scholarly journals The structure of normal lattice supercharacter theories

2020 ◽  
Vol 3 (5) ◽  
pp. 1059-1078
Author(s):  
Farid Aliniaeifard ◽  
Nathaniel Thiem
Keyword(s):  
Normal Lattice

Defects in Crystals

1968 ◽  
Vol 26 ◽  
pp. 244-245
Author(s):  
Kenneth R. Lawless
Keyword(s):  
Electron Microscope ◽  
Point Defects ◽  
Surface Defects ◽  
Chemical Properties ◽  
Material Point ◽  
Crystal Defects ◽  
Defects In Crystals ◽  
Irradiation Effects ◽  
Normal Lattice ◽  
Line Defects

One of the most important applications of the electron microscope in recent years has been to the observation of defects in crystals. Replica techniques have been widely utilized for many years for the observation of surface defects, but more recently the most striking use of the electron microscope has been for the direct observation of internal defects in crystals, utilizing the transmission of electrons through thin samples.Defects in crystals may be classified basically as point defects, line defects, and planar defects, all of which play an important role in determining the physical or chemical properties of a material. Point defects are of two types, either vacancies where individual atoms are missing from lattice sites, or interstitials where an atom is situated in between normal lattice sites. The so-called point defects most commonly observed are actually aggregates of either vacancies or interstitials. Details of crystal defects of this type are considered in the special session on “Irradiation Effects in Materials” and will not be considered in detail in this session.

Normal lattice vibrations and the crystal structure of anisotropic modifications of boron nitride

1998 ◽  
Vol 32 (9) ◽  
pp. 924-932 ◽  
Author(s):  
S. V. Ordin ◽  
B. N. Sharupin ◽  
M. I. Fedorov
Keyword(s):  
Crystal Structure ◽  
Boron Nitride ◽  
Lattice Vibrations ◽  
Normal Lattice

On Polynomially Normal Lattice Configurations

2005 ◽  
Vol 147 (2) ◽  
pp. 137-153
Author(s):  
Mordechay B. Levin ◽  
Meir Smorodinsky
Keyword(s):  
Normal Lattice

Remarks on annihilators preserving congruence relations

2012 ◽  
Vol 62 (3) ◽  
Author(s):  
Sergio Celani
Keyword(s):  
Distributive Lattices ◽  
Normal Lattice ◽  
Topological Interpretation ◽  
Congruence Relations

AbstractIn this note we shall give some results on annihilators preserving congruence relations, or AP-congruences, in bounded distributive lattices. We shall give some new characterizations, and a topological interpretation of the notion of annihilator preserving congruences introduced in [JANOWITZ, M. F.: Annihilator preserving congruence relations of lattices, Algebra Universalis 5 (1975), 391–394]. As an application of these results, we shall prove that the quotient of a quasicomplemented lattice by means of a AP-congruence is a quasicomplemented lattice. Similarly, we will prove that the quotient of a normal latttice by means of a AP-congruence is also a normal lattice.

Self-diffusion in gold single crystals at low temperatures

1968 ◽  
Vol 46 (23) ◽  
pp. 2589-2594 ◽  
Author(s):  
J. L. Whitton ◽  
G. V. Kidson
Keyword(s):  
Single Crystals ◽  
Diffusion Coefficients ◽  
Low Temperatures ◽  
Bulk Diffusion ◽  
Lattice Diffusion ◽  
Fast Diffusion ◽  
Initial Portion ◽  
Self Diffusion ◽  
Normal Lattice ◽  
Structure Sensitive

Self-diffusion in gold single crystals has been studied at temperatures between 335 to 390 °C for times between 15 and 30 min. The concentration profiles, obtained by use of a sensitive sectioning technique, consist of a region that appears to be characteristic of bulk diffusion, followed by a deeply penetrating 'tail' that is structure sensitive. Diffusion coefficients extracted from the initial portion of the curves are somewhat larger than those predicted from an extrapolation of high temperature measurements. The results are interpreted in terms of a combination of normal lattice diffusion and fast diffusion along dislocations.

scholarly journals Critical and co-operative phenomena. IV. A theory of disorder in solids and liquids and the process of melting

1939 ◽  
Vol 170 (943) ◽  
pp. 464-484 ◽  
Keyword(s):  
Continuous Process ◽  
The Other ◽  
Heat Of Fusion ◽  
Essential Difference ◽  
Continuous Change ◽  
Continuous Transition ◽  
Normal Lattice ◽  
Liquid States ◽  
Solid And Liquid States ◽  
Satisfactory Theory

It is probably true to say that at present there is no satisfactory theory of the process of melting. By this is meant that none of the existing theories can account satisfactorily for the sharp transition in properties which occurs at a precise temperature when a pure single component substance melts. An adequate theory must find a reason for the existence of a sharp temperature and must explain the change of volume and the latent heat of fusion in terms of interatomic forces. For this purpose it is necessary to devise a model of the solid and liquid states of such a kind that a change from one phase to the other can be regarded as taking place by a continuous process and represented mathematically by a continuous change of one or more suitable variables. An attempt to construct such a model has been made by the authors in a recent paper (Lennard-Jones and Devonshire 1939). It was based on the hypothesis that the essential difference between a solid and a liquid is that one is ordered and the other disordered and that a change from one state to the other can be followed by a continuous transition of a variable suitably chosen to represent the state of order. For this purpose the concept of disorder used by Bethe (1935) in his theory of binary alloys was used but adapted to a substance consisting only of one component. This was done by considering the distribution of atoms not only on their normal lattice sites (called α -sites) but also on certain other abnormal sites (called β -sites). These latter sites were taken to be certain positions in the interstices of the normal lattice positions. Owing to the repulsive fields of atoms at close quarters these sites must necessarily be positions of higher energy than the normal sites and will rarely be occupied at low temperatures.

Influence of magnesium concentration on the optical properties of ytterbium and holmium co-doped lithium niobate crystal

2016 ◽  
Vol 30 (01) ◽  
pp. 1550260 ◽  
Author(s):  
Li Dai ◽  
Shanshan Jiao ◽  
Zhehua Yan ◽  
Ping Dai ◽  
Gang Lui ◽  
...  
Keyword(s):  
Doping Concentration ◽  
Lithium Niobate Crystal ◽  
Threshold Concentration ◽  
Magnesium Concentration ◽  
Optical Homogeneity ◽  
Czochralski Technique ◽  
Infrared Transmission ◽  
Damage Resistance ◽  
Normal Lattice ◽  
Fundamental Reason

In this paper, a series of Yb (0.5[Formula: see text]mol.%):Ho (0.5[Formula: see text]mol.%):LiNbO3 crystals doped with various concentration of Mg[Formula: see text] (1, 3, 5 and 7[Formula: see text]mol.%) were grown by the Czochralski technique. The ability of optical damage resistance of Mg:Yb:Ho:LiNbO3 crystals increases with increasing the Mg[Formula: see text] doping concentration. The optical homogeneity of Mg:Yb:Ho:LiNbO3 crystals doped with different concentration of Mg[Formula: see text] was detected using the birefringence gradient method. The results demonstrated that the optical homogeneity is getting better with the increase of the Mg[Formula: see text] doping concentration. The studies on the infrared transmission spectra indicated that Mg[Formula: see text] ions first replaces anti-site Nb[Formula: see text] in the form of Mg[Formula: see text] defect, once the concentration of Mg[Formula: see text] reaches or exceeds the threshold concentration, it begins to substitute Li-site and Nb-site of normal lattice and form defect of Mg[Formula: see text][Formula: see text]3Mg[Formula: see text]. Therefore, the change of Mg[Formula: see text] doping concentration is the fundamental reason leading to a violet shift of the OH[Formula: see text] absorption peak.

Exchange between normal lattice occupants

1978 ◽  
Vol 40 (6) ◽  
pp. 999-1002 ◽  
Author(s):  
S. Fernandez Valverde ◽  
G. Duplâtre ◽  
A.G. Maddock
Keyword(s):  
Normal Lattice

scholarly journals Filter Representation of Normal Lattice

1996 ◽  
Vol 1 (1) ◽  
pp. 63
Author(s):  
B. Yallaoui
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Normal Lattice ◽  
Necessary And Sufficient

In this paper we will investigate the properties of normality lattices and their relationships to zero-one measures. We will establish necessary and sufficient conditions for lattices to be normal. These properties are then investigated in the case of separated lattices.

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