Effect of gasketing and assembly design: a novel 10/3.5 mm multi-anvil assembly reaching perovskite pressures

A new design of multi-anvil assembly and modified gasket characteristics with octahedron and truncation edge lengths of 10 and 3.5 mm is presented for reaching pressures and temperatures over 24 GPa and 2000 °C, respectively. Partially dehydroxylated pyrophyllite half-gaskets with a tapered design fully nesting the octahedron have been employed to prevent excessive octahedron extrusion between the cubes. The assembly utilizes an axially placed thermocouple through the octahedral center, allowing two samples to be present at identical high P–T conditions on either side of the thermocouple during a run. A third sample can be used as a packing around the thermocouple, so long as that sample is inert with respect to the thermocouple and surrounding material. The temperature gradient within the sample locations has been well characterized using two-pyroxene thermometry in the CaO–MgO–SiO₂ system and numerical modeling calculations. The results indicate a good agreement in gradient shape, although the numerical model appears to under-estimate the magnitude of temperature change. The assembly maintains stable temperatures and provides low failure rates.     

Technology Use in the Teaching of Mathematics and Science in Elementary Schools

Principals from 80 elementary schools, in predominantly rural Western Pennsylvania, completed and returned a 22-item questionnaire designed to assess the nature and extent of technology use for the teaching of elementary mathematics and science within their buildings. Technologies included calculators, microcomputers, overhead projection panels, videotape, and interactive video. Microcomputers were being used in at least some elementary grade levels for mathematics or science instruction in 84% of the schools. Teachers used microcomputers more frequently in mathematics (82.5%) than in science instruction (55%). Principals reported a lower frequency of calculator use with 63.3% of the schools having some grade levels where calculators were used in mathematics lessons, and 21.5% of schools in science lessons. Further analyses of data suggest that microcomputer and calculator use is more common in the intermediate grades (3–6) than in the primary grades (K-2).     

Nonclassical equations of state for critical and tricritical points

We develop a method by which certain classical equations of state may be modified to produce nonclassical critical scaling behavior. We then apply this method to the classical free energy describing a tricritical point that was originally introduced by Griffiths. The phase behavior of the resulting nonclassical free energy is characterized by the competition between critical scaling and tricritical scaling already envisioned by previous authors.Work supported by the National Science Foundation and the Cornell University Materials Science Center.Footnotes 3–10 of Ref. 1 provide a comprehensive list of experimental investigations of tricritical points in fluid mixtures.     

Quantum mechanics without the projection postulate

I show that the quantum state can be interpreted as defining a probability measure on a subalgebra of the algebra of projection operators that is not fixed (as in classical statistical mechanics) but changes with and appropriate boundary conditions, hence with the dynamics of the theory. This subalgebra, while not embeddable into a Boolean algebra, will always admit two-valued homomorphisms, which correspond to the different possible ways in which a set of determinate quantities (selected by and the boundary conditions) can have values. The probabilities defined by (via the Born rule) are probabilities over these two-valued homomorphisms or value assignments. So any universe of interacting systems, including those functioning as measuring instruments, can be modelled quantum mechanically without the projection postulate.     

Bohr-sommerfeld orbits in the moduli space of flat connections and the Verlinde dimension formula

We show how the moduli space of flatSU(2) connections on a two-manifold can be quantized in the real polarization of [15], using the methods of [6]. The dimension of the quantization, given by the number of integral fibres of the polarization, matches the Verlinde formula, which is known to give the dimension of the quantization of this space in a Kähler polarization.Supported in part by MSRI under NSF Grant 85-05550Supported in part by an NSF Graduate fellowship, and by a grant-in-aid from the J. Seward Johnson Charitable TrustSupported in part by NSF Mathematical Sciences Postdoctoral Research Fellowship DMS 88-07291. Address as of January 1, 1993: Department of Mathematics, Columbia University, New York, NY 10027, USA     

Experimental observations of a left-handed material that obeys Snell's law

We measure two-dimensional profiles of collimated microwave beams transmitted through composite wire and split-ring resonator prisms. Prior experiments suggest these structures have a negative index of refraction, though these claims have been questioned. Our 2D measurements demonstrate that transmission obeys Snell's law with a negative index, confirming the refractive nature of this signal and refuting alternatives posed in the criticisms. In addition, we present preliminary evidence that a flat rectangular slab of this material can focus power from a point source.     

New interpretations of XPS spectra of nickel metal and oxides

A current interpretation of XPS spectra of Ni metal assumes that the main 6 eV satellite is due to a two hole c3d⁹4s² (c is a core hole) final state effect. We report REELS observation in AES at low voltages of losses (plasmons and inter-band transitions) corresponding to the satellite structures in Ni metal 2p spectra. The satellite near 6 eV is attributed to a predominant surface plasmon loss. A current interpretation of Ni 2p spectra of oxides and other compounds is based on charge transfer assignments of the main peak at 854.6 eV and the broad satellite centred at around 861 eV to the cd⁹L and the unscreened cd⁸ final-state configurations, respectively (L is a ligand hole). Multiplet splittings have been shown to be necessary for assignment of Fe 2p and Cr 2p spectral profiles and chemical states. The assignments of Ni 2p states are re-examined with intra-atomic multiplet envelopes applied to Ni(OH)₂, NiOOH and NiO spectra. It is shown that the free ion multiplet envelopes for Ni²⁺ and Ni³⁺ simulate the main line and satellite structures for Ni(OH)₂ and NiOOH. Fitting the NiO Ni 2p spectral profile is not as straightforward as the hydroxide and oxyhydroxide. It may involve contributions from inter-atomic, non-local electronic coupling and screening effects with multiplet structures significantly different from the free ions as found for MnO. A scheme for fitting these spectra using multiplet envelopes is proposed.