Kinetics and mechanism of lead-iodide film growth on lead

The tarnishing rate of Pb with iodine vapor in the temperature and pressure ranges of 423–523 K and 0.615–6.578 kPa, respectively, have been studied. The film-growth kinetics follow the parabolic law. The iodine-vapor-pressure dependence of the isothermal parabolic rate constant has been observed to be k_Pp _I2 ^1/2 which is explained on the basis of the migration of electron holes across the film as the rate-limiting step. The activation energy value for iodination of Pb under normal conditions in an iodine pressure of 0.615 kPa is estimated to be 64 kJ·mol^–1. In contrast, the rate of iodide-film growth has been found to increase considerably under a short-circuit mode of experiments. Such observations have been explained with the help of ion migration as the rate-limiting step for the film-growth process. The iodine-pressure dependence of the rate constant under short-circuit conditions is found to be k_Pp _I2 ^1/3 associated with an activation energy of 51 kJ·mol^–1. Results of the present study have been explained assuming Schottky-Wagner-type point defects in the lead-iodide film, where an equivalent number of vacancies in the cationic and anionic sublattices are present, and taking into account Wagner's electrochemical potential gradient as the main driving force for the film-growth process. The kinetics results have been substantiated through characterization of iodide films by SEM, EDS, EPMA, and XRD analyses.     

Kinetics and Mechanism of Iodide-Film Growth on Lead-Effect of Short-Circuiting and Lower-Valent Dopant

The influence of Ag as a lower-valent dopant onthe kinetics of lead iodination under normal andshort-circuit conditions in iodine pressures of 0.615 to6.578 kPa in the temperature range of 423 to 523 K was investigated. Like pure Pb, Ag-doped Pbalso follows the parabolic law of film growth. Theisothermal parabolic rate constants are found todecrease in the presence of the dopant. The iodinevapor-pressure dependence of isothermal parabolic rateconstants was observed to be k_P p _I2 ^1/2 . Results for normal iodination areexplained in terms of migration of electron holes underthe influence of Cabrera-Mott's electrical field across the film. Theactivation energy for normal iodination of Ag-doped Pbis estimated to be 84 kJmol^-1 comparedto that of 64 kJmol^-1 for pure lead. Therate of iodide-film growth has been found to decrease further undershort-circuit mode of experiments. Such observationshave been explained with the concept of ion migration asthe ratelimiting step for the film-growth process. The iodine pressure dependence of the rateconstants under short-circuit conditions is observed tobe k_P p _I2 ^1/3 associatedwith an activation energy value of 66kJmol^-1. Unlike pure lead, introduction of additional resistances in series to theshort-circuit Pt path during iodination of Ag-doped Pbcaused an increase in the rates with gradual increasedvalue of resistances. Kinetics results are explained by considering the prevalence ofSchottky-Wagner type of point defects in lead iodide.The driving forces for migration of the defect speciesthrough the growing pure PbI₂ films andAg-doped PbI₂ are confirmed to be Wagner's electrochemical potentialgradient and Cabrera-Mott's electrical field,respectively. The iodide films were characterized bySEM, EDS, EPMA, AES, and XRD analyses to substantiatethe kinetic results.     

Sulfidation of iron at high temperatures and diffusion kinetics in ferrous sulfide

The kinetics and mechanism of iron sulfidation have been studied as a function of temperature (950–1200 K) and sulfur pressure (10^–3-0.065 atm). It has been stated that a compact Fe_1–yS scale on iron grows according to the parabolic rate law as a result of outward lattice diffusion of metal ions through cation vacancies. The activation energy of sulfidation increases with sulfur pressure and the 1/n exponent increases with temperature. This nontypical dependence of iron sulfidation kinetics on temperature and pressure results from the analogous effect of both these parameters on defect concentration in ferrous sulfide. The chemical diffusion coefficients,D_FeS, and diffusion coefficients of defects, D_d, in ferrous sulfide have been calculated on the basis of parabolic rate contacts of iron sulfidation and deviations from stoichiometry in ferrous sulfide. It has been shown thatD_FeS is practically independent of cation vacancy concentration whereas the diffusion coefficient of defects depends strongly on that parameter. A comparison of self-diffusion coefficients of iron in Fe_1–yS calculated from the kinetics of iron sulfidation to those obtained from radioisotopic studies indicates that within the range studied of temperatures and sulfur vapor pressures the outward diffusion of iron across the scale occurs preferentially along the c axis of columnar ferrous sulfide crystals.     

Sulfidation properties of an Fe-23.4Cr-18.6Al alloy at temperatures 1073 and 1173 K in H2S-H2 atmospheres of sulfur at pressures 104-10−5 Pa

An investigation is reported on the sulfidation properties of an Fe-23.4Cr-18.6Al(at.%) alloy at 1073 and 1173 K in H₂S-H₂ atmospheres, 10⁴ > P_{S 2} 10⁵Pa. The sulfidation kinetics exhibited an early transient period before onset of parabolic kinetics. Values of the parabolic sulfidation rate constants increased by as much as 10⁵ from their smallest values at low sulfur pressures, P_{S 2} 10^–4 Pa, to maximum values at sulfur pressures P_{S 2} 10² Pa. Multilayered scales were formed, the number and types of layers dependent on sulfur pressure. A fully developed scale at sulfur pressures P_{S 2} > 10^–3 Pa.     

Influence of an Externally-Applied Static Charge on the Oxidation Kinetics of Copper

The kinetics of copper oxidation under theinfluence of an externally-supplied static charge ofeither kind at one of the reaction interfaces of agrowing oxide film on its subsequent thickening weredetermined in the temperature range of 523-1173 K andoxygen-pressure range of 5.06-50.66 kPa. The kineticsconformed to the parabolic rate law under all conditionsof experimentation. In the temperature range of 523-723 K, charge supply of either kind ateither of the oxide interfaces, reduced the ratescompared to normal oxidation. The reduction in rates ismore pronounced with (-)ve charge supply. In thistemperature range, Mott's in situ electrical-potentialgradient across the oxide film is identified as thepredominant driving force for migration of copper ionsduring the subsequent film-thickening process. On the other hand, in the temperature range of 873-973K, a charge supply of either kind enhanced the ratescompared to normal oxidation, where Wagner'selectrochemical-potential gradient acts as the maindriving force for ion diffusion. However, at 1073 K and1173 K, the rates were found to decrease slightlycompared to normal oxidation. The oxygen-pressuredependencies of rate constants at 623 K exhibitedrelations of the type k_P P _O2 ^1/4 for normal and k_p P _O2 ^1/8 (approximately) for oxidation witheither (+)ve or (-)ve charge supply at the oxide/oxygeninterface. However, at 873 K the oxygen-pressuredependencies of rate constants conform to k_P P _O2 ^1/6 for normal as well as for oxidationwith either (+)ve or (-)ve charge supply at theoxide/oxygen interface. The estimated activationenergies are 54 kJ/mol and 160 kJ/mol in Mott's and Wagner's parabolic ranges,respectively. It is established that migration of Cu+ions through the growing film is the rate-limiting stepunder all conditions of experimentation. This study has clearly demonstrated that changes inoxidation rates can be brought about by disturbing theinterfacial defect equilibria with anexternally-supplied static charge when no net currentflows through the oxide film. The estimated self-diffusivityvalues of Cu⁺ ions in the growingCu₂O at 873 K are also reported.     

The corrosion behavior of Fe-Al alloys in H2/H2S/H2O atmospheres at 700–900°C

The corrosion behavior of five Fe-Al binary alloys containing up to 40 at. % Al was studied over the temperature range of 700–900°C in a H₂/H₂S/H₂O mixture with varying sulfur partial pressures of 10^–7–10^–5 atm. and oxygen partial pressures of 10^–24–10^–2° atm. The corrosion kinetics followed the parabolic rate law in all cases, regardless of temperature and alloy composition. The parabolic rate constants decreased with increasing Al content. The scales formed on Fe-5 and –10 at.% Al were duplex, consisting of an outer layer of iron sulfide (FeS or Fe_1–xS) and an inner complex scale of FeAl₂S₄ and FeS. Alloys having intermediate Al contents (Fe-18 and –28 at.% Al) formed scales that consisted of mostly iron sulfide and Al₂O₃ as well as minor a amount of FeAl₂S₄. The amount of Al₂O₃ increased with increasing Al content. The Fe 40 at.% Al formed only Al₂O₃ at 700°C, while most Al₂O₃ and some FeS were detected at T800°C. The formation of Al₂O₃ was responsible for the reduction of the corrosion rates.     

Oxidation Kinetics and Surface Chemistry of an Fe–Cr–Al–Y Alloy Medium Made of 12-μm Diameter Fibers at Elevated Temperatures in Dry Air

Fiber media composed of Fe–Cr–Al–Y alloy are being used increasingly as materials for high-temperature applications for their excellent oxidation resistance. The oxidation kinetics of Fe–Cr–Al–Y alloy fiber medium as a heat-resistant material for high-temperature applications was studied in dry air at 1073, 1188, 1255, and 1318 K. The oxidation process followed the parabolic kinetic law. The alumina-scale growth was found to be influenced by short-circuit diffusion and the presence of stresses related to oxide-scale growth. The surface of the oxide scale formed on the fiber medium was analyzed using X-ray photoelectron spectroscopy, which revealed that the outer surface of the oxide scale formed on the fiber medium composed of 12-m diameter Fe–Cr–Al–Y alloy fibers, consisted of -Al₂O₃, -Al₂O₃, and Cr-oxide. The metastable -Al₂O₃ subsequently partially transformed into the more stable -phase following a time-temperature-transformation relationship. The surface morphology and the cross section of the oxide scale formed on the fiber medium in the temperature range 1073–1318 K in dry air, have been studied by scanning-electron spectroscopy (SEM) and focused-ion beam, respectively.     

Sulfur effects on the internal carburization of Fe-Ni-Cr alloys

Several commercial and laboratory-cast model austenitic alloys have been exposed in both sulfur-free carburizing environments and also in carburizing atmospheres to which additions of H₂S have been made. These studies were concentrated over the temperature range 1223–1323 K at a fixed carbon activity (a_c=0.8) with sulfur activities ranging from 2.2×10^–12 bar to 1.4×10^–9 bar. Under conditions of sulfur adsorption, e.g., 5.5 × 10^–11 bar at 1273 K, the blocking of adsorption sites for methane resulted in a transition from the parabolic kinetics observed during sulfur-free carburization to surface controlled linear kinetics. Higher levels of H₂S promoted the formation of a surface layer of chromium sulfide which reduced internal carburization but became a problem itself. The role of minor alloying elements has been established and the use of thermodynamic phase stability diagrams in defining the optimum conditions for sulfur inhibition of carburization evaluated.     

The corrosion of Fe-Mo alloys in H2/H2O/H2S atmospheres

The corrosion of Fe-Mo alloys containing up to 40 wt.% Mo was studied over the temperature range 600–980C in a H₂/H₂O/H₂S mixture having a sulfur pressure of 10^–5 atm. and an oxygen pressure of 10^–20 atm. at 850C. All alloys were two-phase, consisting of an Fe-rich solid solution and an intermetallic compound, Fe₃Mo₂. The scales formed on Fe-Mo alloys were bilayered, consisting of an outer layer of iron sulfide (FeS) and of a complex inner layer whose composition and microstructure were a function of the reaction temperature and of the Mo content of the alloys. No oxides formed under any conditions. The corrosion kinetics followed the parabolic rate law at all temperatures. The addition of Mo caused only a slight decrease of the corrosion rate. Platinum markers were always located at the interface between the inner and outer scales, indicating that outer scale growth was primarily due to outward diffusion of iron, while the inner scale growth had a contribution from inward diffusion of sulfur.     

Sulfidation properties of nickel-20 wt.% molybdenum alloy in hydrogen-hydrogen sulfide atmospheres at 700°C

The sulfidation kinetics and morphological development of the reaction products for a Ni-20wt.% Mo alloy exposed at 700° C to H₂-H₂S atm at sulfur pressures in the range 1×10^–11 to 2×10^–2 atm are reported. At Ps₂5×10^–11 atm, the reaction product was Mo₂S₃ which grew as an external scale by parabolic kinetics. For 1×10^–1024×10^–10 atm, simultaneous internal precipitation and external growth of MoS₂ occurred by linear kinetics. An external duplex scale was formed at sulfur pressures 2×10^–822×10^–2 atm in which the inner layer was a two-phase mixture of MoS₂ and nickel sulfide, and the outer layer contained solid nickel sulfides and a liquid Ni-Mo sulfide phase. Catastrophic linear kinetics occurred under these latter condition.     

Reoxidation of chromium with densified Cr2O3 Scales

Preoxidized chromium specimens have been high vacuum annealed at 1200° and 1300°C to produce densified Cr ₂O₃ scales. These specimens have been reoxidized at the same temperatures at 10^–6 atm O₂. The initial reoxidation is linear with time and is concluded to reflect a volume diffusion controlled transport through the densified scale. The corresponding parabolic rate constant (w² = k_pt)is given by k_p=1.4 · 10^–2 exp(–235,000/RT)(gram of O) ²/cm⁴ sec. It is tentatively concluded that outward chromium diffusion predominates in an inner layer of the Cr₂O₃ scales and inward oxygen diffusion in an outer layer. Under the experimental conditions it has not been possible to maintain growth of the Cr₂O₃ scales controlled by volume diffusion. The new oxide layer consists of fine crystallites; the oxide grows at grain boundaries within the scales. This causes sideways growth of the scale, breakdown of the originally densified layer, and an increased rate of reaction.     

Influence of temperature and the role of chromium on the kinetics of sulfidation of 310 stainless steel

The sulfidation of 310 stainless steel was studied over the temperature range from 910 to 1285° K. By adjusting the ratio of hydrogen to hydrogen sulfide, variations in sulfur potential were obtained. The effect of temperature on sulfidation was determined at three different sulfur potentials: 39 N·m^–2, 1.4×10^–2 N·m^–2, and 1.5×10^–4 N·m^–2. All sulfide scales contained one or two surface layers in addition to a subscale. The second outer layer (OL-II), furthest from the alloy, contained primarily Fe-Ni-S. The first outer layer0 (OL-I), nearest the subscale, contained Fe-Cr-S. The subscale consisted of sulfide inclusions in the metal matrix. Two different phases were observed in OL-II depending on the temperature and sulfur potential. Below 1065°K OL-II is composed of a mixture of monosulfides of iron and nickel (Fe Ni)_1–xS and pentlandite (Fe_4.5Ni_4.5S₈) with the pentlandite phase exsolved as lamellae upon cooling. At temperatures higher than 1065°K only the pentlandite phase was formed, which melted above 1145°K at sulfur potentials greater than 10^–2 N·m^–2, yielding metal-rich iron-nickel-sulfur. Above 1145°K, and at sulfur potentials less than 10^–2 N·m^–2, OL-II ceased to exist (this temperature is termed transition temperature). Below the transition temperature, where OL-II exists, OL-I could be represented by the general composition (Fe, Cr)_1–xS. This phase on cooling transformed into an array of structures differing in FeCr ratio. These substructures, however, were not observed in quenched samples. Above the transition temperature OL-I changed to a chromium-rich sulfide composition and was associated with a sudden decrease in reaction rate. Subscale formation was found to be due to the dissociation of OL-I at the scale-metal interface, and the extent of subscale growth was found to depend on the temperature and the sulfur potential, as well as the composition of OL-I. At a given temperature and sulfur potential the weight-gain data obeyed the parabolic rate law after an initial transient period. The parabolic rate constants obtained at the sulfur potential of 39 N·m^–2 did not show a break when the logarithm of the rate constant was plotted as a function of the inverse of absolute temperature. Sulfidation carried out at a sulfur potential below 2 × 10^–2 N·m^–2, however, did show a break at 1145°K. This break was found to be associated with the changes which had occurred in the FeCr ratio of OL-I. Below the transition temperature the activation energy was found to be approximately 125 kJ · mole^–1. Above the transition temperature the rate of sulfidation decreased with temperature but depended on the FeCr ratio in the ironchromium-sulfide layers of the OL-I. A reaction mechanism consistent with the experimental results has been proposed in which the diffusion of cations through OL-I is the rate-controlling step. Below the transition temperature the diffusion of Fe and Ni through OL-I contributes to the scale formation, whereas above the transition temperature the diffusion of Cr through OL-I controls the scale formation. Existing literature on the Fe-Ni-S system is compared with the present results.     

Air Oxidation of Ni–Ti Alloys at 650–850°C

The oxidation of pure Ni and three Ni–Ti alloys containing 5, 10, and 15 wt.% Ti over the temperature range 650–850°C in air was studied to examine the effect of titanium on the oxidation resistance of pure nickel. Ni–5Ti is a single-phase solid solution, while the other two alloys consisted of nickel solid solution (-Ni) and TiNi₃. The oxidation of Ni–Ti alloys at 650°C follows an approximately parabolic rate law and produces a decrease in the oxidation rate of pure Ni by forming an almost pure TiO₂ scale. At higher temperatures, Ni–Ti alloys also follow an approximately parabolic oxidation, and their oxidation rates are close to or faster than those of pure Ni. Duplex scales containing NiO, NiTiO₃ and TiO₂ formed. Some internal oxides of titanium formed, especially at 850°C. In addition, the two-phase structure of Ni–10Ti and Ni–15Ti was transformed into a single-phase structure beneath the scales.     

The kinetics and mechanism of catastrophic oxidation of metals

A set of independent methods has been used to study the catastrophic oxidation of copper in the system Cu–Me_xO_y (where Me is Bi, W, Mo, or V). Two stages of the catastrophic oxidation have been revealed: a rapid stage (K10^–4 kg² m^–4 sec^–1) and a super rapid stage when the metal is oxidized within1–5 sec. The weight ratios of metal to oxidizer and the partial oxygen pressure for the superrapid copper oxidation have been established. The mechanism of the catastrophic oxidation of metals is considered.     

Calculations of parabolic reaction rate constants

The oxidation kinetics of only a very limited number of pure metals or binary alloys can be described by the simplest parabolic law, m²=k_pt, Thus for a transient period of faster kinetics, the steady state parabolic law is given by (m–m_i)² = k_p(t–t_i) when the initial weight gain m_i does not contribute to steady state rate control. In such a case, a plot of the kinetics data as m vs t^1/2 is inherently superior to the m² vs t plot for an accurate determination of the steady state parabolic rate constant, as well as for the analysis of the transient, faster kinetics.     

Oxidation and Sulfidation Behavior of AlTiN-Coated Ti–46.7Al–1.9W–0.5Si Intermetallic with CrN and NbN Diffusion Barriers at 850°C

Attempts have been made to improve the high-temperature corrosion behavior of an intermetallic alloy, Ti–46.7Al–1.9W–0.5Si, in an H₂/H₂S/H₂O atmosphere at 850°C using AlTiN coating with and without CrN and NbN diffusion barriers. The oxidation and sulfidation behavior of the uncoated Ti–46.7Al–1.9W–0.5Si alloy followed protective kinetics with a parabolic rate constant of 6×10^–11 g²/cm⁴/s. A multi-layered scale developed: an outer rutile (TiO₂) layer, a continuous layer of -Al₂O₃ beneath the rutile layer, and an inner TiS layer, in which pure W was scattered. Fast outward diffusion of Ti within the substrate resulted in the formation of a zone of high concentration of aluminum (TiAl₃ and TiAl₂) between the scale and substrate.The use of an AlTiN coating greatly increased the oxidation and sulfidation resistance of Ti–46.7Al–1.9W–0.5Si. The use of NbN and CrN diffusion barriers further enhanced its corrosion resistance. The protection of the double-layer coatings persisted even after 240 hr exposure. However the mismatch of thermal expansion coefficients between the coating and substrate led to the development of cracks in some locations within the coatings. A 2.5 m thick AlTiN coating on the Ti–46.7Al–1.9W–0.5Si substrate with an embedded defect was modeled using the general finite element (FE) program ABAQUS. The modeling results showed rapid mode I failure of the coating at a temperature of 774°C. The through-fracture of the nitride film caused the nitride coating to shrink back leading to delamination around the crack in the nitride coating. The cracks formed acted as diffusion paths, for the ingress of oxygen and sulfur species and the outward diffusion of substrate elements, which resulted in the formation of nodular corrosion products with similar morphologies and microstructures to the uncoated alloy in those locations where cracks developed.     

Morphological evolution during sulfidation of an iron-nickel alloy

An Fe-41 wt.% Ni alloy was reacted at 793, 888, and 938K with H₂-H₂S-N₂ mixtures corresponding to equilibrium levels of 3×10^–4–0.65Pa and varying degrees of nitrogen dilution. At 793 K and low values of and , a compact layer of almost pure Fe_1–S was the only product. At values of 5×10³–1×10⁴ Pa, large growths of nickel-rich sulfide whiskers formed on top of the compact layer. At =2.2×10⁴ and = 1.8×10^–3 Pa, the whiskers were replaced by a compact layer of (Ni, Fe)_1–S. Kinetics were irregular at 793 K, but at the higher temperatures parabolic kinetics were observed after an initial period of slow reaction, during which a compact layer of Fe_1–S was the only product. The onset of parabolic kinetics corresponded to the appearance of an additional zone of nickel-rich sulfide. This zone was made up of whiskers, except at high .     

Compositional changes due to the removal of one constituent in an alloy by a surface reaction

The depletion of an alloy by the selective removal of one element is considered when various rate laws apply. Duhamel's technique has been employed to obtain analytical solutions for the change in alloy composition with time. The effect of the depletion of the matrix by selective oxidation on the subsequent oxidation behavior of the alloy is discussed in terms of operating temperature of the alloy.Notation C concentration of solute (g cm^–3) - C _m bulk concentration of solute (g cm^–3) - C(x, t) concentration of solute at distancex from surface after timet(g cm^–3) - t time - x distance - W _o increase in weight due to takeup of oxygen - W _m change in weight due to metal entering the oxide - M _o molecular weight of anion - M _m molecular weight of cation - Z valency of cation - 2M _m/M _o - k _l linear rate constant (g cm^–2 sec^–1) - k _p andk _p parabolic rate constants (g² cm^–4 sec^–1) - k _e andk _e logarithmic rate constants - D diffusion coefficients of solute in metal     

Sulfidation properties of Fe-Cr alloys at 1073 K in H2S-H2 atmospheres of sulfur pressures 10−2 and 10−5 Pa

An investigation is reported on the sulfidation properties of Fe-Cr alloys over their complete compositional range in H ₂ S -H ₂ atmospheres at 1073 K. Sulfidation of alloys containing less than 60 at. % Cr obeyed parabolic kinetics and alloys of larger chromium content and chromium followed linear kinetics. Scales were composed of two distinct layers: an outer columnar grained sulfide and an inner equiaxed grained sulfide layer of increased relative thickness and porosity at larger alloy chromium contents. The scales on quenched specimens were composed of either (CrFe) ₅ S ₆ or (FeCr)S plus small amounts of (FeCr) ₃ S ₄ at =10 ^–2 Pa and of (CrFe) ₅ S ₆ at =10 ^–5 Pa. Internal sulfidation was most pronounced in the high chromium content alloys and at the low sulfur pressure. The parabolic sulfidation rate at =10 ^–2 Pa was large and of practically constant value irrespective of alloy composition. These kinetics at =10 ^–5 Pa, however, increased from a very low value by three orders of magnitude as the alloy chromium content was increased from 5–60 at.%.     

Cracking Behavior of Cr2O3 Scales on Fe–25Cr Alloys Under Creep Deformation at 973 K in Ar Atmosphere

An Fe–25Cr alloy was oxidized in Ar at 973 K with or without external stresses of 30, 35, and 40MPa. A 0.1-m thick Cr₂O₃ scale was formed during pretreatment, after which it grew obeying a parabolic rate law without formation of flaws, i.e., cracks and exfoliation. After the pretreatment, tensile stresses of 30, 35, and 40 MPa were applied to monitor cracking behavior of the oxide scale. Cracking commenced at the alloy grain boundaries by the end of a second-stage creep. In a third stage, cracks formed in the alloy grains, arrayed almost perpendicular to the direction of the tensile stress, with regular intercrack spacings. The average intercrack spacings (L) at grain boundaries are smaller than the intercrack spacing of the grains, and the spacings are given by the power law relation: L()ⁿ, with strain rate exponents n of -0.22 for grains and –0.44 for grain boundaries. It appears that the local strain rate at grain boundaries is much larger than that of the grain as well as that the toughness of the oxide formed on the grain boundaries may be less than that of the grains. Indentation with a Vickers micro hardness tester indicated that the adhesion and fracture toughness of the oxide scale decreased both with growth of the oxide scale and creep deformation of the alloy substrate.