silicon for the chemical and solar industry XIII

selectivity (ratio of dichlorodimethylsilane over total chlorosilanes) and reactivity

(quantity of chlorosilane produced per hour and kg of Si) of the chlorosilane synthesis

in the fluidized bed reactor.

Iron, aluminium, calcium and titanium are usually the main elements in metallurgical

grade silicon. Other elements are referred to as trace elements. Previous studies have

provided a description of the intermetallic phases found in MG-Si material produced

with standard process route [1, 2, 3, 4, 5]. The main intermetallic phases are FeSi2,

Al3FeSi2, FeSi2Ti, Al2CaSi2, Al6CaFe4Si8, CaSi2, Al6Fe4Si6 and TiSi2. Some

studies have been carried out to assess the effect of composition and cooling rate on the

type and amount of particles.

Nevertheless, this empirical knowledge has not yet been fully systematized into an

efficient and practical tool. The purpose of this paper is to present such a tool under

development by SINTEF in collaboration with Elkem. The model is currently based on

gathered literature data covering the major binary and ternary systems. The main

challenge is in integrating it into a predictive microstructure model covering a large

range of compositions and various solidification conditions. This paper will describe

the microstructure model, its calibration and a simple application to illustrate the

potential use in industrial product/process design. Please note that unless otherwise

stated all alloy composition are given in wt%.

Microstructure model

The microstructure model, hereafter referred to as Sistruc, has been initially developed

in 2009 by A.L. Dons following a similar approach as for the Alstruc model [6]. The

main objective of this tool is to be predictive, fast and user-friendly which implies that

one has to balance complexity with some simplifications and approximations. In the

following sections, we will present the main aspects of the current version. One

essential aspect of the current model is that it solves equilibrium phase formation during

solidification. At any step during solidification, the solid-liquid interface is assumed to

be at equilibrium and the phases form accordingly. Possible solid state phase

transformations are not accounted for in the model.

Model equations

Two main values have to be computed by the model to determine the phase formation

path: i) the concentration dependence of the liquidus temperature and ii) the solubility

of the different phases. In addition, for some particles, the model also computes the

particle composition based on the current liquid composition. The generic formula to

compute the liquidus temperature is given by:

௟௜௤

ൌ ͳͶͳͶ ൅෍෍

௜ ௞

ଷ

௞ୀଵ ௜

൅෍෍

௜௝

௜

௝

ஷ௜

௜

( 1 )

where

denotes the solute element (Al, Ca, Fe, Ti, B and P are considered in the model)

and C the concentration in the liquid,

௜ ௞

are the coefficients of the third order polynomials.