Experimental determination of activity interaction coefficients of components in Si-B-Fe and Si-B-Al ternary systems at 1723 K

: The interactions among impurity components in Si-based solution are the important thermodynamic parameters for the purification of silicon materials. A "same concentration" method was used to determine the activity interaction coefficients of Fe to B and Al to B in the silicon solution. Fe and Al were respectively dissolved into the binary Si-B solution at 1723 K with the holding time of 5 h, 7 h, 9 h and 11 h. The equilibrium concentrations of Fe, B in the Si-B-Fe system and Al, B in the Si-B-Al system were determined. The interaction coefficients of Fe to B and Al to B were obtained by fitting the solubility data of B, Fe and Al. The solubility relationships between B and [%Fe] and between B and [%Al] were obtained, respectively. It is found by the SEM and EPMA pictures of samples that the third component Fe or Al added to the binary Si-B solution have been fully alloyed, which verifies the accuracy of the experimental determination results. The significance of the activity interaction coefficient of B on boron removal from industrial silicon was analyzed.


Introduction
Solar grade silicon (SoG-Si) is a key material for solar photovoltaic conversion. A metallurgical route for producing SoG-Si that employs relatively inexpensive metallurgical grade silicon (MG-Si, ~99%) as the raw material is believed to be a promising approach for fabricating solar cells [1][2][3]. However, various impurities in silicon such as iron, aluminum, boron, etc. have a great negative impact on the photoelectric conversion performance of solar grade silicon [4]. In the process of metallurgical production of industrial silicon, boron is mainly removed by refining outside the furnace [5]. The temperature of silicon refining is around 1723 K. So the thermodynamic parameters ε B Fe and ε B Al about the phase equilibria and the liquid phase are necessary, since the boron removal from silicon by refining is relevant to the thermodynamic parameters such as solubility and activity in silicon [6][7][8].
Currently, there are no details on the thermodynamic parameters about boron removal from silicon under high temperature conditions. Therefore, the research on the thermodynamic properties of metallurgical grade silicon has always been a research hotspot in the silicon industry [9]. Liu [10]  solution under the vacuum environment, and calculated the activity interaction coefficients between Fe and Al. Tao [11][12][13] [20][21][22]

Experimental
The Fe (>99.97%), Al (>99.95%), Si (>99.99%) and B (>99.9%) powders were used as the raw materials in the experiments. As shown in the Si-B binary phase diagram ( Fig. 1) [23], the boron concentration on the liquidus at 1723 K is about 5.5% mass ratio. Therefore, the raw materials were matched according the liquidus at 1723 5 K and the raw material composition used to prepare the experimental alloys is shown in Table 1. An excess of B in Si-B-Fe and Si-B-Al systems were ensured.

Fig. 1 Si-B binary phase diagram
The high-purity Si, B, Fe or Al were weighed and mixed uniformly and then placed in a corundum crucible of φ20-mm*33-mm, which were encased a graphite crucible of φ63-mm*90-mm. Since the content of Fe and Al added in the experiment is high, the influence of Al in corundum crucible on the experiment can be neglected. The crucibles were then placed in a vacuum tubular resistance furnace as shown in Fig. 2.
In order to ensure that the materials were not oxidized, the furnace tube was first evacuated, and then a high purity argon gas (99.99%) was continuously supplied during the experiment. The temperature was raised to 1723 K and kept for 5, 7, 9, and 11 hours, respectively. After the full dissolution of B and Fe or Al in silicon solution, the high-temperature graphite crucible is quickly extracted from the furnace tube by molybdenum wire, and the silicon solution is quenched.  [24].
In this study, Fe or Al is added to the Si-B binary system, and the effect of Fe or Al on the activity coefficient of B was obtained. The Wagner equations [25,26] corresponding to the Si-B-Fe system and the Si-B-Al system are shown in the formulas (1) and (2) 8 The results of chemical composition analysis by ICP for the Si-B-Fe and Si-B-Al ternary alloy samples at 1723 K with different holding time are shown in Table 2.
Since the boron is at a saturated state, the activity of B in silicon solution is 1.

xBγB=1 (3)
Given as Therefore, We know from the literature that γ B 0 is 0.24 [27], so the calculation results of Si-B-Fe and Si-B-Al ternary alloy systems by the formulas (3)-(5) and the data of Table 2 are obtained and shown in Table 3.
According to Table 2 and Table 3 (1) and (2), it is seen that the slope of the fitted straight line is the activity interaction coefficient e B Fe or e B Al , which is converted to ε B Fe or ε B Al by the formulas (6) and The results of ε B Fe and ε B Al are shown in Table 4.

Physical characterization techniques
The

Features of and on Si purification
The Si-B-Fe and Si-B-Al alloy solutions at 1723 K are in dynamic equilibrium states with holding time 5 h, 7 h and 7 h, 9 h, respectively. As shown in Fig. 7(a) and Fig. 7(b), the saturation solubility of boron in silicon solution decreases with the increase of Fe and Al contents. Since the affinity of Fe to Si is greater than the affinity of Si and B, Si atoms are more likely to combine with Fe to form a compound, so that the compound formed by Si and B is reduced, resulting in a decrease in the saturation solubility of B. Its atomic behavior diagram is shown in Fig. 8(a). The addition of Al changes the original Si-B phase to the Si-B-Al phase, and Al extrudes a portion of the B atom, reducing the saturation solubility of B in Si. A schematic diagram of its atomic and molecular behavior is shown in Fig. 8(b). 1723K [26,29,30]  The existence of a small amount of Fe and Al is benefit for Si slag refining removes B.   Table 3 Fitting data of Si-B-Fe and Si-B-Al system at 1723 K