Concentration Of Cation Vacancies Research Articles

Effects of Y3+ doping on the microstructure evolution, optical, dielectric, and non-Ohmic properties of Na1/3Cd1/3Bi1/3Cu3Ti4O12 ceramics

In this study, Na1/3Cd1/3(Bi1-xYx)1/3Cu3Ti4O12 (NCBYCTO, x = 0−0.20) ceramics were successfully prepared via solid state method. Their microstructure along with the optical, dielectric, and non-Ohmic properties were investigated systemically. It was shown that Y3+ doping caused the decrease in cation vacancy concentration and the increase in optical energy band. With the increase of Y3+ content, ceramics exhibited a more stable structure, while their average grain size increased from 6.80 μm to 9.12 μm and then decreased to 2.17 μm with the dopant amount. The relative density increased from 94.7 % for the undoped specimen to 95.6 % for the specimen with x = 0.20. The giant dielectric constant (ɛ′ = 44200) at a relatively low dielectric loss (tanδ = 0.048) at 10 kHz was obtained in the specimen with x = 0.08, being more than three times that of undoped sample and demonstrating the outstanding frequency stability in the range of 40−106 Hz. The giant dielectric constant below 106 Hz originated from Maxwell–Wagner relaxation related to the insulating grain boundaries (GBs) and followed the internal barrier layer capacitor model. Besides that, Y3+ doping improved the nonlinearity properties of NCBYCTO ceramics. The specimen with x = 0.20 had the largest nonlinearity coefficient α (∼9.60) and breakdown field strength Eb (∼7.15 kV/cm). At last, the nonlinear J-E characteristics were closely related to the GB conductivity activation energy.

Exploring the electrochemical properties of lithium-ion battery electrodes composed of vacancy-defective zinc-substituted magnetite nanocrystallites

Single phase Zn2+-substituted magnetite nanocrystallites are synthesized via co-precipitation method and used as lithium-ion battery electrodes. The structural properties and vacancy distribution of nanoparticles are evaluated by X-ray diffraction, X-ray photoelectron spectroscopy (XPS), and positron annihilation lifetime spectroscopy (PALS). The Rietveld refinement of the X-ray diffraction patterns shows that the lattice constant increases with Zn2+ content from 8.392 Å for magnetite to 8.448 Å for Zn0.2Fe2.8O4. The XPS measurements show that cation vacancies increase with Zn content on the surface of nanoparticles. Positron annihilation lifetime spectra suggest more concentration of monovacancies and larger size of vacancy clusters in the Zn0.1Fe2.9O4 sample compared with the other two samples, Fe3O4 and Zn0.2Fe2.8O4. Electrochemical measurements show better reversibility, higher initial discharge capacity, and lower electrochemical impedance for the Zn0.1Fe2.9O4 electrode, which are attributed to the higher concentration of vacancy defects in its nanocrystallites. The electrochemical impedance spectroscopy (EIS) shows that the Li+ diffusion coefficient (DLi+) increases with Zn2+ doping from 1.51 × 10–15 cm2s–1 for Fe3O4 to 3.25 × 10–13 cm2s–1 for Zn0.1Fe2.9O4, and 1.43 × 10–13 cm2s–1 for Zn0.2Fe2.8O4. The initial discharge capacities of the samples found to be about 1345.04 mAh g−1 for Fe3O4, 1435.82 mAh g−1 for Zn0.1Fe2.9O4, and 1063.72 mAh g−1 for Zn0.2Fe2.8O4 electrodes, respectively. During first few cycles, the discharge capacity decline faster as Zn content increases. The discharge capacity of the Zn0.2Fe2.8O4 electrode is stable at 410 mAhg−1 from the 60th to the 200th cycle, which is higher than the Fe3O4 electrode (150 mAhg−1) and the Zn0.1Fe2.9O4 electrode (270 mAhg−1). This variance is explained by the cation vacancy concentration and the lattice constant of the samples. The impedance of the electrodes is also affected by the vacancy defects formed during the sample preparation.

Building a depletion-region width modulation model and realizing memory characteristics in PN heterostructure devices.

Memristive systems have potential applications in nonvolatile memories and even unexplored functionalities in electronics. However, progress has been delayed by difficulties in the controllability of memory behaviors and the dependence on material conductivity. Considering this, a new depletion-region width modulation model is proposed to realize and explain memory characteristics. The coexistence of memristive and memcapacitive behaviors is demonstrated in p-CuAlO2/n-ZnO, p+-Si/n-ZnO and p-NiO/n-ZnO heterostructure devices. A high external electric field induces the migration of oxygen ions and electrons/holes between the p-type and n-type semiconductor layers. It can regulate the oxygen vacancy concentration of the n-type side and cation vacancy concentration of the p-type side, changing the depletion-region width and modulating device conductivity and capacitance. Several essential synaptic functions were accurately imitated, including spike-timing-dependent plasticity (STDP) and "learning-experience" behaviors. This work provides new opportunities in fabricating a memristor and memcapacitor based on a PN heterostructure for synaptic simulation.

Enhanced energy storage performance in samarium and hafnium co-doped silver niobate ceramics

Improving energy storage density and efficiency of antiferroelectric materials could promote their use within energy storage field, particularly in the context of pulsed power sources. In this study, Sm and Hf co-doped silver niobate (AgNbO3; AN) ceramics were prepared using traditional solid-state method. Comprehensive analysis of crystal structure, microstructure, defects, absorbance, and energy storage performance of the material was conducted. Results reveal that co-doping increased the concentration of cation vacancies and band gap, decreased the M1–M2 and M2–M3 phase transition temperatures, and enhanced the antiferroelectric phase stability and energy storage performance. The (Ag0.955Sm0.015)(Nb0.95Hf0.05)O3 ceramic exhibited energy storage density of 5.35 J/cm3 and energy storage efficiency of 73% at electric field (E) of 295 kV/cm, demonstrating significant improvement. The (Ag0.955Sm0.015)(Nb0.95Hf0.05)O3 ceramic exhibited excellent thermal stability (<5% in the range of 25 °C-125 °C) and frequency stability (<3% in the range of 1–100 Hz under E = 290 kV/cm). Additionally, the (Ag0.955Sm0.015)(Nb0.95Hf0.05)O3 ceramic exhibited ultrahigh discharge speed (∼18 μs) and high discharge energy density (4.9 J/cm3). These advantages make these ceramics promising materials for energy storage applications.

Indium containing sillenite semiconductor: Synthesis, structural, spectroscopic, and thermogravimetric analysis

AbstractSillenite‐type ceramics are non‐centrosymmetric phases of ongoing research interest because of their structural defects and optoelectronic properties. We report a series of sillenite compounds with a general composition Bi12(Bi3+4/5−3xIn3+5x□1/5−2x)O19.2+3x□0.8−3x for x = 0.03–0.27 to understand how the crystal–physicochemical properties change with a successive filling of empty Bi3+ positions in the tetrahedral site by In3+ cation. Conventional solid‐state synthesis method is used to prepare the microcrystalline samples. Each sample is characterized by X‐ray diffraction, Raman, UV/Vis diffuse reflectance spectroscopy, and thermogravimetry (TG/DSC). X‐ray powder data Rietveld refinement reveals that phase‐pure samples can be obtained for x = 0.03–0.08 in the space group I23. Appearance of starting In2O3 as minor phases with the final products for 0.10 &lt; x &lt; 0.27 suggests for xmax = 0.08. The successive decrease of the lattice parameter indicates the incorporation of smaller In3+ cations in the structure. The effect of the lone electron pairs of Bi3+ and the structural cation vacancies lead to the modification of the interatomic bond lengths. At least one Raman active phonon mode shows hardening for decreasing cation vacancy concentration in the system. The bandgap energy increases with increasing indium content. An additional absorption band at lower energy for x = 0.03–0.08 complements the theoretical study, which completely disappears for x &gt; 0.08. The stronger In–O bonds play pivotal roles in the thermal stability of the phases studied by TGA/DSC analysis.

Using vacancies to tune mechanical and elastic properties in La3−xTe4, Nd3−xTe4, and Pr3−xTe4 rare earth telluride thermoelectric materials

Elastic and mechanical properties in advanced RE3−xTe4 (RE = La, Pr, Nd) thermoelectric materials are found to depend considerably on cation vacancy concentration x. Increasing x, which simultaneously reduces charge carrier concentration from metal-like to semiconductor-like, leads to significant stiffening of elastic constants due to charge carrier effects. The coefficient of thermal expansion in La3−xTe4 determined by high temperature X-ray diffraction correspondingly decreases with x, indicating that thermal expansion may be tuned by x in RE3−xTe4 materials systems. Vickers indentation hardness and fracture toughness tests show similarly significant effects of x on hardness and mode I fracture toughness, both of which decrease with increasing x. The mechanical property trends are counter-intuitive and merit further investigation, but demonstrate overall that higher x in RE3−xTe4 leads to more brittle behavior. The combined results show the importance of intrinsic defects in RE3−xTe4 and the potential to tune the mechanical performance of RE3−xTe4 for practical implementation in next-generation thermoelectric devices.

Passivity Breakdown and Crack Propagation Mechanisms of Lean Duplex (UNS S32001) Stainless Steel Reinforcement in High Alkaline Solution Under Stress Corrosion Cracking

The passivity breakdown and subsequent stress corrosion cracking (SCC) of Type 2001 lean duplex stainless steel (UNS S32001) reinforcement were investigated in a highly alkaline environment containing chlorides at a low temperature. Electrochemical analysis and mechanical testing were utilized to characterize the passive film development. Fractographic analysis was performed, correlating microstructure and corrosion performance, to reveal preferential crack paths. A chloride threshold below 4 wt% Cl− for a high alkaline environment was elucidated, with pitting susceptibility factor values close to unity, having a threshold critical areal cation vacancy concentration for passivity breakdown close to the 1013 cm−2. Pit initiation leading to passivity breakdown and crack nucleation in 4 wt% Cl− was triggered for stresses above σy, developing a low-frequency peak (0.1 Hz to 0.01 Hz) of the cracking process. Current peak deconvolution demonstrated passivity breakdown was triggered by the intensification in the rate of Type II transient and exposure time, while an increase in transient amplitude was related to the crack propagation. The α phase served as a nucleation site for pits, whose propagation was arrested at the γ phase. Predominant intergranular-SCC morphology through the α/γ interface was developed following anodic dissolution given the more active nature of the α phase (most active path); minor transgranular-SCC propagated through γ phase when high-stress concentration was reached, corresponding to slip-step dissolution.

Preparation of Al and Sm Co-doped Apatite-Type Lanthanum Silicate Electrolyte and analysis of the conductivity mechanism

The contradiction between the increasing demand for energy and the scarcity of traditional fossil energy sources is becoming increasingly acute, and it is urgent to accelerate the development and use of new, more efficient, and environmentally friendly energy sources. Apatite-type lanthanum silicate solid oxide electrolyte materials (La9.33Si6O26, LSO) are widely used in the field of fuel cell electrolytes due to their high ionic conductivity and high density. In this paper, Al and Sm co-doped LSO solid electrolytes were successfully prepared by the urea-nitrate combustion method. SEM images, relative density, and linear shrinkage of Al and Sm co-doped lanthanum silicate electrolytes sintered at different temperatures were compared. The results show that the best sintering temperature is 1500°C. The electrical conductivity of La9.33SmxSi5.5Al0.5O25.75+1.5x was analyzed by EIS. The conductivity of La9.33Sm0.2Si5.5Al0.5O26.05 is 2.56 × 10−4 S·cm−1 when measured at 600°C. The reason Al and Sm co-doping enhances the conductance is that Al doping generates oxygen vacancies and increases the interstitial oxygen (Oi) concentration. Doping of Sm not only increases the concentration of Oi but also reduces the concentration of cation vacancies, thus improving the conductivity of the electrolyte.

Effects of local compositional and structural disorder on vacancy formation in entropy-stabilized oxides from first-principles

Entropic stabilization has evolved into a strategy to create new oxide materials and realize novel functional properties engineered through the alloy composition. Achieving an atomistic understanding of these properties to enable their design, however, has been challenging due to the local compositional and structural disorder that underlies their fundamental structure-property relationships. Here, we combine high-throughput atomistic calculations and linear regression algorithms to investigate the role of local configurational and structural disorder on the thermodynamics of vacancy formation in (MgCoNiCuZn)O-based entropy-stabilized oxides (ESOs) and their influence on the electrical properties. We find that the cation-vacancy formation energies decrease with increasing local tensile strain caused by the deviation of the bond lengths in ESOs from the equilibrium bond length in the binary oxides. The oxygen-vacancy formation strongly depends on structural distortions associated with the local configuration of chemical species. Vacancies in ESOs exhibit deep thermodynamic transition levels that inhibit electrical conduction. By applying the charge-neutrality condition, we determine that the equilibrium concentrations of both oxygen and cation vacancies increase with increasing Cu mole fraction. Our results demonstrate that tuning the local chemistry and associated structural distortions by varying alloy composition acts an engineering principle that enables controlled defect formation in multi-component alloys.

A comparative study of the structure, defects, optical, dielectric, and magnetic properties of GdMnO3 multiferroic ceramics synthesized by solid-state reaction and sol-gel methods

In this work, GdMnO3 ceramics were synthesized by solid state reaction and sol-gel methods, and the structure, defects and optical, dielectric and magnetic properties of the synthesized samples were comparatively investigated. The samples synthesized by different methods show a single phase structure without any detectable impurities. The SEM results suggest that the particle size of the specimen obtained by the solid phase route is on the micron scale, while that of the specimen fabricated by the sol-gel route is on the nanometer scale. Compared with the ceramic fabricated by solid-state reaction technology, the specimen synthesized by sol-gel technique possesses lower oxygen vacancies and Mn2+ concentration, and Mn3+ concentration. The positron annihilation analyses show that the cation vacancy concentration of the specimen synthesized by the solid phase approach is higher than that of the specimen synthesized via the sol-gel approach. The compound obtained by the solid phase reaction has better dielectric properties than that obtained with the sol-gel method. The magnetic transition temperature and the effective magnetic moment are influenced by the Mn ion valence state in GdMnO3. The stronger magnetization of the ceramic synthesized via the sol-gel approach is associated with the lower concentration of cation vacancies.

The role of Ge vacancies and Sb doping in GeTe: A Comparative Study of Thermoelectric Transport Properties in SbxGe1-1.5xTe and SbxGe1-xTe Compounds

Optimizing the thermoelectric properties of GeTe-based compounds usually involves the modulation of Ge vacancies and dopants. However, the mixture of vacancies and dopants makes the understanding of the doping mechanism complicated. Herein, two batches of SbxGe1-1.5xTe and SbxGe1-xTe compounds were prepared and the role of Ge vacancies and Sb were systematically studied. Alloying Sb2Te3 in GeTe increases the concentration of cationic vacancies, which boosts the solubility limit of Sb in the GeTe compound. Moreover, such vacancies aggregate and form planar vacancies in SbxGe1-1.5xTe compounds. Both the cationic vacancies and Sb doping in the structure weaken the degree of the rhombohedral distortion. Additionally, doping with Sb in both cases lower the hole concentration effectively but with different regulation mechanism. Apart from the donor characteristic of Sb dopant in the SbxGe1-xTe compounds, the dissolution of Ge-precipitates facilitated by the additional Ge vacancies introduced via alloying with Sb2Te3 reduces the carrier concentration. Furthermore, all-scale hierarchical architectures, including point defects, planar vacancies, and inherent grain boundaries, effectively scatter heat-carrying phonons, resulting in a low lattice thermal conductivity of 1.07 W m−1 K−1 for the Sb0.10Ge0.85Te compound. All these produce a peak ZT value of 1.85 at 724 K for the Sb0.10Ge0.85Te compound.

The structure, optical and magnetic properties of GdMnO3 nano ceramics induced by aluminum substitution

The evolution of Al substitution on the structure, optical and magnetic properties of GdMnO3 was investigated and GdMn1-xAlxO3 (x = 0.00–0.30) nano ceramics were prepared by sol–gel method. All ceramics exhibit the single phase and orthorhombic structure. Al doping causes the change of Raman mode and microscopic morphology of GdMn1-xAlxO3 ceramics. Vacancy concentration firstly decreases and then increases when the Al substitution amount in the range of 0.00–0.15. Vacancy concentration decreases in the Al substitution amount range of 0.15–0.20, and increases in the Al substitution amount range of 0.20–0.30. Optical results indicate that Al doping has an impact on the band gap of GdMnO3 ceramics. Al substitution can adjust the long-range ordering of Gd3+ magnetic moments and magnetic transition temperature. The magnetic transition temperature depends on the local electron density by Al substitution while the magnetization is obviously related to cation vacancy concentration and dilution effect.

The influence of Zr doping on the structure, vacancy defects, and magnetic properties of GdMnO3 ceramics

The influences of the Zr doping on the structure, vacancy defects, and magnetic properties of GdMn1-xZrxO3 (x = 0.00–0.20) ceramic samples synthesized using a solid-state reaction method were investigated. All the GdMn1-xZrxO3 samples formed a single-phase structure, and no phase transformation occurred within the experimental doping range; however, Zr doping caused lattice distortion. The microstructure of the GdMn1-xZrxO3 samples was compact, and Zr doping reduced the grain size. The positron annihilation spectrum (PAS) measurements showed that Zr doping had a great influence on the cation vacancy concentration of GdMn1-xZrxO3 samples. The vacancy concentration increased with increasing Zr doping content from 0.00 to 0.10, and then decreased with the further increase in Zr doping content. XPS results showed that the charge compensation induced by Zr doping was achieved mainly by the decrease of cation valence (forming Mn2+) in the x = 0.00–0.10 ceramics. Appropriate Zr doping obviously improved the transition temperatures and magnetization of the GdMn1-xZrxO3 samples. This investigation demonstrated that the cation vacancy concentration is one of the important factors that could tailor the magnetic properties of GdMn1-xZrxO3ceramics.

The effects of hot isostatic pressing temperature on the structure and properties in GdMnO3 ceramics

In this paper, the effects of hot isostatic pressing (HIP) temperature on the crystal structure, optical, dielectric and magnetic properties of GdMnO 3 ceramics were studied. All samples form a single-phase structure without structural transformation, while HIP temperature induces the changes in lattice parameters. HIP causes the change in Mn ions valence state, oxygen vacancy concentration, Raman vibration modes and microscopic morphology of GdMnO 3 . Vacancy concentration of the samples prepared by HIP at 800 °C increases compared with that of the samples without HIP, then remains unchanged when the HIP temperature is from 800 to 900 °C, and finally decreases with the further increase of HIP temperature. Appropriate HIP temperature can increase the dielectric constant and decrease the dielectric loss. The transition temperature of paramagnetism to antiferromagnetism and magnetization can be significantly affected by HIP temperature. Magnetic transition temperature and magnetization are closely related to Mn 2+ ions concentration and cation vacancy concentration, respectively.

Preparation of praseodymium-doped La9.33(SiO4)6O2 apatite-type solid electrolytes and analysis of the conductivity mechanism

In order to improve the electrical conductivity of lanthanum silicate oxide electrolyte (LSO), La9.33Pr x Si6O26+1.5x (LPSO) solid electrolyte powder doped with praseodymium was synthesized at 600 °C by urea-nitrate combustion method with lanthanum oxide (La2O3) and Praseodymium nitrate hexahydrate (Pr(NO3)3·6H2O) as raw materials. It is shown that the Pr-doped LSO still have the typical apatite structure and occupy the LaII cation vacancy at the 6h position. Optimal sintering temperature is 1550 °C. La9.33Pr0.5Si6O26.75 reaches the highest conductivity (4.80×10−4 S·cm−1 at 600 ºC). The main factor that Pr-doped improves the performance of LSO is that Pr-doped that introduced more interstitial oxygen ions Oi* and increased lattice volume, so improved the transport efficiency of interstitial oxygen. The secondary factor is the decrease in the concentration of cation vacancy after Pr-doped, which reduced the negative defect stacking centers. Thereby, decreases space drag of interstitial oxygen transport which increases conductivity of LSO. The praseodymium doped to enhancement LSO conductivity mechanism that interstitial oxygen concentration-cation vacancies concentration-lattice volume composite enhancement mechanism was proposed.

Modification of grain boundary potential barriers by annealing treatments of PTCR ceramics with identical microstructure and room-temperature resistivity

Semiconducting BaTiO3-based ceramics originating from the same starting powder batch were subjected to different oxidative post-sintering treatments at temperatures between 800 °C and 1200 °C. The annealing profiles were chosen in a way to result in ceramics with same room-temperature and microstructure. However, the different annealing procedures clearly affected the resulting PTCR characteristics above and below the phase transition temperature. Observed changes in electrical properties were investigated by capacitance-voltage measurements and x-ray diffraction. It was found that annealing treatments influence the grain boundary potential barrier height and width by modifying the equilibrium concentration of cation and oxygen vacancies. Moreover, oxidative annealing at 1100 °C appears to influence the temperature development of spontaneous polarization by filling up oxygen vacancies within the grain bulk. These findings not only extent existing knowledge about defect equilibria in barium titanate but also emphasize the strong impact of process parameters on electrical properties of electroceramics.

Fabrication and thermal shock behavior of ZrO2 toughened magnesia aggregates

MgO-based refractories have been regarded as ideal linings for various furnaces owing to high refractoriness and excellent corrosion resistance to basic slag. However, thermal shock damage resulting from poor thermal shock resistance (TSR) of magnesia is the common failing. The present work aimed at improving TSR of magnesia aggregates by introducing microscale monoclinic ZrO2. The results showed that the ZrO2 added could increase cation vacancy concentration and inhibit abnormal growth of MgO grains, which therefore enhanced densification of the specimens. However, when the ZrO2 amount exceeded 15 wt%, densification decreased slightly due to agglomeration of ZrO2 and formation of more microcracks at the MgO grain boundaries. With increasing ZrO2 content, although the flexural strength degraded, the fracture toughness increased constantly because of the toughening effects of crack deflection and crack branching. Besides, although the addition of ZrO2 decreased the thermal conductivity, TSR of the specimens was significantly improved with increasing ZrO2 content due to the increase in toughness and decrease in strength, thermal expansion coefficient as well as Young's modulus. After thermal shock tests, 15 wt% ZrO2 containing specimen exhibited the highest TSR, whose residual strength ratio was about triple of that of the pure magnesia specimen. However, further increasing ZrO2 content to 20 wt% reduced the TSR attributing to the spalling of intergranular ZrO2 agglomerations.

Influence of crystallization temperature and atmosphere on the phase composition, microstructure and electrical properties of Ni–Mn–O thin films

Nickel manganite thin films were prepared by chemical solution deposition from nitrate and acetate precursors on polished alumina substrates. By variation of crystallization temperature between 650 ​°C and 900 ​°C and atmosphere during cooling of the films, the morphology, phase formation and electrical properties of the films were investigated. The electrically conductive spinel phase was formed as a main phase independent of processing conditions exhibiting NTCR characteristics. Cooling down in nitrogen atmosphere favored the decomposition of the spinel phase into nickel oxide and a spinel phase with higher manganese content, but it also reduced the resistance drift of the samples. From this finding it can be deduced that a reduced oxygen partial pressure influences defect equilibria and by that decreases cation vacancy concentration. This supports the assumption that cation redistribution by a cation vacancy diffusion mechanism is a relevant mechanism of resistance drift in such thin films.

Behavior of cation vacancies in single-crystal and in thin-film SrTiO3 : The importance of strontium vacancies and their defect associates

Solid-state diffusion experiments were used to probe the behavior of cation vacancies in the perovskite oxide ${\mathrm{SrTiO}}_{3}$. Two types of nominally undoped (effectively acceptor-doped) ${\mathrm{SrTiO}}_{3}$ systems were studied: (1) single crystals and (2) epitaxial thin films with different Sr/Ti stoichiometries produced by pulsed laser deposition. As diffusion sources, thin films of the perovskite oxide ${\mathrm{BaZrO}}_{3}$ were employed, and diffusion anneals were carried out in air at $1323\ensuremath{\le}T/\mathrm{K}\ensuremath{\le}1523$ for single crystals and at $1073\ensuremath{\le}T/\mathrm{K}\ensuremath{\le}1223$ for thin films. Sample analysis by means of time-of flight secondary ion mass spectrometry (ToF-SIMS) yielded diffusion coefficients of Ba and Zr in ${\mathrm{SrTiO}}_{3}\phantom{\rule{4pt}{0ex}}({D}_{\mathrm{Ba}}$ and ${D}_{\mathrm{Zr}})$. Diffusion profiles in single-crystal samples showed the expected error-function form and yielded ${D}_{\mathrm{Ba}}\ensuremath{\approx}{D}_{\mathrm{Zr}}$ at each temperature, and hence, activation enthalpies of diffusion that are approximately the same, at $(3.0\ifmmode\pm\else\textpm\fi{}0.4)$ eV and $(2.8\ifmmode\pm\else\textpm\fi{}0.4)$ eV. Diffusion profiles in the thin-film samples were unexpectedly complex, showing multiple error-function features. They also yielded ${D}_{\mathrm{Ba}}\ensuremath{\approx}{D}_{\mathrm{Zr}}$ at each temperature, however, but no clear trend was found as a function of Sr/Ti ratio. Comparing results for the two systems, we conclude that the concentration of cation vacancies is orders of magnitude higher in our thin-film samples than in the single crystals. Our results also provide experimental evidence that oxygen vacancies, ${\mathrm{v}}_{\mathrm{O}}^{\ifmmode\bullet\else\textbullet\fi{}\ifmmode\bullet\else\textbullet\fi{}}$, can decrease the activation enthalpy of strontium-vacancy migration by forming ${({\mathrm{v}}_{\mathrm{O}}{\mathrm{v}}_{\mathrm{Sr}})}^{\ifmmode\times\else\texttimes\fi{}}$ defect associates, and we derive an analytical model for the cation diffusivity as a function of temperature and defect concentrations.

Departures from local interfacial equilibrium during metal oxidation

We use irreversible thermodynamics to formulate a model for the formation of a cation-deficient, $p$-type oxide on the surface of a pure metal in which local equilibrium is not necessarily maintained at the oxide interfaces and no a priori assumption regarding a rate limiting step is made. The dissipation rate derived here accounts for most of the conceivable processes that can occur during the oxidation of a metal, including bulk diffusion of cations and surface diffusion along the metal-oxide and gas-oxide interfaces. By including capillary effects in the formulation, shape changes in the oxide, which are usually neglected in most theories, can be described. We examine the steady-state solution of the model in one dimension for planar interfaces, and show that the growth law naturally captures the transition from linear to parabolic kinetics as the film thickens. A characteristic lengthscale for the transition is derived and can be obtained from oxide growth curves as a fitting parameter. Wagner's classical oxidation model is obtained as a limiting case of our more general model. We obtain expressions for the interfacial defect concentrations as a function of the departure from local equilibrium at the interfaces. From these expressions, we show that the exponent for the oxygen pressure dependence of the cation vacancy concentration can deviate from the usual values obtained from equilibrium considerations, and thus measuring nonstandard exponents can indicate a nonequilibrium effect. Our analysis serves to clarify the meaning and validity of the local equilibrium assumption in the context of metal oxidation.