scholarly journals The apparent sizes of atoms in metallic crystals with special reference to aluminium and indium, and the electronic state of magnesium

1940 ◽  
Vol 177 (968) ◽  
pp. 27-37 ◽  
Keyword(s):  
Experimental Data ◽  
Special Reference ◽  
Solid Solutions ◽  
Brillouin Zone ◽  
Abrupt Change ◽  
Atomic Radius ◽  
Previous Suggestion ◽  
Interatomic Distances ◽  
The Face ◽  
Metallic Aluminium

The interatomic distances in crystals of alloys cannot be accounted for by assigning a fixed atomic radius to each kind of atom, and the causes of this variation are discussed with special references to the Brillouin zone characteristics of different structures. According to the theory of Jones, the effect of an overlap across the side of a Brillouin zone is to compress the zone at right angles to the face concerned, and so to expand the crystal lattice in the same direction. This expansion is not a property of an atom which can be transferred to any of its alloys, but is a characteristic of a structure with sufficient electrons to produce an overlap. The lattice spacings of alloys of aluminium and indium with copper, silver, gold, and magnesium are examined, and the apparent sizes of the aluminium and indium atoms are discussed, and are shown to be in agreement with the theory. The previous suggestion, that in metallic aluminium the atoms exist in an incompletely ionized state, is improbable, and is no longer required in order to explain the facts. New experimental data for the lattice spacings of solid solutions of aluminium and indium are presented, and these show that, whilst the curves connecting the a parameter with the composition are smooth and continuous, the corresponding curves for the c parameter show an abrupt change in direction at about 0.75 atomic % of indium or aluminium. This is taken to imply that, although in metallic magnesium with two electrons per atom, the overlap of the first Brillouin zone is in the a direction only, the structure is so near to the stage at which the c overlap sets in that the addition of less than one electron per hundred atoms causes the c overlap to take place.

A New Condition of Formation and Stablity of All Crystalline Systems in a Good Agreement with Experimental Data

2015 ◽  
Vol 11 (3) ◽  
pp. 3224-3228
Author(s):  
Tarek El-Ashram
Keyword(s):  
Experimental Data ◽  
Brillouin Zone ◽  
Electron Concentration ◽  
Free Electron ◽  
Lattice Point ◽  
Valence Electron ◽  
Fermi Gas ◽  
Valence Electron Concentration ◽  
Fermi Sphere ◽  
Good Agreement

In this paper we derived a new condition of formation and stability of all crystalline systems and we checked its validity andit is found to be in a good agreement with experimental data. This condition is derived directly from the quantum conditionson the free electron Fermi gas inside the crystal. The new condition relates both the volume of Fermi sphere VF andvolume of Brillouin zone VB by the valence electron concentration VEC as ;𝑽𝑭𝑽𝑩= 𝒏𝑽𝑬𝑪𝟐for all crystalline systems (wheren is the number of atoms per lattice point).

An accidental visualization of the Brillouin zone in an Ni–W alloyviadiffuse scattering

2013 ◽  
Vol 46 (4) ◽  
pp. 1211-1215 ◽  
Author(s):  
Sascha B. Maisel ◽  
Nils Schindzielorz ◽  
Stefan Müller ◽  
Harald Reichert ◽  
Alexei Bosak
Keyword(s):  
Fermi Surface ◽  
Brillouin Zone ◽  
Expansion Method ◽  
Reciprocal Space ◽  
Three Dimensions ◽  
X Rays ◽  
Solid State Physics ◽  
Seitz Cell ◽  
The Face ◽  
The Given

Solid state physics is built on the concept of reciprocal space. The physics of any given periodic crystal is fully defined within the Wigner–Seitz cell in reciprocal space, also known as the first Brillouin zone. It is a purely symmetry-based concept and usually does not have any eye-catching signature in the experimental data, in contrast with some other geometrical constructions like the Fermi surface. However, the particular shape of the Fermi surface of nickel allowed the visualization of the system of edges (skeleton) of the Wigner–Seitz cell of the face-centred cubic lattice in reciprocal space in three dimensions by the diffuse scattering of X-rays from Ni1−xWx(x= 0.03, 0.05, 0.08) single crystals. Employing a cluster-expansion method with first-principles input, it is possible to show that the observed scattering is inherent to the given nickel alloys and the crystal structures they form. This peculiar feature can be understood by considering the shape of the Fermi surface of pure nickel.

THE EFFECT OF COLD ACCLIMATION ON THE SIZE OF ORGANS AND TISSUES OF THE RAT, WITH SPECIAL REFERENCE TO MODES OF EXPRESSION OF RESULTS

1958 ◽  
Vol 36 (2) ◽  
pp. 209-216 ◽  
Author(s):  
O. Heroux ◽  
N. T. Gridgeman
Keyword(s):  
Experimental Data ◽  
Body Weight ◽  
Special Reference ◽  
Cold Acclimation ◽  
Muscle Mass ◽  
Cold Adaptation ◽  
Organ Weight ◽  
Organ Weights ◽  
White Rats ◽  
Body Weights

In experiments in which two groups of animals of different mean body weight are compared, individual organ weights of the animals can be expressed as absolute weights, as fractional weights, or as absolute weights statistically regressed onto constant body weights. The second, and commonest, mode of expression involves the assumption that the part is directly proportional to the whole, and this is shown to be unlikely for all organs except the muscle mass. Practical as well as theoretical justifications for the use of regressed weights (which utilize the actual slope of the line relating the organ weight to the whole) are given.The experimental data are from white rats kept for 4 weeks in a warm (30 °C.) or a cold (6 °C.) environment. It is shown that cold adaptation had no effect on brain, genitals, and lung weights, but that it reduced the growth of muscle, pelt, fat, skeleton, spleen, and thymus, and that it hypertrophied the liver, intestine, kidney, heart, and adrenals. Apparently cold acclimated rats are smaller than the controls mainly because they have a smaller muscle mass.

scholarly journals Carbides and Nitrides of Zirconium and Hafnium

Materials ◽  
2019 ◽  
Vol 12 (17) ◽  
pp. 2728 ◽  
Author(s):  
Sergey V. Ushakov ◽  
Alexandra Navrotsky ◽  
Qi-Jun Hong ◽  
Axel van de Walle
Keyword(s):  
Experimental Data ◽  
Phase Equilibria ◽  
Ab Initio ◽  
Solid Solutions ◽  
Binary Systems ◽  
Experimental Studies ◽  
Published Data ◽  
Oxygen Solubility ◽  
Melting Temperatures ◽  
Ab Initio Computations

Among transition metal carbides and nitrides, zirconium, and hafnium compounds are the most stable and have the highest melting temperatures. Here we review published data on phases and phase equilibria in Hf-Zr-C-N-O system, from experiment and ab initio computations with focus on rocksalt Zr and Hf carbides and nitrides, their solid solutions and oxygen solubility limits. The systematic experimental studies on phase equilibria and thermodynamics were performed mainly 40–60 years ago, mostly for binary systems of Zr and Hf with C and N. Since then, synthesis of several oxynitrides was reported in the fluorite-derivative type of structures, of orthorhombic and cubic higher nitrides Zr3N4 and Hf3N4. An ever-increasing stream of data is provided by ab initio computations, and one of the testable predictions is that the rocksalt HfC0.75N0.22 phase would have the highest known melting temperature. Experimental data on melting temperatures of hafnium carbonitrides are absent, but minimum in heat capacity and maximum in hardness were reported for Hf(C,N) solid solutions. New methods, such as electrical pulse heating and laser melting, can fill the gaps in experimental data and validate ab initio predictions.

Electronic eigenvalues of copper

1953 ◽  
Vol 220 (1143) ◽  
pp. 513-529 ◽  
Keyword(s):  
Brillouin Zone ◽  
Metallic Copper ◽  
Copper Ion ◽  
Wave Functions ◽  
Free Electrons ◽  
Cubic Crystal ◽  
Conduction Electrons ◽  
Energy Gaps ◽  
The Face ◽  
Cellular Method

The cellular method as developed by Howarth & Jones (1952) is applied to the face-centred cubic crystal, and, in particular, the eigenvalues and wave functions of the 3 d and 4 s electrons in metallic copper are obtained for states whose wave vectors lie at the ends of the three- and four-fold axes in the Brillouin zone. The conduction electrons approximate closely to free electrons inside the first Brillouin zone, but the energy gaps at the zone faces are found to be sensitively dependent upon the potential used to represent the copper ion. The eigenvalues of the 3 d band agree closely with Fletcher’s results for nickel, and show a band width of 3·46 eV. An approximate solution of the Hartree equations for the metal shows the top of the d -band to lie 3·7 eV below the Fermi level in the conduction band.

Phonon Dispersion in ZnSe

1972 ◽  
Vol 50 (21) ◽  
pp. 2596-2604 ◽  
Author(s):  
J. C. Irwin ◽  
J. LaCombe
Keyword(s):  
Experimental Data ◽  
Theoretical Model ◽  
Specific Heat ◽  
Single Crystals ◽  
Raman Spectra ◽  
Density Of States ◽  
Brillouin Zone ◽  
Critical Points ◽  
Phonon Dispersion ◽  
Zone Boundary

Second-order Raman spectra have been obtained from oriented single crystals of ZnSe. The spectra have been interpreted and the results have been used to determine the zone boundary frequencies at the critical points X, L, and W. The resulting set of frequencies are consistent with known polarization selection rules and with a theoretical model. The frequencies in turn serve to determine the parameters in the theoretical model and the resulting model has been used to calculate the phonon dispersion throughout the Brillouin zone, the density of states, and the specific heat. The results are compared to the small amount of experimental data that is available.

scholarly journals III . Mathematical contributions to the theory of evolution.—XII. On a generalised Theory of alternative Inheritance, with special reference to Mendel's laws

1904 ◽  
Vol 203 (359-371) ◽  
pp. 53-86 ◽  
Keyword(s):  
Experimental Data ◽  
General Theory ◽  
Special Reference ◽  
Mathematical Theory ◽  
Individual Case ◽  
Experimental Results ◽  
Theory Of Evolution ◽  
Original Theory ◽  
Growing Mass ◽  
Mendel’S Laws

It seems likely to be of interest at the present time to consider rather at length a fairly full mathematical theory of the pure gamete. We do not venture to call this theory a generalised Mendelian theory of inheritance, partly because it is not even the most general theory of the pure gamete conceivable, partly because Mendel’s original theory of heredity was perfectly clear and perfectly simple, and is not the theory here developed. The pure and simple Mendelian theory seems to have been discarded in the light of recent experimental results by more than one Mendelian, both in this country and abroad. The original Mendelian theory has been replaced by what are termed “ Mendelian Principles.” In this aspect of investigation the fundamental principles propounded by Mendel are given up, and for each individual case a pure gamete formula of one kind or another is suggested as describing the facts, This formula is then emphasised, modified or discarded, according as it fits well, badly, or not at all with the growing mass of experimental data. It is quite clear that it is impossible while this process is going on to term anything whatever Mendelian as far as theory is concerned.

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