Sintering and crystallization of mullite powder prepared by sol-gel processing

Mullite powder with the stoichiometric composition (3Al₂O₃.2SiO₂) was synthesized by a sol-gel process, followed by hypercritical drying with CO₂. Within the limits of detection by X-ray diffraction, the powder was amorphous. Crystallization of the powder commenced at 1200 °C and was completed after 1 h at 1350 °C. In situ X-ray analysis showed no intermediate crystalline phases prior to the onset of mullite crystallization and the pattern of the fully crystallized powder was almost identical to that of stoichiometric mullite. The synthesized powder was compacted and sintered to nearly theoretical density below 1250 °C. The microstructure of the sintered sample consisted of nearly equiaxial grains with an average size of 0.2 m. The effect of heating rate (1–15 °C min^–1) on the sintering of the compacted powder was investigated. The sintering rate increased with increasing heating rate, and the maximum in the sintering curve shifted to higher temperatures. The sintering kinetics below 1150 °C can be described by available models for viscous sintering.     

On a certain inverse problem of temperature and thermal stress fields

Summary The paper discusses the method of solution of an inverse problem of one-dimensional temperature and stress fields for a sphere, a circular cylinder and an infinite plate. The inverse problem describes the dependance of the boundary conditions of different types on the prescribed temperature state or stress state within the body under consideration, in contrast with the direct problem which relates the temperature and stress states to known boundary conditions. To obtain a function describing the temperature of a heating medium and/or the Biot number in a simple form use has been made of the Laplace transformation. The numerical examples for both types of the inverse problems are presented.

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Über ein inverses Problem der Temperatur- und Wärmespannungsfelder

Zusammenfassung Die Arbeit Antersucht die Lösungsmethode des inversen Problems eindimensionaler Temperatur-und Spannungsfelder für eine Kugel, einen Kreiszylinder und eine unendliche Platte. uas inverse Problem beschreibt die Abhängigkeit der Randbedingungen verschiedener Drt vom vorgegebenen Temperatur- oder Spannungszustand innerhalb des betrachteten Körpers im Vergleich zum direkten Problem, welches den Temperatur- und Spannungszustand zu bekannten Randbedingungen in Beziehung setzt. Zum Erhalt einer Funktion, die die Temperatur des erwärmten Mediums und/oder die Biot-Zahl in einer einfachen Form beschreiben, wurde die Laplace-Transformation verwendet. Numerische Beispiele für beide Arten der inversen Probleme werden angegeben.

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Notation a characteristic size of the body, [m] - _t coefficient of linear thermal expansion [1/°C]; [1/°K] - parameter describing a shape of the body; - Laplace transform of the functionf, G, ... - Fourier number (dimensionless time) - Biot number - G shear modulus, [kN·cm^–2] - I (z),K (z) modified Bessel 1^st and 2^nd kind functions of the order - J (z) 1^st kind Bessel function of the order ; - thermal diffusivity, [m²·s^–1]; - , Lame constants, [kN·cm^–2] - Poisson ratio - s parameter of Laplace transformation - _°°(°,Fo), (°,Fo) radial and circumferential stresses [kN·cm^–2] - T(,Fo) absolute temperature at a point (,Fo); [°C, °K] - T _f (Fo) absolute temperature of a medium that heats a body under consideration [°C, °K] - T _m the reference temperature [°C, °K] - dimensionless temperature - u(,Fo) dimensionless displacement - dimensionless coordinate of position With 11 Figures     

Thermal transport properties of helium near the superfluid transition. II. Dilute3He-4He mixtures in the superfluid phase

Measurements of the average thermal conductivity _exp hQ/T and of the thermal relaxation time to reach steady-state equilibrium conditions are reported in the superfluid phase for dilute mixtures of³He in⁴He. Hereh is the cell height,Q is the heat flux, andT is the temperature difference across the fluid layer. The measurements were made over the impurity range 2×10^–9<X(³He)<3×10^–2 and with heat fluxes 0.3<Q<160 µW/cm². Assuming the boundary resistanceR _b , measured forX<10^–5, to be independent ofX over the whole range ofX, a calculation is given for _exp. ForQ smaller than a well-defined critical heat fluxQ _c (X) X ^0.9, _exp is independent of Q and can be identified with the local conductivity _eff, which is found to be independent of the reduced temperature = (T–T)/T for –10^–2. Its extrapolated value at T is found to depart forX10^–3 from the prediction X ^–1 , tending instead to a weaker divergence X ^–a witha0.08. A finite conductivity asX tends to zero is not excluded by the data, however. ForQ >Q _c (X), a nonlinear regime is entered. ForX10^–6, the measurements with the available temperature resolution are limited to the nonlinear conditions, but can be extrapolated into the linear regime forX2×10^–7. The results for _exp(Q),Q _c (X), and _eff(XX) are found to be internally consistent, as shown by comparison with a theory by Behringer based on Khalatnikov's transport equations. Furthermore, the observed relaxation times (X) in the linear regime are found to be consistent forX>10^–5 with the hydrodynamic calculations using the measured _eff(X). ForX<10^–5, a faster relaxation mechanism than predicted seems to dominate. The transport properties in the nonlinear regimes are presented and unexplained observations are discussed.     

Breakup of an anomolously viscous liquid film in a centrifugal force field

An equation is obtained for the breakup radius with consideration of tipping moments and Laplacian pressure forces acting on the liquid ridge at the critical point.Notation K, n rhenological constants - density - surface tension - r current cup radius - R maximum cup radius - r_c critical radius for film breakup - ¯r=¯r=r/R dimensionless current radius - ¯r_c=r_c/R dimensionless critical radius - ₀, _c actual and critical film thicknesses - current thickness - R_r ridge radius - h₀ ridge height - h current ridge height - ₀ limiting wetting angle - current angle of tangent to ridge surface - angle between axis of rotation and tangent to cup surface - angular velocity of rotation - q volume liquid flow rate - v₁ and v meridional and tangential velocities - =4vv _lm/r,=4v_m/r dimensionless velocities - M moments of surface and centrifugal forces - M_v moment from velocity head - p_r pressure within ridge - P_vm pressure from velocity head - p_m, p_pm pressures from centrifugal force components tangent and normal to cup surface - deviation range of breakup radius from calculated value - ¯r_max, ¯r_min limiting deviations of breakup radius - _c angle of tangent to curve _c/°₀=f(¯r) at critical point - t random oscillation of ratio _c/_c Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 1, pp. 51–56, July, 1980.     

Electrical conductivity in hot-pressed nitrogen ceramics

The a.c. and d.c. electrical conductivities of some hot-pressed polycrystalline nitrogen ceramics have been measured between 400 and 1000° C. The materials examined were Si₃N₄, 5.0% MgO/Si₃N₄ and two sialons, Si_(6–z) · Al _z · O _z · N_(8–z) having z 3.2 and z 4.0 respectively. The electrical behaviour of all the materials showed similar general features. The d.c. conductivities were about 10^{–10 –1} cm^–1 at 400° C and rose to between 10^–6 and 10^{–5 –1} cm^–1 at 1000° C. The a.c. Data, taken over the frequency range 15 Hz to 5 kHz showed that below about 500° C the a.c. conductivity ( _a.c.) varied with frequency as _a.c. ^s where 0.7 _d.c.) agreed well with the relation _d.c. = A exp(–B/T ^1/4). Above 700° C both the a.c. and d.c. conductivities followed log T ^–1. Hall effect and thermoelectric power measurements enabled the Hall mobility to be estimated as less than 10^–4 cm² V^–1 sec^–1 at 400° C and showed that the materials were all p-type below 900° C and n-type above 900° C. The electrical properties of all four materials are consistent with the presence of a glassy phase.     

Microwave properties of highly oriented YBa2Cu3O7-δ superconducting thin films

We have performed millimeter-wave frequency (94 GHz) measurements on high-quality YBa₂Cu₃O₇- superconducting films on yttrium-stabilized (100) ZrO₂ and MgO substrates. The 0.2m thin films fabricated by magnetron sputteringin situ with the YBa₂Cu₃O₇- powders as target exhibit superconducting transition temperatures up to 88 K. The critical current density of 6×10⁵ A/cm² at 77 K and the X-ray diffraction spectrum as well as scanning electron microscope photographs indicate these thin films are fullyc-axis oriented, extremely high in density, and universally homogeneous. Millimeter-wave surface resistances have been measured on a hemisphere open resonator in the temperature range of 20 K toT _c and beyond. The surface resistance at 94 GHz and 77 K for these films is found to be about 30 m, nearly 1/4 that for copper, and a drop of two orders in the surface resistance within 4 K is observed, which indicates that these films are good materials for applications in the millimeter-wave range, especially for fabricating microwave devices. We observed such low surface resistance in these thin films due to the near absence of grain and phase boundaries coupled with a high degree of crystalline orientation.     

The Interplay of Electronic and Nuclear Magnetism in PtFe x at Milli-, Micro-, and Nanokelvin Temperatures

We have measured ac susceptibility, nuclear magnetic resonance, and nuclear heat capacity of two PtFe _x samples with concentrations of magnetic impurities x = 11 ppm and 41 ppm at magnetic fields (0 ± 0.05) mTB248 mT. The susceptibility data have been measured at temperatures of 0.3 KT100 mK, no hint for nuclear magnetic ordering could be detected to a temperature of 0.3 K. The nuclear heat capacity data taken at 1.4 KT10 mK show enhanced values which scale with x at low polarization. This effect is described by a model assuming an internal magnetic field caused by the impurities. No indication for nuclear magnetic ordering could be detected to 1.4 K. The nuclear magnetic resonance experiments have been performed on these samples at 0.8 KT0.5 mK and 2.5 mTB22.8 mT as well as on three other samples with x = 5, 10, 31 ppm in a different setup at 40 KT0.5 mK and at 5.4 mTB200 mT. Spin-lattice and effective spin-spin relaxation times ₁and ₂ ^* of ¹⁹⁵ Pt strongly depend on x and on the external magnetic field. No temperature dependence of ₁and ₂ ^* could be detected and the NMR data, too, give no hint for nuclear magnetic ordering to 0.8 K.     

Lead zinc niobate pyrochlore: Structure and dielectric properties

In Pb(B _x B_1–x )O₃ ceramic compositions, it is customary to find a mixture of cubic pyrochlore and perovskite phases after calcination. Based on X-ray diffraction analysis, we concluded that both phases are made up of the same structural unit of BO₆ octahedra. The B and B ions occupy the B sites randomly to the extent that local charge equilibrium is maintained. Thus a general formula for the pyrochlore phase can be expressed as Pb(B _x B_1–x )O₃ · O_p where O p 0.5. An extensive study of the Pb(Zn _x Nb_1–x )O_3.5–1.5x pyrochlore system was made by varying the zinc concentration. We interpret changes in the X-ray diffraction pattern and the lattice constant as indicative of the changing occupancy of the seventh oxygen sites in order to maintain local charge balance. The best combination of the dielectric properties, with a dielectric constant of130 and a factor greater than 1000 at10 MHz, is achieved at a composition of 0.3 x 0.4 and a sintering temperature of 980° C. The temperature coefficient of the dielectric constant measures –0.75 × 10^–3° C^–1. It decreases to –0.54 × 10^–3° C^–1 when5 mol% of PbTiO₃ was mixed with the nominal pyrochlore compositions and sintered. Thus, it may be possible to effect a larger change in the temperature coefficient by judiciously including selective amounts of a second phase which has the best compensating temperature coefficient.     

Electrical properties of polycrystalline ZnO : Cu obtained from freeze-dried ZnO+copper(II) acetate powders

Highly homogeneous mixtures of powders containing ZnO and monohydrated copper(II) acetate, (CH₃COO)₂CuH₂O, AcCuH₂O were obtained by freeze drying. Thermal analysis and high-temperature X-ray diffraction showed that pure freeze-dried AcCuH₂O powder decomposed to CuO, in air, at temperatures above 325 °C. Due to the polymeric nature of AcCuH₂O, the powder mixtures were compacted without pressing additives. Pellets with ZnO+x mol % Cu (x=0.05, 0.5, and 5.0) compositions were sintered in air from 750 to 1150 °C for 1 h. After sintering, the density, shrinkage and mass loss increased as the concentration of AcCuH₂O increased. A microstructural analysis of samples sintered at 950 °C for 1 h revealed Cu-doped ZnO grains with Cu-clusters of x=5.0 mol % Cu; the J–E curves showed that both the breakdown electric field, E_br, and the nonlinearity coefficient, , increased as x increased from 0.05 to 0.5. Complex acceptor defects involving Cu⁺ _Zn in the grain boundary are believed to have compensated for the n-type conductivity of the ZnO grains, giving rise to high E_br values.     

Non-Newtonian properties of emulsions in solutions of surface-active agents

The adsorption of surface-active agents (surfactants) on channels changes the effective viscosity of an emulsion and gives it non-Newtonian properties.Notation a drop radius - C and C° concentration of surfactant near a drop and averaged over the medium - D diffusion coefficient of the surfactant - I second-rank unit tensor - n_i components of the unit normal vector to the drop surface - r radius vector directed from the center of the drop - s surface area of the drop occupied by one molecule of surfactant - t_j and T characteristic times - and sorption and desorption constants - gG and ° true and equilibrium surface concentrations of surfactant - , , and gh₁ effective viscosity and the viscosities of the disperse phase and dispersion medium - volume concentration of the disperse phase - surface tension of the drop - T_j, and characteristic times Indices + and * quantities near and inside the drop - t tangential components of vectors and tensors. The operators div_s and grad_s have the same meaning as the ordinary divergence and gradient operators, but with fixed values of the radius vector ra Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 56, No. 5, pp. 787–793, May, 1989.     

Mixed convection boundary-layer on a vertical cylinder embedded in a saturated porous medium

Summary The mixed convection boundary layer on a vertical circular cylinder embedded in a saturated porous medium is considered. It is found that the flow depends on the parameter =R _a /P _e whereR _a andP _e are the Rayleigh number and Peclet number respectively. gives the ratio of the velocity scale for free convection to that for the forced convection. When is small the solution is, to a first approximation, obtained by a known heat conduction problem. The flow near the leading edge is considered and it is shown that a solution is possible only for ₀, ₀–1.354, and that a stable finite-difference solution away from the leading edge can be obtained only if –1; with <–1 there is a region of reversed flow near the cylinder. The finite-difference scheme is unable to give a satisfactory solution at very large distances from the leading edge, and to overcome this difficulty a simple approximate solution is developed. This solution shows that at large distances along the cyclinder, forced convection eventually becomes the dominant mechanism for heat transfer. This is also confirmed by an asymptotic solution of the full boundarylayer problem.Nomenclature a radius of cylinder - g acceleration of gravity - K permeability of the porous medium - N _u non-dimensional Nusselt number - r radial coordinate - non-dimensionalr=r/a - R _a Rayleigh number=(g T)Ka/ - P _e Peclet number=U ₀ a/ - T temperature - T _w temperature of the cylinder (constant) - T ₀ temperature of the ambient fluid (constant) - T temperature difference=T _w –T ₀ - u Darcy's law velocity in thex direction - U ₀ velocity of the outer flow - v Darcy's law velocity in ther-direction - x coordinate measuring distance along the cylinder - X non-dimensionalx,=x(aP _e )^–1 - equivalent thermal diffusivity - coefficient of thermal expansion - ratio of free to forced convection=R _a /P _e - viscosity of the convective fluid - density of the ambient fluid - non-dimensional temperature - stream function With 2 Figures     

Microstructures of titanium-aluminides produced by laser surface alloying

The microstructures of Ti-Al layers (from 43–80 at %Al) produced by laser surface alloying of titanium substrate with a powder feed technique have been investigated. The laser processing parameters were; 1.8 kW laser power, 3 mm beam diameter, 7 mm s^–1 traverse speed, and values of powder flow rates of aluminium ranging from 0.07–0.11 g s^–1. The microstructures were dendrites of ₂ and interdendritic regions of ₂+ in the Ti-43 at %Al alloy; dendrites of either ₂ or ₂+ with interdendritic in the Ti-50 at %Al alloy; dendrites of ₂+ with interdendritic in the Ti-55 at %Al alloy; single phase in the Ti-60 at %Al alloy and TiAl₃ dendrites and Al solid solution in the interdendritic regions in the Ti-80 at %Al alloy. The microstructures were fine and comparable to those produced by other methods of rapid solidification processing. The microstructures of the Ti-50 and Ti-55 at %Al alloys were in agreement with the existence of the peritectic reactions:L + andL + , in the Ti-Al system.     

Low cost porous mullite-corundum ceramics by gelcasting

A gelcasting process has been successfully employed to fabricate porous mullite-corundum ceramic composites from natural clay and corundum powders. The specimens based on the mullite composition are found with an open porosity of 45–47.9%, mean pore size of 1.28–2.55 m, and nitrogen permeability of 965–5038 m³· m^–2· bar^–1· hr^–1by reactively sintering the gelled mixture of kaolinite and -alumina at 1100–1500°C. The open porosity (_o), mean pore size (d _p), pore size distribution and gas permeability can be controlled by adjusting raw material ratios and sintering temperatures. The gas permeability of the specimens is found to be more dependent on the pore size distribution as well as d _pthan on _o. In addition, the gas transportation mechanism in porous mullite-corundum ceramic composites is dominated by viscous flow.     

Spin-lattice relaxation in gadolinium-doped calcium tungstate

The spin-lattice relaxation of the S-state ion Gd³⁺ in a calcium tungstate host lattice has been examined at 37.5 GHz over the temperature range 1.5 to 30 K. The gadolinium concentrations in the doped single crystals used were about 50 ppm. Single exponential recovery was observed and the spin-lattice relaxation time (T ₁) varied from about 14 msec at 1.5 K to 0.03 msec at 30 K, measured with =90° and =8°. It was found that T ₁ varied with temperature (T) as T ₁ T ^–1 below 8 K and as T ₁ T ^–3 between 8 and 30 K. The experimental data was fitted by the expressions T ₁ ^–1 =35 T+0.5 T ³ and T ₁ ^–1 =35T+0.1 T ^3.6 for crystals of nominal gadolinium concentrations 0.005 wt % and 0.05 wt % respectively. The difference between the observed dependence and the T ^–5 variation predicted in the Raman region for an S-state ion in a perfect lattice is attributed to defects. Measurements in the -plane at 4.2 K showed that T ₁ was anisotropic with a maximum value at =25° about three times greater than the minimum value obtained at =55°. The angular positions at which these features occur show a remarkable coincidence with the acoustic axes of symmetry of the crystal, which have recently been determined by ultrasonic methods.     

On the Bose-Einstein condensation of nonzero-momentum cooper pairs. A second-order phase transition

Based on the BCS Hamiltonian, the normal-to-super phase transition is investigated, approaching the critical temperatureT _c from the high-temperature side. Nonzero-momentum Cooper pairs, that is, pairs of electrons (holes) with antiparallel spins and nearly opposite momenta aboveT _c in the bulk limit, are shown to move like independent bosons with the energy vs. momentump relation=1/2v_F , where _F represents the Fermi velocity (1/2m* _F ² _FFermi energy). The system of free Cooper pairs undergoes a phase transition of the second order with the critical temperatureT _c given byk _B T _c=1/2(²³ _F ³ n/1.20257)^1/3 wheren is the number density of Cooper pairs. The ratio of the jump of the heat capacity, C, to the maximum heat capacity,C _s, is a universal constant: C/C _s=0.60874; this number is close to the universal constant 0.588 obtained by the finite-temperature BCS theory. The physical significance of these results is discussed, referring to the well-known BCS theory, which treats the many-Cooper-pair ground state exactly and the thermodynamic state belowT _c approximately. An explanation is proposed on the question why sodium should remain normal down to 0 K, based on the band structures with the hypothesis that the supercondensate composed of zero-momentum electron and hole Cooper pairs is electrically neutral.     

Transport Properties of Ca1 – x MnO3 – δ + xCeO2(0 < x ≤ 0.15) Mixtures

Data are presented on the temperature-dependent electrical conductivity and thermoelectric power of Ca_{1 – x} MnO_{3 –} + xCeO₂ (0 < x 0.15) mixtures obtained as intermediate products in the synthesis of Ca_{1 – x} Ce _x MnO_{3 –} solid solutions. The electrical properties of the mixtures are shown to be dominated by those of the perovskite-like phase Ca_{1 – x} MnO_{3 –} and to depend on Ca concentration. All of the samples with 0 x 0.15 exhibit n-type conductivity. The charge transport in CaMnO_{3 –} below 930 K is attributable to small-polaron hopping. At higher temperatures, conduction through delocalized states seems to prevail. In the Ca_{1 – x} MnO_{3 –} + xCeO₂ mixtures with 0.05 x 0.15, small-polaron hopping is observed between 160 and 920 K. Below 160 K, the temperature variation of conductivity in the samples with x = 0.1 and 0.15 follows Mott's law.     

Sound propagation in 3He-4He mixtures near the superfluid transition

Measurements of the acoustic attenuation and dispersion in liquid ³He-⁴He mixtures near the superfluid transition T (x) are reported. The frequency range is /2gp=1–45 MHz and the ³He mole fraction X of the mixtures is 0.007, 0.05, 0.15, and 0.36. Comparisons are made with the measurements of Buchal and Pobell for similar mixtures obtained in the kHz region, and on the whole, the consistency between the two experiments is very satisfactory. An analysis is then performed using both the kHz and MHz data. In the normal phase, where the energy dissipation is caused by order parameter fluctuations having a lifetime _F , the attenuation data can all be scaled according to the expression = (T )f(_F. Here (T )^1+y, with y being a function of the mole fraction X and _F(T–T )^–x, with x increasing weakly with X. In the superfluid phase, we attempt a similar scaling representation, which is found to be fairly successful, but where x(T\s-T ) is roughly 15% larger than x(T>T ). In the superfluid phase we also analyze the attenuation data, assuming the additivity of relaxation and fluctuation-dissipation mechanism, and discuss the relaxation times so derived. In contrast to the attenuation, the dispersion data cannot be brought satisfactorily into a scaling representation. However, at T , we find U()-U(0)^y as predicted by Kawasaki, where y is in good agreement with the values from attenuation experiments.Supported by a grant from the National Science Foundation.     

High-frequency dielectric properties of Mg-Al-Si,Ca-Al-Si and Y-Al-Si oxynitride glasses

Recently developed coaxial line techniques [1] have been used to determine, at room temperature, the values of the real () and imaginary (') parts of the dielectric constants for some Mg-Al-Si, Ca-Al-Si and Y-Al-Si oxynitride glasses over the frequency range 500 MHz to 5 GHz. The frequency dependencies of and ' are consistent with the universal law of dielectric response in that (-_t8)^(n–1) and '^(n–1) for all glass compositions; the high experimental value of the exponent (n=1.0±0.1) suggests the limiting form of lattice loss [2] situation. In this frequency range, as previously reported [3] at longer wavelengths, the addition of nitrogen increases the dielectric constant, (); in both the oxide and oxynitride glasses is also influenced by the cation, being increased with cation type in the order magnesium, yttrium, calcium as at lower frequencies.     

Polymorphism of the Ag8S4O4 and Ag6S3O4 compounds

Experimental results of the reaction occurring between aqueous solutions of AgNO₃ and Na₂S₂O₃ were presented in this work. It has been demonstrated that these reagents form two phases to which the summary formulas: -Ag₈S₄O₄ and -Ag₆S₃O₄ were ascribed. The -Ag₈S₄O₄ phase crystallizes in a tetragonal system and has the following parameters of the unit cell: a = b = 0.72052 nm, c = 0.51140 nm, V = 0.26550 nm³, Z = 1, d_x = 6.60 g/cm³. At 223°C -Ag₈S₄O₄ undergoes an irreversible, endothermic polymorphic transition. The heat of this transition amounts 8.03 × 10^–3 J/mol. A high-temperature polymorphic form -Ag₈S₄O₄ melts at 400°C. The -Ag₆S₃O₄ phase crystallizes in a monoclinic system and has the following parameters of the unit cell:a = 2.09616 nm, b = 0.53118 nm, c = 1.49885 nm, = 102.78°, V = 1.62753 nm³, Z = 8, d_x = 6.59 g/cm³. -Ag₆S₃O₄ also undergoes an irreversible, endothermic polymorphic transition at 221°C. The heat of this transition amounts 7.65 × 10^–3 J/mol. A high-temperature form, -Ag₆S₃O₄, melts at 390°C.     

Ultrasonic dispersion and attenuation near the liquid-gas critical point of 3He

We report ultrasonic dispersion and attenuation measurements near the liquid-gas critical point of ³He at frequencies from 0.5 to 5.0 MHz and densities from 0.89 _c to 1.15 _c . The singular part of the sound attenuation and the dispersion on the critical isochore _c = 0.0414 g/cm³ are analyzed in terms of the Kawasaki-Mistura theory. If the Ornstein-Zernike order parameter correlation function is assumed in the analysis, good agreement with our data is achieved, except close to the critical temperature T _cin the high-frequency region, where ^* = /_D 1. Here _D is the characteristic relaxation rate of the critical fluctuations. From a fit of the theory to our data, and assuming the inverse correlation length is expressed by = ₀, where = (T–T_c)/T_c with = 0.63, we obtain ₀ = (3.9 ± 0.4) × 10⁹ m^–1. It is found that a more realistic form of the correlation function, as proposed by Fisher and Langer and calculated by Bray, yields even poorer agreement with out data than does the classical Ornstein-Zernike form for ^* > 10. The same difficulties appear in the analysis of the available data for xenon. Thus, the present mode coupling theory is unable to satisfactorily describe the acoustic experiments on fluids near the liquid-vapor critical point over a large range of reduced frequencies ^*. In the appendix, we reanalyze previously reported ultrasonic data in ⁴He, taking into account the nonsingular term of the thermal conductivity. Using = 0.63, we obtain a good fit of the experiment to the theory in the hydrodynamic region with ₀ = (5.5 ± 1) × 10⁹ m^–1.Supported by a grant from the National Science Foundation.