Portable pop-up spectroscope Phys. Teach. 50, 443 (2012) Video-based spatial portraits of a nonlinear vibrating string Am. J. Phys. 80, 862 (2012) Analyzing simple pendulum phenomena with a smartphone acceleration sensor Graphite sheets are commonly used in introductory physics laboratories to model electric potential patterns for systems such as dipoles and parallel plates. Usually, silvered ink pens are used to draw patterns on the sheets and appropriate voltages are then applied. Quantitative experiments are often done at the intermediate level. Students are often puzzled by the failure of the patterns to confirm to the theoretical figure in the manual that came with the kit. I discuss measuring difficulties and some of the common theoretical methods for analyzing edge effects on the sheets.
The elastic properties, including elastic constants, bulk, and shear moduli, and anisotropic index of hexagonal Mg x Ti 1−x B 2 (0 x 1) are obtained using a first-principles density-functional-theory method. A difference in chemical bonding occurs between Ti-rich and Mg-rich diborides, leading to significantly different elastic properties: a small elastic anisotropy with relatively large bulk and shear moduli for Ti-rich diborides with x < 0.25, and a large elastic anisotropy and relatively small bulk and shear moduli for Mg-rich diborides with x > 0.25. The calculated results reveal a dominant role of the interplanar metal-metal bonds in predicting the extent of shear elastic anisotropy in Mg x Ti 1−x B 2 (0 x 1).
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