Mössbauer studies of the irradiation effects of Y1.6Ca1.4V0.45Sn0.5Fe4.05O12

Y_1.6Ca_1.4V_0.45Sn_0.5Fe_4.05O₁₂ has been bombarded with a 0.56 GeV C⁶⁺ ion beam. The vacancies and vacancy clusters induced by the irradiation change the directions of hyperfine fields around the defects. The reduction of the magnetic hyperfine field is caused by the lower superexchnage field due to the formation of the O^2– vacancies. The change of direction of the hyperfine field has also been observed in Mössbauer spectra. X-ray diffraction showed that the defects give rise to an increase of the lattice constant of the samples.     

New forms of the INAA advance prediction computer program

The development and experimental testing of a new instrumental neutron activation analysis (INAA) Advance Prediction Computer Program (APCP) is described for activation by high-intensity, short-duration reactor pulses. Also presented are the results of extensive experimental testing of the APCP for epithermal INAA. Brief mention is made of other forms of the APCP not yet completed, but in various stages of development.     

Two theorems on integral matrices

The following two results are proved: (1) For a positive definite integral symmetric matrix S of rank (S) < 7 or when rank (S) = 8, S has an odd entry in its diagonal, there is an integral matrix A satisfying AA^t = Sif there is a rational matrix R with RR^t = S (2) Given an integral matrix A of size r×n such that AA^t = mI_r there is then always an integral completion matrix B of size n×n satisfying BB^t = mI_r whenever n-r is less than or equal to 7. This threshold number 7 is the best possible. (Here m, n satisfy the obvious necessary conditions.)     

Capillary induced self-assembly of thin foils into 3Dstructures

Self-assembly of complex structures is common in nature. Self-assembly principles provide a promising way to fabricate three-dimensional, micro- or millimeter scale devices. In the present paper, we present a generalized analytical study of the self-folding of thin plates into deterministic 3D shapes through fluid-solid interactions. Based on the beam theory, a mechanics model is developed, incorporating the two competing components—a capillary force promoting folding and the bending rigidity of the foil that resists folding into a 3D structure. Through an equivalence argument of thin foils of different geometry, an effective folding parameter, which uniquely characterizes the driving force for folding, has been identified. A criterion for spontaneous folding of any shaped 2D patterned foil based on the effective folding parameter is thus established. The model predictions show excellent agreement with experimental measurements made on a variety of materials, indicating that the assumptions used in the analysis arevalid.     

Theoretical study of the bonding in Fe---M dimers

The electronic structures of Fe₂, FeMn, FeCo, FeCu and FeNi have been calculated using Gaussian-76 SCF techniques. Gaussian basis sets contracted to [4s, 2p, 1d] functions are used on each atom resulting in sets of near double zeta accuracy in the valence region. The calculated UHF electronic ground state configurations for these Fe---M dimers are comparable with those experimentally determined. By examining the Mulliken atomic overlap population analysis, a correlation is found between the Mössbauer spectrum and calculated binding strengths in these dimers. Our calculations, fixed at r_e of 2.3 Å, show that the binding strengths decrease from FeCu, FeMn, Fe₂, FeCo, FeNi.     

Studies of archaeological problems by Mössbauer spectroscopy

The recent developments and achievements of the application of Mössbauer spectroscopy to archaeological problems are reviewed. The relevances of Mössbauer spectroscopy in studies of provenance, manufacturing technology and age dating of ancient pottery, as well as the ancient bronzes are discussed.     

Closure of Periodic Points Over a Non-Archimedean Field

The closure of the periodic points of rational maps over a non-archimedeanfield is studied. An analogue of Montel's theorem over non-archimedeanfields is first proved. Then, it is shown that the (nonempty)Julia set of a rational map over a non-archimedean field iscontained in the closure of the periodic points.     

Results concerning composition of sums of three squares

Pairs of integers a, bwhich are sums of 3 squares and for which a bhas the same property are studied. Contributions to two problems in which such pairs occur are obtained.