A sub-regular solution model used to predict the component activities of quaternary systems

Zhang, Bing; Chang, Jiang Guo; Tang, Kai; Lun, Xu Jian; Zhong, Ding Wei; Di, Xu Kuang

doi:10.1016/s0364-5916(97)00031-x

Cited by 2 publications

(5 citation statements)

References 2 publications

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“…The reaction equilibrium between element, M, and dissolved oxygen, O, at the steel/inclusion interface can be described by

x [M] + y [O] = {false(M_{x} O_{y} false)}_{inc}

X_{normalM}^{* x} = \frac{a_{{normalM}_{x} O_{y}}^{*}}{e_{normalM} X_{O}^{* y}}

e_{normalM} = \frac{K_{{normalM}_{x} O_{y}} {false(f_{normalM} \cdot M W_{normalM} false)}^{x} \cdot {false(f_{O} \cdot M W_{O} false)}^{y} \times 100^{x + y}}{M W_{Fe}^{x + y}}

where

K_{{normalM}_{x} {normalO}_{y}}

are the equilibrium constants for the respective deoxidation reactions evaluated at 1873 K shown in Table 1 ,

X_{i}^{*}

is the mole fraction of species i at the interface,

a_{i}

are the activities of the i th oxides in

MnO - {SiO}_{2} - {Al}_{2} {normalO}_{3}

system which are calculated at the interface by the sub‐regular solution model (SRSM), [ 18 ]

M W_{i}

is the molar mass of species i , and

f_{i}

represents the Henrian activity coefficient of i th species with respect to 1 wt. % standard state, calculated using unified interaction parameter formalism.…”

Section: Mathematical Modelmentioning

confidence: 99%

“…The endogenous oxide inclusions encountered within the modeled system as a result of deoxidation belong to the

CaO - MnO - {SiO}_{2} - {Al}_{2} {normalO}_{3}

system. The oxide activities in this system can be represented by the sub regular solution model, [ 18 ] using

a_{M_{x} o_{y}} = X_{M_{x} o_{y}} \exp (\frac{G_{M_{x} o_{y}}^{e x} - G_{M_{x} O_{y}}^{\circ}}{R T})

where

X_{M_{x} O_{y}}

is the mole fraction of an oxide

M_{x} O_{y}

in the oxide system,

G_{M_{x} O_{y}}^{ex}

is the excess partial molar free energy of the oxide in reference to the pure liquid state,

G_{M_{x} O_{y}}^{normalo}

is the molar free energy associated with the oxide's transformation from liquid to solid, and

G_{M_{x} O_{y}}^{ex}

is expressed with a set of formulae in a multi‐component system (

M_{x} O_{y}

= 1–4) in which 1–4 denote four oxide compounds in a quaternary oxide system. The activities calculated using a computerized version of this model in the

MnO - {SiO}_{2}

and

MnO - {SiO}_{2} - {Al}_{2} {normalO}_{3}

systems are shown in Figure 2 a,b, respectively.…”

Section: Model Validationmentioning

confidence: 99%

“…where K M x O y are the equilibrium constants for the respective deoxidation reactions evaluated at 1873 K shown in Table 1, X Ã i is the mole fraction of species i at the interface, a i are the activities of the ith oxides in MnO À SiO 2 À Al 2 O 3 system which are calculated at the interface by the sub-regular solution model (SRSM), [18] MW i is the molar mass of species i, and f i represents the Henrian activity coefficient of ith species with respect to 1 wt. % standard state, calculated using unified interaction parameter formalism.…”

Section: Equilibrium Equationsmentioning

confidence: 99%

“…The endogenous oxide inclusions encountered within the modeled system as a result of deoxidation belong to the CaO À MnO À SiO 2 À Al 2 O 3 system. The oxide activities in this system can be represented by the sub regular solution model, [18] using…”

Section: Oxide Activity Calculationmentioning

confidence: 99%

“…While using a high alumina slag for steel refining, a redistribution of silica and alumina can be observed between the inclusions and the slag (Refer to Figure 5c and 6b). If the alumina activity in the slag is sufficiently high and the silica activity sufficiently low, the silicon activity in the steel may be high enough to reduce the alumina via a reaction similar to Equation (18). The aluminum activity in the steel may then be high enough for Reaction (19) to proceed with replacing silica in the inclusion with alumina.…”

Section: Study Of Al Pickup Ratementioning

confidence: 99%

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Modeling Study of Steel–Slag–Inclusion Reactions During the Refining of Si–Mn Killed Steel

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2022

steel research int.

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“…The reaction equilibrium between element, M, and dissolved oxygen, O, at the steel/inclusion interface can be described by

x [M] + y [O] = {false(M_{x} O_{y} false)}_{inc}

X_{normalM}^{* x} = \frac{a_{{normalM}_{x} O_{y}}^{*}}{e_{normalM} X_{O}^{* y}}

e_{normalM} = \frac{K_{{normalM}_{x} O_{y}} {false(f_{normalM} \cdot M W_{normalM} false)}^{x} \cdot {false(f_{O} \cdot M W_{O} false)}^{y} \times 100^{x + y}}{M W_{Fe}^{x + y}}

where

K_{{normalM}_{x} {normalO}_{y}}

are the equilibrium constants for the respective deoxidation reactions evaluated at 1873 K shown in Table 1 ,

X_{i}^{*}

is the mole fraction of species i at the interface,

a_{i}

are the activities of the i th oxides in

MnO - {SiO}_{2} - {Al}_{2} {normalO}_{3}

system which are calculated at the interface by the sub‐regular solution model (SRSM), [ 18 ]

M W_{i}

is the molar mass of species i , and

f_{i}

represents the Henrian activity coefficient of i th species with respect to 1 wt. % standard state, calculated using unified interaction parameter formalism.…”

Section: Mathematical Modelmentioning

confidence: 99%

“…The endogenous oxide inclusions encountered within the modeled system as a result of deoxidation belong to the

CaO - MnO - {SiO}_{2} - {Al}_{2} {normalO}_{3}

system. The oxide activities in this system can be represented by the sub regular solution model, [ 18 ] using

a_{M_{x} o_{y}} = X_{M_{x} o_{y}} \exp (\frac{G_{M_{x} o_{y}}^{e x} - G_{M_{x} O_{y}}^{\circ}}{R T})

where

X_{M_{x} O_{y}}

is the mole fraction of an oxide

M_{x} O_{y}

in the oxide system,

G_{M_{x} O_{y}}^{ex}

is the excess partial molar free energy of the oxide in reference to the pure liquid state,

G_{M_{x} O_{y}}^{normalo}

is the molar free energy associated with the oxide's transformation from liquid to solid, and

G_{M_{x} O_{y}}^{ex}

is expressed with a set of formulae in a multi‐component system (

M_{x} O_{y}

= 1–4) in which 1–4 denote four oxide compounds in a quaternary oxide system. The activities calculated using a computerized version of this model in the