Synthesis of a single phase of high-entropy Laves intermetallics in the Ti–Zr–V–Cr–Ni equiatomic alloy

The high-entropy Ti–Zr–V–Cr–Ni (20 at% each) alloy consisting of all five hydride-forming elements was successfully synthesised by the conventional melting and casting as well as by the melt-spinning technique. The as-cast alloy consists entirely of the micron size hexagonal Laves Phase of C14 type; whereas, the melt-spun ribbon exhibits the evolution of nanocrystalline Laves phase. There was no evidence of any amorphous or any other metastable phases in the present processing condition. This is the first report of synthesising a single phase of high-entropy complex intermetallic compound in the equiatomic quinary alloy system. The detailed characterisation by X-ray diffraction, scanning and transmission electron microscopy and energy-dispersive X-ray spectroscopy confirmed the existence of a single-phase multi-component hexagonal C14-type Laves phase in all the as-cast, melt-spun and annealed alloys. The lattice parameter a = 5.08 Å and c = 8.41 Å was determined from the annealed material (annealing at 1173 K). The thermodynamic calculations following the Miedema’s approach support the stability of the high-entropy multi-component Laves phase compared to that of the solid solution or glassy phases. The high hardness value (8.92 GPa at 25 g load) has been observed in nanocrystalline high-entropy alloy ribbon without any cracking. It implies that high-yield strength (~3.00 GPa) and the reasonable fracture toughness can be achieved in this high-entropy material.     

Effect of electron concentration on the Laves phase stability of NbCr2–Ni produced by powder metallurgy

The powder metallurgy technology of mechanical alloying followed by hot-pressing consolidation has been used to obtain NbCr₂–Ni Laves phases. High-purity Nb, Cr, and Ni crystalline powders were milled for periods up to 35 h. These powders were vacuum sintered at 1250°C for 0.5 h under 45 MPa. The phase transformations of NbCr₂–Ni Laves phases have been investigated by X-ray diffraction. The grain size decreases and the microstrain increases with increased Ni content. Different phase transformations were observed from NbCr₂–Ni intermetallics. It is found that the electron concentration and phase stability correlation is obeyed in the Nb–Cr–Ni systems. However, the electron concentration corresponding to the C15/C14 phase transition is found to move to a higher value (i.e. 6.103) than the predicted one (i.e. 5.88) in the literature.     

When can we trust theF-approximation of the box-test?

Consider a multivariate context withp variates andk independent samples, each of sizen. To test equality of thek population covariance matrices, the likelihood ratio test is commonly employed. Box'sF-approximation to the null distribution of the test statistic can be used to computep-values, if sample sizes are not too small. It is suggested to regard theF-approximation as accurate if the sample sizesn are greater than or equal to 1+0.0613p ²+2.7265p-1.4182p ^0.5+0.235p ^1.4* In (k), for 5p30,k20.This research was supported by the Deutsche Forschungsgemeinschaft through Ste 405/2-1.     

Rotational equivalence of factor loading matrices with specified values

Under mild assumptions, when appropriate elements of a factor loading matrix are specified to be zero, all orthogonally equivalent matrices differ at most by column sign changes. Here a variety of results are given for the more complex case when the specified values are not necessarily zero. A method is given for constructing reflections to preserve specified rows and columns. When the appropriatek(k – 1)/2 elements have been specified, sufficient conditions are stated for the existence of 2 ^k orthogonally equivalent matrices.This research was supported in part by the National Institute of Health Grant RR-3.     

Icosahedral-phase formation and stability in Ti Zr Co alloys

We present the first report of icosahedral phase i-phase formation in rapidly quenched alloys of Ti Zr Co . Electron diffraction patterns of i TiZrCo 53 27 20 contain features, such as anisotropic spot shapes and arcs of diffuse scattering, that are characteristic of the disordered icosahedral phases found in Ti 3d transition metal Si O and Ti Zr Fe alloys. The features are less prominent than in those alloys, however, suggesting that this i-phase may have structural order intermediate between those strongly disordered i-phases and more ordered Ti Zr Ni i-phases, showing none of these features. The quasilattice constant for a i TiZrCo, 0 51 nm, is close to that of i TiZrNi . The i-phase in rapidly q quenched Ti Zr Co alloys is deeply metastable and transforms exothermically o to the hexagonal Laves phase about 500 C. The Laves phase transforms to the o T bcc solid solution phase b-Ti and the Ti Ni-type fcc structure for 630 C. A 2 reversible transformation between the b-Ti and the hexagonal solid solution phase a-Ti is observed on temperature cycling; the Ti Ni-type fcc phase is 2 stable over the entire temperature range.     

Tests of statistical hypotheses in the case of unequal or disproportionate numbers of observations in the subclasses

General solutions of the analysis of variance in the case of unequal numbers of observations in the subclasses are presented. If we havek criteria for the classification, there will bek! solutions in making a complete analysis and 2^k–1 answers, bearing different meanings, for the sum of squares between subclasses of each criterion. The sum of squares for the interaction of any order, however, will be identical in different solutions of same problem.     

Effect of network connectivity on thermal properties of As30Te70– x Tl x glasses

Alternating differential scanning calorimetry (ADSC) studies were undertaken to investigate the effect of Tl addition on the thermal properties of As₃₀Te_{70– x} Tl _x (6?≤?x?≤?22 at%) glasses. These include parameters such as glass-transition temperature (T _g), changes in specific heat capacity (ΔC _p) and relaxation enthalpy (ΔH ^NR) at the glass transition. It was found that T _g of the glasses decreased with the addition of Tl, which is in contrast to the dependence of T _g in As–Te glasses on the addition of Al and In. The change in heat capacity ΔC _p through the glass transition was also found to decrease with increasing Tl content. The addition of Tl to the As–Te matrix may lead to a breaking of As–Te chains and the formation of Tl⁺Te^?AsTe_2/2 dipoles. There was no significant dependence of the change of relaxation enthalpy, through the glass transition, with composition.     

Maximization of sums of quotients of quadratic forms and some generalizations

Monotonically convergent algorithms are described for maximizing six (constrained) functions of vectors x, or matricesX with columns x₁, ..., x _r . These functions are h₁(x)= _k (xA _kx)(xC _kx)^–1, H₁(X)= _k tr (XA _k X)(XC _k X)^–1, h₁(X)= _{k l} (x _l A _kx _l ) (x _l C _kx _l )^–1 withX constrained to be columnwise orthonormal, h₂(x)= _k (xA _kx)²(xC _kx)^–1 subject to xx=1, H₂(X)= _k tr(XA _kX)(XA_kX)(XC_kX)^–1 subject toXX=I, and h₂(X)= _{k l} (x _l A _kx _l )² (x _l C _kX _l )^–1 subject toXX=I. In these functions the matricesC _k are assumed to be positive definite. The matricesA _k can be arbitrary square matrices. The general formulation of the functions and the algorithms allows for application of the algorithms in various problems that arise in multivariate analysis. Several applications of the general algorithms are given. Specifically, algorithms are given for reciprocal principal components analysis, binormamin rotation, generalized discriminant analysis, variants of generalized principal components analysis, simple structure rotation for one of the latter variants, and set component analysis. For most of these methods the algorithms appear to be new, for the others the existing algorithms turn out to be special cases of the newly derived general algorithms.This research has been made possible by a fellowship from the Royal Netherlands Academy of Arts and Sciences to the author. The author is obliged to Jos ten Berge for stimulating this research and for helpful comments on an earlier version of this paper.     

The temporal architecture of central information processing: Evidence for a tentative time-quantum model

Summary A new, elaborated version of a time-quantum model (TQM) is outlined and illustrated by applying it to different experimental paradigms. As a basic prerequisite TQM adopts the coexistence of different discrete time units or (perceptual) intermittencies as constituent elements of the temporal architecture of mental processes. Unlike similar other approaches, TQM assumes the existence of an absolute lower bound for intermittencies, the time-quantum T, as an (approximately) universal constant and which has a duration of approximately 4.5 ms. Intermittencies of TQM must be multiples T _k=k·T ^* within the interval T ^*T _kL·T ^*M·T ^* with T ^*=q·T and integer q, k, L, and M. Here M denotes an upper bound for multipliers characteristic of individuals, the so-called coherence length; q and L may depend on task, individual and other factors. A second constraint is that admissible intermittencies must be integer fractions of L, the operative upper bound. In addition, M is assumed to determine the number of elementary information units to be stored in short-term memory.     

DEMAND EQUATIONS FOR QUALITATIVELY DIFFERENT FOODS UNDER FIXED‐RATIO SCHEDULES: A COMPARISON OF THREE DATA CONVERSIONS

Concurrent schedules were used to establish 6 hens' preferences for three foods. The resulting biases suggested wheat was preferred over honey‐puffed and puffed wheat, and puffed wheat was the least preferred food. The hens then responded under fixed‐ratio schedules for each food in 40‐min (excluding reinforcer time) sessions, with the response requirement doubling each session until no reinforcers were received. At the smaller ratios, the less preferred the food, the faster the hens' overall response rates (mainly as a result of shorter postreinforcement pauses) and the more reinforcers they received. The relations between the logarithms of the number of reinforcers obtained (consumption) and the response ratio (price) were well fitted by curvilinear demand functions. Wheat produced the smallest initial consumption (ln L), followed by honey‐puffed and puffed wheat, respectively. The response requirement at which the demand functions predicted maximal responding (P_max) were larger for wheat than for the other foods. Normalizing consumption and price, as suggested by Hursh and Winger (1995), moved the data for the three foods towards a single demand function; however, the P_max values were generally largest for puffed wheat. The results of normalization, as suggested by Hursh and Silberberg (2008), depended on the k value used. The parameter k is related to the range of the data, and the same k value needs to be used for all data sets that are compared. A k value of 8.0 gave significantly higher essential values (smaller α values) for puffed wheat as compared to honey‐puffed wheat and wheat, and the P_max values, in normalized standard price units, were largest for puffed wheat. Normalizing demand by converting the puffed and honey‐puffed wheat reinforcers to wheat equivalents (by applying the bias parameter from the concurrent‐schedules procedure) maintained separate demand functions for the foods. Those for wheat had the smallest rates of change in elasticity (a) and, in contrast to the other analyses, the largest P_max values. Normalizing demand in terms of concurrent‐schedule preference appears to have some advantages and to merit further investigation.     

Selecting K of N alternatives

In some decision contexts (e.g. graduate admissions) the task to select a subset of k distinct alternatives from among the N > k > 1 options available. For moderate values of N and k, the number of possible subsets of size k becomes quite large. Assuming alternatives are evaluated using consistent, though not explicit weights, selecting k, rather than 1, empirically excludes a substantial proportion (more than 80%) of the subsets; unfortunately to the unaided decision maker it is not obvious which subsets should be excluded. The tendency of subjects to select excludable subsets can be called an ‘infeasibility’ bias. The experimental evidence surprisingly shows no ‘infeasibility’ bias, as subjects overwhelmingly chose non-excluded selections.     

Energetic effects of dopants on the eutectoid decomposition of Nb–Si in situ composites

The influences of doping elements (Ti, Zr, Hf, V, Ta, Cr, Mo, W and Al) on the heats of formation of Nb, Nb₅Si₃ and Nb₃Si have been studied using first-principles pseudopotential plane-wave method based on density functional theory. Site preferences of dopants in Nb₅Si₃ and Nb₃Si intermetallics are first determined by comparing the heats of formation of the systems with different site occupations of the doping atoms. The partitionings of dopants between the equilibrium phases Nb and Nb₅Si₃ of Nb–Si in situ composites are then discussed and compared with experimental results. Phase partitioning behaviours of the alloying elements are found to depend strongly on the number of their valence electrons. By calculating the enthalpy of reaction regarding the eutectoid decomposition of Nb₃Si phase, we conclude that Ta is a Nb₃Si stabiliser while other dopants destabilise Nb₃Si at the investigated concentration.     

A note on “pattern variants on a square field”

It is shown how results of Prokhovnik on the number of pattern variants that may be formed byk markers on a square network ofm ² positions may be derived more simply by means of a combinatorial theorem of Pólya's, which may also be used to solve systematically many other problems of this type.     

Estimation of the reliability of ratings

A procedure for estimating the reliability of sets of ratings, test scores, or other measures is described and illustrated. This procedure, based upon analysis of variance, may be applied both in the special case where a complete set of ratings from each ofk sources is available for each ofn subjects, and in the general case wherek ₁,k ₂, ...,k _n ratings are available for each of then subjects. It may be used to obtain either a unique estimate or a confidence interval for the reliability of either the component ratings or their averages. The relations of this procedure to others intended to serve the same purpose are considered algebraically and illustrated numerically.The writer wishes to acknowledge the helpful comments and suggestions of Professors E. E. Cureton, Harold Gulliksen, and E. F. Lindquist.     

Analytical derivation of the effective temperature for field-dependent hopping conductivity

The electric-field enhancement of hopping conductivity in amorphous solids can be described in terms of an effective temperature T _eff given by for hopping, at a temperature T and field F, within a uniform distribution of electronic states with localization length γ^?1. We have derived this expression analytically and find at low fields a value for C of 1/2^1/2, which is consistent with the F-independent value C = 0.67 previously obtained numerically for band-tail hopping. With increasing electric field, the decrease in C(F) matches the hopping transport characteristics in amorphous semiconductors (hydrogenated amorphous silicon and hydrogenated amorphous carbon nitride) better than previous numerical simulations.     

On the numerical approximation of the bivariate normal (tetrachoric) correlation coefficient

In this paper a rapid and reliable method is found for estimating the value of the Bivariate Normal Correlation Coefficient, ρ, given values of the joint probability and the normal deviates,h andk, or the related areas. This technique finds useful application in the computational approximation of the tetrachoric correlation coefficient,r, when the underlying distributions may be assumed to be normal.     

Using logistic regression to estimate delay-discounting functions

The monetary choice questionnaire (MCQ) and similar computer tasks ask preference questions in order to ascertain indifference, the perceived equivalence of immediate versus larger delayed rewards. Indifference data are then fitted with a hyperbolic function, summarizing the decline in perceived value with delay time. We present a fitting method that estimates the hyperbolic parameterk directly from survey responses. Binary preferences are modeled as a function of time (X₂) and a transformed reward ratio (X ₁), yielding logistic regression coefficients β₂ and β₁. The hyperbolic parameter emerges ask = β₂/β₁, where the logistic predictedp = .5 (the definition of indifference). The MCQ was administered to 1,073 adolescents and was scored using both standard and logistic methods. The means for ln(k) were similar (standard, −4.53; logistic, −4.51), and the results were highly correlated (ρ = .973). Simulated MCQ data showed thatk was unbiased, except where β₁ ≥ −1, indicating a vague survey response. Jackknife standard errors provided excellent coverage.     

Structural phase transitions in epitaxial SrRuO3 thin films

The microstructural evolution of epitaxial SrRuO₃ thin films from ambient temperature (about 293K) to about 900K has been studied by in-situ transmission electron microscopy. Upon heating from the ambient temperature, the intensities of h, k, 2n+1 and h, -h+2n+1, 0 reflections in selected-area electron diffraction patterns decrease with increasing temperature. Two structural phase transitions were observed at about 673and about 783K, revealed by the vanishing of the h, k, 2n+1 and h,-h+2n+1, 0 reflections respectively. The examination of electron diffraction patterns along several different zone axes, taking into account the possible tilting configurations of RuO₆ octahedra, indicates that, upon heating, the orthorhombic structure of SrRuO₃ transforms into a tetragonal structure at about 673K, and further transforms into a cubic structure at about 783K. Possible structural models for the high-temperature phases are considered.     

The Relation between Motivation and Goal Attainment: A Correlational Meta-Analysis

This meta-analysis investigated the strengths of the relationship between various types of motivations and accompanying future outcomes that individuals intend to change, based upon 337 effect sizes from 62 studies. Considerable variation exists within and between the effect sizes of the 14 types of motivations, ranging from a small negative effect size, r = −.13, I² = 93.85% (k = 13), to a medium positive effect size, r = .38, I² = 0.0% (k = 3). The following factors moderated some of the 14 summary effect sizes: (a) the type of assessment data (self-report vs. physical data); (b) the type of future outcomes (physical behavior, psychological state, and intellectual ability); (c) the use of a motivational intervention; (d) the use of a longitudinal design; and (e) the time period between the point that measured motivation and future outcomes. The moderating effects suggest that the effect size of motivations may fluctuate across various domains, while future outcomes may be almost unaffected or even affected negatively by particular types of motivations, although certain other types of motivations play positive roles.     

Flicker in computer-generated visual displays: Selecting a CRO phosphor and other problems

The visual system's response to flicker is approximated by 6–9 RC stages in series. The CRO phosphor can be represented by one additional RC stage. Therefore, increasing the refresh rate by a factor of k can be k⁵ to k⁸ times more effective in reducing apparent flicker than increasing the phosphor time constant. “Slow” phosphors impair the display of rapid movement and cause undesirable persistence of old picture contents after they have been altered. Behavioral scientists usually should choose fast, efficient phosphors. Display programs should be written so that spatially adjacent points of a display are intensified as close together in time as possible.