Effect of zirconia particle size distribution on the toughness of zirconia-containing ceramics

The zirconia particles in zirconia-containing ceramics have a size distribution similar to Gaussian distribution. The spontaneously martensitic start temperature (M_s) of different particles are not the same. The larger the particle, the higher its M_s. On cooling from high temperature to a value lower than the macro M_s of the materials, the stress-induced and spontaneous transformation will happen, so that the toughness of the materials increases at first, then gradually drops to a value slightly higher than that of the matrix. The size distribution plays an important role in affecting the toughness of the materials. When the average particle size increases, the maximum toughening (K_c)_max and the temperature (T_max) at which (K_c)_max happens will all increase. The toughness at given temperature will increase at first and then drop also to a value slightly higher than that of matrix with increasing of average particle size. The stronger concentration of the size distribution, the higher (K_c)_max will be. The weaker concentration for size distribution (either the range of zirconia particle sizes becomes wider or the scale parameter of the distribution increases), the lower (K_c)_max, but the range of temperature in which the toughness is larger than certain value will become wider. Some suggestions of designing ceramics with high toughness at different temperatures are given.     

Hafnia and hafnia-toughened ceramics

Hafnia (HfO₂) and hafnium-based materials are traditionally regarded as technologically important materials in the nuclear industry, a consequence of their exceptionally high neutron absorption coefficient. Following the discovery of transformation toughening in the mid 1970s, a considerable research effort has been devoted to zirconia (ZrO₂)-toughened ceramics (ZTCs). They are considered to be potentially useful materials for structural applications at low and intermediate temperatures (T<1000 °C). Their unsuitability for high-temperature structural applications (T>1000 °C) is related to the low temperature of the tetragonal to monoclinic transformation in ZrO₂. On the basis that HfO₂ exhibits a similar crystal structure and in particular that its tetragonal to monoclinic transformation temperature (1700 °C) is approximately 700 °C higher than that for ZrO₂, it has been suggested that high-temperature transformation toughening could be possible in HfO₂-toughened ceramics (HTCs). Although the concepts behind this suggestion are universally appreciated, only a limited success has been made of the fabrication and the microstructural and mechanical property evaluation of these materials. The fracture toughness values obtained so far in HfO₂ toughened ceramics are, in fact, considerably lower than those obtained in their ZrO₂ counterparts. A great deal of further research work is therefore required in order to understand fully and to exploit toughened ceramics in the HfO₂-based and HfO₂-containing systems. This review covers the science and technology of HfO₂ and HfO₂-toughened ceramics in terms of processing, phase transformation, microstructure, and mechanical properties.     

An approximate approach for the calculation ofM s in iron-base alloys

Having estimated the critical driving force associated with martensitic transformation,ΔG ^α→M, as $$\Delta G^{\alpha \to M} = 2.1 \sigma + 900$$ whereσ is the yield strength of austenite atM _s, in MN m^?2, we can directly deduce theM _s by the following equation: $$\Delta G^{\gamma \to {\rm M}} |_{M_S } = \Delta G^{\gamma \to \alpha } + \Delta G^{\alpha \to M} = 0.$$ The calculatedM _s are in good agreement with the experimental results in Fe-C, Fe-Ni-C and Fe-Cr-C, and are consistent with part of the data in Fe-Ni, Fe-Cr and Fe-Mn alloys. Some higher “M _s” determined in previous works may be identified asM _a,M _s of surface martensite or bainitic temperature. TheM _s of pure iron is about 800 K. TheM _s in Fe-C can be approximately expressed as $$M_S (^\circ {\text{C}}) = 520 {\text{--- }}\left[ {{\text{\% C}}} \right]{\text{ }}x 320.$$ In Fe-X, the effect of the alloying element onM _s depends on its effect onT ₀ and on the strengthening of austenite. An approach for calculation of ΔG ^γ→α in Fe-X-C is suggested. Thus dM _s/dx _c in Fe-X-C is found to increase with the decrease of the activity coefficient of carbon in austenite.     

Intrinsic size dependence of the phase transformation temperature in zirconia microcrystals

It is argued that because the tetragonal (t) to monoclinic (m) transformation in zirconia is exothermic, this guarantees that the surface free energy of the former is less than that of the latter structure. It is argued further that for pristine, unconstrained, single crystals,A _s M _s 1447 K. It follows then, from a thermodynamic analysis that the reciprocal crystallite size is a linear function of the transformation temperature. Quantitative agreement was obtained between calculated and experimental crystallite size-temperature data which ranged over three orders of magnitude.     

Flaw growth in a polycrystalline lithium-aluminium-silicate glass ceramic

The growth of indentation-produced controlled flaws in a polycrystalline lithium-aluminium-silicate glass ceramic has been studied, over a wide range of temperatures and strain rates. Significant scatter in the fracture stress at elevated temperatures suggests that the extent of slow crack growth is highly sensitive to microstructural details. The initial flaw shape is important inK _IC determination. Up to 1000° C the fracture toughness,K _IC, is essentially strain-rate insensitive. The value ofK _IC decreases with temperature beyond 850° C. Intergranular cavity formation is suggested as the reason. Crack blunting by diffusive crack healing probably occurs at high temperatures. Also, intergranular slow crack growth occurs essentially under Mode I loading.     

Mass and spin diffusion near the λ line in dilute3He-4He mixtures

We examine the possibility of using NMR and other measurements on very weak solutions of ³ He in liquid ⁴ He to investigate the superfluid phase transition. It is found that even for these very weak solutions the mass (D _m) and spin (D _s) diffusion coefficients associated with the ³ He behave in radically different ways:D _m is predicted to diverge asT approaches T from above as (T–T) ^–1/3 , while the behavior ofD _s depends on the type of experiment, and for the ordinary spin-echo type has no particular singularity.Based on a D.Phil. thesis submitted to the University of Sussex by M. A. Eggington.     

The effect of SiO2 on high-temperature deformation and strength of zirconia-toughened alumina

At room temperature, SiO₂ additions may increase the fracture toughness, K _IC, by diminishing the tetragonal phase contents to about 50%, but with ground surfaces the influence on strength is small. A pronounced decrease in strength is observed with rising temperature in the high toughness region from 20°C to M _s, the starting temperature for martensitic transformation. Beyond M _s at lower toughness, the strength behaviour is very similar to nontransforming alumina ceramics, and an even modest increase of the silicate concentration intensively promotes propagation-controlled failure in the brittle creep region (> 900°C) and inelastic deformation. With less than 1% amorphous grain boundary phases, damage-free superplasticity is restricted to small strains of less than 10%. The significance of high-temperature data for tool applications is considered by cutting tests with high feeding rates.     

The spin diffusion coefficient of3He in3He-4He solutions

The transport properties of³He in³He-⁴He solutions with molar concentrations of 5, 9, 14, and 24% have been studied for 0.9 KT2.5 K. The spin diffusion coefficientD _s and the longitudinal relaxation timeT ₁ were measured by the spin-echo method for temperatures both above and below the solution lambda temperatureT . The spin-echo method measures the diffusion coefficient for magnetizationD _s, which differs from the usual diffusion coefficient for particlesD belowT .D _s depends on the³He-³He scattering cross section _FF and the³He-roton/phonon cross section _FB, whileD depends only on _FB. The distinction betweenD _s andD is elaborated in terms of a simple mutual-friction model for diffusion. The two scattering mechanisms are clearly evident in the behavior ofD _s as a function of concentrationx and temperature. The contribution due to the³He-³He scattering is inversely proportional tox, indicating that the³He can be treated in first approximation as a classical gas (the Pomeranchuk model). The predictions of various theoretical models are compared with the results, where possible, but most of the previous theoretical work is not applicable to the concentration range and temperatures of these measurements.Supported in part by the National Science Foundation and the U.S. Office of Naval Research.     

Magnetic Phase Transition and Electronic Anomalies in La1.96−x Y0.04Sr x CuO4 around x∼1/8

La-NMR, Hall coefficient and sound velocity have been measured in order to investigate the correlation between the magnetic ordering, the prominent change of transport properties, the suppression of T _c and the structural transformation around x1/8 in La _1.96–x Y _0.04 Sr _x CuO ₄. By the substitution of 0.04/2 Y for La-sites, the structural transformation to the low temperature tetragonal phase (LTT) is caused at 57±14 K for samples around x0.115. The. prominent decrease of the Hall coefficient followed by the sign reversal and the magnetic ordering are observed around x0.115 below temperatures T _s and T _N, respectively. T _s vs x shows a bell shaped curve with the maximum value of 65 K at x00115 where most prominent suppression of T _c appears. T _N shows similar x dependence to T _s with the maximum value of 40 K at x0.115. The change of the electronic state below T _s and the suppression of T _c become more prominent and the magnetic ordering is observed more wide range of x under the LTT phase.     

Pair breaking, “intrinsic”Tc, and the upper limit ofTc in the cuprates

The presence of magnetic impurities leads to a drastic decrease inT _c in the overdoped region, gaplessness, and the usual temperature dependence ofH _c2. The magnetic moments are localized on the apical oxygen site, and this allows us to explain the increase inT _c with the increase in the number of Cu-O planes in the unit cell. Applied pressure can raiseT _c above the usual value at optimum doping, toward the intrinsicT _c. The cuprates as a class of compounds have an upper limit ofT _c in the rangeT _c,upp=160–170 K.     

The effect of titanium additions onM s of β-CuZn

The effect of titanium additions to binary -CuZn alloys was investigated: the concentration range of at high temperatures (860° C), solid solution hardening of this phase, and the change in martensite temperature,M _s. Titanium in solution produces considerable solid solution hardening, both by replacing copper or zinc. Only replacement of zinc leads to a constant or increasingM _s, while replacing copper decreases it. Ageing of the -phase causes strong hardening and a decrease inM _s. The results have been interpreted considering the role of thermodynamic and mechanical properties in determiningM _s.     

Martensitic transformation of an aged/thermal-cycled Ti30.5Ni49.5Zr10Hf10 shape memory alloy

Ti_30.5Ni_49.5Zr₁₀Hf₁₀ alloy undergoes a B2 B19 one stage martensitic transformation. Martensitic transformation temperatures decrease, but the hardness increases with increasing aging time, resulting from the effect of point defects/atoms rearrangement in B2 phase induced by aging at 450°C. Thermal cycling can also decrease the transformation temperatures while increasing the hardness of the alloy. The strengthening effects of aging and thermal cycling on the M _s (M*) temperature of this alloy follows the expression M _s = T ₀ – KK y, in which K values are affected by different strengthening processes. Experimental results indicate that martensitic transformation temperatures of Ti_30.5Ni_49.5Zr₁₀Hf₁₀ alloy can be more effectively depressed by aging than by thermal cycling. The K value of this aged alloy is smaller than that of aged Ti_40.5Ni_49.5Zr₁₀ alloy due to the former having the higher aged temperature and the less lattice distortion.     

Transport properties of GdB6 and DyB6

The electrical resistance and absolute thermoelectric power (TEP) have been measured for GdB₆ and DyB₆ in the temperature range 2–30 K. The compounds GdB₆ and DyB₆ order antiferromagnetically atT _N 15.2 and 20.3 K, respectively. Above the Néel temperature the resistivity has a small contribution that is linear inT due to electron-phonon scattering, whereas in the same temperature range the spin-disorder TEP (S _spd) has been evaluated and found to be linear inT. A divergence in the temperature derivative of resistance and TEP has been found atT _N that is consistent with the present theories. There is evidence of a low-temperature phase appearing at 7 K in the resistivity and the TEP data of GdB₆. A minimum in the TEP is found in these compounds below 6 K, which is associated mainly with phonon drag and possibly a magnon contribution. A broad peak in the TEP of DyB₆ around 16 K is thought to be due to crystalline electric field effects.     

Correlation between structural relaxation enthalpy and superconducting properties of amorphous Zr70Cu30 and Zr70Ni30 alloys

The anneal-induced change in the superconducting properties together with the irrecoverable relaxation enthalpy (H _i,exo) and recoverable relaxation enthalpy (H _r,endo) of amorphous Zr₇₀Cu₃₀ and Zr₇₀Ni₃₀ alloys was examined. The increase in _i,exo and the degradation ofT _c progress logarithmically with annealing timet _a in a temperature range of 373 to 523 K. The activation energy and the attempted frequency were respectively estimated to be 1.5eV and 6.6 × 10¹³ sec^–1 for the increase in H _i,exo and 1.5eV and 1.9×10¹⁴ sec^–1 for the degradation ofT _c. The recoverable structure relaxation exerts little effect onT _c. Based on the agreement between the kinetic parameters for the changes of H _i,exo andT _c, it appears that the degradation ofT _c on annealing is associated with the irrecoverable structural relaxation as a result of the annihilation of frozen-in defects and the topological and compositional atomic rearrangement. The values of the attempted frequency being of the order of Debye frequency suggest that the irrecoverable structural relaxation processes occur more or less independently from each other. The dressed density of electronic states at the Fermi level,N(E _f)(1+), determined from the measured values of _n and -(dH _c2/dT)_{T c} using GLAG (theory), was found to have a similar annealing dependence to that ofT _c. The degradation ofT _c by the irrecoverable relaxation was thus inferred as resulting from the decrease in due to the decrease inN(E _f) and the increases inM and . Furthermore, the irrecoverable structural relaxation resulted in a significant depression of fluxoid pinning force and was interpreted as due to an enhanced structural homogeneity on the scale of coherence length.     

Systemic Study of Orbital and Spin Nematicity in NaFe<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Co<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>As by NMR

Nematic order, a self-organized state with rotational symmetry broken, has been observed in both copper-oxide and iron-pnictide high temperature superconductors. However, its origin is still a mystery in the iron pnictides although it is considered as a key to understand the mechanism of superconductivity. Here, we report a systemic nuclear magnetic resonance (NMR) study on NaFe_1?x Co _x As (0 ≤x ≤ 0.042) that an orbital order, accompanied by an instant spin nematicity, occurs at at a temperature T ^? far above structural transition temperature T _s in the tetragonal phase. We show that the observed NMR spectra splitting and its evolution is due to an incommensurate orbital order that sets in below T ^? and becomes commensurate below T _s. We show that the electric field gradient asymmetry parameter is a good measure for the orbital order parameter which undergoes a Landau-like 2nd-order phase transition. We further show that the spin nematicity is well accounted for by the observed orbital order.     

Heat conduction in Ba1?xKxBiO3

We have investigated heat conduction of single crystal Ba_1–xK_xBiO₃ in the temperature range of 2–300 K and in a magnetic field of up to 6 Tesla. Temperature dependence of thermal conductivity(T) reveals the participation of both electrons and phonons with their relative contributions that depend critically on the potassium doping concentration. Crystals underdoped with potassium (samples with higherT _c) exhibit a strong suppression of and a glass-like temperature dependence. In contrast, those with a higher potassium content (lowerT _c) show an increase as temperature decreases with a peak near 23 K. Field dependence of(H) is also very sensitive to the level of potassium doping. Crystals exhibiting a large phonon contribution show an initial drop in(H) at low fields followed by a minimum and then a slow rise to saturation as the field increases. The initial drop is due to the additional phonon scattering by magnetic vortices as the sample enters a mixed state. The high field behavior of(H), arising from a continuous break-up of Cooper pairs, exhibits scaling which suggests the presence of an unconventional superconducting gap structure in this material.     

NMR studies of single crystals of H2. V. NMR anisotropy and order parameter distribution ofX (ortho)≤0.55

We report a study of the NMR line shapes in hcp single crystals of H₂ with ortho concentrationsX0.55 in the regime where there is no longer a transition to a long-range orientationally ordered phase. From the anisotropy of the o-H₂ impurity NMR spectrum at low ortho concentration, reached by ortho-para conversion, the crystal orientation is determined. The second momentM ₂ can be represented by a function of the formM ₂=(X, T)f(cos _Hc ), where _Hc is the angle between the applied magnetic field and the crystalc axis. For a single crystal, the anisotropy functionf(cos _Hc ) is found to be independent of temperature and of ortho concentration within experimental error, and is in very good agreement with predictions based on the first term of the high-temperature expansion ofM ₂ and on other, more general symmetry arguments. An order parameter is defined and the distribution functionP() is calculated from the NMR line shapes under the simplifying assumption that the anisotropy of the order parameter, which gives rise to the observed anisotropy ofM ₂, can be neglected. We giveP() as a function ofX at low temperature, where the line shape is only weakly dependent onT, and as a function ofT at constantX. It is found that the line shapes andP() in both situations evolve continuously and give no hint of a phase transition. These results are discussed in relation to those of magnetic spin-glasses, and it is concluded that the orientational regime in solid H₂, called a quadrupolar glass by previous investigators, cannot be distinguished by symmetry from the orientationally disordered phase that occurs at high temperature.Work supported by NSF grants DMR-81-02993 at Duke University and DMR-79-10153 at the University of Pennsylvania.     

Toughening mechanisms in duplex alumina-zirconia ceramics

A series of Al₂O₃-ZrO₂ ceramics has been fabricated using both conventional sintering and a hot-pressing route, which results in various microstructures including (i) Al₂O₃ with well-dispersed ZrO₂ single crystals; (ii) Al₂O₃ With TZP (tetragonal zirconia polycrystals) agglomerates (20 to 50m); and (iii) Al₂O₃-ZrO₂ duplex structures, in which both well-dispersed ZrO₂ single crystals and TZP agglomerates are dispersed. The fracture strength of the composites has been measured by means of three-point bending and the fracture toughness by means of the micro-indentation technique. The microstructural characterization was carried out using scanning and transmission electron microscopy, and phase analysis of the zirconia by means of X-ray diffraction. The high toughness values of 12 M Pa m^1/2 measured for the duplex structure have been correlated with the toughening mechanisms operative and the fracture strength with the matrix grain size and with larger defects present in the structure. A combined toughening process is proposed to account for the improved properties, including transformation toughening, microcrack toughening and crack deflection, which are discussed in context with the property measurements and the microstructural observations.     

A micromechanics theory for the transformation toughening of two-phase ceramics

Summary Based on the principle of thermodynamic equilibrium, the condition of stress-induced phase transformation in a two-phase ceramic is established. The development makes use of the change of potential energy that was calculated with a mean-field approach. In this process the elastic heterogeneity of the constituent phases, and the shape and volume concentration of the randomly oriented metastable ellipsoidal inclusions, are fully accounted for. Both the transformation heightH of the process zone with a steadily growing crack and the fracture toughness increment K of the transforming system are derived. The derived theory is then used to address the effect of inclusion shape and elastic inhomogeneity on the transformation toughening of two-phase ceramics. By considering the metastable ellipsoidal inclusions as phase 1 and the stable matrix as phase 0, it is found that, when ₁/₀>1, flat-like discs always provide a larger transformation-height while spherical ones provide the smallest, and vice versa. As the ratio of ₁/₀ increases, the size of the process zone also increases. For the toughness increment, the results indicate that thin-disc inclusions are again the most effective toughening medium. It is further found that Poisson's ratio of the constituent phases also has a significant effect; the combination ofv ₁0.5 for the inclusions andv ₁0 for the matrix has the best enhancement for fracture toughness. But whenv ₁, the toughness increment K all approaches to an asymptotic value regardless of the values of Poisson's ratios. Some explicit solutions of toughness change for several distinctive shapes of inclusions are also derived for the first time.     

The effect of surface constraint on the phase transformation of Nitinol

Ultra-low-temperature isotropic carbon was vapour deposited on a near equiatomic Ti-Ni (Nitinol) alloy (49.9 at% Ti-50.1 at% Ni) for components used in biomedical applications. The adhering carbon film, and carbide layer formed after annealing, introduced a surface constraint. Differential scanning calorimetry studies show a marked decrease in theA _s andM _f temperatures of such a surface-constrained alloy during phase transformation. TEM foils made of vertical and horizontal sections of carbon-coated Nitinol were examined using transmission electron microscopy. It is proposed that for surface-constrained samples, the martensite plates last to form were close to the surface, and these are first to disappear during reverse transformation. Moreover, for both coated and uncoated samples, the martensitic and reverse transformations can be described by equations of the formf(A) =exp[-(M _s -T)] andf(A) =exp[-(A _f -T)], respectively, wheref(A) is the fraction of austenitic phase present at the specific temperature (T), and and are constants. Finally, the driving force for the martensitic and reverse transformations of both coated and uncoated samples was calculated.