We report the first observation of Bragg scattering of sodium atoms from a standing light wave. We also present a theory which quantitatively predicts the amplitude of the various Bragg orders as a function of the light's detuning and power, and the interaction time. The analog of the Pendello'sung eff'ect, previously observed in Bragg scattering of neutrons from crystals, is predicted and qualitatively observed for first-order Bragg scattering of atoms from a standing light wave PACS numbers: 42.50.Vk Bragg scattering of x rays from crystal planes was demonstrated by W. H. Bragg and his son W. L. Bragg in 1912, in a series of experiments' which won them a Nobel prize in 1915. Bragg scattering of neutron de Broglie waves from crystal planes was first observed in 1946, leading to the Geld of neutron interferometry. This Letter presents the first experimental observation of Bragg scattering of atoms from a standing light wave.This observation provides a beautiful example of the complementarity of particles and waves in that we treat the atomic beam as a wave and the intensity maxima of the standing light wave as crystal planes. Our observation also represents a breakthrough in the coherent manipulation of atoms, completing the technology necessary to construct an atomic interferometer (i.e. , one which acts by interference of atomic-matter waves). Momentum transfer to atoms by light in the absence of spontaneous emission results from an interaction of the induced dipole moment of the atom with the field gradient of the standing light wave. Quantum mechanically, the atom trades a photon via absorption and stimulated emission between the counterpropagating traveling waves which compose the standing light wave, thus gaining momentum in discrete units of 26k, along the k vector of the standing light wave. One can also view this phenomenon as diffraction of an atomic de Broglie wave (Ada =It/p) from the intensity grating (periodicity dl;sbt A, l;sbt/2) of the standing light wave. Thus, constructive interference occurs at discrete angles given by p=kdtt/dl;sh, which again results in momentum transfer to the atom in discrete units of 26k.The difference between Bragg scattering, in which the atoms scatter mainly into one order (i.e. , final momentum state), and the previously observed Kapitza-Dirac scattering, in which a large number of momentum states are populated, results from energy-momentum conservation. The absorption and stitnulated emission of photon pairs changes the momentum but not the laboratory kinetic energy of the atom. The final momentum vectors must lie on a circle of radius p; in momentum space as shown in Fig. 1. The focused waist of a Gaussian light beam has a minimum Heisenberg uncertainty 50'. QW 5mm / P I FIG. l. Comparison of Kapitza-Dirac and Bragg scattering. A tightly focused waist (left) has a large angular uncertainty in the direction of its photons, thus allowing energy conservation for many final momentum states pf -this is the Kapitza-Dirac regime.The observation of Bragg scattering requires...

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This article is concerned with understanding the behavior of polyethylene terephthalate (PET) in the injection stretch blow molding (ISBM) process where it is typically biaxially stretched to form bottles for the packaging industry. A comprehensive experimental study was undertaken, analyzing the behavior of three different grades of PET under constant width (CW), simultaneous (EB), and sequential (SQ) equal biaxial deformation. Experiments were carried out at temperature and strain rate ranges of 80-1108C and 1 s 21 to 32 s 21 , respectively, to different stretch ratios. Results show that the biaxial deformation behavior of PET exhibits a strong dependency on forming temperature, strain rate, stretch ratio, deformation mode, and molecular weight. The tests were also monitored via a high speed thermal image camera which showed an increase in temperature between 58C and 158C depending on the stretch conditions. POLYM. ENG. SCI., FIG. 14. Average surface temperature of PET specimen (calculated from within the boxed area) following EB deformation at 908C and a strain rate of 16 s 21 to a stretch ratio of 3. (a) Before the deformation is conducted. (b) After the deformation is stopped.

During free surface moulding processes such as thermoforming and blow moulding, heated polymer materials are subjected to rapid biaxial deformation as they are drawn into the shape of a mould. In the development of process simulations, it is therefore essential to be able to accurately measure and model this behaviour. Conventional uniaxial test methods are generally inadequate for this purpose and this has led to the development of specialised biaxial test rigs. In the present study, the results of several programmes of biaxial tests conducted at Queen's University are presented and discussed. These have included tests on high impact polystyrene (HIPS), polypropylene (PP) and aPET, and the work has involved a wide variety of experimental conditions. In all cases, the results clearly demonstrate the unique characteristics of materials when subjected to biaxial deformation. PP draws the highest stresses and it is the most temperature-sensitive of the materials. aPET is initially easier to form but exhibits strain hardening at higher strains. This behaviour is increased with increasing strain rate but at very high strain rates, these effects are increasingly mollified by adiabatic heating. Both aPET and PP (to a lesser degree) draw much higher stresses in sequential stretching showing that this behaviour must be considered in process simulations. HIPS showed none of these effects and it is the easiest material to deform.

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