``Average Energy Approximation'' in Spin‐Coupling Calculations

1960 ◽  
Vol 33 (3) ◽  
pp. 941-942 ◽  
Author(s):  
Martin Karplus
Keyword(s):  
Average Energy ◽  
Spin Coupling ◽  
Energy Approximation

scholarly journals Anisotropic and isotropic triple-dipole dispersion energy coefficients for all three-body interactions involving He, Ne, Ar, Kr, Xe, H2, N2, and CO

1996 ◽  
Vol 74 (6) ◽  
pp. 1180-1186 ◽  
Author(s):  
Sean A.C. McDowell ◽  
Ashok Kumar ◽  
William J. Meath
Keyword(s):  
Input Data ◽  
Average Energy ◽  
Interaction Energies ◽  
Tabular Form ◽  
Rare Gases ◽  
Dispersion Energy ◽  
Interacting Species ◽  
Energy Approximation ◽  
Dipole Oscillator ◽  
Three Body

Formulae for the computation of isotropic and anisotropic dipolar dispersion energy coefficients, for two-body and three-body interactions involving H2, N2, CO, and the rare gases, are presented in an average energy approximation. These coefficients are computed to within 1% of the reliable values for these coefficients, which are obtained by using the relevant dipole oscillator strength distributions, with the exception of a few that are recorded in tabular form. The input data required for these formulae are the isotropic and anisotropic polarizabilities and average energies for the interacting species. The results provide the first reliable anisotropic triple-dipole dispersion energy coefficients for interactions involving molecules. Key words: non-additive, anisotropic, interaction energies, triple-dipole dispersion energies.

ON THE SECOND CRITICAL FIELD FOR A GINZBURG–LANDAU MODEL WITH FERROMAGNETIC INTERACTIONS

2004 ◽  
Vol 16 (02) ◽  
pp. 147-174 ◽  
Author(s):  
STAN ALAMA ◽  
LIA BRONSARD
Keyword(s):  
Magnetic Field ◽  
Critical Field ◽  
Order Parameter ◽  
Upper Critical Field ◽  
Average Energy ◽  
Spin Coupling ◽  
P Wave ◽  
Ginzburg Landau ◽  
Landau Model ◽  
Second Critical Field

We consider a two-dimensional Ginzburg–Landau model for superconductors which exhibit ferromagnetic ordering in the superconducting phase, introduced by physicists to describe unconventional p-wave superconductors. In this model the magnetic field is directly coupled to a vector-valued order parameter in the energy functional. We show that one effect of spin coupling is to increase the second critical field Hc2, the value of the applied magnetic field at which superconductivity is lost in the bulk. Indeed, when the spin coupling is strong we show that the upper critical field is no longer present, confirming predictions in the physics literature. We treat the energy density as a measure, and show that the order parameter converges (as the Ginzburg–Landau parameter κ→∞) in an average sense to a constant determined by the average energy.

The chemical shift. I. Approximate theory and application to first row binary fluorides

1970 ◽  
Vol 48 (22) ◽  
pp. 3498-3503 ◽  
Author(s):  
F. G. Herring
Keyword(s):  
Perturbation Theory ◽  
Chemical Shift ◽  
Chemical Shifts ◽  
Average Energy ◽  
Approximate Theory ◽  
Hartree Fock ◽  
Nuclear Shielding ◽  
Energy Approximation

Starting from the approximations of the i.n.d.o.-l.c.a.o.-s.c.f. method and using approximate Hartree–Fock perturbation theory, a method has been developed whereby the nuclear shielding of a nucleus for a first row element may be estimated. The method avoids the use of the average energy approximation. The method is demonstrated by calculating the 19F chemical shifts in the first row binary fluorides relative to the fluorine molecule.

Article

1998 ◽  
Vol 76 (4) ◽  
pp. 483-489 ◽  
Author(s):  
Sean AC McDowell ◽  
W J Meath
Keyword(s):  
Average Energy ◽  
Rare Gases ◽  
Dispersion Energy ◽  
Interacting Species ◽  
Energy Approximation ◽  
Three Body

Average energy approximations for the anisotropic triple-dipole dispersion energy coefficients are tested using reliable results for these coefficients, which are available for all interactions involving the rare gases, H2, N2, CO, O2, and NO. The original average energy approximation does not reproduce any of the anisotropic coefficients to within their estimated uncertainties. More recently derived average energy approximation formulae, requiring the isotropic and anisotropic polarizabilities and average energies for the interacting species as input, reproduce all but 69 of the 680 isotropic and anisotropic coefficients considered to within their estimated uncertainties.Key words: nonadditive, three-body interactions, dispersion energies.

Stopping-power determination for compound by EELS

1994 ◽  
Vol 52 ◽  
pp. 948-949 ◽  
Author(s):  
David C. Joy ◽  
Suichu Luo ◽  
John R. Dunlap ◽  
Dick Williams ◽  
Siqi Cao
Keyword(s):  
Energy Loss ◽  
Electron Energy ◽  
Electron Energy Loss Spectroscopy ◽  
Materials Science ◽  
Average Energy ◽  
Stopping Power ◽  
Accurate Information ◽  
Power Calculation ◽  
Coulomb Collisions ◽  
Electron Energy Loss

In Physics, Chemistry, Materials Science, Biology and Medicine, it is very important to have accurate information about the stopping power of various media for electrons, that is the average energy loss per unit pathlength due to inelastic Coulomb collisions with atomic electrons of the specimen along their trajectories. Techniques such as photoemission spectroscopy, Auger electron spectroscopy, and electron energy loss spectroscopy have been used in the measurements of electron-solid interaction. In this paper we present a comprehensive technique which combines experimental and theoretical work to determine the electron stopping power for various materials by electron energy loss spectroscopy (EELS ). As an example, we measured stopping power for Si, C, and their compound SiC. The method, results and discussion are described briefly as below.The stopping power calculation is based on the modified Bethe formula at low energy:where Neff and Ieff are the effective values of the mean ionization potential, and the number of electrons participating in the process respectively. Neff and Ieff can be obtained from the sum rule relations as we discussed before3 using the energy loss function Im(−1/ε).

Calculation of many-beam dynamic electron diffraction without high-energy approximation

1996 ◽  
Vol 54 ◽  
pp. 128-129
Author(s):  
B. R. Ahn ◽  
N. J. Kim
Keyword(s):  
Electron Diffraction ◽  
Flat Surface ◽  
Dynamic Theory ◽  
High Energy ◽  
Perfect Crystal ◽  
Zone Axis ◽  
Beam Dynamic ◽  
Diffraction Angle ◽  
Energy Approximation ◽  
The Many

High energy approximation in dynamic theory of electron diffraction involves some intrinsic problems. First, the loss of theoretical strictness makes it difficult to comprehend the phenomena of electron diffraction. Secondly, it is difficult to believe that the approximation is reasonable especially in the following cases: 1) when accelerating voltage is not sufficiently high, 2) when the specimen is thick, 3) when the angle between the surface normal of the specimen and zone axis is large, and 4) when diffracted beam with large diffraction angle is included in the calculation. However, until now the method to calculate the many beam dynamic electron diffraction without the high energy approximation has not been proposed. For this reason, the authors propose a method to eliminate the high energy approximation in the calculation of many beam dynamic electron diffraction. In this method, a perfect crystal with flat surface was assumed. The method was applied to the calculation of [111] zone axis CBED patterns of Si.

{10} edge dislocations in YSZ films grown on (100)MgO by PLD

1994 ◽  
Vol 52 ◽  
pp. 530-531
Author(s):  
Jason R. Heffelfinger ◽  
C. Barry Carter
Keyword(s):  
Thin Films ◽  
Semiconductor Lasers ◽  
Vapor Deposition ◽  
Substrate Surface ◽  
Laser System ◽  
Average Energy ◽  
Target Material ◽  
Chemical Vapor ◽  
Buffer Layers ◽  
Organic Chemical

Yttria-stabilized zirconia (YSZ) is currently used in a variety of applications including oxygen sensors, fuel cells, coatings for semiconductor lasers, and buffer layers for high-temperature superconducting films. Thin films of YSZ have been grown by metal-organic chemical vapor deposition, electrochemical vapor deposition, pulse-laser deposition (PLD), electron-beam evaporation, and sputtering. In this investigation, PLD was used to grow thin films of YSZ on (100) MgO substrates. This system proves to be an interesting example of relationships between interfaces and extrinsic dislocations in thin films of YSZ.In this experiment, a freshly cleaved (100) MgO substrate surface was prepared for deposition by cleaving a lmm-thick slice from a single-crystal MgO cube. The YSZ target material which contained 10mol% yttria was prepared from powders and sintered to 85% of theoretical density. The laser system used for the depositions was a Lambda Physik 210i excimer laser operating with KrF (λ=248nm, 1Hz repetition rate, average energy per pulse of 100mJ).

Vibrational and thermal averaging of the indirect nuclear spin-spin coupling constants of CH4, SiH4, GeH4 and SnH4

1997 ◽  
Vol 91 (5) ◽  
pp. 897-907 ◽  
Author(s):  
SHEELA KIRPEKAR ◽  
THOMAS ENEVOLDSEN ◽  
JENS ODDERSHEDE ◽  
WILLIAM RAYNES
Keyword(s):  
Nuclear Spin ◽  
Coupling Constants ◽  
Spin Coupling ◽  
Spin Coupling Constants ◽  
Spin Spin Coupling
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