On the use of tensor paths to estimate the nonproportionality factor of multiaxial stress or strain histories under free-surface conditions

Nonproportional (NP) strain hardening is caused by multiaxial load histories that induce variable principal stress/strain directions, activating cross-slip bands in several directions, due to the associated rotation of the maximum shear planes. This effect increases the strain-hardening behavior observed under proportional loads, those with fixed principal directions, and must be considered in multiaxial fatigue calculations, especially for materials with low stacking fault energy, such as austenitic stainless steels. NP hardening depends on the material and on the shape of the multiaxial load history path in a stress or strain diagram as well. It can be evaluated by a nonproportionality factor \({F_{\rm NP}}\) that varies from zero, for a proportional load history, to one, for a \({90^{\circ}}\) out-of-phase tension–torsion loading with the same normal and effective shear amplitudes. Originally, \({F_{\rm NP}}\) was estimated from the aspect ratio of a convex enclosure that contains the load history path, such as an ellipse or a prismatic enclosure, but such convex enclosure estimates can lead to poor predictions of \({F_{\rm NP}}\). Another approach consists on evaluating the shape of the six-dimensional (6D) path described by the six normal and shear components of the stress tensor, where the stress path contour is interpreted as a homogeneous wire with unit mass. The moment of inertia (MOI) tensor of this hypothetical wire is then calculated and used to estimate \({F_{\rm NP}}\). The use of 6D stress paths to estimate \({F_{\rm NP}}\) is questionable, since 6D formulations implicitly include the effect of the hydrostatic stress, while NP hardening is caused by the deviatoric plastic straining, not by stresses alone or by their hydrostatic component. In this work, the NP factor \({F_{\rm NP}}\) of a multiaxial load history is estimated from the eigenvalues of the MOI tensor of the plastic strain path, which are associated with the accumulated plastic straining in the principal directions defined by the associated eigenvectors. The presented formulation assumes free-surface conditions, but allows a surface pressure, covering the conditions of most critical points, which indeed are located on free surfaces. Experimental results for 14 different tension–torsion multiaxial histories prove the effectiveness of the proposed method.     

A coupled quantum/continuum mechanics study of graphene fracture

A new technique is presented to study fracture in nanomaterials by coupling quantum mechanics (QM) and continuum mechanics (CM). A key new feature of this method is that broken bonds are identified by a sharp decrease in electron density at the bond midpoint in the QM model. As fracture occurs, the crack tip position and crack path are updated from the broken bonds in the QM model. At each step in the simulation, the QM model is centered on the crack tip to adaptively follow the path. This adaptivity makes it possible to trace paths with complicated geometries. The method is applied to study the propagation of cracks in graphene which are initially perpendicular to zigzag and armchair edges. The simulations demonstrate that the growth of zigzag cracks is self-similar whereas armchair cracks advance in an irregular manner. The critical stress intensity factors for graphene were found to be 4.21 MPa\({\sqrt {\rm m}}\) for zigzag cracks and 3.71 MPa\({\sqrt{\rm m}}\) for armchair cracks, which is about 10% of that for steel.     

Bootstrap in semi-functional partial linear regression under dependence

This paper deals with the semi-functional partial linear regression model \(Y={{\varvec{X}}}^\mathrm{T}{\varvec{\beta }}+m({\varvec{\chi }})+\varepsilon \) under \(\alpha \)-mixing conditions. \({\varvec{\beta }} \in \mathbb {R}^{p}\) and \(m(\cdot )\) denote an unknown vector and an unknown smooth real-valued operator, respectively. The covariates \({{\varvec{X}}}\) and \({\varvec{\chi }}\) are valued in \(\mathbb {R}^{p}\) and some infinite-dimensional space, respectively, and the random error \(\varepsilon \) verifies \(\mathbb {E}(\varepsilon |{{\varvec{X}}},{\varvec{\chi }})=0\). Naïve and wild bootstrap procedures are proposed to approximate the distribution of kernel-based estimators of \({\varvec{\beta }}\) and \(m(\chi )\), and their asymptotic validities are obtained. A simulation study shows the behavior (on finite sample sizes) of the proposed bootstrap methodology when applied to construct confidence intervals, while an application to real data concerning electricity market illustrates its usefulness in practice.     

Static mode fatigue crack propagation and generalized stress intensity correlation for fatigue–brittle polymers

Stable fatigue crack propagation is predominantly described by the Paris power law correlation of the crack growth rate with the amplitude cyclic stress intensity. The Paris relationship works well for most ductile materials but does not capture the response for fatigue–brittle materials lacking a cyclic damage mechanism, including ceramics and many polymers. Instead, crack growth rate of fatigue–brittle materials correlates to the peak cyclic stress intensity factor, \(\hbox {K}_{\mathrm{max}}\). This work shows that \(\hbox {K}_{\mathrm{max}}\) correlation of fatigue crack growth is derived directly from static mode crack tip behavior with constant correlation coefficients, and that \(\Delta \hbox {K}\) correlations are not generally applicable for static mode crack propagation in fatigue–brittle polymers. This derivation predicts load ratio, frequency, and waveform effects, which are included in a general static mode fatigue crack propagation law. Fatigue crack propagation data of a known fatigue–brittle polymer are presented to demonstrate static mode crack propagation behavior correlation with \(\hbox {K}_{\mathrm{max}}\) with constant parameters.     

A heuristic reference recursive recipe for adaptively tuning the Kalman filter statistics part-1: formulation and simulation studies

Since the innovation of the ubiquitous Kalman filter more than five decades back it is well known that to obtain the best possible estimates the tuning of its statistics \({\mathbf{X}}_{\mathbf{0}}\), \({\mathbf{P}}_{\mathbf{0}}\), \(\Theta \), R and Q namely initial state and covariance, unknown parameters, and the measurement and state noise covariances is very crucial. The manual and other approaches have not matured to a routine approach applicable for any general problem. The present reference recursive recipe (RRR) utilizes the prior, posterior, and smoothed state estimates as well as their covariances to balance the state and measurement equations and thus form generalized cost functions. The filter covariance at the end of each pass is heuristically scaled up by the number of data points and further trimmed to provide the \({\mathbf{P}}_{\mathbf{0}}\) for subsequent passes. The importance of \({\mathbf{P}}_{\mathbf{0}}\) as the probability matching prior between the frequentist approach via optimization and the Bayesian approach of the Kalman filter is stressed. A simultaneous and proper choice for Q and R based on the filter sample statistics and other covariances leads to a stable filter operation after a few iterations. A typical simulation study of a spring, mass and damper system with a weak nonlinear spring constant by RRR shows it to be better than earlier techniques. Part-2 of the paper further consolidates the present approach based on an analysis of real flight test data.     

The unsteady hydrodynamic force during the collision of two spheres in a viscous fluid

The time-dependent Stokes equations were solved in the vicinity of two spheres colliding in a viscous fluid with viscosity ν to determine the rate of change of the hydrodynamic forces during large accelerations associated with Hertzian mechanical contact of small duration \({\tau_{\rm c}}\). It was assumed that the gap clearance remains finite during contact and is approximately equal to the height σ of surface micro-asperities. The initial condition corresponds to the steady-state axisymmetric solution of Cooley and O’Neill (Mathematika 16:37–49, 1969), and the initial value problem for the time-dependent Stokes streamfunction was solved using Laplace transform methods. Assuming that σ is small compared to the sphere radius a, we used singular perturbation expansions and tangent-sphere coordinates to obtain an asymptotic solution for the viscous flow in the gap and around the moving sphere. The solution provides the dependence of the resistance, added mass and history forces on σ, the sphere velocity and acceleration, and the ratio of the sphere diameters. We found that the relative importance of viscous and mechanical forces during contact depends on a new Stokes number \({St_{\rm c}=\sigma^2/\nu \tau_{\rm c}}\). Integration of Newton’s equation for the motion of the sphere during mechanical contact showed that there is a critical \({St_{\rm c}=O(\sigma/a)}\) for which there is no rebound at the end of contact.     

Microstructure and Magnetic Properties of Sn<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>Ni<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>O<Subscript>2</Subscript> Thin Films Prepared by Flash Evaporation Technique

An effort was made to develop semiconductor oxide-based room temperature dilute magnetic semiconductor (DMS) thin films based on wide band gap and transparent host lattice with transition metal substitution. The Sn\(_{\mathrm {1}-x}\)Ni\(_{x}\textit {O}_{\mathrm {2}}\) (\(x\,= \mathrm {0.00, 0.03, 0.05, 0.07, 0.10, and \,0.15}\)) thin film samples were prepared on glass substrates by flash evaporation technique. All the samples were shown single phase crystalline rutile structure of host SnO\(_{\mathrm {2}}\) with dominant (110) orientation. The Ni substitution promotes reduction of average crystallite size in SnO\(_{\mathrm {2}}\) as evidenced from the reduction of crystallite size from 40 (SnO\(_{\mathrm {2}}\)) to 20 nm (Sn\(_{\mathrm {0.85}}\)Ni\(_{\mathrm {0.15}}\textit {O}_{\mathrm {2}}\)). In the energy dispersive spectra as well as X-ray photoelectron spectra of all the samples show, the chemical compositions are close to stoichiometric with noticeable oxygen deficiency. The crystalline films were formed by coalescence of oval-shaped polycrystalline particles of 100 nm size as evidenced from the electron micrographs. The energy band gap of DMS films decreases from 4 (SnO\(_{\mathrm {2}}\)) to 3.8 eV (x \(=\) 0.05) with increase of Ni content. The magnetic hysteresis loops of all the samples at room temperature show soft ferromagnetic nature except for SnO\(_{\mathrm {2}}\) film. The SnO\(_{\mathrm {2}}\) films show diamagnetic nature and it converts into ferromagnetic upon substitution of 3 % Sn\(^{\mathrm {4+}}\) by Ni\(^{\mathrm {2+}}\). The robust intrinsic ferromagnetism (saturation magnetization, 21 emu/cm\(^{\mathrm {3}}\)). Further increase of Ni content weakens ferromagnetic strength due to Ni-O antiferromagnetic interactions among the nearest neighbour Ni ions via O\(^{\mathrm {2-}}\) ions. The observed magnetic properties were best described by bound magnetic polarons model.     

Rejoinder on: Some recent work on multivariate Gaussian Markov random fields

I thank the discussants, Miguel A. Martinez-Beneito, Fedel Greco, Carlo Trivisano, Stephan R Sain, and Reinhard Furrer, for their insightful and stimulating commentary. The rejoinder is organized in five sections: (1) the M-based models, (2) posterior sensitivity to prior choices for \({\varvec{C}}\) and \({\varvec{\varSigma }}\), (3) stationary and non-stationary (M)GMRFs, (4) various approaches to model formulation and related applications, and (5) statistical computation.     

Structural,magnetic and photocatalytic characterization of Bi<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>La<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>FeO<Subscript>3</Subscript> nanoparticles synthesized by thermal decomposition method

Single-phase La-substituted bismuth ferrite (Bi\(_{\boldsymbol {1-x}}\)La\(_{\boldsymbol {x}}\)FeO\(_{\mathbf {3}}\)) nanoparticles have been synthesized by thermal decomposition of a glyoxylate precursor. The crystal structure transition of BiFeO\(_{\mathbf {3}}\) from the rhombohedral (R3c) to the cubic \(\boldsymbol {Pm}\bar {\mathbf {3}}\boldsymbol {m}\) structure by La addition was confirmed by X-ray diffraction and infrared spectrometry methods. Furthermore, the Bi\(_{\boldsymbol {1-x}}\)La\(_{\boldsymbol {x}}\)FeO\(_{\mathbf {3}}\) nanoparticles showed a weak ferrimagnetism behaviour, while the magnetization increased from 0.18 to 0.48 emu g\(^{\mathbf {-1}}\) with La substitution. The Bi\(_{\boldsymbol {1-x}}\)La\(_{\boldsymbol {x}}\)FeO\(_{\mathbf {3}}\) nanoparticles exhibited strong absorption in the visible region with the optical band gap calculated from Tauc’s plot in the range of 2.19–2.15 eV. Furthermore, the effects of La substitution on the photodegradation of the methylene blue (MB) under visible light were also studied. The photodegradation of MB dye was enhanced from 64 to \(\sim \)99% with increasing La substitution from \(\boldsymbol {x =}\) 0 to 0.1 and then decreased to 8% for \(\boldsymbol {x =}\) 0.15.     

Structural,microstructural and optical properties of $$\hbox {Cu}_{2}\hbox {ZnSnS}_{4}$$ thin films prepared by thermal evaporation: effect of substrate temperature and annealing

Thin films of \(\hbox {Cu}_{2}\hbox {ZnSnS}_{4}\) (CZTS), a promising solar cell absorber, were grown by thermal evaporation of ZnS, Sn and Cu precursors and subsequent annealing in sulphur atmosphere. Two aspects are chosen for investigation: (i) the effect of substrate temperature (\(T_{\mathrm{S}})\) used for the deposition of precursors and (ii) (\(\hbox {N}_{2}{+}\hbox {S}_{2})\) pressure during annealing, to study their impact on the growth of CZTS films. X-ray diffraction analysis of these films revealed the structure to be kesterite with (112) preferred orientation. Crystallite size is found to slightly increase with increase in \(T_{\mathrm{S}}\) as well as pressure during annealing. From optical absorption studies, the direct optical band gap of CZTS films is found to be \({\sim }\)1.45 eV. Room temperature electrical resistivity of the films obtained on annealing the stacks at 10 and 100 mbar pressures is found to be in the ranges 25–55 and 5–25 \(\Omega \) cm, respectively, depending on \(T_{\mathrm{S}}\). Films prepared by annealing the stack deposited at 300\({^{\circ }}\)C under 100 mbar pressure for 90 min are slightly Cu-poor and Zn-rich with compact grain morphology.     

Stability Evaluation and Calibration of Type C Thermocouples at the Pt–C Eutectic Fixed Point

Tungsten–rhenium thermocouples (type C thermocouples) are used to measure temperatures higher than 1500 \({^{\circ }}\)C under protective, inert, or vacuum conditions in a wide range of industries, such as metallurgy, power generation, and aerospace. Generally, the measurement uncertainty of a new tungsten–rhenium thermocouple is about 1 % (20 \({^{\circ }}\)C at 2000 \({^{\circ }}\)C), and a significant drift is always observed above 1200 \({^{\circ }}\)C. Recently, the National Institute of Metrology, China, has spent great efforts to calibrate tungsten–rhenium thermocouples with high-temperature fixed points of up to 2000 \({^{\circ }}\)C. In the present work, three tungsten–rhenium thermocouples made by two manufacturers were calibrated at the Pt–C eutectic fixed point (1738 \({^{\circ }}\)C) and their stability was investigated. A linear fitting and extrapolation method was developed to determine the melting and freezing temperatures of the Pt–C eutectic fixed point for avoiding the effect of thermal resistance caused by the sheath and protection tube. The results show that the repeatability of the calibration is better than 0.9 \({^{\circ }}\)C from the melting curve of the Pt–C fixed point and better than 1.2 \({^{\circ }}\)C from the freezing curve of the Pt–C fixed point, and a good agreement was obtained for the calibration with the melting and freezing temperature plateau through the linear fitting and extrapolation method. The calibration uncertainty of the thermocouples at the Pt–C eutectic fixed point was 3.1 \({^{\circ }}\)C (k \(=\) 2).     

Measurement Uncertainty Budget of the PMV Thermal Comfort Equation

Fanger’s predicted mean vote (PMV) equation is the result of the combined quantitative effects of the air temperature, mean radiant temperature, air velocity, humidity activity level and clothing thermal resistance. PMV is a mathematical model of thermal comfort which was developed by Fanger. The uncertainty budget of the PMV equation was developed according to GUM in this study. An example is given for the uncertainty model of PMV in the exemplification section of the study. Sensitivity coefficients were derived from the PMV equation. Uncertainty budgets can be seen in the tables. A mathematical model of the sensitivity coefficients of \(T_{\mathrm{a}}\), \(h_{\mathrm{c}}\), \(T_{\mathrm{mrt}}\), \(T_{\mathrm{cl}}\), and \(P_{\mathrm{a}}\) is given in this study. And the uncertainty budgets for \(h_{\mathrm{c}}\), \(T_{\mathrm{cl}}\), and \(P_{\mathrm{a}}\) are given in this study.     

The parameters governing the coefficient of dispersion of cubes in rotating cylinders

Axial dispersion of cubic particles in horizontal, rotating cylinders was investigated using discrete element modelling simulations. We found that, similar to the behavior of spheres, the axial dispersion coefficient of cubes depends on (1) the rotational speed of the cylinder \({\omega }\), (2) the acceleration due to gravity g and (3) the particle size d, satisfying the relationship \({D}_\mathrm {ax}\propto {\omega }^{1-2{\lambda }}{g}^{{\lambda }}{d}^{2-{\lambda }}\) with \({\lambda }\approx 0.15\) (\({\lambda }\approx 0.1\) for beds of spheres) (Third et al. in Powder Technol 203:510–517, 2010). This observation suggested that, although particle shape influences significantly the rate of axial dispersion (cubes disperse almost twice as fast as spheres of equal volume), the parameters controlling the coefficient of dispersion are independent of particle shape.     

Fast crack propagation correlated with crack tip stress in 2D hexagonal atomic lattices

We construct strip finite element models of 2D hexagonal atomic lattices with initial cracks to simulate dynamic crack propagation under mode \(\mathrm{I}\) displacement loading, in which the atomic bonds of 2D lattices are represented by Timoshenko beam elements. Series of 2D lattices, including graphene, hexagonal boron nitride and virtual graphene-like materials, are modeled by varying the nonlinear constitutive relations of beam elements. Branching and oscillation phenomena inevitably occur in fast-propagating crack when the crack speed reaches a critical value, which is closely related to the stress field near the crack tip. Our results reveal that the size of nominal plastic zone \(r_{p}\) around crack front varies with different 2D lattices at both crack initiation and branching. The critical branching speeds \(V_{\mathrm {C}}\) change with material properties, and is correlated with the local stresses around the crack front. Further, we find that \(V_{\mathrm {C}}\) increases with the increment of conditional yield stresses of 2D lattices, but \(V_{\mathrm {C}}\) decreases with the increment of \(r_{p}\) monotonously and linearly at crack branching. Therefore, nonlinear zone, formed by redistributed singular stresses at crack tip, dominates crack kinking or branching during fast crack propagation.     

Network structure dependence on unconstrained isothermal-recovery processes for shape-memory thiol-epoxy “click” systems

The shape-memory response (SMR) of “click” thiol-epoxy polymers produced using latent catalysts, with different network structure and thermo-mechanical properties, was tested on unconstrained shape-recovery processes under isothermal conditions. Experiments at several programming temperatures (\(T_{\mathrm{prog}}\)) and isothermal-recovery temperatures (\(T_{\mathrm{iso}}\)) were carried out, and the shape-memory stability was analyzed through various consecutive shape-memory cycles. The temperature profile during the isothermal-recovery experiments was monitored, and it showed that the shape-recovery process takes place while the sample is becoming thermally stable and before stable isothermal temperature conditions are eventually reached. The shape-recovery process takes place in two different stages regardless of \(T_{\mathrm{iso}}\): a slow initial stage until the process is triggered at a temperature strongly related with the beginning of network relaxation, followed by the typical exponential decay of the relaxation processes until completion at a temperature below or very close to \(T_{\mathrm{g}}\). The shape-recovery process is slower in materials with more densely crosslinked and hindered network structures. The shape-recovery time (\(t_{\mathrm{sr}}\)) is significantly reduced when the isothermal-recovery temperature \(T_{\mathrm{iso}}\) increases from below to above \(T_{\mathrm{g}}\) because the network relaxation dynamics accelerates. However, the temperature range from the beginning to the end of the recovery process is hardly affected by \(T_{\mathrm{iso}}\); at higher \(T_{\mathrm{iso}}\) it is only slightly shifted to higher temperatures. These results suggest that the shape-recovery process can be controlled by changing the network structure and working at \(T_{\mathrm{iso}} < T_{\mathrm{g}}\) to maximize the effect of the structure and/or by increasing \(T_{\mathrm{iso}}\) to minimize the effect but increasing the shape-recovery rate.     

A comparative study on dielectric behaviours of Au/(Zn-doped PVA)/<Emphasis Type="Italic">n</Emphasis>-4H-SiC (MPS) structures with different interlayer thicknesses using impedance spectroscopy methods

Three different thicknesses (50, 150 and 500 nm) Zn-doped polyvinyl alcohol (PVA) was deposited on n-4H-SiC wafer as interlayer by electrospinning method and so, Au/(Zn-doped PVA)/n-4H-SiC metal–polymer–semiconductor structures were fabricated. The thickness effect of Zn-doped PVA on the dielectric constant (\(\varepsilon ^{\prime }\)), dielectric loss (\(\varepsilon ^{{\prime }{\prime }}\)), loss-tangent (tan \(\delta \)), real and imaginary parts of electric modulus (\(M^{\prime }\) and \(M^{{\prime }{\prime }})\) and ac electrical conductivity \((\sigma _{\mathrm{ac}})\) of them were analysed and compared using experimental capacitance (C) and conductance (\(G/\omega \)) data in the frequency range of 1–500 kHz at room temperature. According to these results, the values of \(\varepsilon ^{\prime }\) and \(\varepsilon ^{{\prime }{\prime }}\) decrease with increasing frequency almost exponentially, \(\sigma _{\mathrm{ac}}\) increases especially, at high frequencies. The \(M^{\prime }\) and \(M^{{\prime }{\prime }}\) values were obtained from the \(\varepsilon ^{\prime }\) and \(\varepsilon ^{{\prime }{\prime }}\) data and the \(M^{\prime }\) and \(M^{{\prime }{\prime }}\) vs. f plots were drawn for these structures. While the values of \(\varepsilon ^{\prime }\), \(\varepsilon ^{{\prime }{\prime }}\) and tan \(\delta \) increase with increasing interlayer thickness, the values of \(M^{\prime }\) and \(M^{{\prime }{\prime }}\) decrease with increasing interlayer thickness. The double logarithmic \(\sigma _{\mathrm{ac}}\) vs. f plots for each structure have two distinct linear regimes with different slopes, which correspond to low and high frequencies, respectively, and it is prominent that there exist two different conduction mechanisms. Obtained results were found as a strong function of frequency and interlayer thickness.     

Measurement of the Water Relaxation Time of $${\upvarepsilon }$$-Polylysine Aqueous Solutions

\({\upvarepsilon }\)-Polylysine is an effective food preservative. In this paper, the \({\upbeta }\)-relaxation time of \({\upvarepsilon }\)-polylysine aqueous solutions, which represents the rotational speed of a single water molecule, was measured by broadband dielectric spectroscopy at various temperatures and concentrations. The broadband dielectric spectrum of each sample containing water ranging from 35 wt% to 75 wt% at temperatures ranging from \(0\,^{\circ }\hbox {C}\) to \(25\,^{\circ }\hbox {C}\) was measured using a co-axial semirigid cable probe. The measured dielectric spectra of the samples were composed of several Debye relaxation peaks, including a shortest single molecular rotational relaxation time of water, the \({\upbeta }\)-relaxation time, longer than that of pure water. This result represents that \({\upvarepsilon }\)-polylysine suppresses the molecular kinetics of water. It is also found that the \({\upbeta }\)-relaxation time of an \({\upvarepsilon }\)-polylysine solution that contained more than 35 wt% water showed a typical Arrhenius plot in the temperature range from \(0\,^{\circ }\hbox {C}\) to \(25\,^{\circ }\hbox {C}\). The activation energy of each sample depends on the water content ratio of the sample. As indicated by its long \({\upbeta }\)-relaxation time, \({\upvarepsilon }\)-polylysine is expected to possess high abilities of suppressing freezing and ice coarsening.     

Canadian Field Soils IV: Modeling Thermal Conductivity at Dryness and Saturation

The thermal conductivity data of 40 Canadian soils at dryness \((\lambda _{\mathrm{dry}})\) and at full saturation \((\lambda _{\mathrm{sat}})\) were used to verify 13 predictive models, i.e., four mechanistic, four semi-empirical and five empirical equations. The performance of each model, for \(\lambda _{\mathrm{dry}}\) and \(\lambda _{\mathrm{sat}}\), was evaluated using a standard deviation (SD) formula. Among the mechanistic models applied to dry soils, the closest \(\lambda _{\mathrm{dry}}\) estimates were obtained by MaxRTCM \((\textit{SD} = \pm ~0.018\,\hbox { Wm}^{-1}\cdot \hbox {K}^{-1})\), followed by de Vries and a series-parallel model (\(\hbox {S-}{\vert }{\vert }\)). Among the semi-empirical equations (deVries-ave, Advanced Geometric Mean Model (A-GMM), Chaudhary and Bhandari (C–B) and Chen’s equation), the closest \(\lambda _{\mathrm{dry}}\) estimates were obtained by the C–B model \((\pm ~0.022\,\hbox { Wm}^{-1}\cdot \hbox {K}^{-1})\). Among the empirical equations, the top \(\lambda _{\mathrm{dry}}\) estimates were given by CDry-40 \((\pm ~0.021\,\hbox { Wm}^{-1}\cdot \hbox {K}^{-1}\) and \(\pm ~0.018\,\hbox { Wm}^{-1}\cdot \hbox {K}^{-1}\) for18-coarse and 22-fine soils, respectively). In addition, \(\lambda _{\mathrm{dry}}\) and \(\lambda _{\mathrm{sat}}\) models were applied to the \(\lambda _{\mathrm{sat}}\) database of 21 other soils. From all the models tested, only the maxRTCM and the CDry-40 models provided the closest \(\lambda _{\mathrm{dry}}\) estimates for the 40 Canadian soils as well as the 21 soils. The best \(\lambda _{\mathrm{sat}}\) estimates for the 40-Canadian soils and the 21 soils were given by the A-GMM and the \(\hbox {S-}{\vert }{\vert }\) model.     

Theoretical and experimental approaches to measuring mechanical properties of Zn<Subscript>1−x</Subscript>Co<Subscript>x</Subscript>O binary tetrahedral bulk semiconductors

We prepared a \({{\text{Zn}}_{1 - {\text{x}}}}{{\text{Co}}_{\text{x}}}{\text{O}}\) system as polycrystalline nanoparticles with various compositions \((x=0.01, 0.02, 0.03, 0.04, 0.05, {\text{and}} \; 0.10)\) using sol–gel techniques and use zinc acetate dihydrate and cobalt acetate tetrahydrate as precursors. Nanoparticles were pressed under a pressure of 4 tons for 5 min into 2 mm thick disk shaped compacts 10 mm in diameter, which were then annealed at 500 °C for 30 min under a 5B Ar atmoshpere. We carried out X-ray diffraction, scanning electron microscopy, and Vickers microhardness analyses of Co doped \({\text{Zno}}\)-based nano bulk materials in detail, focusing especially on theoretical and experimental mechanical analyses. We found that calculated values were higher than the Vickers microhardness experimental results. Doping ZnO with Co did not lead to significant changes in the a and c axes. The calculated hardness values are larger than those from the experiments. Acoording to the SEM and EDS images grain size decreases as Co doping increases and the amount of Zn decreases with Co doping, respectively.