Effective conductivity of a composite of poly-dispered spherical particles in a linear continuum

Rayleigh's method is used to find the electric potentials of a composite of poly-dispered spherical particles in a linear continuum in an external electric field. Based on the solutions of potentials, analytical formula for the effective electric conductivity is derived. Based on the formula, several factors, such as the number of spherical inclusions, the spatial distribution of the spheres, the contrast ratio _i / _h (where, _i and _h are the conductivities of the spherical inclusion and the host medium, respectively) and volume fraction of the inclusions, are discussed. Our results show that at high volume fraction, the effective conductivity is also affected by the spatial distribution of the inclusions.     

Kinetics of Solid State Reactions With Fractal Reagent

In the present research we theoretically studied the kinetics of nucleation-limited solid state reactions as influenced by the fractal properties of solid reagent. We consider the model of equal-sized primary particles assembled in fractal cluster. The geometry of such an object is assumed to be described solely by its fractal dimension D and by upper (R _max) and lower (R _min) cutoffs of fractality further identified with the overall size of the object and the size of the primary particle correspondingly. Depending on the ratio between R _max, R _min and the radius of the critical nucleus R _nucl the following cases are considered: (1) R _max R _nucl. In this case the reaction kinetics is described by the equation: = 1 – B{ln(k + 1)}^D/(D–3), where B, k are constants. Numerical solution of this equation gives rise to n-order reaction kinetics with n > 1. (2) R _min R _nucl R _max. In this case under certain conditions there can exist non-trivial critical density _crit 0, 1 that favors the formation of the critical nuclei of the new phase. The asymptotic kinetic equation for large times corresponds to n-order reaction with n = (D + 3)/(D + 1). (3) R _min R _nucl R _max. In this case the reaction follows the first-order kinetics with D-dependent rate constant.     

Thermal Resistance of 4He Below but Very Near the Superfluid Transition

We report high-resolution measurements at saturated vapor pressure of the thermal resistivity R of superfluid ⁴He over the reduced-temperature range 3×10^–7<t1–T/T <3×10^–5 (T is the transition temperature for Q=0) and heat-current-density range 4<Q<200 W/cm². For smaller Q and t, no thermal resistance was detectable below a transition at T _c(Q)<T . For Q10 W/cm² we find that the results can be described well by R=(t/t ₀)^–2.8 K cm/W with t ₀=(Q/Q ₀)^0.904 and Q ₀=393 W/cm². Thus R has an incipient divergence at T which is, however, supplanted by T _c(Q) where R remains finite. The results imply RQ ^(m–1) with m=3.53±0.02. This differs from the original assumption m=3 of Gorter and Mellink, and from experimental results obtained well below T . However, it agrees with measurements by Leiderer and Pobell at larger currents and further below but still close to T . Our measurements could not resolve a critical heat current for the onset of resistance.     

Transport in the low-temperature limit of a Landau Fermi liquid

The Boltzmann equation for Landau quasiparticles is solved for T 0 by a specialization of a method discussed by Sykes and Brooker. The quasiparticle distribution function is expanded in Legendre polynomials, assuming a boundary condition which imposes axial symmetry, and even-order terms are assumed to relax together with relaxation time _e , odd-order terms with relaxation time _o . By letting wavelength , with finite, one obtains a first-sound solution, and by lettingT 0, and then , one obtains a zero-sound solution. When these solutions are used to calculate the pressure, it is found that the first-sound solution is consistent with hydrodynamics, exhibiting viscosity = _s , while the zero-sound velocityc ₁=[^–1(B₁+4/3_s)]^1/2, so that phenomenologically zero-sound propagates like a longitudinal elastic wave in a glass. A higher zero-sound mode is also predicted, but is heavily damped. The heat flux is calculated and found to obey Vernotte's equation, which contains an intertial term, added to Fourier's law, that becomes significant asT 0.     

Effect of phase fluctuations upon penetration depth

The temperature dependence of the static penetration (T) has been used as a guide to the nature of the superconducting state in high-T _c materials. It has been argued that an algebraic temperature dependence in the ratio (T)/(0) [(T) — (0)]/(0) at low temperature is evidence for d-wave pairing. This paper examines the effect of superconducting phase fluctuations upon (T) and finds an algebraic dependence over a broad range of temperature.     

Two-particle tunneling current in Josephson junctions

The contribution to the tunneling current of a Josephson junction from the Two-particle tunneling, to the 2nd order approximation in the barrier transparency, is investigated. Expressions for the current onset amplitudes corresponding to eV = _1,2 are given together with the full expressions for the voltage and the temperature dependencies of the two-particles current. The theory has ben developed to take also into account corrections due to depairing mechanisms, which lead to the smearing of the current singularities. Introducing a depairing parameter , which accounts for the probability of these processes, I–V curves in the voltage region of the onset of single and two particle current are obtained. It is shown that, though having the same functional dependence, spreading occurs over a voltage range of different widths. In particular, it is shown that the width of the single-particle structure is twice larger the one for the two-particle. A careful investigation of the I–V curves in the region 2 -eV is presented and some aspects of the interesting voltage region near ¦₁-₂¦ is discussed.     

Structure of martensite formed in Cu-Al-Fe single crystals duringin situ HVEM pseudoelastic tensile experiment

Single crystals of the CuAlFe alloy, containing 14.5 wt% Al and 2.2 wt% Fe were subjected toin situ tensile experiment using straining attachment in a 1 MV electron microscope. Loadelongation curves were obtained for three foil plane/tensile direction orientations: (001) [0 1 0], (0 0 1) [1 1 0] and (1 1 0) [¯1 1 2]. Each crystal was subjected to two cycles of pseudoelastic deformation up to maximum 2% strain, showing almost complete shape recovery. Structure observations and electron diffraction pattern indicated that during deformation of samples of (0 0 1) [1 1 0] and (1 1 0) [1 1 2] orientations, formation of ₁ martensite was observed and only at later stages narrow needles of ₁ nucleate in front of ₁. During pseudoelastic deformation in the (0 0 1) [1 0 0] direction, martensite forms as a mixture of narrow plates possessing either 2H or 18R structures. The following crystallographic relationship between the parent phase and both types of martensite was observed: [1 00] ₁ [101] ₁ and (0 0 1) ₁ (0 1 0)₁;(0 0 1) ₁ (0 1 0) ₁ and [1 1 0] ₁ [0 0 1] ₁. From the character of sidebands reflections presence of 1 0 1 1 0¯1 static displacement waves was inferred.     

Axi-symmetric natural frequencies and response of a spinning liquid column under strong surface tension

Summary The response of a solidly rotating anchored finite liquid column consisting of frictionless liquid is subjected to axial harmonic excitation. The response of the free liquid surface elevation and velocity distribution has been determined analytically in the elliptic (>2 ₀) and hyperbolic frequency range (>2 ₀). For the liquid surface displacement the response has been evaluated numerically as a function of the forcing frequency/2 ₀. In addition the first natural stuck-edge frequency has been determined and compared with the slipping case.List of symbols a radius of liquid bridge - h length of liquid bridge - I ₀,I ₁ modified Besselfunctions - J ₀,J ₁ Besselfunctions - p liquid pressure - r, ,z cylindrical polar coordinates - t time - u, v, w velocity distribution in rotating liquid - Weber number - z₀ axial excitation amplitude - elliptic case (>2 ₀) - hyperbolic case (>2 ₀) - liquid density - surface tension - liquid surface displacement - acceleration potential - ₀ rotational speed - axial forcing frequency - natural frequency of rotating system - _0n natural frequency of harmonic axial response     

On the dispersion of gases under the action of the medium

Some general regularities of dispersion of a gas emerging from a nozzle submerged in a liquid are considered. A condition for establishment of the so-called maximum dispersion state is formulated.Notation ₀ coefficient of surface tension at the liquidgas boundary - contact angle of wetting of the nozzle material surface by the liquid - p_at atmospheric pressure - p air pressure - density of the liquid - g gravitational acceleration - h height of the liquid column - ₁, and _g dynamic viscosity coefficients of the liquid and gas, respectively - R and r radii of the bubble and nozzle, respectively - Q and F dimensionless criteria - , , , , and undetermined coefficients - ratio of the circumference of a circle to its diameter     

Hydrodynamics of a vortex ring

We considered the kinematics and dynamics of a vortex ring in an incompressible fluid in toroidal coordinates. We obtained the change in the pressure difference along the boundary between two flow regions in the case of a moving torus.Notation , , toroidal coordinates - (V ;V ;V ) velocity of a fluid particle and its projections in toroidal coordinates - g ,g ,g metric tensor components - the Jacobian of transition to curvilinear coordinates - V ₀ velocity at the center of a vortex ring on its symmetry axis - x, y, z Cartesian coordinates - z, y, cylindrical coordinates - a distance from the axis of a torus (V=0) to its axis of symmetry (Oz) - angle between the Oy axis and the line that connects a fluid particle on the streamline =const, which represents a circle [16], with the center of this circle - U _z,U _y velocities in the cylindrical system of coordinates - ₀ stream function of a stationary vortex ring - velocity circulation - U V ₁, velocity of a rectilinear flow at infinity - ₁ stream function of a rectilinear flow - = ₀ + ₁ superposition of two flows - n=k ⁴=V ₁/V ₀ velocity ratio coefficient - R radius of a vortical region - U velocity of fluid particles at the boundary in polar coordinates (r, ) with the center at the coordinate origin (point 0) - fluid density - p ₀,p pressure at infinity and at a certain point of flow - pressure difference Polotsk State University, Polotsk, Belarus. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 4, pp. 531–536, July–August, 1995.     

Stability of the nonequilibrium state of a superconductor irradiated by an electromagnetic field

Irradiation of a superconductor by an electromagnetic field with a frequency ₀ larger than twice the energy gap (order parameter) decreases the order parameter . We obtain the quasiparticle distribution function n and the dependence of the order parameter on the power of the electromagnetic field P by solving numerically the kinetic equations for n and in the steady state. We take ₀/₀ = 2.1, 8, and 20, where ₀ is the equilibrium value of the order parameter at T = 0 K. In the examples considered the dependence of on the pumping power P becomes double-valued above a critical power. We allow phonons also to be out of thermal equilibrium. To discuss the stability of the steady state thus obtained, we derive kinetic equations for small deviations of the quasiparticle distribution function and the order parameter from the steady state n and by means of the nonequilibrium Green's function theory. Assuming n, exp(i kr – t), (k) is computed using n _s/, where n _sis the steadystate quasiparticle distribution function for arbitrary . It is concluded in general that the steady state on the upper branch ( > _{c 2}) is stable with respect to both spatially homogeneous and inhomogeneous fluctuations, and the lower branch ( > _{c 2}) is unstable; _{c 2}is the value where the upper and lower branches of (P) coalesce.This work is partly supported by a Grant-in-Aid for Special Project Research from the Ministry of Education, Science and Culture of Japan.     

Anisotropic spin diffusion and multiple spin echoes in3He-4He solutions

We propose a ₁-t₁-₂ pulse-NMR experiment to detect the spin-diffusion anisotropy, =D-D, in degenerate spin-polarized³He-⁴He mixtures, where D and dare the transverse and longitudinal spin diffusion coefficients. In such an experiment the nonlinearity of the dynamics produces multiple spin echoes (MSE). At the ³He concentration x₃ 4% the spinrotation parameter vanishes (M 0), so that the nonlinearity of the equations of motion is entirely due to the anisotropy. In this situation, detection of MSE amounts to observation of D. For slight anisotropy, i.e. D/D 0.25, we use a perturbation scheme similiar to that developed by Einzel et al. (in that case, for small M and small demagnetizing field) to calculate the second and third echo heights. For larger anisotropy we numerically calculate the echo heights. We find that for D/D = 0.5 the heights are 2 % of the first echo, and should be detectable. The (₁, ₂) tip-angle dependence of the D echoes is different from that of the M and demagnetization echoes, and furthermore, they occur at right angles to these echoes (in spin space). Thus, even when small spin-rotation and demagnetization effects are present, the ₁-t₁-₂ experiment provides a sensitive means of detecting the anisotropy.     

Correlation between magnetic hysteresis and magnetic relaxation in YBaCuO single crystals

The dependence of the magnetic momentm obtained from the hysteresis loops on the speed of the magnetic field sweep =dH _ext/dt is explained on the basis of Anderson's interpretation of the magnetic flux creep. In addition, a phenomenological model is suggested which predicts a linear dependence ofm on ln with the slope m/ ln , numerically equal to the relaxation rate m/ ln(t) from the usual magnetic relaxation. Such linear relations betweenm and ln were observed experimentally in single crystals of YBaCuO. Preliminary experiments on the complementary time dependent relaxation ofm after a simulated step change ofH _ext gave mostly relaxation rates close to the predicted values. The model here presented also enables one to compare the critical state in the superconductor at a field sweep rate with the critical state at some timet _eff after a step change ofH _ext. The values of analyzed in our experiments actually correspond to the critical state at timest _eff between0.04 and4 sec after an imaginary large step change ofH _ext.     

On the calculation of plastic energy dissipation rate during stable crack growth

An approximate analysis is presented for the calculation of the plastic energy dissipation rate during stable growth of a centrally located through crack. in a sheet subjected to gradually increasing uniaxial tension normal to the crack plane.It is shown that the plastic energy dissipation rate is a function of the slow growth parameter (_p/)·(d/da)+(_p/a), where _p is the plastic enclave width in the plane of the crack and d/da is the rate of increase of the gross stress with respect to stable growth. At the point of instability this parameter becomes equal to _p/a. By assuming that this parameter is zero at the point of instability, a simple expression is obtained for the plastic energy dissipation rate.The analysis excludes the energy dissipation rate resulting from energy changes in an inner fracture zone in the immediate neighborhood of the crack tip in which it is presumed that fracture processes such as vacancy formation, crack initiation by dislocation pile ups etc., are active. The analysis is not applicable in this inner zone as deformation is not homogeneous.

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Zusammenfassung Es wurde eine mehr oder weniger genaue Analyse für die Kalkulation eines plastischen Energiezerstreuungsverhältnisses während stabilem Wachstums eines zentral lokalisierten Durchrißes in einer einfachen Anspannungsplatte präsentiert.Man zeigte, daß das plastische Energiezerstreuungsverhältnis eine Funktion des langsam wachsenden Parameters ist, wobei _p die eingeschlossene, plastische Weite in der Rißebene und d/da das Wachstumsverhältnis des Rohdruckes mit Rücksicht auf das stabile Wachstum, darstellt.Diese Analyse schließt das Energiezerstreuungsverhältnis vom Energiewechsel in einer inneren Bruchzone in der unmittelbaren Nähe der Rißspitze aus. Man nahm nicht an, daß these Veränderung homogen, sondern auf Vakanzen, Verschiebungen, etc. begründet sei.

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Résumé On présente une analyse approchée pour le calcul de la vitesse de dissipation de l'érgie de déformation plastique au cours de l'extension stable d'une fissure située au centre d'une tôle et traversant celle-ci de part en part, lorsque cette tôle est sujette à une contrainte uniaxiale, normale au plan de la fissure, et graduellement croissante.On montre que cette vitesse de dissipation est fonction du paramètre d'extension lente: où _p est la largeur de l'enclave de déformation plastique dans le plan de la fissure, et d/da le taux d'accroissement de la tension nominale par rapport à l'extension de la fissure dans des conditions stables.Au point d'instabilité, ce paramètre devient égal à _p/a, en supposant que sa valeur soit nulle, on aboutit à une expression simple de la vitesse de dissipation de 1'énergie de déformation plastique.L'analyse ne considère pas la vitesse de dissipation qui résulte de modifications de l'énergie au sein d'une zone de rupture interne, et située dans le voisinage immédiat de la pointe de la fissure. Dans cette zone, l'on présume que les processus de fissuration tels que la formation de lacunes, ou l'amorçage d'une fissure par empilements de dislocations, etc., sont particulièrement actifs. L'analyse n'est pas applicable dans cette zone interne, car les déformations n'y sont pas homogènes.

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Notations 2a Crack length - t Thickness of sheet - W Width of sheet - Gross stress applied at infinity normal to the crack plane - A, ₀, n Parameters in a Ramburg-Osgood representation of the octahedral shear stresss-hear strain curve - _oct Octahedral shear stress at any point near the crack tip - _oct Octahedral shear strain at any point near the crack tip. - _infoct ^supel Octahedral shear stress at any point near the crack tip given by elastic analysis - _oli Octahedral shear stress at yield - _oli/₀ - _infoct ^supel /_oli - \5m _oct/_oli - E Young's modulus - E _s Secant modulus - G Shear modulus - G _s Secant modulus of the octahedral stress-strain curve - u _p Plastic energy density at any point inside the plastic enclave at the crack tip - U _p Plastic energy dissipated in the plastic enclave per unit thickness - v Poisson's ratio - r, Polar co-ordinates with the crack tip as origin - K Stress intensity factor - _p Plastic enclave width given by Irwin's formula - f ₁, f ₂, f ₃ Functions of , defining the stress field near the crack tip - f _e f _inf1 ^sup2 –f ₁ f ₂+f _inf2 ^sup2 +3f _inf3 ^sup2 - _oct Limiting octahedral shear stress beyond which homogeneous plastic deformation is not possible since fracture processes such as vacancy formation etc., become active. - \5m_{0 infoct} ^supu /_oli - C (_p/)·(d/da)+(_p/da); slow growth parameter - B (G·A/_o1i)· ⁿ      

Preparation of superconducting Bi-Sr-Ca-Cu-O ceramics by the sol-gel method

Superconducting Bi-(Pb)-Sr-Ca-Cu-O ceramics were prepared through the sol-gel method using an aqueous solution of metal acetates containing acetic acid and tartaric acid. The conditions of gelation and conversion of gel to Bi₂Sr₂CaCu₂O_x phase were studied by thermal analysis, infrared absorption spectroscopy and X-ray diffraction technique. It was found that transparent gels were obtained from the solutions containing tartaric acid, with a molar ratio of C₄H₆O₆/Cu of about 0.4. The gel matrix was assumed to be composed of carboxylate anions and metal cations. A gel of molar composition BiSrCaCu = 2223 was decomposed to CaCO₃, CaO, CuO and Bi_1-x Sr_xO_y (x = 0.2 to 0.3) at low temperatures of 270 to 600 ° C and produced Bi₂Sr₂CaCu₂O_x phase at 800 ° C via complex intermediate states. A rapid cooling of the heated product increasedT _c (end) in the gel of molar composition BiSrCaCu = 2223, while a slow cooling increasedT _c (end) in the lead-containing gel of molar composition BiPbSrCaCu = 1.850.351.92.03.1. The latter showedT _c (onset) at 115 K andT _c (end) at 105K.     

Die Entwicklung von Längswirbeln in zeitlich anwachsenden Grenzschichten an konkaven Wänden

Zusammenfassung Messungen des Anwachsens von Längswirbeln in zeitlich anwachsenden Grenzschichten an konkav gekrümmten Wänden (Görtler-Taylor-Wirbel) ergaben drei deutlich getrennte Bereiche: Es traten zunächst Wirbel mit der Wellenläge 0,9 auf (=Grenzschichtdicke, =Höhe einer Zelle, die zwei gegensinnig drehende Wirbel enthält). Je nach Größe der mit der Verdrängungsdicke ₁ der Grenzschicht gebildeten Reynolds-Zahl erschienen dann kurze Zeit später Wirbel mit 2,5, wenn war. Im Bereiche dagegen traten stattdessen bei den hier durchgeführten Versuchen immer Wirbel mit der Wellenlänge 6,5 auf. Bei werden die ersten Tollmien-Schlichting-Wellen mit der Wellenlänge _TS 6· angefacht. In ihren wandnahen Bereichen der Wellentäler könnten sich dann die oben genannten Längswirbel der Wellenlänge 6,5· ausbilden, die die zwei-in eine dreidimensionale Störung allseits gleicher Größenordnung verwandeln können.

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The development of longitudinal vortices in boundary layers growing with time along concave walls

Summary Measurements of the growth of longitudinal vortices in boundary layers growing with time along concave walls (Görtler-Taylor vortices) rendered three distinctly separated regions. First, vortices with a wave-length 0.9 appeared (-boundary layer thicness, =height of a cell containing two counterrotating vortices). Then, depending on the Reynolds number R _{a 1}/v ₁=displacement thickness), vortices with 2.5 appeared shortly afterwards, provided . In the region , however, the wave-length was 6.5. For the first Tollmien-Schlichting waves with _TS 6 were excited. In the wave-throughs close to the wall the abovementioned longitudinal vortices with wave length 6.5 may then be formed. This might transform the two-dimensional into a three-dimensional flow of equal order of magnitude in all directions.

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Zeichenerklärungen R _a Innenradius - Re _a Reynolds-Zahl gebildet mit dem InnenradiusR _a - Reynolds-Zahl gebildet mit der Verdrängungsdicke ₁ - kritische Taylor-Zahl - h Standhöhe der Flüssigkeit im Zylinder - t Zeit - z Anzahl - Steigungswinkel der Geraden - Grenzschichtdicke - ₁ Verdrängungsdicke - Wellenlänge (enthält ein gegensinnig rotierendes Längswirbelpaar) - v kinematische Zähigkeit - Winkelgeschwindigkeit Indizes K Knickpunkt der Geradensteigung - L unterhalb des Knickpunktes der Geradensteigung - TS Tollmien-Schlichting - e Einsatz der Wirbelentstehung     

The mechanism of adhesion of moist powders to solid surfaces in the presence of a temperature field

An examination is made of the basic factors which influence the creation of forces causing powders to adhere to solid surfaces in the presence of a temperature field. An experimental investigation has been conducted on an apatite concentrate.Notation p_c capillary pressure - density of fluid - g acceleration due to gravity - h_cap, h limiting and actual height of capillary rise - surface tension - r radius of equivalent capillary - q specific suction force - k_w water saturation coefficient - V_w volume of water in pores - V_pore volume of pores - Wg humidity by weight - R particle radius - polar angle - _c area of contact - N total adhesive force - _m, _w specific weight of powder and water     

Heat conduction in a multilayer composite wedge

A new method for analytically solving a problem of steady-state heat conduction for multilayer composite wedge-shaped bodies is suggested based on a generalization of the integral Mellin transform.Notation T temperature - _rr, thermal conductivity coefficients - thickness of composite material layers (1) - N₁(), N ₂ ⁽¹⁾ (), N ₂ ⁽²⁾ () auxiliary local functions from the rapid variable =r/ - m(r, p) auxiliary function entering the core of the generalized integral Mellin transform - ₀ half of the wedge aperture angle Moscow Institute of Chemical Engineering. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 64, No. 4, pp. 487–491, April, 1993.     

Fracture stress difference of notched polycarbonate between atmospheric pressure and a hydrostatic pressure

Experimental data on fracture stress of polycarbonate (PC) with and without various artificial notches have been obtained at atmospheric pressure and a high hydrostatic pressure (400 MPa). The difference in fracture stress, _F, between both pressures was directly proportional to the intensity of pressure,P, and was inversely proportional to the stress concentration factor of the notch,K _n such that _F following the form of the Kaieda-Oguchi formula, _F. By using the combined stress concentration factor,K _nc, of superposed notch and craze, and by considering the change in elastic modulus due to pressure, the experimental data agreed with the modified Kaieda-Oguchi formula. The stress concentration factor of the craze was calculated by using the Dugdale model.     

Sintering mechanisms and microstructural development of coprecipitated mullite

Coprecipitated mullite precursor powders of the bulk compositions 78 wt% Al₂O₃+22 wt% SiO₂ (high-Al₂O₃ material) and 72 wt% Al₂O₃+28 wt% SiO₂ (low-Al₂O₃ material) have been used as starting materials. The precursor powders were calcined at 600, 950, 1000, 1250, and 1650 C, and test sintering runs were performed at 1550, 1600, 1650, 1700, and 1750 C. Homogeneous and dense ceramics were obtained from cold isostatically pressed (CIPed) powders sintered in air at 1700 C. Therefore, all further sintering experiments were carried out at 1700 C. After pressureless sintering, sample specimens were hot isostatically pressed (HIPed) at 1600 C and 200 bar argon gas pressure. Sintering densifications of low Al₂O₃ materials ranged between 94% and 95.5%. There was no clear dependency between densification and calcination temperature of the starting powders. High-Al₂O₃ compositions displayed sintering densities which increased from 97% at 600 C calcination temperature to 99% at 950 C calcination temperature. Higher calcination temperatures first caused slight lowering of the sintering density to 95.5% (calcination temperature 1250 C) but later the density strongly decreased to a value of 85% (calcination temperature 1650 C). HIPing of pressureless sintered specimens prepared from powders calcined between 600 and 1100 C yielded 100% density. At the given sintering temperature of 1700 C, the microstructure of sample specimens was influenced by Al₂O₃/SiO₂ ratios and by calcination temperatures of the starting powders. Homogeneous and dense microstructures consisting of equiaxed mullite plus some minor amount of -Al₂O₃ were produced from high-Al₂O₃ powders calcined between 600 and 1100 C. Low-Al₂O₃ sample specimens sintered from precursor powders calcined between 600 and 1100 C were less dense than high-Al₂O₃ materials. Their microstructure consisted of relatively large and elongated mullite crystals which were embedded in a fine-grained matrix of mullite plus a coexisting glass phase. The different microstructural developments of high- and low-Al₂O₃ compositions may be explained by solid-state and liquid-phase sintering, respectively. The microstructure of HIPed samples was very similar to that of pressureless sintered materials, but without any pores occurring at grain boundaries.