Thermal shock resistance of laminated ceramic matrix composites

The thermal shock resistance capability of laminated ceramic matrix composites is investigated through the study of three-dimensional transient thermal stresses and laminate failure mechanisms. A (–45°/45°)_s SiC/borosilicate glass laminate is utilized as a reference composite system to demonstrate the analytical results. The maximum allowable temperature change, T _max, has been taken as a measure of the thermal shock resistance capability of composites. The effects of fibre orientation, volume fraction, thermal expansion coefficient. Young's modulus, and thermal conductivity on the thermal shock resistance capability, expressed in terms of the maximum allowable temperature change, T _max, have been assessed. Numerical computations are also performed for six composite systems.     

New equations for enthalpy of vaporization from the triple point to the critical point

Two new equations are proposed for the enthalpy of vaporization from the triple point to the critical point. One of these equations containing four parameters is exceptionally good for fitting the data. The other equation containing three parameters is quite adequate for fitting the data but it is exceptionally suited for interpolation when the data do not cover the entire range. These equations have been tested using the enthalpy of vaporization of water from the triple point to the critical point and are compared with other equations.Nomenclature T _c Critical temperature, K - T _t Triple point, K - T _x Any particular temperature, K - T _r Reduced temperature - P _r Reduced pressure - R Gas constant - P Vapor pressure - X (T _c–T)/T _c - Y (T _c–T)/T - X _x (T _c–T)/(T _c–T _x) - X _t (T _c–T)/(T _c–T _t) - H _vt Enthalpy of vaporization at the triple point, kJ · mol^–1 - H _vx Enthalpy of vaporization at any temperature x, kJ · mol^–1 - Z _v Compressibilty factor of the saturated vapor - Z ₁ Compressibilty factor of the saturated liquid Relative deviation = 100[H_v(obs)–H_v(cal)]/H_v(obsd) Standard deviation = { [H _v(obs)–H _v(cal)]²/(No. points — No. parameters)}^0.5     

Thermal-stress resistance and fracture toughness of two tool ceramics

The thermal-stress resistance and fracture strength behaviour of two oxide ceramics (a hot-pressed pure Al₂O₃ and a composite ceramic NTK-HC2) subjected to severe thermal shocks have been investigated. The damage resistance parameter (K _IC/ _f)² for both ceramics is also determined for a wide range of temperatures (25° to 800° C) and cross-head rates (10^–2 cm min^–1 2.5 m sec^–1). Fracture strength behaviour of these two oxide ceramics is shown to follow Hasselman's model where the instantaneous strength loss at the critical quenching temperature may be calculated using appropriate (K _IC/ _f)² values to give good agreement with experimental results. Repeated shocks show some further degradation in the retained strength for both ceramics so that these materials are susceptible to thermal fatigue. It is found that both materials possess similar resistance to crack initiation (i.e. similar T _c and retained strength after shocking through T _c) but the pure oxide ceramic has higher resistance to crack propagation.     

Supercooling of In2Bi and InBi Melts

The effect of melt overheating T ⁺ on the critical supercooling T ^– of liquid In₂Bi and InBi is studied by cyclic thermal analysis. It is shown that, the T ^– for In₂Bi is 2.0 K, independent of the melt preheating temperature. In contrast, the T ^– for InBi varies jumpwise with T ⁺: T ^– 1.0–1.6 K at T ⁺ < 5 K, and T ^– 16 K at T ⁺ = 5–300 K, independent of the cooling rate (varied from 0.002 to 8.0 K/s). The solidification behaviors of In₂Bi and InBi are shown to correlate with the structures of their liquid and solid phases.     

Damage-tolerant laminated composites in thermal shock

Alumina is very susceptible to thermal shock which often leads to catastrophic failure. The addition of tape-cast nickel layers to laminated alumina can increase its tolerance to damage induced during thermal shock. The fracture behaviour after thermal shock of laminated composites showed non-catastrophic failure during loading at room temperature. The retained strength of the laminates was determined for a wide range of quenching-temperature differences (T= 150–1200C). The retained strength and critical quenching-temperature difference, T _c, of the laminated composites were a significant improvement over the values for the respective monolithic alumina. This improvement in behaviour can be related to the compressive residual stress in the alumina layers and ductile-layer crack blunting.     

Effect of stress on the superconducting transition temperature of SrTiO3

The superconducting transition temperatures of several specimens of reduced SrTiO₃ and of Nb-doped SrTiO₃ have been investigated as functions of hydrostatic and uniaxial compressive stresses up to 1.8 kbars. Decreases inT _c as large as 0.12 K have been observed in specimens under hydrostatic pressure. Because of the lowT _c and small compressibility of SrTiO₃, (lnT _c)/P and (lnT _c)/(lnV) are orders of magnitude greater than the corresponding effects in elemental superconductors. The effect of uniaxial stress onT _c varied with the direction of stress. Compression along a [111] direction caused large decreases inT _c, while both small increases and small decreases inT _c have been observed for [100] compression. It is believed that the present results reveal the presence of a sensitive volume dependence in one or more of the parameters important to superconductivity in SrTiO₃, and that no significant electron-transfer effects occurred in the range of stresses of this experiment.     

Interaction between a dislocation and various divalent impurity in KCl single crystals for the Fleischer's model taking account of the Friedel relation

The interaction between a dislocation and the impurity in KCl : Mg²⁺ (0.035 mol% in the melt), KCl : Ca²⁺ (0.035 and 0.065 mol% in the melt) and KCl : Ba²⁺ (0.050 and 0.065 mol% in the melt) was investigated from the strain-rate cycling test during the Blaha effect measurement. This was carried out at 77–254 K. As a result, it was found that the Fleischer's model taking account of the Friedel relation seems to be suitable for KCl : Ca²⁺ and KCl : Ba²⁺. However, it was not appropriate for KCl : Mg²⁺. Furthermore, the values of T _c, H(T _c) and G ₀ were obtained for the specimens. T _c is the critical temperature at which effective stress is zero. H(T _c) and G ₀ are the enthalpy and the Gibbs free energy of activation for the breakaway of the dislocation from the impurity, respectively. H(T _c) was almost the same for the specimens except KCl : Mg²⁺. G ₀ increased with increasing the divalent cation size. In addition, the tetragonality around the divalent ion-positive ion vacancy pair was estimated on the basis of G ₀ for the each specimen.     

Analysis of thermal fatigue behaviour of brittle structural materials

The effect of the level of maximum temperature (T _max), the temperature range (T) and the mode of convective heat transfer on the thermal fatigue resistance of brittle structural materials is analysed. Expressions are derived for the number of thermal cycles to failure in terms of the appropriate mechanical and thermal properties, crack growth parameter, T andT _max. For simultaneous changes inT _max and T commonly used in practice, the change in thermal fatigue life is governed by both the thermal stress intensity exponent (n) and the activation energy (Q) for subcritical crack growth, in contrast to the results of other studies. For constantT _max but variable T, thermal fatigue life is affected byn only, whereas, for constant T but variableT _max, the value ofQ alone governs changes in fatigue-life. Heat transfer by natural or forced convection will result in differences in thermal fatigue resistance. Recommendations are made for the design and analysis of thermal fatigue experiments. Figures-of-merit for the selection of materials with high thermal fatigue resistance are presented.     

Prediction of thermal fatigue life of ceramics

On the assumption that the thermal fatigue life of ceramics is determined mainly by the duration over which a crack reaches a small critical length, a prediction of the life was made by application of fracture mechanics to ceramics based on subcritical crack growth. Approximated formulae, such asN/N(T _N /T _N ) ⁿ , were derived, whereN andN are the lives for temperature differences of T _N and T _N , respectively, andn is a material constant. Experimental examination showed that the formulae proved to be valid for glass, sintered mullite under moderate shock severity, and zirconia. Data given by other authors also prove their validity. The deviation of the life from the formulae for sintered mullite under a thermal shock of extremely low severity, suggests that a certain mechanism, for example strengthening, is needed to understand the life of the sintered mullite. Moreover,n determined from the thermal shock experiments is comparable with that given in data determined by a mechanical method.     

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.     

The high-temperature thermal expansion of BiPbSrCaCuO superconductor and the oxide components (Bi2O3, PbO,CaO, CuO)

The thermal expansion of superconducting Bi_1.6Pb_0.4Sr₂Ca₂Cu₃Ox (BiPbSrCaCuO) and its oxide components Bi₂O₃, PbO, CaO and CuO have been studied by high-temperature dilatometric measurements (30–800°C). The thermal expansion coefficient for the BiPbSrCaCuO superconductor in the range 150–830°C is =6.4×10^–6K^–1. The temperature dependences of L/L of pressed Bi₂O₃ reveals sharp changes of length on heating (T ₁=712°C), and on cooling (T ₂=637°C and T ₃=577°C), caused by the phase transition monoclinic-cubic (T ₁) and by reverse transitions via a metastable phase (T ₂ and T ₃). By thermal expansion measurements of melted Bi₂O₃ it is shown that hysteresis in the forward and the reverse phase transitions may be partly caused by grain boundary effect in pressed Bi₂O₃. The thermal expansion of red PbO reveals a sharp decrease in L/L, on heating (T ₁=490°C), related with the phase transition of tetragonal (red, a=0.3962 nm, c=0.5025 nm)-orthorhombic (yellow, a=0.5489 nm, b=0.4756 nm, c=0.5895 nm). The possible causes of irreversibility of the phase transition in PbO are discussed. In the range 50–740°C the coefficient of thermal expansion of pressed Bi₂O₃ (_m=3.6 × 10^–6 and _c=16.6×10^–6K^–1 for monoclinic and cubic Bi₂O₃ respectively), the melted Bi₂O₃ (_m=7.6×10^–6 and _c=11.5×10^–6K^–1), PbO (_t=9.4×10⁶ and _or=3.3×10^–6K^–1 for tetragonal and orthorhombic PbO respectively), CaO (=6.1×10^–6K^–1) and CuO (=4.3×10^–6K^–1) are presented.     

Thermodynamic properties of the layered superconductor 2H-NbSe2

The specific heat in the normal and superconducting states of single crystals of the transition metal dichalcogenide superconductor 2H-NbSe ₂ was measured from 1.7 to 9 K by use of a thermal relaxation method. The thermodynamic critical field and the specific heat behavior are different from those predicted by the BCS theory. The anisotropy and strong coupling effects in the thermodynamic properties are made evident through comparison with the Clem-Sheahen-Gubser relations, which take account of these effects near T _c and 0 K. A simple semiempirical model is proposed to explain the temperature dependences of the thermodynamic critical field and the superconducting electronic specific heat. Under the assumption of a spheroidal Fermi surface based on the tight-binding approximation, the model takes into account effects of the anisotropy and the strong coupling interaction in the expression for the energy gap _k (t)= ₀ (t)(1+ ₂ cos ₂ ). The strong coupling parameter 2 ₀ (0)/K _B T _c and the energy gap anisotropy parameter ₂ are the only two adjustable parameters. The thermodynamic behavior deduced from the model gives good agreement with experimental results for values of 2 ₀ (0)/k _B T _c5.0 and ₂ -–0.6.Supported by a Grant in Aid for Special Research from the Ministry of Education.     

Theory for incongruent crystallization: Application to a ZBLAN glass

Equations which describe incongruent nucleation and subsequent crystal growth have been derived. A ZrF₄-BaF₂-LaF₃-AlF₃-NaF glass was used to test the validity of these equations. Nucleation rate measurements were fitted to theory and some growth rate measurements were found in reasonable agreement with theoretical predictions. Both nucleation theory and crystal growth theory were used for computer simulations of the crystallization behaviour during heat treatments. Some heat treatments were performed in a differential scanning calorimeter to verify the theories. The experimental results were in good agreement with the numerical data. Using these theoretical results it is possible to estimate fibre scattering losses due to crystallization. Depending on drawing temperature, estimated losses can vary from 0.014 (310 °C) to 25 (320 °C) or more dB km^–1.Nomenclature a _s the chemical activity of component A in solution referred to the activity of the component in crystalline form - c _c ^A the concentration of A in the crystalline form (mol m^–3) - c _r ^A the concentration of A in the liquid at the interface (mol m^–3) - c ₁ ^A the concentration of A far from the interface in the bulk (mol m^–3) - c _e ^A the equilibrium concentration of A (mol m^–3) - D the diffusion coefficient (m²s^–1) - G the free energy difference between the liquid and the crystal, equal to the molar Gibbs' free enthalpy of component A in solution minus the molar Gibbs' enthalpy of the crystalline form of A (J mol^–1). - -G free energy difference between crystal A and pure liquid A (J mol^–1) - G _a activation energy for growth (J mol^–1) - G _r free energy difference between the liquid (of composition c _r ^A ) at the interface and the pure liquid A - G ₁ free energy difference between the liquid (of compositionc ₁ ^A ) far from the interface and the pure liquid A - H _f heat of fusion of the pure component A (J mol^–1) - I the nucleation frequency (1 m^–3 s^–1) - k Boltzmann constant (J K^–1) - K a constant of the order 10³²–10³³ Pa m^–3 K^–1 - r the radius of the spherical crystal - R gas constant (J mol^–1 K^–1) - t time (s) - T temperature (K) - T T ₁ - T the undercooling of the melt of compositionx ^A (T ₁ is the liquidus of the melt and depends onx _A). - T ₁ liquidus temperature (K) - T _m melting temperature of pure component A (K) - T _p temperature at the top of the DSC peak (K) - u crystal growth rate (ms^–1) - V _m molar volume of the crystallizing phase (mol m^–3) - x _A molar fraction of the precipitating component A in the melt (for an example: see Appendix) - viscosity (Pa s) - jump distance of the order of molecular dimensions (m) - ₀ frequency of vibration (s^–1) - surface tension of the crystal-liquid interface (J m^–2) - the thickness of the diffusion layer     

Effect of Biexciton on Cooper Pairing in High Tc Superconductors

In this paper, we have modified the Cooper theory by considering a biexcitonic attractive interaction for high T _c superconductors. We have developed an expression for (2/K _B T _c) as a function of phonon and biexciton mediated coupling constants. For the sake of simplicity, we use a two-square-well potential model (electron–phonon and electron–biexciton). The calculated values of (2/K _B T _c) show good agreement with experimental values.     

The equilibrium humidity of dispersed solids at different temperatures

The use of the free energy of water vapor as a unique characteristic of saturated air permits the level of dehydration of dispersed solids to be determined unambiguously. The moist air diagram is computed for compensation of the moisture fluctuation of the surrounding air, corresponding to a change of the temperature of drying.Notation F₁ free energy of water vapor in air - F₂ free energy of bound water in dispersed solid - T₁ temperature of drying air, °C - T₂ temperature of dispersed solid, °C - T₃ temperature of air in laboratory, °C - P₁ water vapor pressure (absolute air humidity) - p_s saturated water vapor pressure at temperature T₁ - relative humidity of air, % - R gas constant - M molecular weight of water - W moisture content of dispersed solid - L₂ internal binding energy (thermal effect) of water in dispersed solid Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 20, No. 5, pp. 787–791, May, 1971.     

Thermal fatigue in polycrystalline alumina

Damage accumulation in polycrystalline alumina subjected to cyclic thermal loading was studied via non-destructive elastic modulus and internal friction measurements. These nondestructive techniques were sensitive to cracks formed by thermal loading. Thermal shock damage was observed to saturate as a function of an increasing cumulative number of thermal shock cycles. The observed power law relationship between the damage saturation and thermal shock difference implies a fatigue-like power law relation in stress. The exponent has a value of approximately 12 for the range of T included in this study. Thermal shock damage induced changes in internal friction were found to be a function of a crack damage parameter. These thermal fatigue results of polycrystalline (unreinforced) alumina are also compared to thermal fatigue results for SiC whisker-alumina composites.     

Transport properties and determination of the basic parameters of superconductors with overlapping bands

The thermoconductivity and ultrasonic attenuation in non-single-band super-conductors are investigated. It is proved that the ratio ₂/₁ atT T _c is equal to that atT=0. It is also shown that ultrasonic measurements and data on the phonon thermoconductivity can be used very effectively for definition of the basic parameters of the superconductors with overlapping bands.     

Quantum fluctuations in continuous superconducting films

Motivated by recent experiments on ultrathin continuous superconducting films, we study the dependence ofT _c and (for zero temperatures) on the film thicknessd. Using field-theoretical methods, we express the Coulomb interaction in terms of a fluctuating potential, and the fluctuation correction to the free energy (in one-loop approximation) is determined. Based on the standard dirty-limit expressions for the response functions, we findT _c and by a numerical investigation of the gap equation. Generally, we find that the decrease ofT _c and vs.d ^–1 is quite similar, but depends sensitively on both the large-wave-vector cut-off and the strength of the interaction. In particular, however, for a strong interaction (Coulomb interaction), the order parameter is more strongly suppressed than the critical temperature, which is due to long-wavelength fluctuations of the phase and the potential.     

New Universal Relations for Liquid-Vapor Phase Equilibrium

Universal relations between the saturation pressure p _LV and the value of =h _LV/ _LV–p _LV, where h _LV .is the latent heat of evaporation and _LV is the volume change of the vapor-liquid transition, and the product of the orthobaric densities _L and _V of the liquid and vapor at coexistence have been discovered. In the temperature range from the triple point to T/T _c0.9, these relations obey a power law with universal exponents. At temperatures 0.9<T/T _c1, p _LV and depend linearly on ln( _{L V}) with retention of universality for substances of different nature.     

Growth and Characterization of YBCO Thin Films by Sequential Deposition and Annealing

A novel thin film growth procedure, sequential deposition and annealing (SDA), which contains the advantages of both in situ and ex situ procedures, was proposed. Y₁Ba₂Cu₃O_{7 – x} (YBCO) high temperature superconducting thin films were grown and characterized by the SDA procedure. Purely c-axis-oriented YBCO thin films with no foreign phases and other oriented grains were successfully prepared. The superconducting transition properties of SDA-grown YBCO thin films were measured by measurement of inductance and resistance. The inductance measurements gave a T _c ^onset of 85 K and a T _c of 5 K. The resistance measurements gave a T _c ^onset of 90 K and a T _c of 5 K. Atomic force microscopy studies showed that SDA-grown YBCO thin films had micrometer-size grains surrounded by many nanometer-size grains. The nanometer-size grains in SDA-grown YBCO thin films are responsible for degradation of superconducting transition properties.