Interdiffusion and Association Phenomena in the System NiO-Al2O3

The rate of formation of NiAl₂O₄ by reaction between single crystals of NiO and Al₂O₃ can be described by k = 1.1 × 10⁴ exp (−108,000 ± 5,000/ RT ) cm²/s. In NiO the behavior of D as a function of concentration supports the Lidiard theory of diffusion by impurity-vacancy pairs. A good fit of the theory to the experimental results was obtained by assuming that Al³⁺ ions diffuse as [Al_Ni· V_Ni]'pairs. The diffusion coefficient of pairs, D_p , obeys the equation 6.6 × 10⁻² exp (−54,000 ± 3,000/ RT ) cm²/s. The free energy of association for pairs was calculated to range from 6.5 kcal/mol at 1789°C to 9.0 kcal/mol at 1540°C. The interdiffusion coefficients in the spinel showed a constant small increase with increasing concentration of Al³⁺ dissolved in the spinel.     

Sodium Diffusion in SiO2 Glass

Diffusion of the radioactive tracer ²²Na in a commercial SiO₂ glass was investigated from 170° to 1000°C. The temperature dependence curve had discontinuities at about 573° and 250°C. The resulting Arrhenius equations are D = 3.44 × 10² exp(-21.1 kcal/RT) cm²/sec between 1000° and 573°C, D = 0.398 exp(-25.8 kcal/RT) cm²/sec between 573° and 250°C, and D = 2.13 exp(-28.3 kcal/RT) cm²/sec between 250° and 170°C. The two anomalies are discussed in terms of "quartz-like" and "cristobalite-like" precrystalline elements in the structure of the glass. Comparison of the Na diffusion in SiO, glass with that in soda-silica and soda-lime-silica glasses shows that SiO₂ glass occupies a boundary position with respect to these systems. A possible diffusion mechanism is discussed.     

Grain-Boundary Diffusion of Cr in Pure and Y-Doped Alumina

The diffusive transport of chromium in both pure and Y-doped fine-grained alumina has been investigated over the temperature range 1250°–1650°C. From a quantitative assessment of the chromium diffusion profile in alumina, as obtained from electron microprobe analysis, it was found that yttrium doping retards cation diffusion in the grain-boundary regime by over an order of magnitude. The Arrhenius equations for the undoped and Y-doped samples were determined to be: δ D _b=(4.77±0.24) × 10⁻⁷ exp (−264.78±47.68 (kJ/mol)/RT)(cm³/s) and δD_b=(6.87±0.18) × 10⁻⁸ exp (−284.91±42.57 (kJ/mol)/RT)(cm³/s), respectively. Finally, to elucidate the mechanism for this retardation, the impact of yttrium doping on diffusion activation energies and prefactors was examined.     

Oxygen Self-Diffusion in Single-Crystal Mn-Zn Ferrite

Self-diffusion coefficients for the oxygen ion in single-crystal Mn-Zn ferrite were determined by the gas-solid isotope exchange technique. The oxygen volume diffusion coefficients can be expressed as D =6.70 × 10⁻⁴ exp (-330 (kJ /mol) /RT)m₂/s (>1350°C), D=3.94 × 10⁻¹⁰ exp (−137 (kJ/mol)/RT)m²/s (1100° to 1350°C), and D=7.82 × 10⁴ exp (−507 (kJ/mol)/RT)m²/s (<1100°C).     

Oxygen Self-Diffusion in Magnesium- or Titanium-Doped Alumina Single Crystals

Oxygen Setf-diffusion coefficients have been measured in single crystals of N₂O₃ doped with Mg or Ti under an oxygen partial pressure of 20 kPa in the temperature range 1400° to 1700°C. Diffusion coefficients in Mg-doped crystals obey the equation D_o (cm²/s) = 1 × 10¹¹∼ (1×10¹³) exp[−915 ± 50(kJ/mol)/ RT ]. The diffusivity of oxygen in Ti-doped A1₂O₃ is lower than Mg-doped A1₂O₃. A vacancy mechanism explains these results.     

Interdiffusion in the System MgO-MgAl2O4

Interdiffusion coefficients in single-crystal MgO were determined using an MgO-MgAl₂O₄ diffusion couple. For a concentration of 1 mol% Al₂O₃ in MgO, the interdiffusion coefficient can be expressed as D =2.0±0.2 exp (−76,000±3,000/ RT ) for the MgO-MgAl₂O₄ couple. This relation compares well with previous measurements in the MgO-Al₂O₃ system. The interdiffusion coefficients, which increased with the mol fraction of cation vacancies, were in the range of 10⁻⁸ to 10⁻¹⁰ cm²s⁻¹ for the concentrations and temperatures studied. Diffusion was enhanced below 1640°C if powdered MgAl₂O₄ was used. Self-diffusion coefficients for Al³⁺ ions in MgO were calculated; Al³⁺ diffuses faster than Cr³⁺ in MgO.     

High-Temperature Creep and Kinetic Demixing in (Co,Mg)O

The creep behavior of fine-grained (Co_0.5Mg_0.5)O and (Co_0.25Mg_0.75)O has been characterized as part of an investigation of kinetic demixing in solid-solution oxides due to a nonhydrostatic stress. (i) For low stresses and small grain sizes, the dominant deformation mechanism for both compositions is diffusional creep limited by the transport of oxygen along grain boundaries. The oxygen grain-boundary diffusivity, D _o ^b is independent of oxygen partial pressure. The values of ω D _o ^b , where ω is the grain-boundary width, that have been determined from the steady-state diffusional creep rates are given by ω D _o ^b =4.7×10⁻⁸ exp[-230 (kJ/mol)/ RT ] (cm³/s) for (Co_0.5Mg_0.5)O in the range 950° to 1200°C and ω D _o ^b =7.4 × 10⁻⁸ exp[-263 (kJ/mol)/ RT ] (cm³/s) for (Co_0.25Mg_0.75)O in the range 1100° to 1250°C. Since oxygen diffusion controls the rate of diffusional creep, kinetic demixing is not observed in deformed samples of either composition. (ii) For high stresses and large grain sizes, the dominant deformation mechanism in both cases is dislocation-climb-controlled creep, where the rate of dislocation climb is controlled by oxygen lattice diffusion. Based on the positive dependence of creep rate on oxygen partial pressure, it is concluded that oxygen diffuses through the lattice by an interstitial mechanism.     

Chemical Diffusion in Nickel Oxide

The chemical diffusion coefficient was measured for undoped, single-crystalline NiO at 900° to 1200°C and within an oxygen partial pressure of 10⁻⁵ to 0.21 atm. Electrical conductivity was used to monitor the reequilibration kinetics after the oxygen pressure was suddenly changed over the initially equilibrated NiO crystal. The chemical diffusion coefficient was calculated vs the reequilibration degree indicating the most stable range of investigations. The chemical diffusion coefficient value is virtually the same for the oxidation and reduction experiments, giving, respectively: D_chem.=(1.64 × 10⁻²) exp[-(22,480±800)/RT] D_chem.=(9.68 × exp[-(21,430±2600)/RT] It has been stated that chem is independent of the oxygen pressure and thus of oxide composition. The electrical conductivity depends on the oxygen partial pressure in the power (l/n) = (1/5.45), indicating that doubly ionized cation vacancies are the predominant defects. Deviation from the linear dependence of log α vs logp^o2 was observed at <10⁻⁵ atm, indicating formation of anion vacancies of interstitials.     

Oxygen Self-Diffusion in Lithium-Doped Single-Crystal Magnesium Oxide

Oxygen self-diffusion coefficients for a single-crystal MgO doped with 400 ppm Li were determined at 848° to 1300°C by isotope exchange technique using ¹⁸O as the tracer. The diffusion coefficient increased with increasing temperature in the lower temperature range, as described by D = 7.8 × 10⁻⁴ exp[−279 (kJ/mol)/RT] cm²/s, which was interpreted to be an extrinsic diffusion due to the oxygen vacancies introduced by substitutional Li ions. The oxygen diffusivity tended to decrease above 1050°C, presumably becauuse of evaporation of Li₂O.     

Diffusion of Oxygen in Fused Silica

Oxygen diffusion in fused silica was measured over the range 850° to 1250°C by means of heterogeneous isotope exchange. In this temperature range and at 1 atm oxygen pressure the diffusion coefficients can be represented by the relation: D = 2 × 10⁻⁹ exp (-29 kcal/ RT). The oxygen diffusion coefficients are almost directly proportional to the oxygen pressure which suggests that the oxygen is diffusing in a molecular form.     

Raman Spectrometric Determination of the Oxygen Self-Diffusion Coefficients in Oxides

New methods of determining the oxygen self-diffusion coefficients (D*_o) in oxides have been developed using Raman spectroscopy combined with the ¹⁶O–¹⁸O exchange technique. From the depth-profiles of the ¹⁸O concentration in the ¹⁶O–¹⁸O exchanged oxides, which was measured by Raman microscope with a spatial resolution of 5 μm, D *_o was determined for 2.8 mol% Y₂O₃-containing tetragonal zirconia polycrystall (the depth-profile method). Thus-obtained results are expressed as D *_O,D-P= 1.82(^+0.41_−0.40) × 10⁻¹·exp{−(139.3 ± 0.2) [kJ/mol]/ RT } [cm²/s] in the temperature range of 700–950^°C. We also determined D *_o for the same sample from the Raman spectrometric monitoring of the ambient gas during the ¹⁶O–¹⁸O exchange reaction (the gas-monitoring method). Thus-obtained results are expressed as D *_O,G-M= 1.14(^+0.05_−0.04) × 10⁻² exp{−(117.5 ± 0.4) [kJ/mol]/ RT } [cm²/s] in the temperature range of 700–1165°C. The results obtained from the above two different methods virtually agree with each other, indicating that reliable D *_o can be obtained by either of these two methods. We demonstrate that Raman spectroscopy is a useful tool for determining D *_o in oxides.     

Ion-Probe Measurement of Oxygen Self-Diffusion in Single-Crystal Al2O3

Anion self-diffusion coefficients normal to (1102) were obtained for single-crystal Al₂O₃ in a 1.3 × 10 ³ N/m² (10⁻⁵ torr) vacuum at 1585° to 1840°C. Tracer was supplied from an initial 650 to 1300 A Al₂¹⁸O₃ layer produced by the oxidation of vapor-deposited Al metal films in an ¹⁸O₂ atmosphere at 520°C. Concentration gradients extended over depths of 3000 to 5000 A and were measured by mass spectrometry of material sputtered from the samples with a beam of Ar⁺ ions. Crystals which had not been preannealed to remove surface damage displayed enhanced diffusion. Diffusion coefficients from preannealed crystals may be described by D₀ =6.4×10⁵cm²/s, with an activation energy of 188 ± 7 kcal/mol. The diffusion is interpreted as an extrinsic vacancy mechanism.     

Sintering of Zinc Sulfide

The mechanisms of the sintering of ZnS were determined by measurement of the rate of growth of the necks between polycrystalline spheres. In vacuum (10⁻⁶ mm Hg) at temperatures higher than 600° C the mechanism of sintering is that of volume diffusion with coefficient D_v, = 1.06 × 10⁻² exp (-26,400/RT); below 600°C surface diffusion predominates, with coefficient D₃, = 9.14 × 10_-3 exp (-5700/RT). In Zn vapor (10⁻² mm Hg) between 550° and 650°C the predominating mechanism of sintering is surf ace diffusion, D₃, = 7.06 × 10⁻² exp (-8600/RT). It has been found that in an argon atmosphere the diffusion coefficient is much lower.     

Diffusion of Oxygen in Vitreous Silica

The diffusivity of the oxygen ion in vitreous silica has been directly determined by exchange measurements employing the stable isotope ¹⁸O and mass spectrometer analysis. It was found that over the temperature range 925° to 1225°C the results can be represented by the equation D = 1.51 × 10⁻² exp (-71,200/ RT ) cm² sec⁻¹. These results are compared with other measurements of oxygen diffusion in silicate glasses. It is proposed that the controlling diffusion step in silicate glasses and nonstoichiometric silica is the rupture of a single oxygen bond to silicon and that the diffusion mechanism is interstitial motion through voids in the lattice. An analysis of theoretical expressions for the pre-exponential term D _O shows that present theories are unable to predict D _O for oxygen diffusion in glasses. It is also shown that the mechanism for electrical conduction in vitreous silica or in electrolytically purified quartz is not migration of oxygen ions.     

Deviation from Stoichiometry in Cr2O3 at High Oxygen Partial Pressures

The deviation from stoichiometry, δ, in Cr₂−δO₃ was measured by a tensivolumetric method in the high pO₂ range of ≊10⁴ to 10⁴ Pa at 1100°C. The value of δ, or chromium vacancy concentration, was≊9×10⁻⁵ mol/mol Cr₂O₃ in air for Cr₂O₃ with 99.999% purity. The chemical diffusion coefficient, DT, determined from equilibration data was ≊4.6× cm²·s⁻¹ at 1100°C for pO₂= 2.2 ×10¹ Pa. The self-diffusion coefficient of Cr ions was calculated from and δ and found to be≊1.6×10-17 cm²-s⁻¹, in good agreement with recently measured values.     

Kinetics of NiCr2O4 Formation and Diffusion of Cr3+ Ions in NiO

The reaction kinetics for NiCr₂O₄ formation and the diffusion of Cr³⁺ ions into single-crystal NiO were studied between 1300° and 1600°C in air. The experimental activation energy for NiCr₂O₄ formation was about 83 kcal/mol. After incubation, NiCr₂O₄ formed by a diffusion-controlled process. The origin of pores at the NiO/NiCr₂O₄ interface is discussed. The concentration profiles of Cr³⁺ in NiO were linear because the interdiffusion coefficient was directly proportional to the mol fraction Cr³⁺. Theoretical considerations indicate that the interdiffusion coefficient equals 3/2 the self-diffusion coefficient of Cr³⁺, which is rate-determining. The interdiffusion coefficient at 1 mol% Cr₂O₃ can be expressed as =4×10⁻³ exp (−55,000/RT) cm² s⁻¹.     

Interdiffusion of Calcium in Soda-Lime-Silica Glass at 880° to 1308°C

The interdiffusion of calcium in soda-lime-silica glass under the action of a concentration gradient was studied. Pairs of glass blocks differing by 2.9 mole % in CaO content were fused together to form diffusion couples and were held at 880° to 1308°C. The couples were allowed to cool to room temperature and the diffusion which had taken place was measured by optical interferometry and by an electron microprobe. The diffusion coefficients varied from 4.4 × 10⁻¹⁰cm²/sec at 880°C to 8.0 × 10⁻⁸ cm²/sec at 1308°C. The activation energy was 42,000 cal/mole. It is concluded that oxygen diffuses simultaneously with the calcium, maintaining the electrical neutrality of the glass.     

Self-Diffusion Coefficient of Oxygen in Single-Crystal Forsterite

Self-diffusion coefficients of the oxygen ion in single-crystal forsterite were determined by the gas-solid isotope exchange technique. The results in the 1472° to 1734°C range were described by D =2.85 (10⁻² exp (−416 kJ/mol/RT)cm²/s. In preparing the diffusion sample, argon-ion milling gave a less defective surface condition than did chemical polishing.     

Sintering and Grain-Growth Kinetics of MgAl2O4

The sintering and grain-growth kinetics of finely divided MgAl₂O₄ were determined from 1300° to 1600°C for densities up to 96% of theoretical. These results show that sintering is governed by volume diffusion and that the temperature dependence of the diffusivities is 157 exp [(-118 kcal/mol)/ RT ] cm²/s. Grain growth follows the expression ( G ²- G ₀²)= Kt , where K =51.3 exp [(-110 kcal/mol)/ RT ] cm²/s.     

Oxygen Self-Diffusion in Single-Crystal Y2O3

Self-diffusion coefficients of the oxygen ion in single-crystal Y₂O₃ were determined by the gas-solid isotope exchange technique. The results in the range 1100° to 1500°C are described by D=7.3 X 10^-6 exp [-19l(kJ/mol)/RT] cm²/s. Comparison of the results with those for oxides with the fluorite-type structure indicates that the regularly arranged vacant anion sites in the C-type structure do not contribute eflectively to oxygen ion diffusion .