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Brigham Young University

Astrophysics and Astronomy

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Full-Text Articles in Physical Sciences and Mathematics

Model Of Electron Correlation In Solids, Everett G. Larson, Walter R. Thorson Sep 1966

Model Of Electron Correlation In Solids, Everett G. Larson, Walter R. Thorson

Faculty Publications

The usual Hartree-Fock model (energy-band theory) does not always give an adequate description of electronic structure in a solid, because it ignores the effects of electron correlation. It was shown first by Wigner that such a situation always develops in an electron ''gas'' at sufficiently low density; a solid structure described by ''resonance'' of Heitler-London pair bonds between electrons localized on neighboring atoms is then a good model of the system.The transition from a Bloch-type state to such a highly correlated state as a function of electron density (lattice parameter) is a problem of considerable interest for the theory of …

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Pressure Calibration To 100 Kbar Based On The Compression Of Nacl, R. N. Jeffrey, J. Dean Barnett, H. B. Vanfleet, H. Tracy Hall Jul 1966

Pressure Calibration To 100 Kbar Based On The Compression Of Nacl, R. N. Jeffrey, J. Dean Barnett, H. B. Vanfleet, H. Tracy Hall

Faculty Publications

An independent determination has been made of the transformation pressures assigned to the high-pressure transformations in Ba and Bi which are generally used for calibration points. The metals were imbedded in NaCl, and the transitions were detected by the resistance change of the metal while the NaCl lattice parameter was simultaneously measured by x-ray diffraction. The NaCl compression values determined at the fixed points were related to pressure by reference to the semiempirical compression curve of Decker. The Ba I-II and Bi III-V transformations at room temperature were assigned thermodynamic equilibrium values of 53.3 ±1.2 kbar and 73.8 ±1.3 kbar, …

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X-Ray Diffraction Studies On Tin To 100 Kilobars, J. Dean Barnett, Vern E. Bean, H. Tracy Hall Feb 1966

X-Ray Diffraction Studies On Tin To 100 Kilobars, J. Dean Barnett, Vern E. Bean, H. Tracy Hall

Faculty Publications

The high-pressure equilibrium phase diagram of tin is investigated, and the crystal structure of Sn II at 98 kbar and 25degrees C is shown to be body-centered tetragonal with a=3.70 Angstroms, c=3.37 Angstroms, c/a=0.91, and with two atoms per unit cell. The linear compressibility of white tin is given at 25degrees C up to the high-pressure transformation at 92 kbar, and the latent heat of the transformation is measured as 225 cal/g-atom.

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Equation Of State Of Nacl And Its Use As A Pressure Gauge In High-Pressure Research, Daniel L. Decker Jan 1965

Equation Of State Of Nacl And Its Use As A Pressure Gauge In High-Pressure Research, Daniel L. Decker

Faculty Publications

The pressure as a function of lattice parameter and temperature has been calculated for NaCl over a pressure range of 0 to 500 kbar for temperatures between 0degrees and 1500degrees C. The calculation used the Mie-Gruneisen equation of state with Born-Mayer type repulsion terms between first and second nearest neighbors. The Gruneisen constant was expanded about its value at room temperature and atmospheric pressure; the first coefficient in the expansion being evaluated by forcing the calculated thermal expansion at atmospheric pressure to fit the experimental results of Enck. The two empirical parameters in the repulsion terms were evaluated using the …

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Diffraction Of Spherical Scalar And Vector Waves At Axial Points Of A Circular Aperture And Disk, Keith Leon Mcdonald Jun 1962

Diffraction Of Spherical Scalar And Vector Waves At Axial Points Of A Circular Aperture And Disk, Keith Leon Mcdonald

Faculty Publications

The following work treats Kottler's saltus problem of diffraction of electromagnetic waves emitted by a Hertzian oscillator source and the analogous Kirchhoff's scalar problem of waves emitted by a point source. The medium is a homogeneous isotropic dielectric. In the vector case a new exact solution of the basic integrals is presented, at axial points only, (a) behind a circular aperture in a "black'' screen, and (b) behind its complementary "black'' disk. The relative time-averaged intensity of energy flow is plotted for the disk only. It is shown that the scalar theory predicts considerably larger values than the electromagnetic theory …

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A Note On K-Commutative Matrices, D. W. Robinson Nov 1961

A Note On K-Commutative Matrices, D. W. Robinson

Faculty Publications

Let A and B be square matrices over a field in which the minimum polynomial of A is completely reducible. It is shown that A is k commutative with respect to B for some non-negative integer k if and only if B commutes with every principal idempotent of A. The proof is brief, simplifying much of the previous study of k-commutative matrices. The result is also used to generalize some well-known theorems on finite matrix commutators that involve a complex matrix and its transposed complex conjugate.

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