### Abstract

During intermixing in phase separating A/B diffusion couple the actual atomic fractions of A atoms (c_{α} and c_{β}) on the left as well as on the right hand side of the α/β interface gradually will decrease (from unity) as well as increase (from 0) until the equilibrium c_{α} and c_{β} will be reached (α and β refer to the A- and B-rich phases, separated by the interface). At the same time the interface will also be shifted. Assuming that the atomic flux across the interface, J_{I}, is proportional to the deviations from the equilibrium (Δ_{α}=c_{α}-c_{α} and Δ_{β}=c_{β}-c_{β}) the J_{I}=(1/Ω)[K_{Iαβ}Δ_{α}+K_{Iβα}Δ_{β}) relation is obtained, where Ω=Ω_{A}=Ω_{B} is the atomic volume. It is shown that the K_{Iαβ} and K_{Iβα} interface transfer coefficients are positive, independent of the interface velocity, equal to each other for symmetric miscibility gap, and can be given as K_{Iβα}=K_{Iαβ}=K=z_{v}aΓ_{Iαβ}c_{α}ξ. Here Γ_{Iαβ} is the jump frequency from α to β phase across the interface, a is the lattice spacing, z_{v} is the vertical coordination number.ξ=[1+exp(ZV(c_{α}-c_{β})/kT)], where Z is the coordination number, V is the well-known solid solution parameter, proportional to the heat of mixing, and kT has its usual meaning. The above expression justifies the conjecture, frequently used in the literature, that only one interface transfer coefficient is enough for the description of the mass transfer across an interface. For short diffusion times the finite value of Γ_{Iαβ} will restrict the flux, leading to finite permeability with linear kinetics of interface shift. It is also shown that for an order of magnitude estimation of the critical interface shift (giving the transition from interface to diffusion control) the x_{c}=aΓ(c_{β})/Γ_{Iαβ}, relation can be used, where Γ(c_{β}) is the jump frequency in the β phase at c_{β}. Thus x_{c} is practically independent of the value of V and only the composition dependence of the jump frequencies is important. For composition independent jump frequencies x_{c}≅a, (i.e. it cannot be detected), while for the case when the diffusivity changes by seven orders of magnitude from pure A to B,x_{c} is about 150 nm.

Original language | English |
---|---|

Pages (from-to) | 203-209 |

Number of pages | 7 |

Journal | International Journal of Heat and Mass Transfer |

Volume | 113 |

DOIs | |

Publication status | Published - Jan 1 2017 |

### Fingerprint

### Keywords

- Interdiffusion
- Interface
- Interface transfer coefficient
- Phase separation
- Second phase growth

### ASJC Scopus subject areas

- Condensed Matter Physics
- Mechanical Engineering
- Fluid Flow and Transfer Processes

### Cite this

**Atomic interpretation of the interface transfer coefficients for interdiffusion in AB binary phase separating system.** / Beke, D.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Atomic interpretation of the interface transfer coefficients for interdiffusion in AB binary phase separating system

AU - Beke, D.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - During intermixing in phase separating A/B diffusion couple the actual atomic fractions of A atoms (cα and cβ) on the left as well as on the right hand side of the α/β interface gradually will decrease (from unity) as well as increase (from 0) until the equilibrium cα and cβ will be reached (α and β refer to the A- and B-rich phases, separated by the interface). At the same time the interface will also be shifted. Assuming that the atomic flux across the interface, JI, is proportional to the deviations from the equilibrium (Δα=cα-cα and Δβ=cβ-cβ) the JI=(1/Ω)[KIαβΔα+KIβαΔβ) relation is obtained, where Ω=ΩA=ΩB is the atomic volume. It is shown that the KIαβ and KIβα interface transfer coefficients are positive, independent of the interface velocity, equal to each other for symmetric miscibility gap, and can be given as KIβα=KIαβ=K=zvaΓIαβcαξ. Here ΓIαβ is the jump frequency from α to β phase across the interface, a is the lattice spacing, zv is the vertical coordination number.ξ=[1+exp(ZV(cα-cβ)/kT)], where Z is the coordination number, V is the well-known solid solution parameter, proportional to the heat of mixing, and kT has its usual meaning. The above expression justifies the conjecture, frequently used in the literature, that only one interface transfer coefficient is enough for the description of the mass transfer across an interface. For short diffusion times the finite value of ΓIαβ will restrict the flux, leading to finite permeability with linear kinetics of interface shift. It is also shown that for an order of magnitude estimation of the critical interface shift (giving the transition from interface to diffusion control) the xc=aΓ(cβ)/ΓIαβ, relation can be used, where Γ(cβ) is the jump frequency in the β phase at cβ. Thus xc is practically independent of the value of V and only the composition dependence of the jump frequencies is important. For composition independent jump frequencies xc≅a, (i.e. it cannot be detected), while for the case when the diffusivity changes by seven orders of magnitude from pure A to B,xc is about 150 nm.

AB - During intermixing in phase separating A/B diffusion couple the actual atomic fractions of A atoms (cα and cβ) on the left as well as on the right hand side of the α/β interface gradually will decrease (from unity) as well as increase (from 0) until the equilibrium cα and cβ will be reached (α and β refer to the A- and B-rich phases, separated by the interface). At the same time the interface will also be shifted. Assuming that the atomic flux across the interface, JI, is proportional to the deviations from the equilibrium (Δα=cα-cα and Δβ=cβ-cβ) the JI=(1/Ω)[KIαβΔα+KIβαΔβ) relation is obtained, where Ω=ΩA=ΩB is the atomic volume. It is shown that the KIαβ and KIβα interface transfer coefficients are positive, independent of the interface velocity, equal to each other for symmetric miscibility gap, and can be given as KIβα=KIαβ=K=zvaΓIαβcαξ. Here ΓIαβ is the jump frequency from α to β phase across the interface, a is the lattice spacing, zv is the vertical coordination number.ξ=[1+exp(ZV(cα-cβ)/kT)], where Z is the coordination number, V is the well-known solid solution parameter, proportional to the heat of mixing, and kT has its usual meaning. The above expression justifies the conjecture, frequently used in the literature, that only one interface transfer coefficient is enough for the description of the mass transfer across an interface. For short diffusion times the finite value of ΓIαβ will restrict the flux, leading to finite permeability with linear kinetics of interface shift. It is also shown that for an order of magnitude estimation of the critical interface shift (giving the transition from interface to diffusion control) the xc=aΓ(cβ)/ΓIαβ, relation can be used, where Γ(cβ) is the jump frequency in the β phase at cβ. Thus xc is practically independent of the value of V and only the composition dependence of the jump frequencies is important. For composition independent jump frequencies xc≅a, (i.e. it cannot be detected), while for the case when the diffusivity changes by seven orders of magnitude from pure A to B,xc is about 150 nm.

KW - Interdiffusion

KW - Interface

KW - Interface transfer coefficient

KW - Phase separation

KW - Second phase growth

UR - http://www.scopus.com/inward/record.url?scp=85019887695&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85019887695&partnerID=8YFLogxK

U2 - 10.1016/j.ijheatmasstransfer.2017.05.074

DO - 10.1016/j.ijheatmasstransfer.2017.05.074

M3 - Article

AN - SCOPUS:85019887695

VL - 113

SP - 203

EP - 209

JO - International Journal of Heat and Mass Transfer

JF - International Journal of Heat and Mass Transfer

SN - 0017-9310

ER -