11.01.2016  Ausgabe 3/2016 Open Access
Coupling Inward Diffusion and Precipitation Kinetics; the Case of Nitriding IronBased Alloys
 Zeitschrift:
 Metallurgical and Materials Transactions A > Ausgabe 3/2016
1 Introduction
2 Theoretical Background
2.1 Inward Diffusion
2.2 Precipitation
2.2.1 Nucleation
2.2.2 Growth and coarsening
2.3 Specific Aspects Related to Excess N Uptake Upon Nitriding Ironbased Alloys
3 Model Implementation
3.1 Numerical Methods
3.2 Simulation Settings
Parameter  853 K (580 °C)  823 K (550 °C)  793 K (520 °C) 

ln γ
_{N}
^{0}
 9.92  10.01  10.25 
ln γ
_{V}
^{0}
 −7.57  −7.61  −7.65 
ɛ
_{N}
^{N}
 1.34  1.34  1.34 
ɛ
_{V}
^{V}
(X
_{V} as atomic fraction)  −3.22 + 79.8X
_{V}
 −3.38 + 86.1X
_{V}
 −3.54 + 93.16X
_{V}

ɛ
_{N}
^{V}
= ɛ
_{V}
^{N}
 −36.2  −37.7  −39.4 
K
_{sp} for VN  8.0 × 10^{−12}
 2.5 × 10^{−12}
 0.7 × 10^{−12}

Parameter  Value  Reference 

β, NH_{3} reaction rate coefficient (m s^{−1}) (\( P_{{{\text{H}}_{ 2} }} \) in atm, T in Kelvin) 
\( 9\times 1 0^{  4} \, P_{{{\text{H}}_{ 2} }} exp\left( {  \frac{64220}{RT}} \right) \)
 [34] 
C
_{N,Eq}
^{0}
, N content in unstrained ferrite in equilibrium with NH_{3}/H_{2} gas mixture (# of atoms m^{−3}) (r
_{N} in atm^{−1/2}) 
\( \ln \left( {\frac{{C_{\text{N,eq}}^{0} }}{{r_{\text{N}} }}} \right) = 75.39  \frac{10579}{T} \)
 [27] 
D
_{N}
^{*}
, N selfdiffusion coefficient in dilute bcc FeN alloy (m^{2} s^{−1}) 
\( 6.6 \times 10^{  7} \exp \left( {  \frac{77900}{RT}} \right) \)
 [54] 
D
_{V}
^{*}
, V selfdiffusion coefficient in bcc Fe2 wt pct V alloy (m^{2} s^{−1}) 
\( 3.92 \times 10^{  4} exp\left( {  \frac{240998}{RT}} \right) \)
 [55] 
a
_{
α
}, αFe lattice parameter (nm)  0.2850 + 3.55 × 10^{−6}
T + 5.49 × 10^{−10}
T
^{2}
 [56] 
a
_{VN}, VN lattice parameter (nm)  0.4134 − 1.06 × 10^{−4}
T
^{1/2} + 6.09 × 10^{−6}
T
 [57] 
γ
_{VN/α
}, VN/α interface energy (J m^{−2})  0.25  [58] 
\( \bar{V}_{\text{N}}^{{{\alpha }}} \), partial atomic volume of N in the αFe matrix (Å^{3})  9.8  [59] 
μ
_{
α
}, αFe shear modulus (GPa)  96.1 − 0.038T
 [60] 
K
_{VN}, VN bulk modulus (GPa)  353 − 0.05T
 
f related to excess N  0.8  [31] 
B related to excess N (# of atoms nm^{−2})  9.6  see text 