Achieving 5.9% elastic strain in kilograms of metallic glasses: Nanoscopic strain engineering goes macro

The ideal elastic limit is the upper bound of the achievable strength and elastic strain of solids. However, the elastic strains that bulk materials can sustain are usually below 2%, due to the localization of inelastic deformations at the lattice scale. In this study, we achieved >5% elastic strain in bulk quantity of metallic glass, by exploiting the more uniform and smaller-magnitude atomic-scale lattice strains of martensitic transformation as a loading medium in a bulk metallic nanocomposite. The self-limiting nature of martensitic transformation helps to prevent lattice strain transfer that leads to the localization of deformation and damage. This lattice strain egalitarian strategy enables bulk metallic materials in kilogram-quantity to achieve near-ideal elastic limit. This concept is verified in a model in situ bulk amorphous (TiNiFe)-nanocrystalline (TiNi(Fe)) composite, in which the TiNiFe amorphous matrix exhibits a maximum tensile elastic strain of ∼5.9%, which approaches its theoretical elastic limit. As a result, the model bulk composite possesses a large recoverable strain of ∼7%, a maximum tensile strength of above 2 GPa, and a large elastic resilience of ∼79.4 MJ/m³. The recoverable strain and elastic resilience are unmatched by known high strength bulk metallic materials. This design concept opens new opportunities for the development of high-performance bulk materials and elastic strain engineering of the physiochemical properties of glasses.     

Non-propagating crack behaviour at giga-cycle fretting fatigue limit

Fretting fatigue fracture of industrial machines is sometimes experienced after a long period of operation. It has been a question whether the fatigue limit which means infinite life really exists in fretting fatigue or not. Fretting fatigue tests in ultra high cycle region up to 10⁹ cycles were performed. Test results showed that the S‐N curve had a knee point around 2 × 10⁷ cycles and a clear fatigue limit was observed in the giga‐cycle regime for partial slip conditions. An electropotential drop technique was applied to detect the crack growth behaviour under the contact pad. The real‐time measurement of crack depth during the fretting fatigue test at the fatigue limit showed that a crack initiated at an early stage and then ceased to grow after 2 × 10⁷ cycles and the crack became a non‐propagating crack. These results indicated that the fatigue limit exists in fretting fatigue and infinite endurance is achieved by the mechanism of forming a non‐propagating crack.     

Mapped infinite elements for exterior wave problems

Recently, a new type of infinite elements which uses r^?1 decay was proposed. They were applied to exterior wave problems and good results were obtained. In two-dimensional problems, however, it was necessary to move the origin of the r^?1 decay in order to model the outgoing wave more accurately, because it decays roughly as r^?1/2. In this paper, the mapped infinite elements with r^?1/2 decay and the necessary numerical integration procedure are presented. These elements do not require any artificial movement of the origin. Several example problems are solved. The results show that the infinite elements with r^?1/2 decay here give much more accurate values than the infinite elements with exponential decay and any damper elements.     

Determination of compositional fluctuation region in solid solution of lanthanum-modified lead zirconate titanate

A method was developed to determine a compositional fluctuation region in Pb_1–y La _y (Zr _x Ti_1–x )_1–(y/4)O₃ (PLZT) solid solution in the tetragonal region. The compositional fluctuation in PLZT extends two-dimensionally on the phase diagram. The method described in this paper utilized the fact that the compositional fluctuation region extends to the composition lines whose lattice spacing corresponds to the higher or lower fluctuation limit. The fluctuation limits of the lattice spacings were estimated from X-ray diffraction analysis. This method revealed that the compositional fluctuation in PLZT is difficult to be eliminated by using a conventional dry method (mixed oxide method). The shape of the region indicated that homogenization of Zr⁴⁺ and Ti⁴⁺ was more difficult as compared with that of Pb²⁺ and La³⁺.     

Small Polarons in Dense Lattice Systems

There is considerable evidence for the persistence of small polaron like entities in colossal magnetoresistance oxides, which are dense electronic systems with electron density n1 per site. This has brought up again the question of whether and how small (narrow band) polaronic states survive in a dense electronic system. We investigate this question in a simple one band Holstein polaron model, in which spinless electrons on a tight binding lattice cause an on-site lattice distortion x ₀ . In the small polaron limit, each electron is localized, and the electron hopping t_ij is neglected. We develop a systematic approach in powers of t_ij, identify classical t ⁰ , quantum mean field t ¹ , and quantum fluctuation t ² terms, and show that the last two terms are relatively small, even for dense systems, so long as the narrowed polaron bandwidth t*=t exp(–u) is much smaller than the Einstein phonon energy ₀ . (Here u=(x ² ₀ /2x ² _zp) with x_zp being the zero point phonon displacement.) The relevance of these results for CMR oxides is briefly discussed.     

Discretizing randomly perturbed circle maps

Let f be a C² expanding map of the circle and = d m be the absolutely continuous invariant measure for this system. We formulate a model for a discrete approximation for by perturbing the measure and then discretizing it. We show that whenever the distance between lattice points of the discretization decays polynomially (but not linearly) in the perturbation parameter , then as tends to 0, the discretized density converges to in a suitable Hölder norm. Namely, if < ^1+c for some c > 0, then || , ||(c) 0 as 0, where , is the discretized density. We also show that the rate of convergence is + c. This strengthens the work of Kifer, who shows (in a more general setting), weak convergence of the discretized perturbed measure to .     

The high-field thermal and electrical magnetoconductivities of Pb

The limiting high-magnetic-field behavior of the electrical and thermal magnetoconductivities of a Pb single crystal withB along [001] have been extracted from data taken in fields of up to 4.3 T in the liquid ⁴ He temperature range. The electrical conductivity varies asB ^–2 in the limit of high fields, with the coefficient exhibiting aT ⁵ dependence, the same as is found for the zero-field resistivity. The analogous coefficient for the thermal magnetoconductivity shows aT ³ dependence, but there are no zero-field data available for comparison. The lattice conductivity has also been determined and is shown to obey aT ² dependence only below 3 K, with a more rapid dependence between 3 and 4 K.     

The Effect of Autocorrelation on the Hotelling T2 Control Chart

One of the basic assumptions for traditional univariate and multivariate control charts is that the data are independent in time. For the latter, in many cases, the data are serially dependent (autocorrelated) and cross‐correlated because of, for example, frequent sampling and process dynamics. It is well known that the autocorrelation affects the false alarm rate and the shift‐detection ability of the traditional univariate control charts. However, how the false alarm rate and the shift‐detection ability of the Hotelling T² control chart are affected by various autocorrelation and cross‐correlation structures for different magnitudes of shifts in the process mean is not fully explored in the literature. In this article, the performance of the Hotelling T² control chart for different shift sizes and various autocorrelation and cross‐correlation structures are compared based on the average run length using simulated data. Three different approaches in constructing the Hotelling T² chart are studied for two different estimates of the covariance matrix: (i) ignoring the autocorrelation and using the raw data with theoretical upper control limits; (ii) ignoring the autocorrelation and using the raw data with adjusted control limits calculated through Monte Carlo simulations; and (iii) constructing the control chart for the residuals from a multivariate time series model fitted to the raw data. To limit the complexity, we use a first‐order vector autoregressive process and focus mainly on bivariate data. © 2014 The Authors. Quality and Reliability Engineering International Published by John Wiley & Sons Ltd.     

An isomorphism theorem between the 7-adic integers and a ring associated with a hexagonal lattice

The primary goal of this paper is to prove that a ring defined by L. Gibson and D. Lucas is isomorphic to the ring of 7-adic integers. The ring, denoted byR ₂, arises naturally as an algebraic structure associated with a hexagonal lattice. The elements ofR ₂ consist of all infinite sequences in /(7). The addition and multiplication operations are given in terms of remainder and carries tables. The Generalized Balanced Ternary, denoted byG, is the subring ofR ₂ consisting of all the finite sequences ofR ₂. IfI _k is the ideal ofG consisting of all those sequences whose firstk digits are zero, then the second goal of the paper is to show that the inverse limit ofG/I _k is also isomorphic to the 7-adic integers.     

Weak coupling theory of phonon linewidths in a two-dimensional lattice above a liquid helium substrate

The one-ripplon-n-phonon contributions to the linewidths of lattice resonances have been calculated by first-order perturbation theory to all ordersn in a weak coupling theory. Approximations are made in the expressions for the ripplon-phonon coupled mode coordinates and frequencies which limit the quantitive application of the theory to areal densities 10⁷ cm^–2. A maximum in the linewidth as a function of temperature is predicted which results from the cutoff of scattering from ripplons of large wave vector by the Debye-Waller factor.This work was supported by NSF grant DMR-79-20833.     

Transistor Doping-Predictions for Superconductivity in the Charge Order Model

Transistor doping of potential superconductors promises to illuminate inherent levels and limits for the materials in question. Here some of these limits are quantitatively predicted on a charge order or radical model for a variety of experiments. This model is based on a universal T _c scaling with anionic radical concentration. It is applicable to systems with covalently bonded, high electronegativity components. For the cuprates its general features are a linear increase of T _c with holes, which are normalized per total hole carrying species (e.g., O^– radical density). This dependence proceeds up to optima, corresponding to a uniform alternate hole charge order limit and T _c decreases thereafter with various slopes. The optima are quantitatively calibrated through the deleterious influence of the Blocking layer as measured by its O content. Amongst the predictions is a general limit of T _c ^max 167 K for oxide superconductors, obtainable in infinite layer type compounds (CaCuO₂). Other predictions are optimal T _c 83 K for La₂CuO₄ and maximum values potentially near 500 K for borides or carbides.     

The Polaron: Ground State, Excited States, and Far from Equilibrium

We describe a variational approach for solving the Holstein polaron model with dynamical quantum phonons on an infinite lattice. The method is simple, fast, extremely accurate, and gives ground and excited state energies and wavefunctions at any momentum k. The method can also be used to calculate coherent quantum dynamics for inelastic tunneling and for strongly driven polarons far from equilibrium.     

Studies on structural and electrical properties of copper-doped zinc oxide powders prepared by a solid state method at high temperatures

Abstract

The synthesis, crystal structure and electrical conductivity properties of Cu-doped ZnO powders (in the range of 0.25 – 15 mole %) is reported. I-phase samples, which were indexed as single phase with a hexagonal (wurtzite) structure in the Cu-doped ZnO binary system, were determined by X-ray diffraction. The limit solubility of Cu in the ZnO lattice at this temperature is 5 mole % at 1000°C. The impurity phase was determined as CuO when compared with standard XRD data using the PDF program. We focused on single I-phase ZnO samples which synthesised at 1000°C because the limit solubility range is widest at this temperature. It was observed that the lattice parameters a increased and c decreased with Cu doping concentration. The morphology of the I-phase samples was analysed with a scanning electron microscope. The electrical conductivity of the pure ZnO and single I-phase samples were studied using the four-probe dc method at temperatures between 100 and 950°C in an air atmosphere. The electrical conductivity values of pure ZnO and 5 mole % Cu-doped ZnO samples at 100°C were 2 × 10^?6 and 1.4 × 10^?4 ohm^?1 cm^?1, and at 950°C they were 1.8 and 3.4 ohm^?1 cm^?1, respectively. In other words, the electrical conductivity slightly increased with Cu doping concentration. Also, it was observed that the activation energy of the I-phase samples was decreased with Cu doping concentration.     

The Universality of Energy Spectrum of Phonon and Vacancy Excitations in Solid Helium

The most careful measurements on the specific heat C(T) and dP/dT (P is the pressure, T is the temperature) are analysed using a model where the thermodynamic properties of ³He and ⁴He crystals are described by a sum of phonon and vacancy contributions. The analysis, in which the Debye model of phonons and the Hetherington model for wide-band vacancies are used, yields a universal molar volume depence for the Debye temperature Θ _D and the vacancy activation energy Q _V , and constant values for the Grüneisen parameters in the molar volume range of 14–24 cm³/mol. The Θ _D values are found to be in good agreement with the data obtained from the elastic moduli measurements and with Horner’s theoretical calculations. The Q _V values are in good agreement with the X-ray measurements on the temperature dependences of ³He and ⁴He crystal lattice parameters analysed in terms of the Hetherington model.     

Inelastic neutron scattering from vortex lattice in type-II superconductors. II. The London model

The inelastic neutron scattering from the vortex lattice in type-II superconductors is considered. Use is made of the London model to describe the vibration of the vortex lattice. We find that the differential cross section has sharp peaks besides the Bragg peaks when the transferred momentumq approaches the reciprocal lattice vectorG. These peaks are due to excitation of the vibrational modes and diverge as ¦q –G¦^–2. We also calculate the Debye-Waller factor, which is extremely small.     

Texture dependent stress corrosion failure of commercial titanium sheets in bromine-methanol solution

The stress corrosion cracking (SCC) characteristics of -titanium sheets in a bromine-methanol solution have been studied in the annealed and cold-rolled conditions using longitudinal and transverse specimens. The times to failure for annealed longitudinal specimens were longer than those for similarly tested transverse specimens. The cold-rolled specimens developed resistance to SCC, but failed by cleavage when notched, unlike the intergranular separation in annealed titanium. The apparent activation energy was found to be texture dependent and was in the range 30 to 51 kJ mol^–1 for annealed titanium, and 15kJ mol^–1 for cold-rolled titanium. The dependence of SCC behaviour on the texture is related to the changes in the crack initiation times. These are caused by changes in the passivation and repassivation characteristics of the particular thickness plane. The thickness planes are identified with the help of X-ray pole figures obtained on annealed and cold-rolled material. On the basis of the activation energy and the electrochemical measurements, the mechanism of SCC in annealed titanium is identified to be the one involving stress-aided anodic dissolution. On the other hand, the results on the cold-rolled titanium are in support of the hydrogen embrittlement mechanism consisting of hydride precipitation. The cleavage planes identified from the texture data match with the reported habit planes for hydride formation.     

Statistical monitoring of nonlinear product and process quality profiles

In many quality control applications, use of a single (or several distinct) quality characteristic(s) is insufficient to characterize the quality of a produced item. In an increasing number of cases, a response curve (profile) is required. Such profiles can frequently be modeled using linear or nonlinear regression models. In recent research others have developed multivariate T² control charts and other methods for monitoring the coefficients in a simple linear regression model of a profile. However, little work has been done to address the monitoring of profiles that can be represented by a parametric nonlinear regression model. Here we extend the use of the T² control chart to monitor the coefficients resulting from a parametric nonlinear regression model fit to profile data. We give three general approaches to the formulation of the T² statistics and determination of the associated upper control limits for Phase I applications. We also consider the use of non‐parametric regression methods and the use of metrics to measure deviations from a baseline profile. These approaches are illustrated using the vertical board density profile data presented in Walker and Wright (Comparing curves using additive models. Journal of Quality Technology 2002; 34:118–129). Copyright © 2007 John Wiley & Sons, Ltd.     

Structural and magnetic properties of nanocrystalline Mg–Cd ferrites prepared by oxalate co-precipitation method

Polycrystalline spinel ferrites with general formula Mg_1−x Cd _x Fe₂O₄ (x = 0.0, 0.2, 0.4, 0.6, 0.8, 1.0) were prepared by oxalate co-precipitation method using high purity sulfates. The samples were sintered at 1,050 °C for 5 h. The structural properties of these samples were investigated by XRD, SEM and FTIR techniques. The X-ray diffraction analysis confirms the formation of single phase cubic spinel structure of all the samples. The lattice constant, X-ray density, physical density, porosity, crystallite size, site radii (r _A, r _B), bond length (A–O, B–O) on tetrahedral (A-site) and octahedral (B-site) were calculated for the samples. The lattice constant increases with increase in Cd²⁺ content. The X-ray density increases with increase in Cd²⁺ content. The crystallite size calculated by Scherrer formula is in the range of 27.79–30.40 nm. Physical densities are calculated by Archimedes principle. The SEM study shows that the grain size increases with increasing Cd²⁺ content. The FTIR spectra shows two strong absorption bands around 576 and 431 cm⁻¹ on the tetrahedral and octahedral sites, respectively. The dependence of saturation magnetization on Cd²⁺ content suggests that A–B and B–B super exchange interaction are comparable in strength. Neel’s two sub lattice model is applicable up to x ≤ 0.4, while Y–K three sub lattice models (canted spin) is predominant for x ≥ 0.4.     

A double torsion fracture mechanics and Auger electron spectroscopy approach to the study of stress corrosion cracking in low alloy steels

The applicability of the double torsion fracture mechanics test to the study of stress corrosion cracking (SCC) in steels was assessed by evaluating the behaviour of the low alloy steels AISI 4140 and En3OA, exhibiting both high (1400 MNm^–2) and low (765 MNm^–2) yield strengths respectively. An optical method for measuring crack growth rate and a load relaxation method for computing it were compared and found to give similar results. The test was shown to be eminently suitable for the study of SCC in high yield strength steels and those in a temper embrittled condition. The influence of trace impurities on the SCC susceptibility was examined using Auger electron spectroscopy to determine the type and amount of grain boundary segregants. The degree of segregation of trace impurities was shown to have a profound effect on the stress intensity-crack velocity (K-V) diagram by reducingK _IC and increasing the reaction rate as shown by the increased slope in stage III of theK-V diagram. An anomalously low threshold stress intensity was observed in as-quenched AISI 4140 and this was attributed to residual stresses produced by the phase transformations occurring during quenching.