Lattice relaxation around tetragonal and rhombic defects in alkali halides

1979 ◽  
Vol 57 (8) ◽  
pp. 1209-1215
Author(s):  
B. P. Clayman
Keyword(s):  
Nearest Neighbor ◽  
Alkali Halides ◽  
Nearest Neighbors ◽  
Lattice Relaxation ◽  
Force Constants ◽  
Tetragonal Symmetry ◽  
Model Calculations ◽  
Host Interactions ◽  
Rhombic Symmetry ◽  
Rigid Ion Model

The relaxation of the crystal lattice around impurity pair defects in alkali halides is calculated based on a rigid ion model. Pairs with tetragonal symmetry—fourth nearest neighbors along the [001] axis—and those with rhombic symmetry—second nearest neighbors along the [110] axis— are both considered, for all cases where experimental evidence exists for resonant or gap modes. These are: NaCl with F−, Li+, and Ag+; KI with Cl−, Br−, Na+, and Rb+; KCl with Na+; and NaBr with Li+. Relaxation spaces with 72 ions (tetragonal) and 50 ions (rhombic) are used and results reported for all ions within the spaces. The nearest neighbor central force constants coupling the impurity ions and their nearest neighbors are calculated in the rigid ion approximation and the results compared with earlier dynamical model calculations. Because the dynamical models assumed that only one perturbed force constant was needed to characterize all the impurity–host interactions, and significant directional inhomogeneity of the force constants was a result of the present calculations, only qualitative comparisions could be made.

Lattice relaxation around impurity pairs in alkali halides

1976 ◽  
Vol 54 (19) ◽  
pp. 2010-2017
Author(s):  
T. L. Templeton ◽  
B. P. Clayman
Keyword(s):  
Nearest Neighbor ◽  
Molecular Model ◽  
Linear Chain ◽  
Alkali Halides ◽  
Lattice Relaxation ◽  
Resonant Absorption ◽  
Force Constants ◽  
Chain Model ◽  
Absorption Frequencies ◽  
Good Agreement

The rigid ion model is applied to the calculation of the relaxation of the lattice around single impurities and pairs of impurities in alkali halide host-defect systems. The calculated relaxation of nearest neighbors is typically a few percent of the host crystal lattice constant. Relaxation falls off with increasing distance from the defects. Nearest neighbor force constants derived from this calculation are, in some cases, in good agreement with those obtained by fitting the resonant absorption frequencies of the vibrational modes of these impurity centres to a molecular model. In other cases the extreme anisotropy of the relaxed force constants is seen to prevent the application of a simple molecular model. The calculated force constants, when used in a linear chain model, give good qualitative agreement with experiment.

Molecular Model Calculations of Pair–Modes in Alkali Halides

1974 ◽  
Vol 52 (16) ◽  
pp. 1492-1501 ◽  
Author(s):  
R. W. Ward ◽  
B. P. Clayman
Keyword(s):  
Short Range ◽  
Nearest Neighbor ◽  
Molecular Model ◽  
Alkali Halides ◽  
Nearest Neighbors ◽  
Local Mode ◽  
Relevant Parameter ◽  
Model Calculations ◽  
Short Range Force ◽  
Range Force

The molecular model, developed by Jaswal for [100] aligned impurity pairs, has been extended to account for [110] aligned pairs and used to study U center (H−H− and D−D−) pairs in KCl and (Cl−Cl− and Na+Na+)-induced pair–modes in the gap of KI. In this model the impurity ions in the pair and their nearest neighbors are allowed to vibrate while the rest of the lattice is held fixed. For [110] and [100] aligned pairs, this gives 12- and 17-ion molecules respectively. The potential energy is treated in the rigid ion approximation with short range forces between the nearest neighbors only. After the single relevant parameter of the model, the nearest neighbor force constant, is fitted to the U center local mode frequency, the model can account for the experimentally observed frequencies and polarizations of the three U center pairs in KCl. Similarly, after fitting to the single ion Cl− gap mode at 77 cm−1 in KI, the model predicts 3 infrared active pair–modes whose frequencies are in close agreement with experiment. In KI:Na+, where no single ion resonance has been observed, the calculated results suggest that the absorption lines are due to [110] aligned Na+ ions, with a large softening of the short range force constants occurring around the defect. The KI:Br− and NaCl:F− systems are also considered.

Observation of Superlattice Dislocations on Cube Planes in Ni3Al

1973 ◽  
Vol 31 ◽  
pp. 174-175 ◽  
Author(s):  
J. M. Oblak ◽  
W. H. Rand
Keyword(s):  
Nearest Neighbor ◽  
Antiphase Boundary ◽  
Nearest Neighbors ◽  
High Energy ◽  
Cross Slip ◽  
Octahedral Plane ◽  
Trapping Mechanism ◽  
Slip Traces

The energy of an a/2 <110> shear antiphase. boundary in the Ll2 expected to be at a minimum on {100} cube planes because here strue ture is there is no violation of nearest-neighbor order. The latter however does involve the disruption of second nearest neighbors. It has been suggested that cross slip of paired a/2 <110> dislocations from octahedral onto cube planes is an important dislocation trapping mechanism in Ni3Al; furthermore, slip traces consistent with cube slip are observed above 920°K.Due to the high energy of the {111} antiphase boundary (> 200 mJ/m2), paired a/2 <110> dislocations are tightly constricted on the octahedral plane and cannot be individually resolved.

Temporal Changes in Habitat Selection and Nest Spacing in a Colony of Ross' and Lesser Snow Geese

The Auk ◽  
1983 ◽  
Vol 100 (2) ◽  
pp. 335-343 ◽  
Author(s):  
M. Robert McLandress
Keyword(s):  
Nearest Neighbor ◽  
Average Distance ◽  
Habitat Preferences ◽  
Nearest Neighbors ◽  
Nest Density ◽  
Snow Goose ◽  
Snow Geese ◽  
Lesser Snow Geese ◽  
Average Size ◽  
Island Habitats

Abstract I studied the nesting colony of Ross' Geese (Chen rossii) and Lesser Snow Geese (C. caerulescens caerulescens) at Karrak Lake in the central Arctic of Canada in the summer of 1976. Related studies indicated that this colony had grown from 18,000 birds in 1966-1968 to 54,500 birds in 1976. In 1976, geese nested on islands that were used in the late 1960's and on an island and mainland sites that were previously unoccupied. Average nest density in 1976 was three-fold greater than in the late 1960's. Consequently, the average distance to nearest neighbors of Ross' Geese in 1976 was half the average distance determined 10 yr earlier. The mean clutch size of Ross' Geese was greater in island habitats where nest densities were high than in less populated island or mainland habitats. The average size of Snow Goose clutches did not differ significantly among island habitats but was larger at island than at mainland sites. Large clutches were most likely attributable to older and/or earlier nesting females. Habitat preferences apparently differed between species. Small clutches presumably indicated that young geese nested in areas where nest densities were low. The establishment of mainland nesting at Karrak Lake probably began with young Snow Geese using peripheral areas of the colony. Young Ross' Geese nested in sparsely populated habitats on islands to a greater extent than did Snow Geese. Ross' Geese also nested on the mainland but in lower densities than Ross' Geese nesting in similar island habitats. Successful nests with the larger clutches had closer conspecific neighbors than did successful nests with smaller clutches. The species composition of nearest neighbors changed significantly with distance from Snow Goose nests but not Ross' Goose nests. Nesting success was not affected by the species of nearest neighbor, however. Because they have complementary antipredator adaptations, Ross' and Snow geese may benefit by nesting together.

scholarly journals Tropical Balls and Its Applications to K Nearest Neighbor over the Space of Phylogenetic Trees

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 779
Author(s):  
Ruriko Yoshida
Keyword(s):  
Supervised Learning ◽  
Phylogenetic Trees ◽  
Nearest Neighbor ◽  
Nearest Neighbors ◽  
High Dimensional ◽  
Learning Method ◽  
Dimensional Vector ◽  
K Nearest Neighbor ◽  
K Nearest Neighbors

A tropical ball is a ball defined by the tropical metric over the tropical projective torus. In this paper we show several properties of tropical balls over the tropical projective torus and also over the space of phylogenetic trees with a given set of leaf labels. Then we discuss its application to the K nearest neighbors (KNN) algorithm, a supervised learning method used to classify a high-dimensional vector into given categories by looking at a ball centered at the vector, which contains K vectors in the space.

scholarly journals Chi-Squared Distance Metric Learning for Histogram Data

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Wei Yang ◽  
Luhui Xu ◽  
Xiaopan Chen ◽  
Fengbin Zheng ◽  
Yang Liu
Keyword(s):  
Nearest Neighbor ◽  
State Of The Art ◽  
Metric Learning ◽  
Nearest Neighbors ◽  
Distance Metric Learning ◽  
Distance Metric ◽  
Projected Gradient Method ◽  
Proper Distance ◽  
Chi Squared ◽  
Real World Datasets

Learning a proper distance metric for histogram data plays a crucial role in many computer vision tasks. The chi-squared distance is a nonlinear metric and is widely used to compare histograms. In this paper, we show how to learn a general form of chi-squared distance based on the nearest neighbor model. In our method, the margin of sample is first defined with respect to the nearest hits (nearest neighbors from the same class) and the nearest misses (nearest neighbors from the different classes), and then the simplex-preserving linear transformation is trained by maximizing the margin while minimizing the distance between each sample and its nearest hits. With the iterative projected gradient method for optimization, we naturally introduce thel2,1norm regularization into the proposed method for sparse metric learning. Comparative studies with the state-of-the-art approaches on five real-world datasets verify the effectiveness of the proposed method.

scholarly journals Erratum: Force constants of the metaborate ion in alkali halides

1973 ◽  
Vol 58 (4) ◽  
pp. 1782-1782
Author(s):  
J. C. Decius ◽  
C. R. Becker ◽  
W. J. Fredericks
Keyword(s):  
Alkali Halides ◽  
Force Constants

scholarly journals The K Nearest Neighbor Algorithm for Imputation of Missing Longitudinal Prenatal Alcohol Data

2021 ◽  
Author(s):  
Ayesha Sania ◽  
Nicolo Pini ◽  
Morgan Nelson ◽  
Michael Myers ◽  
Lauren Shuffrey ◽  
...  
Keyword(s):  
Missing Data ◽  
Missing Values ◽  
Nearest Neighbor ◽  
Learning Algorithm ◽  
Drinking Behavior ◽  
Nearest Neighbors ◽  
First Trimester ◽  
Epidemiologic Studies ◽  
K Nearest Neighbor ◽  
Timeline Followback

Abstract Background — Missing data are a source of bias in epidemiologic studies. This is problematic in alcohol research where data missingness is linked to drinking behavior. Methods — The Safe Passage study was a prospective investigation of prenatal drinking and fetal/infant outcomes (n=11,083). Daily alcohol consumption for last reported drinking day and 30 days prior was recorded using Timeline Followback method. Of 3.2 million person-days, data were missing for 0.36 million. We imputed missing data using a machine learning algorithm; “K Nearest Neighbor” (K-NN). K-NN imputes missing values for a participant using data of participants closest to it. Imputed values were weighted for the distances from nearest neighbors and matched for day of week. Validation was done on randomly deleted data for 5-15 consecutive days. Results — Data from 5 nearest neighbors and segments of 55 days provided imputed values with least imputation error. After deleting data segments from with no missing days first trimester, there was no difference between actual and predicted values for 64% of deleted segments. For 31% of the segments, imputed data were within +/-1 drink/day of the actual. Conclusions — K-NN can be used to impute missing data in longitudinal studies of alcohol use during pregnancy with high accuracy.

Monte Carlo simulations of long-range order kinetics in B2 phases

1995 ◽  
Vol 10 (3) ◽  
pp. 591-595 ◽  
Author(s):  
K. Yaldram ◽  
V. Pierron-Bohnes ◽  
M.C. Cadeville ◽  
M.A. Khan
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Nearest Neighbor ◽  
Vacancy Concentration ◽  
Relaxation Times ◽  
Nearest Neighbors ◽  
Migration Energy ◽  
Ordering Kinetics ◽  
Migration Barriers ◽  
Temperature Dependences

The thermodynamic parameters that drive the atomic migration in B2 alloys are studied using Monte-Carlo simulations. The model is based on a vacancy jump mechanism between nearest neighbor sites, with a constant vacancy concentration. The ordering energy is described through an Ising Hamiltonian with interaction potentials between first and second nearest neighbors. Different migration barriers are introduced fur A and B atoms. The results of the simulations compare very well with those of experiments. The ordering kinetics are well described by exponential-like behaviors with two relaxation times whose temperature dependences are Arrhenius laws yielding effective migration energies. The ordering energy contributes significantly to the total migration energy.

scholarly journals Lattice Dynamics of Simple Harmonic and Anharmonic Shell Models

1967 ◽  
Vol 20 (5) ◽  
pp. 495 ◽  
Author(s):  
J Oitmaa
Keyword(s):  
Dipole Moment ◽  
Shell Model ◽  
Lattice Dynamics ◽  
Higher Order ◽  
Force Constants ◽  
Dynamical Equations ◽  
Normal Coordinates ◽  
Shell Models ◽  
Rigid Ion Model ◽  
Explicit Expressions

The lattice dynamics of harmonic and anharmonic shell models are reviewed. It is shown that the various dynamical equations for the shell model can be expressed in the same form as those for the rigid ion model, but with modified force constants. The anharmonic shell model leads to higher order contributions to the dipole moment, quadratic and cubic in the normal coordinates, for which explicit expressions are obtained.

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