Spin-Up-Spin-Down Pair Distribution Function at Metallic Densities

1972 ◽  
Vol 50 (15) ◽  
pp. 1756-1763 ◽  
Author(s):  
B. B. J. Hede ◽  
J. P. Carbotte
Keyword(s):  
Distribution Function ◽  
Kinetic Energy ◽  
Potential Energy ◽  
Born Approximation ◽  
Pair Distribution Function ◽  
Short Range ◽  
Electron Gas ◽  
Scattering Effects ◽  
Wide Range ◽  
Short Range Correlations

Correlations in an electron gas are particularly important at metallic densities because the potential energy cannot be ignored in comparison with the kinetic energy; in particular, interactions are not weak as r → 0, so that a simple Born approximation does not hold in this limit. Short-range correlations between oppositely-spinned electrons can be accounted for by an infinite series of particle–particle ladder diagrams. It leads to a Bethe–Goldstone type of equation which can be solved by an angle-averaged approximation. The resultant spin-up-down p.d.f. is positive over a wide range of metallic densities. A further correction by including particle–hole scattering effects changes the previous results only slightly.

scholarly journals Total scattering and pair distribution function analysis in modelling disorder in PZN (PbZn1/3Nb2/3O3)

IUCrJ ◽  
2016 ◽  
Vol 3 (1) ◽  
pp. 20-31 ◽  
Author(s):  
Ross E. Whitfield ◽  
Darren J. Goossens ◽  
T. Richard Welberry
Keyword(s):  
Distribution Function ◽  
Diffuse Scattering ◽  
Pair Distribution Function ◽  
Short Range ◽  
Function Analysis ◽  
Qualitative Comparison ◽  
Total Scattering ◽  
Local Ordering ◽  
Pdf Analysis ◽  
Short Range Correlations

The ability of the pair distribution function (PDF) analysis of total scattering (TS) from a powder to determine the local ordering in ferroelectric PZN (PbZn1/3Nb2/3O3) has been explored by comparison with a model established using single-crystal diffuse scattering (SCDS). While X-ray PDF analysis is discussed, the focus is on neutron diffraction results because of the greater extent of the data and the sensitivity of the neutron to oxygen atoms, the behaviour of which is important in PZN. The PDF was shown to be sensitive to many effects not apparent in the average crystal structure, including variations in the B-site—O separation distances and the fact that 〈110〉 Pb2+ displacements are most likely. A qualitative comparison between SCDS and the PDF shows that some features apparent in SCDS were not apparent in the PDF. These tended to pertain to short-range correlations in the structure, rather than to interatomic separations. For example, in SCDS the short-range alternation of the B-site cations was quite apparent in diffuse scattering at (½ ½ ½), whereas it was not apparent in the PDF.

scholarly journals Genetic algorithm for the pair distribution function of the electron gas

2011 ◽  
Vol 3 (4) ◽  
pp. 283-289 ◽  
Author(s):  
Fernando Vericat ◽  
César O. Stoico ◽  
C. Manuel Carlevaro ◽  
Danilo G. Renzi
Keyword(s):  
Genetic Algorithm ◽  
Distribution Function ◽  
Pair Distribution Function ◽  
Electron Gas

Obtaining structural information from the atomic pair distribution function

2004 ◽  
Vol 219 (3) ◽  
Author(s):  
Thomas Proffen ◽  
Katharine L. Page
Keyword(s):  
Distribution Function ◽  
Atomic Structure ◽  
Pair Distribution Function ◽  
Short Range ◽  
Structural Information ◽  
Atomic Pair Distribution Function ◽  
Atomic Pair ◽  
Medium Range ◽  
Macroscopic Properties ◽  
Modelling Techniques

AbstractThe knowledge of the detailed atomic structure of modern materials is the key to understanding the their macroscopic properties. The atomic pair distribution function (PDF) reveals short-range and medium-range structural information. In this paper we present an overview of refinement and modelling techniques. In short, we will be trying to answer the question: What can I learn from my PDF?

scholarly journals Energy of Midlatitude Transient Eddies in Idealized Simulations of Changed Climates

2008 ◽  
Vol 21 (22) ◽  
pp. 5797-5806 ◽  
Author(s):  
Paul A. O’Gorman ◽  
Tapio Schneider
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Radiative Forcing ◽  
General Circulation ◽  
Thermal Structure ◽  
Circulation Model ◽  
Static Stability ◽  
Eddy Kinetic Energy ◽  
Available Potential Energy ◽  
Wide Range

Abstract As the climate changes, changes in static stability, meridional temperature gradients, and availability of moisture for latent heat release may exert competing effects on the energy of midlatitude transient eddies. This paper examines how the eddy kinetic energy in midlatitude baroclinic zones responds to changes in radiative forcing in simulations with an idealized moist general circulation model. In a series of simulations in which the optical thickness of the longwave absorber is varied over a wide range, the eddy kinetic energy has a maximum for a climate with mean temperature similar to that of present-day earth, with significantly smaller values both for warmer and for colder climates. In a series of simulations in which the meridional insolation gradient is varied, the eddy kinetic energy increases monotonically with insolation gradient. In both series of simulations, the eddy kinetic energy scales approximately linearly with the dry mean available potential energy averaged over the baroclinic zones. Changes in eddy kinetic energy can therefore be related to the changes in the atmospheric thermal structure that affect the mean available potential energy.

Temperature dependence of short-range correlations in the homogeneous electron gas

1991 ◽  
Vol 44 (24) ◽  
pp. 13291-13297 ◽  
Author(s):  
Herwig K. Schweng ◽  
Helga M. Böhm ◽  
Andreas Schinner ◽  
Wilhelm Macke
Keyword(s):  
Temperature Dependence ◽  
Short Range ◽  
Electron Gas ◽  
Short Range Correlations
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