. and J. Safarian. Mechanisms of graphite crucible degradation in contact with Si–Al melts at high temperatures and vacuum conditions. Vacuum, Vol. 171, 2020, id. 108993. 10.1016/j.vacuum.2019.108993.Search in Google Scholar
[54] Wolf, K. J., A. Smeda, M. Müller, and K. Hilpert. Investigations on the influence of additives for SO2 reduction during high alkaline biomass combustion. Energy and Fuels, Vol. 19, No. 3, 2015, pp. 820–824. 10.1021/ef040081a.Search in Google Scholar
[55] Sakai, S. and K. D. Jordan. Structures and vibrational frequencies of HBeOH, HBOH, HCOH, HMgOH, HAlOH, and HSiOH. Chemical Physics Letters, Vol. 130, No. 1–2, 1986, pp. 103–110. 10.1016/0009-2614(86)80434-1.Search in Google Scholar
[56] Safarian, J., K. Tang, K. Hildal, and G. Tranell. Boron removal from silicon by humidified gases. Metallurgical and Materials Transactions E, Vol. 1, No. 1, 2014, pp. 41–47. 10.1007/s40553-014-0007-8.Search in Google Scholar
[57] Chapman, S. and T. G. Cowling. The mathematical theory of non-uniform gases, D. Burnet, Ed., Cambridge University Press, Cambridge, 1991, pp. 93–96.Search in Google Scholar
[58] Muñoz-Esparza, D., J. M. Buchlin, K. Myrillas, and R. Berger. Numerical investigation of impinging gas jets onto deformable liquid layers. Applied Mathematical Modelling, Vol. 36, No. 6, 2012, pp. 2687–2700. 10.1016/j.apm.2011.09.052.Search in Google Scholar
[59] Nguyen, A. V. and G. M. Evans. Computational fluid dynamics modelling of gas jets impinging onto liquid pools. Applied Mathematical Modelling, Vol. 30, No. 11, 2006, pp. 1472–1484. 10.1016/j.apm.2006.03.015.Search in Google Scholar
[60] Standish, N. and Q. L. He. Drop generation due to an in the steelmaking vessel impinging jet and the effect of bottom blowing in the steel making vessel. ISIJ International, Vol. 29, No. 6, 1984, pp. 455–461. 10.2355/isijinternational.29.455.Search in Google Scholar
[61] Visuri, V.-V., M. Järvinen, J. Savolainen, P. Sulasalmi, E.-P. Heikkinen, and T. Fabritius. A mathematical model for the reduction stage of the AOD process. Part II: model validation and results. ISIJ International, Vol. 53, No. 4, 2013, pp. 613–621. 10.2355/isijinternational.53.613.Search in Google Scholar
[62] Visuri, V.-V., M. Järvinen, P. Sulasalmi, E.-P. Heikkinen, J. Savolainen, and T. Fabritius. A mathematical model for the reduction stage of the AOD process. Part I: derivation of the model. ISIJ International, Vol. 53, No. 4, 2013, pp. 603–612. 10.2355/isijinternational.53.603.Search in Google Scholar
[63] Koria, S. C. and K. W. Lange. Penetrability of impinging gas jets in molten steel bath. Steel Research, Vol. 58, No. 9, 1987, pp. 421–426. 10.1002/srin.198700241.Search in Google Scholar
© 2022 Arman Hoseinpur et al., published by De Gruyter
This work is licensed under the Creative Commons Attribution 4.0 International License.
Articles in the same Issue
- Research Articles
- Numerical and experimental research on solidification of T2 copper alloy during the twin-roll casting
- Discrete probability model-based method for recognition of multicomponent combustible gas explosion hazard sources
- Dephosphorization kinetics of high-P-containing reduced iron produced from oolitic hematite ore
- In-phase thermomechanical fatigue studies on P92 steel with different hold time
- Effect of the weld parameter strategy on mechanical properties of double-sided laser-welded 2195 Al–Li alloy joints with filler wire
- The precipitation behavior of second phase in high titanium microalloyed steels and its effect on microstructure and properties of steel
- Development of a huge hybrid 3D-printer based on fused deposition modeling (FDM) incorporated with computer numerical control (CNC) machining for industrial applications
- Effect of different welding procedures on microstructure and mechanical property of TA15 titanium alloy joint
- Single-source-precursor synthesis and characterization of SiAlC(O) ceramics from a hyperbranched polyaluminocarbosilane
- Carbothermal reduction of red mud for iron extraction and sodium removal
- Reduction swelling mechanism of hematite fluxed briquettes
- Effect of in situ observation of cooling rates on acicular ferrite nucleation
- Corrosion behavior of WC–Co coating by plasma transferred arc on EH40 steel in low-temperature
- Study on the thermodynamic stability and evolution of inclusions in Al–Ti deoxidized steel
- Application on oxidation behavior of metallic copper in fire investigation
- Microstructural study of concrete performance after exposure to elevated temperatures via considering C–S–H nanostructure changes
- Prediction model of interfacial heat transfer coefficient changing with time and ingot diameter
- Design, fabrication, and testing of CVI-SiC/SiC turbine blisk under different load spectrums at elevated temperature
- Promoting of metallurgical bonding by ultrasonic insert process in steel–aluminum bimetallic castings
- Pre-reduction of carbon-containing pellets of high chromium vanadium–titanium magnetite at different temperatures
- Optimization of alkali metals discharge performance of blast furnace slag and its extreme value model
- Smelting high purity 55SiCr automobile suspension spring steel with different refractories
- Investigation into the thermal stability of a novel hot-work die steel 5CrNiMoVNb
- Residual stress relaxation considering microstructure evolution in heat treatment of metallic thin-walled part
- Experiments of Ti6Al4V manufactured by low-speed wire cut electrical discharge machining and electrical parameters optimization
- Effect of chloride ion concentration on stress corrosion cracking and electrochemical corrosion of high manganese steel
- Prediction of oxygen-blowing volume in BOF steelmaking process based on BP neural network and incremental learning
- Effect of annealing temperature on the structure and properties of FeCoCrNiMo high-entropy alloy
- Study on physical properties of Al2O3-based slags used for the self-propagating high-temperature synthesis (SHS) – metallurgy method
- Low-temperature corrosion behavior of laser cladding metal-based alloy coatings on EH40 high-strength steel for icebreaker
- Study on thermodynamics and dynamics of top slag modification in O5 automobile sheets
- Structure optimization of continuous casting tundish with channel-type induction heating using mathematical modeling
- Microstructure and mechanical properties of NbC–Ni cermets prepared by microwave sintering
- Spider-based FOPID controller design for temperature control in aluminium extrusion process
- Prediction model of BOF end-point P and O contents based on PCA–GA–BP neural network
- Study on hydrogen-induced stress corrosion of 7N01-T4 aluminum alloy for railway vehicles
- Study on the effect of micro-shrinkage porosity on the ultra-low temperature toughness of ferritic ductile iron
- Characterization of surface decarburization and oxidation behavior of Cr–Mo cold heading steel
- Effect of post-weld heat treatment on the microstructure and mechanical properties of laser-welded joints of SLM-316 L/rolled-316 L
- An investigation on as-cast microstructure and homogenization of nickel base superalloy René 65
- Effect of multiple laser re-melting on microstructure and properties of Fe-based coating
- Experimental study on the preparation of ferrophosphorus alloy using dephosphorization furnace slag by carbothermic reduction
- Research on aging behavior and safe storage life prediction of modified double base propellant
- Evaluation of the calorific value of exothermic sleeve material by the adiabatic calorimeter
- Thermodynamic calculation of phase equilibria in the Al–Fe–Zn–O system
- Effect of rare earth Y on microstructure and texture of oriented silicon steel during hot rolling and cold rolling processes
- Effect of ambient temperature on the jet characteristics of a swirl oxygen lance with mixed injection of CO2 + O2
- Research on the optimisation of the temperature field distribution of a multi microwave source agent system based on group consistency
- The dynamic softening identification and constitutive equation establishment of Ti–6.5Al–2Sn–4Zr–4Mo–1W–0.2Si alloy with initial lamellar microstructure
- Experimental investigation on microstructural characterization and mechanical properties of plasma arc welded Inconel 617 plates
- Numerical simulation and experimental research on cracking mechanism of twin-roll strip casting
- A novel method to control stress distribution and machining-induced deformation for thin-walled metallic parts
- Review Article
- A study on deep reinforcement learning-based crane scheduling model for uncertainty tasks
- Topical Issue on Science and Technology of Solar Energy
- Synthesis of alkaline-earth Zintl phosphides MZn2P2 (M = Ca, Sr, Ba) from Sn solutions
- Dynamics at crystal/melt interface during solidification of multicrystalline silicon
- Boron removal from silicon melt by gas blowing technique
- Removal of SiC and Si3N4 inclusions in solar cell Si scraps through slag refining
- Electrochemical production of silicon
- Electrical properties of zinc nitride and zinc tin nitride semiconductor thin films toward photovoltaic applications
- Special Issue on The 4th International Conference on Graphene and Novel Nanomaterials (GNN 2022)
- Effect of microstructure on tribocorrosion of FH36 low-temperature steels
Articles in the same Issue
- Research Articles
- Numerical and experimental research on solidification of T2 copper alloy during the twin-roll casting
- Discrete probability model-based method for recognition of multicomponent combustible gas explosion hazard sources
- Dephosphorization kinetics of high-P-containing reduced iron produced from oolitic hematite ore
- In-phase thermomechanical fatigue studies on P92 steel with different hold time
- Effect of the weld parameter strategy on mechanical properties of double-sided laser-welded 2195 Al–Li alloy joints with filler wire
- The precipitation behavior of second phase in high titanium microalloyed steels and its effect on microstructure and properties of steel
- Development of a huge hybrid 3D-printer based on fused deposition modeling (FDM) incorporated with computer numerical control (CNC) machining for industrial applications
- Effect of different welding procedures on microstructure and mechanical property of TA15 titanium alloy joint
- Single-source-precursor synthesis and characterization of SiAlC(O) ceramics from a hyperbranched polyaluminocarbosilane
- Carbothermal reduction of red mud for iron extraction and sodium removal
- Reduction swelling mechanism of hematite fluxed briquettes
- Effect of in situ observation of cooling rates on acicular ferrite nucleation
- Corrosion behavior of WC–Co coating by plasma transferred arc on EH40 steel in low-temperature
- Study on the thermodynamic stability and evolution of inclusions in Al–Ti deoxidized steel
- Application on oxidation behavior of metallic copper in fire investigation
- Microstructural study of concrete performance after exposure to elevated temperatures via considering C–S–H nanostructure changes
- Prediction model of interfacial heat transfer coefficient changing with time and ingot diameter
- Design, fabrication, and testing of CVI-SiC/SiC turbine blisk under different load spectrums at elevated temperature
- Promoting of metallurgical bonding by ultrasonic insert process in steel–aluminum bimetallic castings
- Pre-reduction of carbon-containing pellets of high chromium vanadium–titanium magnetite at different temperatures
- Optimization of alkali metals discharge performance of blast furnace slag and its extreme value model
- Smelting high purity 55SiCr automobile suspension spring steel with different refractories
- Investigation into the thermal stability of a novel hot-work die steel 5CrNiMoVNb
- Residual stress relaxation considering microstructure evolution in heat treatment of metallic thin-walled part
- Experiments of Ti6Al4V manufactured by low-speed wire cut electrical discharge machining and electrical parameters optimization
- Effect of chloride ion concentration on stress corrosion cracking and electrochemical corrosion of high manganese steel
- Prediction of oxygen-blowing volume in BOF steelmaking process based on BP neural network and incremental learning
- Effect of annealing temperature on the structure and properties of FeCoCrNiMo high-entropy alloy
- Study on physical properties of Al2O3-based slags used for the self-propagating high-temperature synthesis (SHS) – metallurgy method
- Low-temperature corrosion behavior of laser cladding metal-based alloy coatings on EH40 high-strength steel for icebreaker
- Study on thermodynamics and dynamics of top slag modification in O5 automobile sheets
- Structure optimization of continuous casting tundish with channel-type induction heating using mathematical modeling
- Microstructure and mechanical properties of NbC–Ni cermets prepared by microwave sintering
- Spider-based FOPID controller design for temperature control in aluminium extrusion process
- Prediction model of BOF end-point P and O contents based on PCA–GA–BP neural network
- Study on hydrogen-induced stress corrosion of 7N01-T4 aluminum alloy for railway vehicles
- Study on the effect of micro-shrinkage porosity on the ultra-low temperature toughness of ferritic ductile iron
- Characterization of surface decarburization and oxidation behavior of Cr–Mo cold heading steel
- Effect of post-weld heat treatment on the microstructure and mechanical properties of laser-welded joints of SLM-316 L/rolled-316 L
- An investigation on as-cast microstructure and homogenization of nickel base superalloy René 65
- Effect of multiple laser re-melting on microstructure and properties of Fe-based coating
- Experimental study on the preparation of ferrophosphorus alloy using dephosphorization furnace slag by carbothermic reduction
- Research on aging behavior and safe storage life prediction of modified double base propellant
- Evaluation of the calorific value of exothermic sleeve material by the adiabatic calorimeter
- Thermodynamic calculation of phase equilibria in the Al–Fe–Zn–O system
- Effect of rare earth Y on microstructure and texture of oriented silicon steel during hot rolling and cold rolling processes
- Effect of ambient temperature on the jet characteristics of a swirl oxygen lance with mixed injection of CO2 + O2
- Research on the optimisation of the temperature field distribution of a multi microwave source agent system based on group consistency
- The dynamic softening identification and constitutive equation establishment of Ti–6.5Al–2Sn–4Zr–4Mo–1W–0.2Si alloy with initial lamellar microstructure
- Experimental investigation on microstructural characterization and mechanical properties of plasma arc welded Inconel 617 plates
- Numerical simulation and experimental research on cracking mechanism of twin-roll strip casting
- A novel method to control stress distribution and machining-induced deformation for thin-walled metallic parts
- Review Article
- A study on deep reinforcement learning-based crane scheduling model for uncertainty tasks
- Topical Issue on Science and Technology of Solar Energy
- Synthesis of alkaline-earth Zintl phosphides MZn2P2 (M = Ca, Sr, Ba) from Sn solutions
- Dynamics at crystal/melt interface during solidification of multicrystalline silicon
- Boron removal from silicon melt by gas blowing technique
- Removal of SiC and Si3N4 inclusions in solar cell Si scraps through slag refining
- Electrochemical production of silicon
- Electrical properties of zinc nitride and zinc tin nitride semiconductor thin films toward photovoltaic applications
- Special Issue on The 4th International Conference on Graphene and Novel Nanomaterials (GNN 2022)
- Effect of microstructure on tribocorrosion of FH36 low-temperature steels