436,175 research outputs found
Pairwise transitive 2-designs
We classify the pairwise transitive 2-designs, that is, 2-designs such that a
group of automorphisms is transitive on the following five sets of ordered
pairs: point-pairs, incident point-block pairs, non-incident point-block pairs,
intersecting block-pairs and non-intersecting block-pairs. These 2-designs fall
into two classes: the symmetric ones and the quasisymmetric ones. The symmetric
examples include the symmetric designs from projective geometry, the 11-point
biplane, the Higman-Sims design, and designs of points and quadratic forms on
symplectic spaces. The quasisymmetric examples arise from affine geometry and
the point-line geometry of projective spaces, as well as several sporadic
examples.Comment: 28 pages, updated after review proces
Vibrational entropy of L12 Cu3Au measured by inelastic neutron scattering
The phonon density of states of elemental Au, Cu, and Cu3Au with L12 chemical order were measured by inelastic neutron scattering and used to calculate the vibrational entropy of formation of the ordered compound from the elemental metals. A vibrational entropy of formation of (0.06±0.03) kB/atom at 300 K was obtained, with the vibrational entropy of the ordered alloy being larger than that of the elemental metals. The phonon DOS of the disordered Cu3Au was simulated by adding the phonon DOS curves of fcc Cu, L12 Cu3Au, and fcc Au to match the numbers of first-nearest-neighbor pairs in a disordered alloy. The vibrational entropy obtained with this simulated DOS disagrees with calorimetric data and theoretical estimates, indicating that the phonon DOS of disordered Cu3Au depends on chemical order at spatial lengths larger than is set by first-nearest-neighbor pairs
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