Electrical Resistivity of Titanium Diboride and Zirconium Diboride

The electrical resistivities of hot-pressed samples of Ti_{1- x} Zr _x B₂ ( x = 0.0, 0.3, 0.5, 0.7, 1.0) were measured by a four-point ac technique over the range 298 to 1573 K in an argon atmosphere. The hot-pressed samples for the intermediate compositions were found to be mixtures of two solid-solution phases. The resistivities for all compositions were found to increase linearly with temperature and can be described by ρ( T ) =ρ₂₉₈+φ( T - 298). The room-temperature resistivity ρ298 (μΩ cm) and the temperature coefficient of resistivity φ (nΩ·cm/K) for ZrB₂ were determined to be 7.8 and 10, both of which increase with the content of TiB₂. These values for TiB₂ were determined to be 20.4 and 36, respectively.     

Processing and Properties of TiB2 with MoSi2 Sinter-additive: A First Report

The densification of non-oxide ceramics like titanium boride (TiB₂) has always been a major challenge. The use of metallic binders to obtain a high density in liquid phase-sintered borides is investigated and reported. However, a non-metallic sintering additive needs to be used to obtain dense borides for high-temperature applications. This contribution, for the first time, reports the sintering, microstructure, and properties of TiB₂ materials densified using a MoSi₂ sinter-additive. The densification experiments were carried out using a hot-pressing and pressureless sintering route. The binderless densification of monolithic TiB₂ to 98% theoretical density with 2–5 μm grain size was achieved by hot pressing at 1800°C for 1 h in vacuum. The addition of 10–20 wt% MoSi₂ enables us to achieve 97%–99%ρ_th in the composites at 1700°C under similar hot-pressing conditions. The densification mechanism is dominated by liquid-phase sintering in the presence of TiSi₂. In the pressureless sintering route, a maximum of 90%ρ_th is achieved after sintering at 1900°C for 2 h in an (Ar+H₂) atmosphere. The hot-pressed TiB₂–10 wt% MoSi₂ composites exhibit high Vickers hardness (∼26–27 GPa) and modest indentation toughness (∼4–5 MPa·m^1/2).     

Optical Properties of Dysprosium-Doped Low-Phonon-Energy Glasses for a Potential 1.3 μm Optical Amplifier

Dysprosium-doped glasses were prepared in the system of gallium-based sulfide, tellurite, zirconium-baed and indium-based fluorides and their optical properties were studied. From the absorption cross sections of five f-f bands, three Judd-Ofelt parameters, ω _t ( t = 2, 4, 6), of Dy³⁺ ion were determined. The compositional variaton of the ω₂value showed the order sulfide > tellurite > fluorozirconate > fluoroindate, whereas the ω₆ value showed the opposite tendency. Compositional variaton of the fluorescence intensity ratio of the (⁴F_9/2⁶H_13/2)/(⁴F_9/2)→⁶H_15/2) is explained by the ratio of ω₂/ω₆ of doped Dy³⁺. The emission probabilities A and the branching ratio β from ⁶H_9/2 and ⁶F_11/2 levels, which are the doublet initial level of the 1.3 μm luminescence, were calculated for the glasses, and it was found that both values showed a tendency similar to that of ω₂ against the glass composition. In the sulfide glass, A was 2.6 × 10³S^-1 and β was 93%, both the highest in all of the glasses investigated. By 1.06 μm pumping of a Nd: YAG laser, the sulfide glass showed strong 1.3 μm emission and the lifetime was 25 μs, resulting in a quantum efficiency of 7%. This value is higher than that of the Pr³⁺:¹G₄ level in ZBLAN glass with β= 60%.     

Synthesis of Y-Doped BaTiO3–(Bi1/2K1/2)TiO3 Lead-Free Positive Temperature Coefficient of Resistivity Ceramics and Their PTC Effects

As a lead-free positive temperature coefficient of resistivity (PTCR) material, (1– x mol%) BaTiO₃– x mol% (Bi_1/2K_1/2) TiO₃– y mol% Y₂O₃–0.5 mol% TiO₂ (BT– x BKT–2 y Y–0.5TiO₂) systems were prepared by the conventional solid-state reaction method. All samples containing <2 mol% BKT sintered in air possessed relatively low room-temperature resistivity (ρ₂₅) and high positive temperature coefficient (PTC) effect. However, when the BKT content exceeded 2 mol%, the sample was not semiconductive after sintering in air. The effects of sintering schedule on the properties of PTCR ceramics were discussed. The results showed that the optimum composition of BT–1BKT–0.2Y–0.5TiO₂, sintered at 1330°C for not-soaking and then fast quenched in air, achieved rather low ρ₂₅ of 28 Ω·cm and a high jump of resistivity (maximum resistivity [ρ_max]/minimum resistivity [ρ_min]) of 4.0 orders of magnitude with T _c about 155°C. The ρ₂₅ of the as-sintered sample could be further reduced to about 10 Ω·cm by annealing in N₂ at 450°C for 30 min, accompanied decrease on the PTC effect.     

THE COMPARISON OF LEAST SQUARES AND THIRD-ORDER PERIODOGRAM PROCEDURES IN THE ESTIMATION OF BIFREQUENCY

Abstract. Given a stretch of time series values, the third-order periodogram is investigated as a criterion for use in the estimation of bifrequencies, that is of frequency triples (ω₁ω₂, ω₃) with ω₃= 2ω -ω₁ω₂. The least squares estimates of such frequencies are compared with estimates derived by maximizing the modulus of the third-order periodogram. It is found that neither estimation procedure is uniformly better than the other.     

A note on estimation by least squares for harmonic component models

Abstract. Let observations ( X ₁,…, X _n ) be generated by a harmonic model such that X _t = A ₀ cos  ω ₀ t + B ₀ sin  ω ₀ t + ε _t , where A ₀, B ₀, ω ₀ are constants and ( ε _t ) is a stationary process with zero mean and finite variance. The estimation of A ₀, B ₀, ω ₀ by the method of least squares is considered. It is shown that, without any restriction on ω in the minimization procedure, the estimate     is an n -consistent estimate of ω ₀, and hence (     ) has the usual asymptotic distribution.
The extension to a harmonic model with k >1 components is discussed. The case k =2 is considered in detail, but it was only found possible to establish the result under the restriction that both angular frequencies lie in the interval         

Preparation and Dielectric Properties of Low-Temperature-Sinterable (Zr0.8Sn0.2)TiO4 Powder

Low-temperature-sinterable (Zr_0.8Sn_0.2)TiO₄ powders were prepared using 3 mol% Zn(NO₃)₂ additive and then compared with powders prepared using 3 mol% ZnO additive and no additives. Sintering at 1200°C for 2 h produced a dielectric ceramic with ρ= 98.6% of theoretical density (TD), ɛ_r= 38.4, Q × f (GHz) = 42000, and τ _f =−1 ppm/°C. Sintering at 1250°C resulted in an excellent dielectric with ρ= 99% of TD, epsilon_r= 40.9, Q × f (GHz) = 49000, and τ _f =−2 ppm/°C. Scanning electron microscopy showed a microstructure with grains measuring 0.5 to 1 μm, and transmission electron microscopy revealed secondary phase in the grain boundaries.     

Densification, Sintering Reactions, and Properties of Titanium Diboride With Titanium Disilicide as a Sintering Aid

In the present investigation, we explore the feasibility of using TiSi₂ as a sintering aid to densify titanium diboride (TiB₂) at a lower sintering temperature (<1700°C). The hot-pressing experiments were conducted in the temperature range of 1400°–1650°C for 1 h in an argon atmosphere and TiSi₂ addition to TiB₂ was restricted up to 10 wt%, with an overall objective to densify the materials with a fine microstructure as well as to assess the feasibility of enhancing the mechanical and electrical properties. When all the materials were hot pressed at 1650°C, the hot-pressed TiB₂– X % TiSi₂ ( X =0, 2.5, 5, 10 wt%) composites were found to be densified to more than 98%ρ_th (theoretical density), except monolithic TiB₂ (∼94%ρ_th). An interesting observation is the formation of a Ti₅Si₃ phase and this phase formation is described by thermodynamically feasible sintering reactions. Our experimental results suggest that the optimal TiB₂–5 wt% TiSi₂ composite can exhibit an excellent combination of properties, including a high hardness of 25 GPa, an elastic modulus of 518 GPa, an indentation toughness of ∼6 MPa·m^1/2, a four-point flexural strength of more than 400 MPa, and an electrical resistivity of 10 μΩ·cm.     

Mechanical Properties of Partially Dense Alumina Produced from Powder Compacts

The elastic modulus ( E ), the critical strain energy release rate ( G _c), and the flexural strength (σ) have been determined for two partially dense alumina bodies produced from the same powder but with different initial densities. The mechanical properties were measured for specimens fabricated at four different relative densities. The measured elastic modulus, critical strain energy release rate, and a calculated critical stress intensity factor ( K _c) were observed to be linearly related to (ρ–ρ₀)/(1 –ρ₀), where ρ is the current relative density and ρ₀ is the initial relative density of the powder compact. With the observed linear relations for E, G _c (or K _c), and the assumption that the crack length responsible for failure was present in the initial powder compact and shrunk in proportion to the relative density change, a Griffith equation was constructed to estimate the strength at any relative density. This relation was in good agreement with measurements.     

Wear Mechanisms of TiB2 and TiB2–TiSi2 at Fretting Contacts with Steel and WC–6 wt% Co

Unlubricated fretting wear tests on TiB₂ and TiB₂–5 wt% TiSi₂ ceramics against two different mating materials (bearing grade steel and WC–6 wt% Co balls) were performed with a view to understand the counterbody-dependent difference in friction and wear properties. The fretting experiments were conducted systematically by varying load (2–10 N) at an oscillating frequency of 4 Hz and 100 μm linear stroke, for a duration of 100,000 cycles. Adhesion, abrasion, and three-body wear have been observed as mechanisms of material damage for both the TiB₂/steel and TiB₂/WC–Co tribosystems. The third body is predominantly characterized as tribochemical layer for TiB₂/steel and loose wear debris particles for TiB₂/WC–Co tribocouple. An explanation on differences in tribological properties has been provided in reference to the counterbody material as well as microstructure and mechanical properties of flat materials.     

ASYMPTOTIC BEHAVIOUR OF DISCRETE LINEAR PROCESSES

Abstract. We consider the linear process Y _n (ω) =Σ A _k (ω) · X _n-k (ω) on a probability space (Ω, P ) and ask for sufficient conditions in order to get a limit theorem for ( Y _k ) if the corresponding limit theorem for ( X _k ) is true.     

THIRD-ORDER ASYMPTOTIC PROPERTIES OF ESTIMATORS IN GAUSSIAN ARMA PROCESSES WITH UNKNOWN MEAN

Abstract. This paper deals with the third-order asymptotic theory for Gaussian autoregressive moving-average (ARMA) processes with unknown mean μ. We are interested in the estimation of ρ = ( α₁…, α_p, β₁…, β_q ), where α ₁…, α_ρ and β ₁…, β_q are the coefficients of the autoregressive part and the moving-average part, respectively. First, we investigate the third-order asymptotic optimality of the bias adjusted maximum likelihood estimator (MLE) of ρ in the presence of the nuisance parameters μ and ² (innovation variance). Next, for a Gaussian AR(1μ μ, ²), we propose a mean corrected estimator α_c1c2 of the autoregressive coefficient. We make a comparison between the bias adjusted estimator α_c1c2* and the bias adjusted MLE, in terms of their probabilities of concentration around the true value, or equivalently, in terms of their mean squared errors. Finally some numerical studies are provided in order to verify the third-order asymptotic theory.     

Knudsen and Langmuir Evaporation Studies of Stannic Oxide

A Knudsen study of the reaction SnO₂( c ) = SnO( g ) +½O₂( g ) yielded for the enthalpy of dissociation of SnO( g ), D°₀= 5.44 × 0.1 ev/molecule, which is in agreement with literature values (average 5.5 × 0.1 ev/molecule) obtained by various methods. Langmuir studies indicated an evaporation coefficient upper limit of 0.1 for the measured reaction. The Langmuir enthalpy of activation (Δ H *₂₉₈= 134 × 2.9 kcal/mole), as calculated by the second-law method, is less than that measured for the equilibrium reaction (Δ H *₂₉₈= 143.4 × 1.1 kcal/mole), but probably should be considered to agree within experimental error. Electron micrographs showed evidence of stepwise evaporation that depends on the crystallographic orientation of the polycrystalline grains.     

Process-Structure-Reflectance Correlations for TiB2 Films Prepared by Chemical Vapor Deposition

The process-structure-reflectance interrelationships for TiB₂ films prepared by CVD were determined using statistically designed experiments. A hot wall CVD reactor employing graphite substrates and the TiCl₄+ BCl₃+ H₂ reagent system were used at pressures of 2.7 and 6.7 kPa. Single-phase polycrystalline TiB₂ films were obtained. An increasing percentage of the grains were oriented with their (001) planes parallel to the substrate as the deposition temperature was increased and as the BCl₃:TiCl₄ ratio decreased. Grain size increased from ∼0.5 to 3 µm as the deposition temperature was increased from 900° to 1100°C and as the coating rate was decreased from 0.6 to 0.1 µm/min. Fine-grained, smooth, highly reflective films were obtained at low deposition temperatures and high BCl₃:TiCl₄ ratios.     

Assessment of the Thermodynamic Values for PuO1.5 and High-Temperature Determination of the Values for PuC1.5

Thermodynamic values for PUO_1.5 were assessed using an improved method for estimating fef ° 1.5 and new data for S°₂₉₈ 1.5. Based on the assessment, a value of ΔH°₂₉₈, 1.5=–828 kJ/mol is recommended. Measurements of (CO) pressure over the nominal equilibrium 1.5+ 1.5+ C were performed between 1348 and 1923 K, yielding pressures between 0.644 and 11600 Pa. Second- and third-law analyses were used to obtain a value for ΔH°₂₉₈ 1.5=–93.3°3.3 kJ/mol.     

High-Temperature Hydroxylation of Mullite

A plane-parallel, polished, 0.9 mm thick, single-crystal (001) plate of 2:1 mullite was treated for 6 h at 1600°C in an Ar/H₂O (90/10) gas mixture at 100 kPa. Optical microscopy studies and infrared (IR) reflection spectroscopy studies of the lattice vibrations yielded no evidence for change with respect to the untreated reference crystal. However, IR absorption spectroscopy showed that structurally bound OH groups were formed by the heat treatment in the Ar/H₂O gas mixture. IR absorption depth profile analysis showed a rather homogeneous OH distribution through the crystal. Five different hydroxyl groups were separated according to dipole orientations and peak positions: E ‖ a , ω _{a 1}= 3447 cm⁻¹, ω _{a 2}= 3579 cm⁻¹; E ‖ b , ω _{b 1}= 3456 cm⁻¹, ω _{b 2}= 3544 cm⁻¹; and E ‖ c , ω _{c 1}= 3498 cm⁻¹. All IR peaks were strongly broadened (between 90 and 150 cm⁻¹) because of a distribution in O-H binding distances caused by the real structure of mullite.     

Porous Glass-Ceramics with a Skeleton of the Fast-Lithium-Conducting Crystal Li1+xTi2−xAlx(PO4)3

Porous glass-ceramics with a skeleton of the fast-lithium-conducting crystal Li_{1+ x} Ti_{2− x} Al _x (PO₄)₃ (where x = 0.3–0.5) were prepared by crystallization of glasses in the Li₂O─CaO─TiO₂─Al₂O₃–P₂O₅ system and subsequent acid leaching of the resulting dense glass-ceramics composed of the interlocking of Li_{1+ x} Ti_{2− x} Al _x (PO₄)₃ and β-Ca₃(PO₄)₂ phases. The median pore diameter and surface area of the resulting porous Li_{1+ x} Ti_{2− x} Al _x (PO₄)₃ glass-ceramics were approximately 0.2 μm and 50 m²/g, respectively. The electrical conductivity of the porous glass-ceramics after heating in LiNO₃ aqueous solution was 8 × 10⁻⁵ S/cm at 300 K or 2 × 10⁻² S/cm at 600 K.     

Preparation of Porous Ca10(PO4)6(OH)2 and β-Ca3(PO4)2 Bioceramics

Submicrometer-sized, pure calcium hydroxyapatite (HA, (Ca₁₀(PO₄)₆(OH)₂)) and β-tricalcium phosphate (β-TCP, Ca₃(PO₄)₂) bioceramic powders, that have been synthesized via chemical precipitation techniques, were used in the preparation of aqueous slurries that contained methyl cellulose to manufacture porous (70%–95% porosity) HA or β-TCP ceramics. The pore sizes in HA bioceramics of this study were 200–400 μm, whereas those of β-TCP bioceramics were 100–300 μm. The pore morphology and total porosity of the HA and β-TCP samples were investigated via scanning electron microscopy, water absorption, and computerized tomography.     

Alkoxy-Derived KTiOPO4 (KTP) Fibers

Crack-free and dense KTiOPO₄ (KTP) fibers could be successfully synthesized through metallo-organics. A homogeneous, drawable KTP precursor solution was prepared from the reaction of (ⁿBuO)₂P(O)(OH), Ti(OEt)₄, and KOEt. KTP precursor fibers crystallized to a single-phase KTP at 650°C for 0.5 h. KTP fibers were a few centimeters in length and 10–150 μm in diameter. The density of the KTP fibers was higher than 2.97 g/cm³ (>98% of theoretical density).     

The Limiting Distribution of the Residual Processes in Nonstationary Autoregressive Processes

The weak limit of the partial sums of the normalized residuals in an AR(1) process y _t = ρ y _{t −1} + e _t is shown to be a standard Brownian motion W ( x ) when |ρ| ≠ 1. However, when |ρ| = 1, the weak limit is W ( x ) plus an extra term due to estimation of ρ. Asymptotic behaviour of the partial sums is investigated with ρ = exp( c )/ n ) in the vicinity of unity, yielding a c -dependent weak limit as n ←∞, whose limit is again W ( x ) as | c | ←∞. An extension is made to nonstationary AR( p ) processes with multiple characteristic roots on the unit circle. The weak limit of the partial sums has close resemblance to that for the polynomial regression.