Fedirko, Viktor

Matychak, Yaroslav

Pohrelyuk, Iryna

Tkachuk, Oleh

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The Open-Access Journal for the Basic Principles of Diffusion Theory, Experiment and ApplicationKinetic peculiarities of two-component diffusion saturation of titaniumunder rarefied nitrogen-oxygen-containing mediumYaroslav Matychak, Oleh Tkachuk∗, Iryna Pohrelyuk, Viktor FedirkoPhysico-Mechanical Institute of National Academy of Sciences of Ukraine, Lviv, Ukraine∗tkachuk@ipm.lviv.uaPreviously, it was investigated the kinetics of single-component diffusion saturation of titanium by theinterstitial elements (nitrogen or oxygen) [1]. It is clear that diffusion saturation of the materials bytwo and more components allows to change the properties of surface layers more considerably com-pared with single-component saturation. But it requires the theoretical knowledge about the kineticsof formation of diffusion zone, its composition and distribution of the elements. The aim of this workis to investigate analytically the peculiarities of simultaneous two-component (nitrogen and oxygen)diffusion saturation of titanium under rarefied controlled gaseous medium.Kinetics of the compatible diffusion of nitrogen and oxygen in titanium is complicated and many-sided.The two-component (nitrogen and oxygen) diffusion saturation of titanium under rarefied controlledgaseous medium (PN  PO2) will be considered. Will be accepted that nitrogen µG1 (PN) and oxygenµG2 (PO2) potentials in gaseous medium (Fig. 1) such that concentrations of nitrogen CS1 and oxygenCS2 on the titanium surface equilibrium with the medium do not exceed their maximum solubilities,according to the phase diagrams. For T=800 ◦C they are 16 at.% and 33 at.%, respectively [2].Figure 1: Scheme of mass transfer in system Ti-G(N, O2)It should be noted that very often in the case of two-component diffusion the influence of onecomponent is more significant than the other component. It will be accepted that oxygen (com-ponent 2) diffuses independently, while it affects the chemical potential (µ1(x,τ) = d11C1(x,τ) +d12C2(x,τ), µ2(x,τ) = d22C2(x,τ)) and diffusion ability (D12 = d12L11, D21 = 0, L11 – Onsager kineticcoefficient) of nitrogen (component 1). We have a system of the differential equations for descriptionof the diffusion of these components:D11∂2C1(x,τ)∂x2+D12∂2C2(x,τ)∂x2=∂C1(x,τ)∂τ, D22∂2C2(x,τ)∂x2=∂C2(x,τ)∂τ. (3)Since the aim of diffusion treatment of titanium is strengthening of its near-surface layers, then thehalf-space has been chosen as the object of investigation. The following boundary (x = 0,x = ∞) andinitial (τ= 0) conditions will be set for solution of a system of the differential equations:C1(0,τ)+λ12C2(0,τ) =CS1 = const, −D22∂C2(x,τ)∂x∣∣∣x=0= H[CS2 −C2(0,τ)], (4)C1(x,0) =C2(x,0) = 0; C1(∞,τ) =C2(∞,τ) = 0, where CS1 = µG1 /d11, CS2 = µG2 /d22.The condition of ideal contact (µG1 = µS1) on the surface was be set in the boundary condition (2) fornitrogen. Surface concentration C2(0,τ) for oxygen was proposed to consider as a function of time. Itis taken into account by mass transfer coefficient H. The solution of the system of equations (1) withthe boundary conditions (2) is following:C1(x,τ) =CS1 −CS2 [(λ12+α12) f1(x,τ)−α12 f2(x,τ)], C2(x,τ) =CS2 f2(x,τ), (5)here f1(x,τ) = erfc[x2√D11τ]− exp[H√D11D22x+H2τD22]· erfc[H√τ√D22+x2√D11τ],f2(x,τ) = erfc[x2√D22τ]− exp[HxD22+H2τD22]· erfc[H√τ√D22+x2√D22τ], α12 =D12D22−D11 .In particular, the time dependences of surface concentrations of components are following:C1(0,τ)=CS1−CS2λ12 f (0,τ), C2(0,τ)=CS2 f (0,τ), where f (0,τ)= 1−exp[H2τ/D22]·erfc[H√τ/D22] .(6)On the basis of obtained solutions (3), (4), the time dependences of surface concentrations of nitrogenand oxygen in titanium (Fig. 2a) and their spatial distributions in the diffusion zone (Fig. 2b) aftersaturation at T = 800◦C for 3h were calculated. The curves were plotted according to the followingparameters: D11 = 1.2 · 10−2 · exp(−45250/RT ) cm2/s, D12 = λ12D11, D22 = 0.8 · exp(−48000/RT )cm2/s, CS1 = 16 at. %, CS2 = 33 at. % [2], H = 5 ·10−7 cm/s, λ12 = 0.5.Figure 2: Time dependence of surface concentration of nitrogen and oxygen (a) and their spatial distributions intitanium after saturation at T = 800◦C for 3h. For nitrogen: curves 1 are for λ12 = 0.5, curve 1’ is for λ12 = 0; foroxygen: curves 2Surface concentrations of oxygen and nitrogen depend on the saturation duration (Fig. 2a). The surfaceoxygen concentration (curve 2) increases gradually to equilibrium value with the medium because ofslow oxygen delivery to titanium surface. The surface nitrogen concentration (curve 1), despite onthe constant chemical potential on the surface, decreases with increase of exposure because of theincrease of surface oxygen concentration. The diffusion zone with nonuniform distribution of oxygenand, especially nitrogen is formed in the near-surface layer of titanium as a result of gasing (Fig. 2b).The depth of the diffusion zone is determined by the distribution of oxygen concentration (curve 2),because the oxygen diffusion coefficient is two orders of magnitude larger than nitrogen diffusioncoefficient. Distribution of nitrogen taking into account the influence of oxygen (curve 1) and withoutsuch consideration (curve 1’) is different substantially. Nitrogen is pushed from titanium surfaceinto the more distant zone because of the influence of diffusion dissolved oxygen. Under the certaintime and temperature parameters the nitrogen distribution (curve 1) is nonmonotonic, its maximumconcentration is not fixed on the titanium surface, but in the more distant zone from surface. Suchcharacter of nitrogen distribution is agreed with the experimental data [3].References[1] Ya. Matychak, I. Pohrelyuk, V. Fedirko, O. Tkachuk, In: J. Sieniawski, W. Ziaja (Eds.): Titaniumalloys – Advances in properties control. InTech, Rijeka, 45–68 (2013)[2] E. Fromm, E. Gebhardt: J. Sieniawski, W. Ziaja (Eds.): Gase und Kohlenstoff in Metallen.Springer-Verlag, Berlin-Heidelberg-New York (1976)[3] H. Dong, X.Y. Li: J. Sieniawski, W. Ziaja (Eds.): Oxygen boost diffusion for the deep-case hard-ening of titanium alloys. Materials Science & Engineering A 280, 303–310 (2000)

Kinetic peculiarities of two-component diffusion saturation of titanium under rarefied nitrogen-oxygen-containing medium

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Kinetic peculiarities of two-component diffusion saturation of titanium under rarefied nitrogen-oxygen-containing medium

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