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Complete Kinetic Maps for Binary Alloys Forming Two Insoluble Oxides Under High Oxygen Pressures

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Abstract

The oxidation under high pressures of a single oxidant of binary A–B alloys forming two insoluble oxides involves the internal oxidation of the most reactive component B when its concentration falls below an upper critical concentration defined by means of a criterion due to Wagner. However, this oxidation mode is no longer stable for alloys sufficiently dilute in B. The paper predicts the nature of the oxidation modes stable in this alloy region and calculates the critical contents of B required for the corresponding transitions.

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Acknowledgments

Financial support by the National Natural Scientific Foundation of China (NSFC) under the research projects (No. 50571107 and 50671114) is gratefully acknowledged.

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Authors and Affiliations

  1. State Key Laboratory for Corrosion and Protection, Institute of Metal Research, Chinese Academy of Sciences, Wencui Road 62, 110016, Shenyang, China

    F. Gesmundo, S. Wang & Y. Niu

  2. DICHEP, University of Genova, Fiera del Mare, Pad. D, 16129, Genoa, Italy

    F. Gesmundo

Authors
  1. F. Gesmundo
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  2. S. Wang
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  3. Y. Niu
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Corresponding author

Correspondence to Y. Niu.

Glossary

DO, DA, DB

Diffusion coefficients of oxygen, A and B in the alloy

F, FS

Fraction of the BO precipitate present at a distance x from the alloy surface and the corresponding value at the alloy surface, respectively

fv

Volume fraction of internal oxide inside the internal oxidation zone

\( {\text{f}}_{\text{v}}^{*} \)

Critical value of fv for the transition from internal to external oxidation of B

h

Defined as the product γ φ 1/2B

kc(AO), kc(BO)

Parabolic rate constants for the growth of AO, BO in terms of thickness of metal consumed by oxidation

kp(AO), kp(BO)

Parabolic rate constants for the growth of AO, BO in terms of weight gain per unit surface area

K(AO), K(BO)

Equilibrium constants for the formation of AO, BO

KS(A)

Sievert’s constant for the dissolution of oxygen in A

Ksp(BO)

Solubility product of BO inside the alloy

Jsp(BO)

Product of the mole fractions of O and B dissolved in A as a function of x

NA°, NB°

Mole fractions of A and B in the bulk alloy

NA(E), NB(E)

Mole fractions of A, B for the equilibrium between the A–B alloy and the two oxides

NA, NB

Mole fractions of A and B in the alloy as functions of x

NB°(α), NB°(β)

Mole fractions of B in the bulk alloys corresponding to the limits of stability of external AO and BO scales, respectively

NB°(i)

Critical mole fraction of B for the transition from internal to external oxidation of B

NB°(i,1)

Minimum mole fraction of B required for the stability of its internal oxidation

NO

Mole fraction of oxygen dissolved in the alloy

NO s°

Mole fraction of oxygen dissolved in pure A under the P(O2) for the A/AO equilibrium

NO s(E)

Mole fraction of oxygen dissolved in the A–B alloy under the P(O2) for the equilibrium between the alloy and a mixture of the oxides of A and B

pA, pB

Parameters involved in the relation between the parabolic rate constants for the growth of AO, BO and the oxygen pressure

P(O2)°

Oxygen pressure for the equilibrium between pure A and its oxide

P(O2,E)

Oxygen pressure for the equilibrium between an A–B alloy and a mixture of the oxides of A and B

r

Parameter introduced in Ref. [17] defined as F/FS

S

Σ (DO t)1/2

t

Time

uA

½ [kc(AO)/DA]1/2

uO

½ [kc(AO)/DO]1/2

x

Distance inside the alloy measured from the original location of the alloy surface

X

Thickness of metal consumed by oxidation at time t

Y

Dimensionless distance parameter introduced in Ref. [17]

α

Parameter appearing in Eq. 20 introduced in Ref. [17]

γ

Constant parameter involved in the kinetics of internal oxidation

γB

Activity coefficient of B in the alloy

ΔGf°(AO), ΔGf°(BO)

Standard free energy changes for the formation of the oxides AO and BO

Δ(AO), Δ(BO)

Defined as ΔGf°(AO)/RT and ΔGf°(BO)/RT

ε

Ratio between NB°(i,1) and NB(E)

ξ

Distance of the front of internal oxidation of B from the original location of the alloy surface

ϑA, ϑB

Parameters in the expressions of the parabolic rate constants for the growth of external AO, BO scales as functions of the oxygen pressure in the gas and at the alloy/scale interface (constant at constant temperature)

ξ

Distance of the front of internal oxidation of B from the original location of the alloy surface

Π(BO)

Excess solubility parameter for the internal precipitation of BO in A

ρ(BO)

Ratio between the molar volumes of BO(per unit mole of metal) and the alloy

Σ = ∂ ln [Jsp(BO)/∂x]

Evaluated at the alloy/scale interface (with x = X)

φA, φB

Ratio between the diffusion coefficient of oxygen and that of A or B in the alloy

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Gesmundo, F., Wang, S. & Niu, Y. Complete Kinetic Maps for Binary Alloys Forming Two Insoluble Oxides Under High Oxygen Pressures. Oxid Met 73, 65–81 (2010). https://doi.org/10.1007/s11085-009-9169-7

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  • DOI: https://doi.org/10.1007/s11085-009-9169-7

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