Fracture toughness and crack morphology in indentation fracture of brittle materials

The relationship between the indentation fracture toughness, K _c, and the fractal dimension of the crack, D, has been examined on the indentation-fractured specimens of SiC and AIN ceramics, a soda-lime glass and a WC-8%Co hard metal. A theoretical analysis of the crack morphology based on a fractal geometry model was then made to correlate the fractal dimension of the crack, D, with the fracture toughness, K _IC, in brittle materials. The fractal dimension of the indentation crack, D, was found to be in the range 1.024–1.145 in brittle materials in this study. The indentation fracture toughness, K _c, increased with increasing fractal dimension, D, of the crack in these materials. According to the present analysis, the fracture toughness, K _IC, can be expressed as the following function of the fractal dimension of the crack, D, such that $$In K_{IC} = {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}\{ In[2\Gamma E/(1 - \nu ^2 )] - (D - 1)In r_L \}$$ Where Γ is the work done in creating a unit crack surface, E is Young's modulus, v is Poisson's ratio, and r _L is r _min/r _max, the ratio of the lower limit, r _min, to the upper limit, r _max, of the scale length, r, between which the crack exhibits a fractal nature (r _min ?r?r _max). The experimental data (except for WC-8%Co hard metal) obtained in this study and by other investigators have been fitted to the above equation. The factors which affect the prediction of the value of K _IC from the above equation have been discussed.     

Application of Fourier transform infrared spectroscopy in cement Alkali quantification

Alkali in cement is responsible for the Alkali–silica-reaction phenomenon that manifests itself in the form of premature cracking in concrete structures such as bridge decks and concrete pavements. X-ray fluorescence spectroscopy (XRF) is commonly used for cement Alkali quantification but a simpler and faster analytical procedure based on Fourier transform infrared spectroscopy (FTIR) has been expanded for this purpose. An analytical absorption band at 750 cm^?1 in the FTIR spectra of cement samples belonging to Alkali solid solution of tricalcium aluminate [C₃A(ss)] is used for Alkali quantification. Regression analysis of a plot correlating FTIR absorption band area ratio (750/923 cm^?1) to equivalent Alkali Na₂O _e (Na₂O _e  = % Na₂O + 0.658 × % K₂O) measured by XRF shows a linear correlation coefficient, R ², of 0.97. High Alkali cement samples show a higher microstructural disorder coefficient, C _d, which is a reactivity criterion introduced by Bachiorrini and co-authors (Proceedings of the seventh international conference on concrete alkali-aggregate reactions? 1986) for ASR-susceptible aggregates. Results of this research indicate applicability of FTIR technique to quantitatively predict cement vulnerability to ASR through the \( A_{{750\,{\text{cm}}^{ - 1} }} \) to \( A_{{923\,{\text{cm}}^{ - 1} }} \) band area ratio and the magnitude of the disorder coefficient (C _d).     

An analytical approach and experimental confirmation of dislocation–twin boundary interactions in titanium

The morphology of $ \{ 10\overline{1} 2\} \left\langle {\overline{1} 011} \right\rangle $ { 10 1 ¯ 2 } 〈 1 ¯ 011 〉 deformation twins formed in commercial purity titanium during an initial pass of equal-channel angular pressing was studied by transmission electron microscopy (TEM). The corresponding diffraction patterns show a symmetry line splitting of $ (10\overline{1} 2) $ ( 10 1 ¯ 2 ) twin boundaries (TB) which is related to the presence of interfacial defects. A simple modeling for the interaction between non-screw a-slip lattice dislocations (Burgers vector b =  $ \frac{1}{3}[\overline{1} \overline{1} 20] $ 1 3 [ 1 ¯ 1 ¯ 20 ] ) and the $ (10\overline{1} 2) $ ( 10 1 ¯ 2 ) twin plane is used according to crystallographic geometry and vector conservation. The results show that dislocation dissociation into different Frank partial dislocations on the interfacial plane is more favorable than its transmission to the other side of the interface. The formation of the Frank partials at the TB can produce a small change in the TB misorientation angle and this is consistent with the symmetry line splitting of the $ (10\overline{1} 2) $ ( 10 1 ¯ 2 ) twin boundaries observed by TEM.     

Investigation of the oxidation of sialons with infrared reflection spectroscopy

Hot-pressedβ-sialons (Si_6-z Al _z O _z N_8-z formed in the Si₃N₄-Al₂O₃-AIN and Si₃N₄-SiO₂-AIN systems have been investigated using infrared reflection spectroscopy (IRRS). Asz increases, the IRRS bands decrease in frequency. The decrease can be explained by the decrease in the force constants of the chemical bondings. IRRS has been applied to the study of the oxidation sialons at 1200 and 1300°C as a function of time. The technique has sensitively detected cristobalite, mullite and glass phases on the oxidized surface. This is considered to be effective for understanding the oxidation kinetics of sialons.     

Thermal Conductivity of n-Aluminium Nitride-Added MgB2 Superconductor in Normal and Superconducting State

Thermal conductivity (k) of 0, 5, 10, and 15 wt.% aluminium nitride (n-AlN)-added polycrystalline MgB ₂ superconductors, synthesized by solid reaction is discussed both in the normal and superconducting states between 20 and 300 K. The prepared samples are characterized using X-ray diffraction (XRD) and field electron gun scanning electron microscope (FEG–SEM). Resistivity measurement confirms a decrease in superconducting transition temperature of MgB ₂ (T _c=38.5 K) with n-AlN addition and decreases to ～35 K in case of 15 wt.% n-AlN-added MgB ₂ sample. Thermal conductivity of both MgB ₂ and n-AlN-added MgB ₂ pellets does not show any hump around T _c, and the absolute values of k decrease with increasing n-AlN in MgB ₂. Temperature dependence of the thermal conductivity of MgB ₂ and n-AlN-added MgB ₂ has been analyzed, assuming the role of both electrons and phonons. The Wiedemann–Franz law does not work well for the present samples, which indicates inelastic scattering (L _eff < L ₀). Thermal conductivity of MgB ₂ and n-AlN-added MgB ₂ pellets is explained by assuming effective Lorentz number, L _eff= 0.1 L ₀. Electronic thermal conductivity in superconducting state ( \(k_{\text {el}}^{\mathrm {s}} )\) follows “two-gap model” and has been used to estimate the values of band gaps, relative contribution of each band in thermal transport, and intraband scattering relaxation time. The estimated values are fairly consistent with the previously reported results for MgB ₂. We further confirm that n-AlN addition in MgB ₂ introduces disorders in π bands, which reduce the π band gapsand intraband relaxation time ( \(\tau _{\pi }^{\text {im}})\) . The lattice contribution of thermal conductivity in both normal and superconducting states is analyzed in the terms of Callaway’s model, assuming various phonon scatterings. Our analysis indicates that the lattice thermal conductivity of MgB ₂ is dominated by phonon-sheet-like fault scattering. Addition of n-AlN in MgB ₂ enhances the phonon scattering from sheet-like faults, and dislocations induced strain field scattering by >7 times compared to that for pure MgB ₂ pellets.     

Hyperfine Fields and Magnetic Structure in the B Phase of CeCoIn5

We re-analyze Nuclear Magnetic Resonance (NMR) spectra observed at low temperatures and high magnetic fields in the field-induced B phase of CeCoIn₅. The NMR spectra are consistent with incommensurate antiferromagnetic order of the Ce magnetic moments. However, we find that the spectra of the In(2) sites depend critically on the direction of the ordered moments, the ordering wavevector and the symmetry of the hyperfine coupling to the Ce spins. Assuming isotropic hyperfine coupling, the NMR spectra observed for H ∥[100] are consistent with magnetic order with wavevector $\mathbf{Q}=\pi(\frac{1+\delta}{a},\frac{1}{a},\frac{1}{c})$ and Ce moments ordered antiferromagnetically along the [100] direction in real space. If the hyperfine coupling has dipolar symmetry, then the NMR spectra require Ce moments along the [001] direction. The dipolar scenario is also consistent with recent neutron scattering measurements that find an ordered moment of 0.15μ _B along [001] and $\mathbf{Q_{n}}=\pi(\frac{1+\delta}{a},\frac{1+\delta}{a},\frac{1}{c})$ with incommensuration δ=0.12 for field $\mathbf{H}\parallel[1\bar{1}0]$ . Using these parameters, we find that a hyperfine field with dipolar contribution is consistent with findings from both experiments. We speculate that the B phase of CeCoIn₅ represents an intrinsic phase of modulated superconductivity and antiferromagnetism that can only emerge in a highly clean system.     

Internal oxidation of Fe-Si alloys in γ-phase region

Internal oxidation measurements of Fe-0.070, 0.219, 0.483, and 0.920 wt % Si alloys were made in the γ-phase region in order to discuss kinetics of internal oxidation, to evaluate the diffusion coefficient of oxygen in the internal oxidation layer, and to determine the diffusion coefficient of oxygen in γ-iron. Internal oxidation of these alloys was conducted at temperatures between 1223 and 1323 K using a powder mixture of iron and Fe₂O₃. The internal oxidation front in Fe-Si alloys with between 0.070 and 0.483 wt % Si advances in parallel to the specimen surface. The internal oxidation in these alloys obeys a parabolic rate law, which indicates that the internal oxidation is controlled by an oxygen diffusion process in the alloy. The diffusion coefficient of oxygen, D _O ^IO , in the internal oxidation layer where SiO₂ particles disperse was determined by using the thermodynamic data for the solution of oxygen in γ-iron. D _O ^IO increases with the increase of the volume fraction of the oxide, f ^IO, in the oxidation layer at a given temperature. The diffusion coefficient of oxygen, D _O, in γ-iron was evaluated by extrapolating D _O ^IO to f ^IO=0. D _O may be given by the following equation: $$D_O = \left( {6.42\begin{array}{*{20}c} { + 4.37} \\ { - 2.60} \\ \end{array} } \right) \times 10^{ - 5} exp \left[ { - \frac{{159 \pm 5(kj mol^{ - 1} )}}{{RT}}} \right]m^2 \sec ^{ - 1} $$ .     

The Influence of Corundum Content and Sintering Temperature on the Mechanical Properties of CaO–ZrO<Subscript>2</Subscript>–Al<Subscript>2</Subscript>O<Subscript>3</Subscript> Ceramic Composites

We have studied the mechanical properties (Vickers microhardness H_V and fracture toughness K_C) of nanostructured CaO–ZrO₂–Al₂O₃ ceramic composites as dependent on the content of corundum (0 ≤ \(C_{Al_{2}O_{3}}\) ≤ 25%) and the temperature of sintering (1250°C ≤ T₁ ≤ 1500°C). Optimum value of the corundum content (\(C_{Al_{2}O_{3}}\) = 5%) and optimum regime (T₁ = 1300°C, 5 min; T₂ = 1200°C, 4 h) of two-stage sintering are established, which favor attaining the best mechanical characteristics of ceramic composites (H_V = 12.25 GPa, K_C = 8.47 MPa m^1/2).     

Rational formulas for traces in zero-dimensional algebras

We present a rational expression for the trace of the multiplication map Times _r : A → A in a finite-dimensional algebra ${A := \mathbb {K}[x_1,\ldots,x_n] /\mathcal {I}}$ in terms of the generalized Chow form of ${\mathcal{I}}$ . Here, ${\mathcal{I} \subset \mathbb {K}[x_1,\ldots,x_n]}$ is a zero-dimensional ideal, ${\mathbb {K}}$ is a field of characteristic zero, and r(x ₁,..., x _n ) a rational function whose denominator is not a zero divisor in A. If ${\mathcal {I}}$ is a complete intersection in the torus, we get numerator and denominator formulas for traces in terms of sparse resultants.     

Dislocation structures in a { \bar{1} 104}/��11 \bar{2} 0�� low-angle tilt grain boundary of alumina (��-Al2O3)

An alumina (??-Al₂O₃) bicrystal with a ( $ \bar{1} $ 104)/[11 $ \bar{2} $ 0] 2^o low-angle tilt grain boundary was fabricated by diffusion bonding at 1500 °C in air, and the grain boundary was observed by transmission electron microscopy (TEM). High-resolution TEM observations revealed that the grain boundary consists of at least two kinds of dislocations. One is a perfect dislocation which has a Burgers vector of 1/3[ $ \bar{1} $ 2 $ \bar{1} $ 0]. The other is dissociated into two partial dislocations with a stacking fault on the (0001) plane, and each partial dislocation has a 1/6[ $ \bar{1} $ 101] edge component. It is suggested from structural considerations that the dissociated-dislocation pair originates from a b = 1/3[02 $ \bar{2} $ 1] perfect dislocation (i.e., 1/3[02 $ \bar{2} $ 1] ?? 1/6[02 $ \bar{2} $ 1] + 1/6[02 $ \bar{2} $ 1]). This dissociation produces a stacking fault in the anion sublattice. The stacking fault energy is estimated to be roughly 1.3 Jm^?2 based on the elastic theory. The authors discuss the dislocation structures and the stacking fault formed on the (0001) plane in detail.     

High temperature creep of polyvinyl chloride

The creep behaviour of polyvinyl chloride (PVC) has been studied in the temperature range 280 to 340° F under constant stress varying from 3.4 to 22.7 p.s.i. It is shown that the steady-state creep rate is an exponential function of stress as suggested by Norton but the exponent decreases with temperature. The activation energy for creep is determined using an activated-state rate process and it is found to be a decreasing function of stress with a higher value at temperatures 320° F and above. It is shown that the time dependent strain can be represented by $$\gamma = \gamma _0 + \dot \gamma _s t + \gamma _T \left[ {1 - \exp \left( { - K\dot \gamma _s t} \right)} \right]$$ where γ ₀ is the instantaneous strain on stressing, \(\dot \gamma _s\) the secondary creep rate, γ _T transient strain, and K is a constant. Scanning electron micrograph studies of the fracture surface and the change in activation energy apparently support the probability of two different deformation mechanisms i.e., domain flow and chain segmental or molecular flow at temperatures below and above 320° F, respectively.     

Insights into the structural,electronic, and magnetic properties of Fe2−x Ti x O3/Fe2O3 thin films with x = 0.44 grown on Al2O3 (0001)

The interface between hematite (α-Fe ₂ ^III O₃) and ilmenite (Fe^IITiO₃), a weak ferrimagnet and an antiferromagnet, respectively, has been suggested to be strongly ferrimagnetic due to the formation of a mixed valence layer of Fe²⁺/Fe³⁺ (1:1 ratio) caused by compensation of charge mismatch at the chemically abrupt boundary. Here, we report for the first time direct experimental evidence for a chemically distinct layer emerging at heterointerfaces in the hematite—Ti-doped-hematite system. Using molecular beam epitaxy, we have grown thin films (~25 nm thickness) of α-Fe₂O₃ on α-Al₂O₃ (0001) substrates, which were capped with a ~25 nm thick Fe_2?x Ti _x O₃ layer (x = 0.44). An additional 3 nm cap of α-Fe₂O₃ was deposited on top. The films were structurally characterized in situ with surface X-ray diffraction, which showed a partial low index orientation relationship between film and substrate in terms of the [0001] axis and revealed two predominant domains with \( (0001) _{{{\text{Fe}}_{2} {\text{O}}_{3} }} \;||\;(0001) _{{{\text{Al}}_{2} {\text{O}}_{3} }}, \) one with \( [10\bar{1}0]_{{{\text{Fe}}_{2} {\text{O}}_{3} }} \;||\;[10\bar{1}0]_{{{\text{Al}}_{2} {\text{O}}_{3} }}, \) and a twin domain with \( [01\bar{1}0]_{{{\text{Fe}}_{2} {\text{O}}_{3} }} \;||\;\;[10\bar{1}0]_{{{\text{Al}}_{2} {\text{O}}_{3} }}. \) Electron energy loss spectroscopy profiles across the Fe_2?x Ti _x O₃/Fe₂O₃ interface show that Fe²⁺/Fe³⁺ ratios peak right at the interface. This strongly suggests the formation of a chemically distinct interface layer, which might also be magnetically distinct as indicated by the observed magnetic enhancement in the Fe_2?x Ti _x O₃/α-Fe₂O₃/Al₂O₃ system compared to the pure α-Fe₂O₃/Al₂O₃ system.     

Synthesis,Crystal Structure,Vibrational and Magnetic Properties of a New Organic–inorganic Hybrid Material: 2-Amonium-methyl-1-Ethylpyrrolidinium Tetrachlorocuprate (II)

Synthesis, crystal structure, vibrational study and magnetic properties of the compound (C₇H₁₈N₂) CuCl₄ are reported. The latter crystallizes in the monoclinic system (space group P2 ₁, Z = 4) with the following unit cell dimensions: a = 7.569(5) Å b = 14.174(5) Å, c = 13.193(2) Å and β = 105.53(3)^°. Besides, its structure was solved using 5754 independent reflections down to R = 0.0475. The atomic arrangement can be described by alternating organic and inorganic layers stacked in the [\(\bar {1}\)01] direction, made up of tetrahedral of tetrachlorocuprate CuCl\(_{4}^{2-}\) sandwiched between two organic layers. In crystal structure, the inorganic layer, built up by independent monomeric [CuCl₄]^2?, is connected to the organic ones through hydrogen bonding in order to build a three-dimensional network. The magnetic behavior of (C₇H₁₈N₂) CuCl₄ samples was investigated as a function of temperature and applied field. At hightemperature paramagnetic behavior, and at low temperature, evidence for weak ferromagnetism, reinforced by a hysteresis loop at 2 K is observed. The magnetic behavior of (C₇H₁₈N₂) CuCl₄ is attributed to Cu (II) due to the presence of an active Jahn–Teller effect in the d ⁹ electronic system, which give rise to short-range weak ferromagnetism.     

Effects of Bi doping on dielectric and ferroelectric properties of PLBZT ferroelectric thin films synthesized by sol–gel processing

[Pb _0·95(La_1???y Bi _y ) _0·05][Zr_0·53Ti_0·47]O₃ (PLBZT) ferroelectric thin films have been synthesized on indium tin oxide (ITO)-coated glass by sol–gel processing. PLBZT thin films were annealed at a relatively low temperature of 550 °C in oxygen ambient. Effects of Bi doping on structure, dielectric and ferroelectric properties of PLBZT were investigated. Bi doping is useful in crystallization of PLBZT films and promoting grain growth. When the Bi-doping content ${\mathit{y}}$ is not more than 0·4, an obvious improvement in dielectric properties and leakage current of PLBZT was confirmed. However, when the Bi-doping content is more than 0·6, the pyrochlore phase appears and the remnant polarization P _r of PLBZT thin films is smaller than that of $\left({Pb}_{{1-x}} {\bf La}_{x}\right)\!\!\left({Zr}_{{1-y}} {Ti}_{y}\right){O}_{3}$ (PLZT) thin films without Bi doping. PLBZT thin films with excessive Bi-doping content are easier to fatigue than PLZT thin films.     

Generalized fracture mechanics of ductile steels

The generalized fracture mechanics approach is applied to two ductile steels, namely mild steel and 18/8 stainless steel in plane stress. The theory defines a fracture parameter \(\mathcal{T}\) , which is a truly plastic analogue of theJ contour integral and, for an edge crack specimen, is given by $$\mathcal{T} = k_1 ( \in _0 )cW_{0_c } $$ wherek ₁ is an explicit function,c is the crack length andε ₀, W_0c are respectively the strain and input energy density at fracture, remote from the crack. The functionk ₁(ε _o) is derived experimentally and the constancy of \(\mathcal{T}\) with respect to crack length and applied load is demonstrated. The variation of \(\mathcal{T}\) with crack extension during slow growth is investigated, as is the rate dependence of \(\mathcal{T}\) in mild steel.     

Quasi-static Thermal Deflection of a Thin Clamped Hollow Circular Disk Due to Heat Generation

This paper deals with the determination of the thermal deflection in a thin clamped hollow circular disk defined as a ≤ r ≤ b; 0 ≤ z ≤ h under an unsteady temperature field due to internal heat generation within it. A thin hollow circular disk is considered having an arbitrary initial temperature and subjected to heat flux at the outer circular boundary (r = b) where an inner circular boundary (r = a) is at zero heat flux. Also, the upper surface (z = h) and the lower surface (z = 0) of the disk are at zero temperature. The governing heat conduction equation has been solved by using an integral transform technique. The inner and outer edges of the disk are clamped ${\frac{\partial \omega }{\partial r}=0}$ at r = a, r = b. The results are obtained in a series form in terms of Bessel’s functions and are illustrated graphically.     

A new correlation for the viscosity of gaseous fluorocarbon refrigerants

A new generalized correlation is presented for the low-pressure gaseous viscosity of fluorocarbon refrigerants. The following empirical equation is obtained based on the most reliable experimental data for 16 fluorocarbons: $$\eta \xi = \left( {0.5124T_r - 0.0517} \right)^{0.82} Z_c ^{ - 0.81}$$ where η is the viscosity in μPa·s and ξ is the viscosity parameter defined using the critical temperature T _c in K, the critical pressure P _c in MPa, and the molar mass M in g·mol^?1 as follows: $$\xi = T_c ^{1/6} M^{ - 1/2} P_c ^{ - 2/3}$$ The applicable ranges are 0.6<T _r<1.8 and 0.253<Z _c<0.282. The availability of the correlating equation for both pure fluorocarbons and their mixtures has been investigated based on the experimental data of these authors and those in the literature. It is found that the present correlation is useful for the prediction of the viscosity of pure fluorocarbons and their binary mixtures at atmospheric pressure with mean deviations less than 1.6%.     

Electrical resistivity of molybdenum in the temperature range 1500 to 2650 K

Measurement of the electrical resistivity of molybdenum in the temperature range 1500 to 2650 K by a subsecond-duration pulse-heating technique is described. The specimens were of the National Bureau of Standards Molybdenum Standard Reference Material 781 for Enthalpy and Heat Capacity. The electrical resistivity of molybdenum in the temperature range 1500 to 2650 K is expressed by the following function (standard deviation = 0.2%): 1 $$\rho = - 6.7083 + 2.8949{\text{x10}}^{{\text{ - 2}}} T + 5.2985{\text{x10}}^{{\text{ - 7}}} T^2 $$ where T is in K and ρ is in ΜΩ · cm. The estimated inaccuracy in the electrical resistivity data does not exceed 1%.     

Features in the formation of Ge/Si multilayer nanostructures under ion-beam-assisted crystallization

A method of combined ion-beam crystallization of the Ge/Si multilayer nanostructures is proposed. Using atomic-force microscopy and electron microscopy, we observed the formation of an array of germanium quantum dots with lateral dimensions 〈a〉 = 12–15 nm at the following conditions: silicon-substrate temperature T = 330–350°C, ion-beam energies E _Ge + = 30–40 eV, $E_{Ar^ + }^0 = 230 - 240$ eV (primary pulsed defect formation mode), $E_{Ar^ + } = 130 - 140$ eV (permanent diffusion stimulation mode), and ion-beam fluences $f_{Ge^ + } = 1.5 \times 10^{14} cm^{ - 2} s^{ - 1} $ , $f_{Ar^ + } = 5 \times 10^{12} cm^{ - 2} s^{ - 1} $ . The Raman spectroscopy data indicate the experimental possibility of low-temperature ion-stimulated growth of the spacer layers of silicon (T = 420–450°C, $E_{Ar^ + } = 80 - 90$ eV, $E_{Si^ + } = 30 - 40$ eV, $f_{Si^ + } = 3.5 \times 10^{14} cm^{ - 2} s^{ - 1} $ ) and the formation of multilayer structures with Ge _x Si_{1 ? x} quantum dots (x > 0.85).