Thermochemical Processes Episode 10

262 Thermochemical Processes: Principles and Models and tate dA Ar e2r2 dx Hence the rate of formation of the molecules MaAb cm 2 s 1 ( ) dt D Jb J a C D e2 1b2 Ai 0 .te.tc C ta/bdA x where x is the instantaneous thickness of the product, and A0 and Ai are the chemical potentials of A at the outer and inner faces of the reaction product. For the oxidation of Ni.mC D 2/, ( ) O .oxide/gas/ D D 2 te.tNi2C C tO2 / dlnpO2 O2.metal/oxide/ Here, te ¾ 1 and tO2 is negligible, and thus the rate of oxidation is determined by the partial conductivity due to the Ni2C ions. If the oxidizing gas is pure oxygen, and tNi2C remains approximately constant over the oxide thickness k G° x 8e2 Ni2C x where G° is the Gibbs free energy change of the reaction 2Ni C O2 ! 2NiO Furthermore, using the Nernst–Einstein equation to substitute in the general equation above yields Z pO .oxide/gas/ D .DM C D0/dlnpO moles/cm s pO2.metal/oxide/ The carburizing and oxidation of transition metals These two processes provide examples of the moving boundary problem in diffusing systems in which a solid solution precedes the formation of a compound. The thickness of the separate phase of the product, carbide or Gas–solid reactions 263 Carbide Metal Cs Gas (CH4) CII, I CI, II x 0 x direction Figure 8.1 Schematic of the carburization of a metal oxide, increases with time thus moving the boundary of the solid solution phase away from the gas–solid interface. In the kinetics of formation of carbides by reaction of the metal with CH4, the diffusion equation is solved for the general case where carbon is dissolved into the metal forming a solid solution, until the concentration at the surface reaches saturation, when a solid carbide phase begins to develop on the free surface. If the carbide has a thickness at a given instant and the diffusion coefficient of carbon is DI in the metal and DII in the carbide, Fick’s 2nd law may be written in the form (Figure 8.1) Metal ∂c D DI ∂xc.x > / Carbide ∂c D DII ∂xc.0 x / for each phase. When the metal/carbide boundary moves away from the free surface of the sample by an increment d, the flux balance at this interface reads .CII,I CI,II/d D DII ∂c C DI ∂c υ Cυ 264 Thermochemical Processes: Principles and Models where CII,I is the concentration of carbon in the carbide at the carbide/metal interface, and CI,II is that in the metal at the same interface. Introducing the relationships and definitions which were used earlier D DII ; I 2 .DIIt/1/2 and replacing CI,II Cs CII 1 erf ./1/2 I erf II where Cs is the carbon concentration in the carbide at the gas/carbide interface, the solutions of Fick’s equations may be represented as follows: The concentration of carbon in the carbide phase is Cx D Cs BII erf 2.DIIt/1/2 0 x and in the metal phase Cx D BI 1 erf 2.DIt/1/2 x > and substituting into the flux balance equation at the interface .Cs CII,I/ CI,II exp. 2/ x 1/2 erf ./1/2[1 erf .1/2/] and BII exp. 2/ BI exp .2/ II,I I,II 1/2 ./1/2 where CII,I CI,II is the difference in the content of carbon between the carbide and metal phases at equilibrium. The equation for the rate of oxidation of the transition metals at high temper-atures, which form a solid solution of oxygen before the oxide appears at the surface has the same form as that derived for the carburizing of the metal, and Gas–solid reactions 265 the weight change/unit area, m/A, can be expressed as a function of time by the formula A D [K.oxide formation/ C K0.oxygen dissolution/]pt D K00pt where K D 2.CI,II CII,I/Doxide and using the definition of given above K0 D 1/21 erfI.1/2/Dmetal exp. 2/ where CII,I CI,II reflects difference between the the oxygen content of the oxide at the oxide–metal interface, and the saturation solubility of oxygen in the metal and is the ratio of the oxygen diffusion coefficients Doxide/Dmetal. There can be little doubt that the carburization process occurs by the inward migration of interstitial carbon atoms, and the major sources of evidence support the view that the oxidation process in the IVA metals, Ti, Zr, and Hf, and in the VA metals Nb and Ta, involves a predominant inward migra-tion of oxygen ions with some participation of the metallic ions in the high temperature regime (>1000°C). The mechanism of oxidation is considerably affected by the dissolution of oxygen in the metal, leading to a low-temperature cubic or logarithmic regime, an intermediate region of parabolic oxidation, and then a linear regime in which the vaporization of the oxide can play a signif-icant part. The temperature ranges in which each of these regimes operates varies from metal to metal and to summarize, the parabolic region extends from about 400–1100°C in the Group IVA elements, but the situation is much more complicated in the Group VA elements because of the complexity of the oxide layers which are found in the oxidation product of Nb and Ta. In these latter elements, the parabolic regime is very limited, and mixtures of linear and parabolic regimes are found as a function of the time of oxidation. It is clear that the dissolution of oxygen in these metals occurs by the inward migration of oxygen, and conforms to the parabolic law. In the oxidation of the Group IVA metals the only oxide to be formed is the dioxide, even though the Ti–O system shows the existence at equilibrium of several oxides. This simplicity in the oxide structure probably accounts for the wide temperature range of parabolic oxidation, although the non-stoichiometry of monoclinic ZrO2 has been invoked to account for the low-temperature behaviour of the oxidation reaction. The mechanisms at low temperature are complicated by a number of factors, including the stresses in the oxide layer which, unlike the behaviour at high temperatures, cannot be relieved during oxidation. Several explanations are given invoking the relative transport numbers of electrons and ions, the formation of pores at the oxide/metal interface, and unrelieved 266 Thermochemical Processes: Principles and Models stresses in the metal which change during the oxidation period as the oxygen solution becomes more concentrated. Whatever the mechanism(s), it is signifi-cant that the oxide is protective for a useful period of time, allowing zirconium cladding to be used for the UO2 fuel rods in a nuclear reactor, but this lifetime is terminated in breakaway corrosion. At high temperatures the change in mechanism to a linear oxidation rate, after a short period of parabolic oxidation, indicates that the stresses in the oxide layer which arise from the rapid rate of formation, cause rupture in the oxide, allowing the ingress of oxygen. The cracks which are formed in the oxide will probably vary in morphology and distribution as a function of time of oxidation, due to the sintering process and plastic flow which will tend to close up the cracks. The oxidation of the Group VA elements, Nb and Ta is complicated by the existence of several oxides which are formed in sequence. For example, the sequence in niobium oxidation is Nb–[O]solid solution–NbO–NbO2–Nb2O5 The pentoxide layer always appears to be porous to oxygen gas and therefore provides no oxidation protection. The lower oxides grow more slowly, and can adapt to the metal/oxide interfacial strains, and provide protection. The low temperature oxidation conforms to a linear rate law after a short interval of parabolic behaviour, corresponding to the formation of a solid solution and a thin layer of oxide which is probably an NbO–NbO2 (sometimes referred to as NbOx) layer in platelet form, which decreases in thickness as the tempera-ture increases. This mechanism is succeeded by a parabolic behaviour over a longer period of time which eventually gives way to a linear growth rate as the temperature increases above about 600°C. It is probable that the parabolic behaviour in this regime is rate-determined by the formation of more substan-tial NbO–NbO2 layers before the pentoxide is formed. The oxidation kinetics of the metals molybdenum and tungsten in Group VI reflect the increasing contribution of the volatility of the oxides MoO3 and WO3 as the temperature increases. At temperatures below 1000°C, a protec-tive oxide, is first formed, as in the case of niobium, followed by a linear rate when a porous layer of the trioxide is formed. There appears to be no signif-icant solubility of oxygen in these metals, so the initial parabolic behaviour is ascribed to the formation of the dioxide. At higher temperatures the porous layer of oxide is restricted in thickness by increasing vaporization, and this process further restricts the access of oxygen to the surface until a steady state is reached, depending on the state of motion of the oxidizing atmosphere. The oxidation of metallic carbides and silicides The expected oxidation mechanisms of carbides and silicides can be analysed from a thermodynamic viewpoint by a comparison of the relative stabilities ... - tailieumienphi.vn