Measurement of the Boltzmann Constant <Emphasis Type="Italic">k</Emphasis><Subscript>B</Subscript> Using a Quasi-Spherical Acoustic Resonator

There is currently great interest in the international metrological community for new accurate determinations of the Boltzmann constant k _B, with the prospect of a new definition of the unit of thermodynamic temperature, the kelvin. In fact, k _B relates the unit of energy (the joule) to the unit of the thermodynamic temperature (the kelvin). One of the most accurate ways to access the value of the Boltzmann constant is from measurements of the velocity of the sound in a noble gas. In the method described here, the experimental determination has been performed in a closed quasi-spherical cavity. To improve the accuracy, all the parameters in the experiment (purity of the gas, static pressure, temperature, exact shape of the cavity monitored by EM microwaves, etc.) have to be carefully controlled. Correction terms have been computed using carefully validated theoretical models, and applied to the acoustic and microwave signals. We report on two sets of isothermal acoustic measurements yielding the value k _B = 1.380 647 74(171) × 10⁻²³ J · K⁻¹ with a relative standard uncertainty of 1.24 parts in 10⁶. This value lies 1.9 parts in 10⁶ below the 2006 CODATA value (Mohr et al., Rev. Mod. Phys. 80, 633 (2008)), but, according to the uncertainties, remains consistent with it.     

Cylindrical Acoustic Resonator for the Re-determination of the Boltzmann Constant

The progress towards re-determining the Boltzmann constant k _B using two fixed-path, gas-filled, cylindrical, acoustic cavity resonators is described. The difference in the lengths of the cavities is measured using optical interferometry. Thus, a literature value for the density of mercury is not used, in contrast with the presently accepted determination of k _B. The longitudinal acoustic resonance modes of a cylindrical cavity have lower quality factors Q than the radial modes of gas-filled, spherical cavities, of equal volume. The lower Qs result in lower signal-to-noise ratios and wider, asymmetric resonances. To improve signal-to-noise ratios, conventional capacitance microphones were replaced with 6.3 mm diameter piezoelectric transducers (PZTs) installed on the outer surfaces of each resonator and coupled to the cavity by diaphragms. This arrangement preserved the shape of the cylindrical cavity, prevented contamination of the gas inside the cavity, and enabled us to measure the longitudinal resonance frequencies with a relative standard uncertainty of 0.2 × 10⁻⁶. The lengths of the cavities and the modes studied will be chosen to reduce the acoustic perturbations due to non-zero boundary admittances at the endplates, e.g., from endplate bending and ducts and/or transducers installed in the endplates. Alternatively, the acoustic perturbations generated by the viscous and thermal boundary layers at the gas–solid boundary can be reduced. Using the techniques outlined here, k _B can be re-determined with an estimated relative standard uncertainty of 1.5 × 10⁻⁶.     

Microstructural effects on the phase transitions and the thermal evolution of elastic and piezoelectric properties in highly dense,submicron-structured NaNbO<Subscript>3</Subscript> ceramics

The dielectric, piezoelectric and elastic coefficients, as well as the electromechanical coupling factors, of NaNbO₃ submicron-structured ceramics have been obtained by an automatic iterative method from impedance measurements at resonance. Poled thin discs were measured from room temperature up to the depoling one, close to 300 °C. Dielectric thermal behaviour was determined also for unpoled ceramics up to the highest phase transition temperature. Ceramics were processed by hot-pressing from mechanically activated precursors. Microstructural effects on the properties are discussed. The suppression of the classical maximum in dielectric permittivity in unpoled ceramics at the phase transition at 370 °C was found when a bimodal distribution of grain sizes, with a population of average grain size of 110 nm in between much coarser grains, is observed. The appearance of a phase transition at 150 °C took place when Na vacancies are minimised. The occurrence of a non-centrosymmetric, ferroelectric phase, in the unpoled ceramic from room temperature to ~300 °C, highly polarisable resulting in high ferro–piezoelectric properties was also observed in the ceramic which presents grain size below 160 nm. Maximum values of k _p = 14%, d ₃₁ = −8.7 × 10⁻¹² C N⁻¹ and N _p = 3772 Hz m at room temperature, and k _p = 18%, d ₃₁ = −25.4 × 10⁻¹² C N⁻¹ and N _p = 3722 Hz m at 295 °C were achieved in the best processing conditions of the ceramics.     

Thermal Expansion of Simulated Fuels with Dissolved Fission Products in a UO2 Matrix

As a part of the DUPIC (direct use of spent PWR fuel in CANDU reactors) fuel development program, the thermal expansion of simulated spent fuel pellets with dissolved fission products has been studied by using a thermo-mechanical analyzer (TMA) in the temperature range from 298 K to 1773 K to investigate the effects of fission products forming solid solutions in a UO₂ matrix on the thermal expansions. Simulated fuels with an equivalent burn-up of (30 to 120) GWd/tU were used in this study. The linear thermal expansions of the simulated fuel pellets were higher than that of UO₂, and the difference between these fuel pellets and UO₂ increased monotonically with temperature. For the temperature range from 298 K to 1773 K, the values of the average linear thermal expansion coefficients for UO₂ and simulated fuels with an equivalent burn-up of (30, 60, and 120) GWd/tU are 1.19 × 10⁻⁵ K⁻¹, 1.22 × 10⁻⁵ K⁻¹, 1.26 × 10⁻⁵ K⁻¹, and 1.32 × 10⁻⁵ K⁻¹, respectively.     

The three isentropic exponents of wet steam

Real gas isentropic changes may be described using the three well known ideal gas relations,pv ^k =const, p^(1−k)T^k=const andTv ^k-1=const, where exponent k has for each equation a different value k_{p, ν}, k_{p, T} and k_{T, ν} respectively. In this paper the three isentropic exponents theory for real gases is extended to the two phase region. As an application the numerical values of the three exponents are calculated for wet steam.     

Thermal and dielectric properties of the LTCC composites based on the eutectic system BaO–Al<Subscript>2</Subscript>O<Subscript>3</Subscript>–SiO<Subscript>2</Subscript>–B<Subscript>2</Subscript>O<Subscript>3</Subscript>

The low-temperature co-fired ceramic (LTCC) composites containing quartz based on the eutectic system BaO–Al₂O₃–SiO₂–B₂O₃ are fabricated at the sintering temperature below 980 °C. Preparation process and sintering mechanism were described and discussed, respectively. The results indicated that the addition of quartz to the eutectic system can availably improve dielectric properties of the LTCC composites. In addition, The LTCC composites with optimum compositions, which were obtained by the regulation of an Al₂O₃ content in the composite, can express excellent dielectric properties (permittivity: 5.94, 5.48; loss: 7 × 10⁻⁴, 5 × 10⁻⁴), considerable CTE values (11.7 ppm. °C⁻¹, 10.6 ppm. °C⁻¹) and good mechanical properties (128 MPa,133 MPa).     

On the thermal mechanism of microwave breakdown of high-temperature superconducting films

Theoretical arguments supporting the thermal nature of the microwave breakdown of high-temperature superconducting films are compared with experimental data. A comparison of the theoretical and experimental values of the threshold field for breakdown of a uniform film, B _f, and the threshold field for breakdown at nonsuperconducting defects, B _d, confirms the dependence corresponding to a thermal mechanism: B _f, B _d∝ (T _c-T ₀)^1/2. It is shown that the space-time picture of the observed breakdown is apparently due to overheating of the film near defects with a size of 10⁻⁵–10⁻⁶ m. The amplitude of the breakdown field may ultimately be limited by the abrupt decrease in the energy of critical disturbances for the initiation of breakdown. Pis’ma Zh. Tekh. Fiz. 24, 12–17 (June 12, 1998)     

Elevated temperature sliding wear behavior of WCP-reinforced ferrous matrix composites

WC_P-reinforced ferrous matrix composites were processed by direct addition of WC_P (100–150 μm) and the melt of the matrix alloy to a rotating mold at 1000 rpm. Dry sliding wear behaviors of the composites containing about 80 vol.% of WC_P and high-speed steel counterpart were investigated at room temperature and 400 °C against a rotating die steel ring. And wear experiments were performed under loads of 50, 100, and 150 N and a fixed sliding velocity of 30 m/s. Results show that at room temperature, both materials exhibited a marked increase in wear rate with load applied. Wear rates of the composites and high-speed steel under loads of 50, 100, and 150 N at room temperature achieved 1.61 × 10⁻⁶, 2.14 × 10⁻⁶, 3.56 × 10⁻⁶, and 3.11 × 10⁻⁶, 23.08 × 10⁻⁶, 57.39 × 10⁻⁶ g/m, respectively. At a testing temperature of 400 °C, the composites exhibited a marked increase in wear rates and high-speed steel exhibited mild wear (characterized by extremely low wear rates) over the range of loads considered in these experiments. Wear rates of both the composites and high-speed steel at 400 °C achieved 2.42 × 10⁻⁶, 5.19 × 10⁻⁶, 6.64 × 10⁻⁶, and 4.1 × 10⁻⁶, 8.92 × 10⁻⁶, 26.02 × 10⁻⁶ g/m, respectively, under different loads. Finally, the wear-mechanism was discussed in this article.     

Thermal Diffusivity and Heat of Formation of Harzburgite and Its Major Constituent Minerals

The thermal diffusivity, D, and its temperature dependence of Oman harzburgite rock and its major mineral olivine have been evaluated from the basic properties such as seismic velocities, density, and Debye temperature. The Arrhenius-type temperature dependence of the diffusivity was utilized to evaluate the heat of formation, ΔH _D. The diffusivity values, 1.80mm² · s⁻¹ and 2.1mm² · s⁻¹ obtained at room temperature for harzburgite and olivine, respectively, are consistent with available data. The diffusivity values for Oman harzburgite are overestimated by an amount of 0.27mm² · s⁻¹ relative to those of PNG harzburgite. The ΔH _D value (−2.40 kJ · mol⁻¹) for harzburgite rock of the Oman ophiolite suite is comparable with that (−2.90 kJ · mol⁻¹) of the harzburgite rock of Papua New Guinea. The disagreements in the thermal diffusivity and heat of formation values may be partly due to ignoring the effect of pyroxene in Oman harzburgite.     

Influence of sputtering power on the physical properties of magnetron sputtered molybdenum oxide films

Thin films of molybdenum oxide were formed on glass and silicon substrates by sputtering of molybdenum target under various sputtering powers in the range 2.3–6.8 W/cm², at a constant oxygen partial pressure of 2 × 10⁻⁴ mbar and substrate temperature 523 K employing DC magnetron sputtering technique. The effect of sputtering power on the core level binding energies, chemical binding configurations, crystallographic structure, surface morphology and electrical and optical properties was systematically studied. X-ray photoelectron spectroscopic studies revealed that the films formed at sputtering powers less than 5.7 W/cm² were mixed oxidation states of Mo⁵⁺ and Mo⁶⁺. The films formed at 5.7 W/cm² contained the oxidation state Mo⁶⁺ of MoO₃. Fourier transform infrared spectra contained the characteristic optical vibrations. The presence of a sharp absorption band at 1,000 cm⁻¹ in the case of the films formed at 5.7 W/cm² was also conformed the existence of α-phase MoO₃. X-ray diffraction studies also confirmed that the films formed at sputtering powers less than 5.7 W/cm² showed the mixed phase of α-and β-phase of MoO₃ where as at sputtering power of 5.7 W/cm² showed single phase α-MoO₃. The electrical conductivity of the films increased from 8 × 10⁻⁶ to 1.2 × 10⁻⁴ Ω⁻¹ cm⁻¹, the optical band gap decreased from 3.28 to 3.12 eV and the refractive index decreased from 2.12 to 1.94 with the increase of sputtering power from 2.3 to 6.8 W/cm², respectively.     

Improvements in the Dynamic Plane Source Method

Three sources of errors in the extended dynamic plane source (EDPS) method caused by the discrepancy between experiment and model are analyzed. The source effect is eliminated by introducing the nuisance parameter R ₀ and the surface effect by a surrounding vacuum. The original model assumes a constant heating power but a constant current is used in the experiment. Suppression of this effect leads to a new solution of the heat equation designated as the constant-current model. The measurements on polymethylmetacrylate (PMMA) in vacuum, evaluated by the constant-current model, provided results of λ = 0.191 W.m⁻¹.K⁻¹ and a = 0.118 ×10⁻⁶ m ².s ^{− 1}, which are in good agreement with published values. The total standard uncertainty was estimated as 1.5 % for both thermophysical properties.     

Crystal structure and negative thermal expansion of solid solution Y<Subscript>2</Subscript>W<Subscript>3−<Emphasis Type="Italic">x</Emphasis></Subscript>Mo<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>O<Subscript>12</Subscript>

A new series of solid solutions Y₂W_3−x Mo _x O₁₂ (0.5 ≤ x ≤ 2.5) were successfully synthesized by the solid state method. Their crystal structure and negative thermal expansion properties were studied using high-temperature X-ray powder diffraction and the Rietveld method. All samples of rare earth tungstates and molybdates were found to crystallize in the same orthorhombic structure with space group Pnca, and show the negative thermal expansion phenomena related to transverse vibration of bridging oxygen atoms in the structure. Thermal expansion coefficients (TEC) of Y₂W_3−x Mo _x O₁₂ were determined as −16.2 × 10⁻⁶ K⁻¹ for x = 0.5 and −16.5 × 10⁻⁶ K⁻¹ for x = 2.5 in the identical temperature range of 200–800 °C. High-temperature XRD data and bond length analysis suggest that the difference between W–O and Mo–O bond is responsible for the change of TECs after the element substitution in this series of solid solutions.     

Experimental Study of the Critical Behavior of the Isochoric Heat Capacity of Aqueous Ammonia Mixture

The isochoric heat capacity of a NH₃ + H₂O (0.2607 mole fraction of ammonia) mixture has been measured in the near- and supercritical regions. Measurements were made in the single- and two-phase regions including the coexistence curve using a high-temperature, high-pressure, nearly constant-volume adiabatic calorimeter. Measurements were made along 38 liquid and vapor isochores in the range from 120.03 kg · m⁻³ to 671.23 kg · m⁻³ and at temperatures from 478 K to 634 K and at pressures up to 28 MPa. Temperatures at the liquid–gas phase transition curve, T _S(ρ), for each measured density (isochore) and the critical parameters (T _C and ρ _C) for the 0.2607 NH₃ + 0.7393  H₂O mixture were obtained using the quasi-static thermograms technique. The expanded uncertainty of the heat-capacity measurements at the 95 % confidence level with a coverage factor of k = 2 is estimated to be 2 % to 3 % in the near-critical and supercritical regions, 1.0 % to 1.5 % in the liquid phase, and 3 % to 4 % in the vapor phase. Uncertainties of the density, temperature, and concentration measurements are estimated to be 0.06 %, 15mK, and 5×10⁻⁵ mole fraction, respectively. An unusual behavior of the isochoric heat capacity of the mixture was found near the maxcondetherm point (in the retrograde region). The value of the Krichevskii parameter was calculated using the critical properties data for the mixture and vapor-pressure data for the pure solvent (H₂O). The derived value of the Krichevskii parameter was used to analyze the critical behavior of the strong (C _P , K _T ) and weakly (C _V ) singular properties in terms of the principle of isomorphism of critical phenomena in binary mixtures. The values of the characteristic parameters (K ₁, K ₂), temperatures (τ ₁, τ ₂), and the characteristic density differences (Δρ ₁, Δρ ₂) were calculated for the NH₃ + H₂O mixture by using the critical-curve data.     

Preparation of SiB4±x and SiB6 plates by chemical vapour deposition of SiCl4 + B2H6 system

SiB_4±x and SiB₆ plates were prepared by chemical vapour deposition (CVD) using SiCl₄, B₂H₆ and H₂ gases under the conditions of deposition temperatures (T _dep) from 1323–1773 K, total gas pressures (P _tot) from 4–40 kPa and B/Si source gas ratio (m _B/Si=2B₂H₆/SiCl₄) from 0.2–2.8. The effects of CVD conditions on the morphology, structure and composition of the deposits were examined. High-purity and high-density SiB_4±x and SiB₆ plates about 1 mm thick were obtained at the deposition rates of 71 and 47 nm s⁻¹, respectively. The lattice parameter, composition and density of CVD SiB_4±x plates were dependent on their non-stoichiometry. The lattice parameter,a, was 0.6325 nm, butc ranged from 1.262–1.271 nm.The B/Si atomic ratio ranged from 3.1–5.0, and the density ranged from 2.39–2.45×10³ kg m⁻³. The CVD SiB₆ plates showed constant values of lattice parameters (a=1.444 nm,b=1.828 nm,c=0.9915 nm), composition (B/Si=6.0) and density (2.42×10³ kg m⁻³), independent of CVD conditions.     

Properties of Va metal-B films prepared by r.f.-sputtering

Nb_100−x B _x alloy films were prepared by the r.f.-sputtering method in the chemical composition range of 30 ≦x ≦ 76. Nb_100−x B _x (30 ≦x ≦ 54) films consisted of the amorphous state, and NbB₂ crystal phase was observed on Nb_100−xB_x (67 ≦x ≦ 76) films. A remarkable preferred orientation with the (001) plane of NbB₂ in parallel to the film surface was observed on Nb₃₃B₆₇ film. d.c. electrical conductivity of Nb_100−xB_x (30 ≦x ≦ 76) films decreased with increasing content of boron in the range from 7.3×10³ to 7.6 ×10²Ω⁻¹cm⁻¹. Micro-Vickers hardness of Nb_100−x B _x (30 ≦x ≦ 76) films exhibited the values of 1070 to 2060 kg mm².     

Microstructure and microwave dielectric characteristics of CaO–B2O3–SiO2 glass ceramics

CaO–B₂O₃–SiO₂ (CBS) glass powders are prepared by traditional glass melting method, whose properties and microstructures are characterized by Differential thermal analysis (DTA), X-ray diffraction (XRD) and scanning electron microscopy (SEM). It is found that the pure CBS glass ceramics possess excellent dielectric properties (ε _r = 6.5, tan δ = 5 × 10⁻³ at 10 GHz), but a higher sintering temperature (>900 °C) and a narrow sintering temperature range (about 10 °C). The addition of a low-melting-point CaO–B₂O₃–SiO₂ glass (LG) could greatly decrease the sintering temperature of CBS glass to 820 °C and significantly enlarge the sintering temperature range to 40 °C. The CBS glass ceramic with 30 wt% LG glass addition sintered at 840 °C exhibits better dielectric properties: ε _r ≈ 6, tan δ < 2 × 10⁻³ at 10 GHz, and the major phases of the sample are CaSiO₃, CaB₂O₄ and SiO₂.     

Investigation of the quasi-ternary system LaMnO3–LaCoO3–“LaCuO3”. II: The series LaMn0.25?xCo0.75?xCu2xO3?δ and LaMn0.75?xCo0.25?xCu2xO3?δ

This paper investigates the crystal structure, thermal expansion, and electrical conductivity of two series of perovskites (LaMn_0.25−x Co_0.75−x Cu_2x O_3−δ and LaMn_0.75−x Co_0.25−x Cu_2x O_3−δ with x = 0, 0.025, 0.05, 0.1, 0.15, 0.2, and 0.25) in the quasi-ternary system LaMnO₃–LaCoO₃–“LaCuO₃”. The Mn/Co ratio was found to have a stronger influence on these properties than the Cu content. In comparison to the Co-rich series (LaMn_0.25−x Co_0.75−x Cu_2x O_3−δ), the Mn-rich series (LaMn_0.75−x Co_0.25−x Cu_2x O_3−δ) showed a much higher Cu solubility. All compositions in this series were single-phase materials after calcination at 1100 °C. The Co-rich series showed higher thermal expansion coefficients (α_max = 19.6 × 10⁻⁶ K⁻¹) and electrical conductivity (σ_max = 730 S/cm at 800 °C) than the Mn-rich series (α_max = 10.6 × 10⁻⁶ K⁻¹, σ_max = 94 S/cm at 800 °C). Irregularities in the thermal expansion curves indicated phase transitions at 150–350 °C for the Mn-rich series, while partial melting occurred at 980–1000 °C for the Co-rich series with x > 0.15. I. Arul Raj—on leave from Central Electrochemical Research Institute, Karaikudi, 630006 India.     

Hot deformation of AA6082-T4 aluminum alloy

High-temperature tensile deformation of 6082-T4 Al alloy was conducted in the range of 623–773 K at various strain rates in the range of 5 × 10⁻⁵ to 2 × 10⁻² s⁻¹. Stress dependence of the strain rate revealed a stress exponent, n of 7 throughout the ranges of temperatures and strain rates tested. This stress exponent is higher than what is usually observed in Al–Mg alloys under similar experimental conditions, which implies the presence of threshold stress. This behavior results from dislocation interaction with second phase particles (Mg₂Si). The experimental threshold stress values were calculated, based on the finding that creep rate is viscous glide controlled, based on creep tests conducted on binary Al–1Mg at 673 K, that gave n a value of 3. The threshold stress (σ _o) values were seen to decrease exponentially with temperature. The apparent activation energy for 6082-T4 was calculated to be about 245 kJ mol⁻¹, which is higher than the activation energy for self-diffusion in Al (Q _d = 143 kJ mol⁻¹) and for the diffusion of Mg in Al (115–130 kJ mol⁻¹). By incorporating the threshold stress in the analysis, the true activation energy was calculated to be about 107 kJ mol⁻¹. Analysis of strain rate dependence in terms of the effective stress (σ − σ _o) using normalized parameters, revealed a single type of deformation behavior. A plot of normalized strain rate () versus normalized effective stress (σ − σ _o)/G, on a double logarithmic scale, gave an n value of 3. Ehab A. El-Danaf—on leave from the Department of Mechanical Design and Production, College of Engineering, Cairo University, Egypt.     

Study of the structural and dielectric properties of Bi<Subscript>2</Subscript>O<Subscript>3</Subscript> and PbO addition on BiNbO<Subscript>4</Subscript> ceramic matrix for RF applications

In this paper, the structural and dielectric properties of BNO (BiNbO₄) was investigated as a function of the external RF frequency and temperature. The BNO Ceramics, prepared by the conventional mixed oxide method and doped with 3, 5 and 10 wt. % Bi₂O₃–PbO were sintered at 1,025 °C for 3 h. The X-ray diffraction patterns of the samples sintered, shown the presence of the triclinic phase (β-BNO). In the measurements obtained at room temperature (25 °C) was observed that the largest values of dielectric permittivity (ε′ _r ) at frequency 100 kHz, were for the samples: BNO5Bi (5 wt. % Bi₂O₃) and BNO5Pb (5 wt. % PbO) with values ε′ _r ~ 59.54 and ε′ _r ~ 78.44, respectively. The smaller values of loss tangent (tan δ) were for the samples: BNO5Bi and BNO3Pb (3 wt. % PbO) with values tan δ ~ 5.71 × 10⁻⁴ and tan δ ~ 2.19 × 10⁻⁴, respectively at frequency 33.69 MHz. The analysis as a function of temperature of the dielectric properties of the samples, obtained at frequency 100 kHz, showed that the larger value of the relative dielectric permittivity was about ε′ _r ~ 76.4 at temperature 200 °C for BNO5Pb sample, and the value smaller observed of dielectric loss was for BNO3Bi sample at temperature 80 °C, with about tan δ ~ 5.4 × 10⁻³. The Temperature Coefficient of Capacitance (TCC) values at 1 MHz frequency, present a change of the signal from BNO (−55.06 ppm/°C) to the sample doped of Bi: BNO3Bi (+86.74 ppm/°C) and to the sample doped of Pb: BNO3Pb (+208.87 ppm/°C). One can conclude that starting from the BNO one can increase the doping level of Bi or Pb and find a concentration where one have TCC = 0 ppm/°C, which is important for temperature stable materials applications like high frequency capacitors. The activation energy (H) obtained in the process is approximately 0.55 eV for BNO sample and increase with the doping level. These samples will be studied seeking the development ceramic capacitors for applications in radio frequency devices.     

Synthesis and characterization of Al2?xScx(WO4)3 ceramics for low-expansion infrared-transmitting windows

A low thermal-expansion material was synthesized with potential application in thermal-shock-resistant infrared-transmitting windows. The material is derived from a solid solution of Al₂(WO₄)₃, which has positive thermal expansion, and Sc₂(WO₄)₃ with a negative thermal expansion. An optimum composition of Al_0.5Sc_1.5(WO₄)₃ was identified by synthesizing solid solutions, Al_2−x Sc _x (WO₄)₃, by a solid-state route with compositions ranging from x = 0 to 2.0. A single orthorhombic phase was obtained at all compositions. A composition corresponding to x = 1.5 had a low coefficient of thermal expansion of −0.15 × 10⁻⁶/°C in the temperature range 25–700 °C. A low temperature solution combustion process was developed for this optimum composition, resulting in a single-phase powder with a surface area of ~14 m²/g and average particle size (as determined from surface area) of 92 nm. The powder was consolidated by slip-casting, sintering, and hot-isostatic pressing into visibly translucent disks with a peak in-line transmittance of 73 % at 2300 cm⁻¹. Significant infrared absorption in a 1-mm-thick disk of this material begins near 2200 cm⁻¹ and features three absorptions arising from 2-phonon transitions at 2002, 1847, and 1676 cm⁻¹. The infrared and Raman spectra are interpreted in terms of 1-, 2-, and 3-phonon vibrational transitions.