Prediction Expressions of Component Activity Coefficients in Si-Based Melts
- PDF / 448,576 Bytes
- 8 Pages / 593.972 x 792 pts Page_size
- 15 Downloads / 218 Views
COMPONENT activities in Si-based melts, such as Fe, Ca, Al, Ti, B, P, and others, are indispensable data for understanding various purification processes to produce solar grade silicon, such as slag refining, plasma refining, vacuum refining, and directional solidification. For example, when removal of Al and B in slag treatment proceeds via oxidation, their distribution coefficients depend on their activity coefficients in Si-based melts; in vacuum refining the separation coefficients of impurities Bi and Ca also involve their activity coefficient.[1] In order to get them, the Wagner interaction parameter formalism (WIPF)[2] usually becomes first method in one’s mind. However, component activity data and the Wagner interaction parameters of Si-based ternary melts still are quite limited because their measurements often are difficult, time-consuming, and expensive. Recently, some key data of binary silicon melts were available in the literatures.[3–7] The aim of this work is to provide an alternative method of predicting component activities in some Si-based multicomponent melts. That is an expression of the molecular interaction volume model (MIVM)[8] for them.
II.
MOLECULAR INTERACTION VOLUME MODEL (MIVM)
For a solution system containing C components, there are C types of molecular cells and molecular pair interaction taken into account. Its molar excess Gibbs energy can be expressed as " GEm
¼ RT
C X i¼1
# /i Dep xi ln þ ; xi 2kT
½1
where xi is molar fraction of component i, /i ¼ xi Vmi =Vm is molar volume fraction of component i, Vmi and Vm are molar volumes of component i and the system, respectively. Excess potential energy function of the system is Dep ¼ 2ep
C X
Zi xi eii ;
½2
i¼1
where Zi is the nearest atoms or first coordination number and eii is pair-potential energy of i i, and the mixing potential energy function of molecules ep can be chosen as[9] ! ! C C C C X X 1X 1X xj Bji eji ep ¼ Zi xi xji eji ¼ Zi xi ; PC 2 i¼1 2 i¼1 j¼1 j¼1 j¼1 xji Bji ½3
DONG-PING TAO, Professor, is with the Faculty of Metallurgical and Energy Engineering, Kunming University of Science and Technology, Kunming 650093, Yunnan, P.R. China. Contact e-mail: [email protected]. Manuscript submitted June 18, 2013. Article published online October 5, 2013. 142—VOLUME 45B, FEBRUARY 2014
where Bji is pair-potential energy parameter which is defined as ½4 Bji ¼ exp eji eii =kT Thus, one can achieve a novel model of molar excess Gibbs energy GEm METALLURGICAL AND MATERIALS TRANSACTIONS B
C C GEm X Vmi 1X ¼ xi ln PC Zi xi 2 i¼1 RT i¼1 j¼1 xj Vmj Bji
PC
j¼1 xj Bji lnBji PC j¼1 xj Bji
!
½5 Then, under conditions of i 6¼ C, d ¼ 1, and i ¼ C, d ¼ 0 where C is number of all components in a solution, based on the relation between partial molar and molar excess Gibbs energies E Gi ¼ RT ln ci ¼ GEm þ d @GEm =@xi T;P;x½i;C
C1 X xj @GEm =@xj T;P;x½j;C ;
½6
j¼1
where subscript symbol x½j; C represents that xj and xC are two P variables for partial differentiation and xC ¼ 1 C1 j¼1 xj is a subordinate
Data Loading...
