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Showing papers in "Journal of the American Ceramic Society in 1972"


Journal ArticleDOI
TL;DR: In this article, the content of free ZrO2 in partially stabilized zirconia ceramics by X-ray diffraction techniques was determined by linear calibration curves.
Abstract: Linear calibration curves were developed for determining the content of free ZrO2 in partially stabilized zirconia ceramics by X-ray diffraction techniques. Two methods were studied. The matrix method, in which free ZrO2 was considered to be distributed in a matrix (the cubic phase), gave approximately equal mass absorption coefficients for the monoclinic and cubic phases. The polymorph technique, in which the cubic phase was considered to be a polymorph of ZrO2 and in which integrated intensities were used, gave the better results.

1,302 citations



Journal ArticleDOI
TL;DR: In this article, a method of comparing the kinetics of isothermal solid-state reactions based on the classical equation for analysis of nucleation-and growth processes is described, where plots of In In (1-α) vs In (time), where α is the fraction reacted, are used to distinguish reaction mechanisms.
Abstract: A method of comparing the kinetics of isothermal solid-state reactions based on the classical equation for analysis of nucleation-and-growth processes is described. In this method, plots of In In (1-α) vs In (time), where α is the fraction reacted, are used to distinguish reaction mechanisms. Even nonintegral slopes obtained for values of the fraction reacted from 0.15 to 0.50 may indicate whether the reaction rate is diffusion- or phase-boundary-controlled. The problems of ascertaining zero time and self-cooling (or heating) of the reacting sample can be observed in the analysis but do not cause severe difficulties in interpretation, as they can for analyses based on reduced-time plots. The analysis is applied to the dehydroxylation of kaolinite and of brucite and the decomposition of BaCO3.

636 citations



Journal ArticleDOI
TL;DR: In this article, the electrical relaxation associated with alkali diffusion in Na2O·3SiO2 glass was studied from 0.2 Hz to 700 kHz at −1° to 163°C.
Abstract: The electrical relaxation associated with alkali diffusion in Na2O·3SiO2 glass was studied from 0.2 Hz to 700 kHz at –1° to 163°C. A formalism for analysis of electrical relaxation in conducting dielectrics which associates the nonexponential decay of the electric field to zero and the dispersions in the dielectric constant and the conductivity with a distribution of relaxation times for the electric field was developed and is shown to be in qualitative accord with current molecular theories of electrical relaxation in alkali silicate glasses. A relation between the dc conductivity, the limiting high-frequency dielectric constant, and the average electric field or conductivity relaxation time was derived and is verified experimentally for the Na2O·3SiO2 glass. The distribution of electric-field relaxation times for the glass is broad, asymmetric on a logarithmic scale, and weighted in favor of the shorter relaxation times; the distribution narrows with increasing temperature. A reduced electrical relaxation curve which can be used to compare electrical and mechanical relaxations in Na2O·3SiO2 glass was generated.

252 citations


Journal ArticleDOI
TL;DR: In this paper, high-density translucent polycrystalline bodies of stoichiometric aluminum silicate (mullite) were obtained by vacuum-hot-pressing of high-purity submicron mixed oxide powders.
Abstract: Highly dense translucent polycrystalline bodies of stoichiometric aluminum silicate (mullite) were obtained by vacuum-hot-pressing of high-purity submicron mixed oxide powders. The powders were prepared by the hydrolytic decomposition of mixed metal alkoxides. X-ray diffraction and electron microscopy indicated that the initially amorphous needlelike fine particulates transform into highly crystalline orthorhombic mullite at ∼1200°C. Optimum hot-pressing conditions were 5 kpsi and 1500°C for 30 min. Densities within experimental error of the theoretical value of 3.19 g/cm3 were obtained. A typical microstructure consisted of fine interlocking needlelike grains arranged in an overall mosaic or “jigsaw” pattern. Microprobe traverses across the samples indicated homogeneous dispersion of SiO2 in the AlO3 matrix. Room-temperature mechanical properties were measured and correlated with the microstructure and crystal structure of the ceramic compact. A slightly higher melting temperature than has been previously reported was observed for the 3Al2O3·2SiO2 studied. All specimens exhibited a smooth surface finish and excellent thermal-shock resistance from 1200°C to room temperature.

223 citations


Journal ArticleDOI
TL;DR: Extensive grain growth was observed by scanning electron microscopy in very porous Al2O3 compacts, even at densities <40% of theoretical after ∼7% shrinkage at 1700°C, the grain size increased from ∼03 to 051 μm in a compact having a relative green density of 031 as mentioned in this paper.
Abstract: Extensive grain growth was observed by scanning electron microscopy in very porous Al2O3 compacts, even at densities <40% of theoretical After ∼7% shrinkage at 1700°C, the grain size increased from ∼03 to 051 μm in a compact having a relative green density of 031 During grain growth in highly porous compacts, the grains appear initially to be chainlike, then to be oblong, and finally to be equiaxed The proposed mechanism of initial grain growth involves the filling of necks between adjacent grains followed by the movement of the grain boundary through the smaller grain Although grain growth in very porous compacts is quite different from coalescence and ordinary grain growth, the kinetics are similar

207 citations


Journal ArticleDOI
TL;DR: Partially stabilized zirconia (PSZ) ceramics in the system CaO-ZrO2 were characterized by optical microscopy as mentioned in this paper, which revealed that the microstructure provided an effective stress-relieving mechanism during thermal shock.
Abstract: Partially stabilized zirconia (PSZ) ceramics in the system CaO-ZrO2 were characterized. The microstructure, as revealed by optical microscopy, consisted of grains of pure ZrO2 distributed in a matrix of fully stabilized material. Electron microscopy showed that the matrix grains have a complex substructure of 1000-A domains of cubic and monoclinic ZrO2. The grains appeared to fit Ubbelohde’s concept of a hybrid single crystal. Evidence obtained indicated that the substructure provides an effective stress-relieving mechanism during thermal shock. It is proposed that initiation of phase inversion in pure ZrO2 domains, even at subtransition temperatures (by thermal stresses), creates an extremely large microcrack density. On the basis of Hasselman’s thermal-shock criterion, only quasi-static crack propagation occurs during thermal shock of PSZ; evidence is presented to support this concept.

204 citations


Journal ArticleDOI
David G. Grossman1
TL;DR: In this paper, the strength of tetrasilicic-mica glass-ceramics has been investigated and two regions of strength dependence on grain size were found, where the strength increases as the 1/5 power of the mica-plate diameter and decreases above a critical plate diameter.
Abstract: Tetrasilicic-mica glass-ceramics are formed from glasses in the simple quaternary system K2O-MgF2-MgO-SiO2. The mica phase crystallizes as small (400-A) spherical grains at #625°C and recrystallizes into larger booklets at 940°C. The mica platelets grow by a dissolution and reprecipitation mechanism, thereby increasing the aspect ratio during growth. Two regions of strength dependence on grain size are found. When the mica platelets are very small, the strength increases as the 1/5 power of the mica-plate diameter. Above a critical plate diameter, the strength decreases, being inversely proportional to the first power of the mica-plate diameter. In the second region, the strength appears to be controlled by the interfacial shear stresses developed as a result of the thermal expansion mismatch between the mica platelets and the residual glass.

194 citations


Journal ArticleDOI
TL;DR: In this article, high-temperature diffusion kinetics and phase relations between couples of fused SiO2 or cristobalite and sapphire or mullite were investigated in air and in helium.
Abstract: High-temperature diffusion kinetics and phase relations between couples of fused SiO2 or cristobalite and sapphire or mullite were investigated in air and in helium. Subsolidus liquid formation between sapphire and cristobalite indicates the existence of a metastable system without mullite. A liquid phase is considered to be essential for the nucleation of mullite. The growth rate of mullite exceeded its dissolution rate in semi-infinite fused-SiO2-sapphire couples above 1634°C. The inter-facial liquid compositions provided data for a minor revision of the mullite liquidus curve. Diffusion coefficients calculated from the Al profiles vary greatly with concentration and temperature, resulting in a large range of values for apparent activation energy, which decreases with increasing Al2O3 content (∼310 to ∼60 kcal/mol for ∼4 to ∼22 wt% Al2O3). The diffusion process in the liquid is considered to be cooperative movement of oxygen-containing Al and Si complexes whose nature changes with composition and temperature; this change in the diffusing species contributes to the range in the values of experimental apparent activation energies.

171 citations


Journal ArticleDOI
K. H. Härdtl1, Detlev Hennings1
TL;DR: In this paper, it was shown experimentally that A-site vacancies predominate in La-substituted lead titanate-zirconate (PLZT) solid solutions.
Abstract: It was shown experimentally that A-site vacancies predominate in La-substituted lead titanate-zirconate (PLZT) solid solutions. The formation of B-site vacancies is favored under increased PbO vapor pressure, but preparation of PLZT-perovskite phases with B-site vacancies only is impossible since the increase in the partial pressure of PbO is naturally limited by the condensation of liquid PbO at the grain boundaries of the ceramic.

Journal ArticleDOI
TL;DR: In this article, a model was proposed to explain the phenomenon of electrode polarization in glasses containing alkali oxides, where the application of a dc potential to Pt electrodes on an alkali-containing glass causes a large electric field to develop in the immediate vicinity of the anode.
Abstract: A model is proposed to explain the phenomenon of electrode “polarization” in glasses containing alkali oxides. The application of a dc potential to Pt electrodes on an alkali-containing glass causes a large electric field to develop in the immediate vicinity of the anode. This high-field region is formed by local dissociation of the alkali oxides and displacement of the dissociated ions from the region. A major hypothesis of the model is that the nonbridging oxygen ions in this region can move and can determine the electrical characteristics of the sample. Large electric fields can also develop at a partially blocking cathode as a result of the pileup of alkali ions beneath the cathode surface. Permanent compositional changes occur near both electrodes under such conditions. The model was confirmed by dc electrical measurements, electron-microprobe data, and oxygen-evolution data. Important physical parameters of the model were calculated from the data.

Journal ArticleDOI
TL;DR: In this article, the strength degradation and crack propagation in Al2O3 are shown to depend on the initial strength and grain size of the material, and the strength retained after thermal shock and the extent of crack propagation decrease with increasing initial strength.
Abstract: Strength degradation and crack propagation in Al2O3 are shown to depend on the initial strength and grain size of the material. The strengths of single-crystal sapphire and polycrystalline Al2O3 specimens with grain sizes of 10, 34, and 40 μm decreased discontinuously at the critical quenching temperature. In contrast, the strength of polycrystalline Al2O3 with a grain size of 85 μm decreased gradually as the quenching temperature increased. The strength retained after thermal shock and the extent of crack propagation decrease with increasing initial strength and grain size, respectively, in Al2O3.

Journal ArticleDOI
TL;DR: In this article, a stoichiometric NiAl2O4, CuAl 2O4 and ZnAl 2 O4 spinels were prepared and equilibrated at temperatures from 600° to 1400°C.
Abstract: Stoichiometric NiAl2O4, CuAl2O4, and ZnAl2O4 spinels were prepared and equilibrated at temperatures from 600° to 1400°C. The parameters u and x, denoting the oxygen position and fraction of divalent cations on tetrahedral sites, respectively, were determined from a detailed X-ray diffraction analysis. In NiAl2O4, x increased from 0.07 at 595° to 0.26 at 1391°C; in CuAl2O4, x decreased from 0.68 at 613° to 0.64 at 1195°C; and in ZnAl2O4, x decreased from 0.96 at 905° to 0.94 at 1197°C. The form of the temperature dependence of x could not be described using theoretically based equations advanced in the literature. A more general equation which allows for a non-distributional contribution to the configurational entropy was derived and observed to properly describe the temperature dependence; the results indicate that short-range order is of definite significance in these intermediate aluminate spinels.

Journal ArticleDOI
TL;DR: In this article, the dimensional changes and the thermograms of cement specimens were determined during temperature cycles (+5° to - 60°C, 0.33°C/min).
Abstract: The dimensional changes and the thermograms of cement specimens were determined during temperature cycles (+5° to - 60°C, 0.33°C/min). In each case, freezing processes at -8° and -40°C and melting processes at -11° and 0°C were observed. The results could be explained by a theory previously developed for the porous-glass-water system. At the higher temperature, freezing occurs on the outer surface of the specimen; at the lower temperature, it occurs in the pores after redistribution of the water. Because water does not freeze in pores filled on adsorption, it migrates out of these pores when the relative humidity (expressed in terms of the vapor pressure of undercooled water), unavoidably decreases on cooling. Expansion is deleterious when the water content of the paste is significantly greater than the equilibrium value at the prevailing relative humidity. The effects of the water/ cement ratio, degree of saturation, air entrainment, sample dimensions, and cooling rate were consistent with the theory.

Journal ArticleDOI
TL;DR: The effect of water on the growth of cracks in glass is discussed in this article, where it is believed that crack motion is caused by a stress-enhanced chemical reaction between water and glass and is influenced strongly by the crack-tip OH− ion concentration.
Abstract: The effect of water on the growth of cracks in glass is discussed. Crack motion is believed to result from a stress-enhanced chemical reaction between water and glass and is influenced strongly by the crack-tip OH− ion concentration. This hypothesis is supported by the observation that crack-velocity data can be correlated with measurements of pH in slurries of ground glass and water. Variation of the measured pH from 5 to 12, depending on glass composition, suggests a wide pH variation at crack tips. The types of chemical reactions that establish the slurry pH are discussed, and it is noted that the slurries behave as weak acids, buffered solutions, or salts of weak acids, depending on glass composition.

Journal ArticleDOI
TL;DR: In this article, nonisothermal techniques for analyzing initial-stage sintering are reviewed and compared with results from isothermal experiments performed on the same materials (UO2 and ThO2 gel).
Abstract: Nonisothermal techniques for analyzing initial-stage sintering are reviewed. It is shown that in principle they permit the determination of all the sintering parameters (rate law, activation energy, and diffusion coefficients) normally obtained from isothermal experiments. Comparison with results from isothermal experiments performed on the same materials (UO2 and ThO2 gel) demonstrates the validity and accuracy of the nonisothermal techniques.


Journal ArticleDOI
S. K. Rhee1
TL;DR: Based on the wetting properties of a-Al2O3 and pyrolytic graphite by liquid metals, the critical surface energy for spreading was determined and compared with the surface energy of the ceramics as mentioned in this paper.
Abstract: Based on the wetting properties of a-Al2O3, and pyrolytic graphite by liquid metals, the critical surface energy for spreading was determined and compared with the surface energy of the ceramics. The surface energy γ-8 (ergs/cm2) of the (0001) surface of a-Al2O3 is estimated to be 892–0.12T (°C), that of the c plane of pyrolytic graphite 1139–0.13T (°C), and that of the a plane of pyrolytic graphite 1300–0.17T (°C). Also, the liquid-solid interfacial energies were calculated and found compatible with the values reported in the literature. The surface energy of liquid Ag or liquid Cu is not significantly affected by carbon.

Journal ArticleDOI
TL;DR: In this paper, the fatigue behavior of polycrystalline alumina was investigated and cyclic fatigue effect characterized by a frequency and amplitude dependence was also observed; possible mechanisms of cyclic fatigues in brittle materials are discussed.
Abstract: The fatigue behavior of a polycrystalline alumina was investigated. Stress conditions consisted of a static tensile stress and a static tensile stress with superposed sinusoidal cyclic stress. The alumina exhibited the expected static fatigue behavior; a cyclic fatigue effect characterized by a frequency and amplitude dependence was also observed. Possible mechanisms of cyclic fatigue in brittle materials are discussed.

Journal ArticleDOI
TL;DR: In this article, multiorganometallic compounds were used to prepare high-purity submicron-size lead lanthanum zirconate-titanate (PLZT) powders which can be consolidated at low sintering temperatures to high-density piezoelectric and electrooptic ceramic bodies.
Abstract: Multiorganometallic compounds were used to prepare high-purity submicron-size lead lanthanum zirconate-titanate (PLZT) powders which can be consolidated at low sintering temperatures to high-density piezoelectric and electrooptic ceramic bodies. Simultaneous hydrolytic decomposition of lead isoamyloxide, lanthanum isopropoxide, and zirconium and titanium tertiary amyloxides produced quaternary titanate powders with particle sizes of 75 to 300 A and analyzed purity of 99.92%; the major contaminant was Na from an intermediate reaction product. Homogeneity and stoichiometry of the powders before and after processing were demonstrated by electron microscopy and chemical analysis. High-temperature X-ray diffraction indicated an amorphous material up to ∼600°C, where the crystalline phase was first observed. Powders prepared in this manner sintered to high-density fine-grained transparent bodies with uniform microstructure. The experimental results suggest that less rigorous consolidation methods are required with high-purity homogeneous precursor materials with fine particle size.

Journal ArticleDOI
Bruce A. Scott1, Gerald Burns1
TL;DR: In this paper, high purity single crystals of PbZrO3 suitable for electrical measurements were grown from solutions in the PbO-ZRO2-PbF2-B2O3 system.
Abstract: High-purity single crystals of PbZrO3 suitable for electrical measurements were grown from solutions in the PbO-ZrO2-PbF2-B2O3 system. Dielectric, hysteresis-loop, and optical measurements confirmed the existence of an intermediate ferroelectric (FE) form, previously observed only in ceramics, just below the transition temperature (Tc#232°C). The temperature stability range of the FE phase, which cooling curve measurements show to vary from 12° to 26°C, appears to be related to crystal stoichiometry. The maximum value of spontaneous polarization is P8(max)#24 μC/cm2, assuming that the FE phase possesses rhombohedral symmetry.

Journal ArticleDOI
TL;DR: In this paper, the authors studied the changes in the hysteresis loops which occur with aging, a s shown in Fig. 1, and indicated that process (2) or (3) is its principal cause.
Abstract: N THE ferroelectric and piezoelectric applications of BaTiOa I and Pb(Zr,Ti)O,, dependence on time of many of their physical properties is encountered; this phenomenon is usually detrimental but is sometimes useful. Since aging is commonly considered to be related to the mobility of the ferroelectric domain structure, information on the nature of the aging process can be obtained by studying the changes in the hysteresis loops which occur with aging, a s shown in Fig. 1. A “fresh” ceramic sample of BaTiO, (just cooled to a temperature below the Curie point) exhibits a normal loop which on aging constricts gradually, resulting in decreasing remanent polarization. The rate and amount of constriction during aging are very sensitive to impurities and to slight variations in the Ba-Ti ratio. In the extreme case, the remanent polarization vanishes. This behavior can easily be confused with the double hysteresis loops exhibited by BaTiO, and PbZrO, as a result of fieldenforced paraelectric-ferroelectric and antiferroelectric-ferroelectric transitions, respectively. The constriction disappears if the sample is subjected to strong ac fields for prolonged times; this process is called deaging. The extremely constricted loop can be viewed as the result of reestablishment of the aged domain pattern after each half cycle. Strong fields are needed to disturb this pattern; however, after this disturbance a memory of the original state is retained, demonstrating that aging involves stabilization of the domain pattern. There is a general agreement’ that such stabilization occurs, but several mechanisms are possible: (1) Gradual equilibration of the domain pattern with respect to sizes and types of domains, with minimization of elastic and dielectric free energy.’*’ (2) Segregation of impurities and vacancies on domain walls and crystal boundaries. (3) Ordering of impurities and vacancies inside the ferroelectric domains with respect to the polar axis. Microscopy of single crystals and ceramics has demonstrated that process (1) occurs; however, its role in stabilization of the domain pattern is unclear. In the present work, an experiment was conducted that demonstrated aging simply and indicated clearly that process (2) or (3) is its principal cause. The ceramic samples were solid

Journal ArticleDOI
TL;DR: In this article, a single-crystal sapphire crack was shown to break up after annealing into channels of cylindrical voids and ultimately into rows of spherical pores, with the thicker gap spacings in the original crack remaining open.
Abstract: Cracks introduced into single-crystal sapphire broke up after annealing, first into channels of cylindrical voids and ultimately into rows of spherical pores, with the thicker gap spacings in the original crack remaining open. Breakup of the cylindrical voids on subsequent annealing conformed to the models for surface-diffusion-controlled material transport. At the temperatures of measurement, the magnitudes of the calculated surface diffusivities agree well with values reported previously.

Journal ArticleDOI
TL;DR: In this article, the effect of oxygen activity on the sintering of high-purity Cr2O3 is shown, and the theoretical density is approached at the equilibrium O2 partial pressure needed to maintain the Cr2 O3 phase (Po2=2×10−12 atm).
Abstract: The effect of oxygen activity on the sintering of high-purity Cr2O3 is shown. Theoretical density was approached at the equilibrium O2 partial pressure needed to maintain the Cr2O3 phase (Po2=2×10−12 atm). The presence of N2 in the atmosphere during sintering did not prevent final sintering. The addition of 0.1 wt% MgO at this equilibrium pressure effectively controlled the grain growth and further increased the sintered density to very near the theoretical value. The solute segregation of MgO at the grain boundaries, followed by nucleation of spherulites of magnesium chromite spinel on the boundaries, accounted for the grain-growth control. It is speculated that these isolated spherulites locked the grain boundaries together, changing the fracture mode of the sintered oxide from inter-to intragranular and also that larger MgO additions produced a more continuous spinel formation at the boundaries, resulting in decreased sintered density. Weight loss, which was also monitored as a function of O2 activity, correlated with the changing predominant volatile species in the Cr-O system.

Journal ArticleDOI
TL;DR: In this article, a high-vacuum Auger electron spectrometer was used to analyze the intergranular fracture surface of Magnesia-doped alumina for surface composition, and the presence of excess Ca at the grain boundary was explained by the fact that its ionic radius is relatively large compared to those of Al and Mg.
Abstract: Magnesia-doped alumina was fractured in a high-vacuum Auger electron spectrometer, and the resulting intergranular fracture surface was analyzed for surface composition. Calcium was present on the fracture surface in amounts of ∼2 to 5 at.%. There was no indication of Mg on the fracture surface. The bulk Ca concentration was 5 to 15 ppm, whereas MgO was present at the 1000-ppm level. The presence of excess Ca at the grain boundary can be explained by the fact that its ionic radius is relatively large compared to those of Al and Mg. Sputtering profiles normal to the fracture surface indicate that the segregated Ca is concentrated in a region near tha intergranular fracture surface.

Journal ArticleDOI
TL;DR: In this article, the lattice parameter of wustite (Fe2O) single crystals was measured at high temperatures and the plots of both lattice parameters vs composition and lattice parametrization vs temperature were linear.
Abstract: The lattice parameter of wustite (Fe2O) single crystals was measured at high temperatures. Plots of both lattice parameter vs composition and lattice parameter vs temperature were linear, and no appreciable changes in slope were detected at the boundaries of the subphases suggested by Vallet and Raccah.

Journal ArticleDOI
TL;DR: In this paper, thermal expansion and compressibility were measured on the orthorhombic compounds HfTiO4, Hf1.26Ti0.74O4 and ZrTiO2.
Abstract: Using X-ray diffraction techniques, thermal expansion and compressibility were measured on the orthorhombic compounds HfTiO4, Hf1.26Ti0.74O4, and ZrTiO4 (both quenched and cooled slowly from 1300°C). The thermal expansion of HfTiO4 is highly anisotropic; the thermal expansion coefficients along the crystallographic axes are αa=+(8.7±0.5)×10−6°C−1, αb=−(5.2±0.5)×10−6°C−1, and αc=+ (5.3±0.5)×10−6°C−1. The thermal expansion of Hf1.26Ti0.74O4 was similar to that of HfTiO4 but that of ZrTiO4 was markedly less anisotropic. The compressibilities of HfTiO4 and ZrTiO4 also differed markedly. All compounds investigated, however, behaved similarly in exhibiting a polymorphic transition to a high-pressure phase having the monoclinic baddeleyite (ZrO2) structure. The polymorphism can be explained qualitatively on the basis of crystal structure.

Journal ArticleDOI
TL;DR: In this article, a simplified structural model for mullite was proposed, which consists of independently vibrating structural units, giving plausible frequency assignments which agree well with other published data for silicates and aluminates.
Abstract: Simplified structural models for mullite were investigated, and ir frequencies were calculated for the simplest model which gave the theoretical number of ir-active frequencies compatible with the observed spectrum. This model, which consists of independently vibrating structural units, gives plausible frequency assignments which agree well with other published data for silicates and aluminates. These assignments explain the spectral changes observed during formation of mullite from heated clay minerals. The model does not take into account the changes in stoichiometry and distortion caused by compositional variations.

Journal ArticleDOI
TL;DR: In this article, the authors determined the fracture strength of Li2O-SiO2 glass-ceramics as a function of nucleation treatment and volume fraction of crystals present.
Abstract: Variations in the thermal expansion coefficients, elastic moduli, and fracture strengths of Li2O-SiO2 glass-ceramics were determined as a function of nucleation treatment and volume fraction of crystals present. Strength enhancement was attributed to a decrease in the mean free path between crystals as crystallization proceeds. It is postulated that the eventual reduction in strength in some glass-ceramics is caused by the development of localized cracks at the crystal-glass interface as a result of the volumetric changes which occur during crystallization.