Graphene's structure bears on both the material's electronic properties and fundamental questions about long range order in two-dimensional crystals. We present an analytic calculation of selected area electron diffraction from multi-layer graphene and compare it with data from samples prepared by chemical vapor deposition and mechanical exfoliation. A single layer scatters only 0.5% of the incident electrons, so this kinematical calculation can be considered reliable for five or fewer layers. Dark-field transmission electron micrographs of multi-layer graphene illustrate how knowledge of the diffraction peak intensities can be applied for rapid mapping of thickness, stacking, and grain boundaries. The diffraction peak intensities also depend on the mean-square displacement of atoms from their ideal lattice locations, which is parameterized by a Debye-Waller factor. We measure the Debye-Waller factor of a suspended monolayer of exfoliated graphene and find a result consistent with an estimate based on the Debye model. For laboratory-scale graphene samples, finite size effects are sufficient to stabilize the graphene lattice against melting, indicating that ripples in the third dimension are not necessary.

[1] Pulsar detection and timing experiments are applications where adaptive filters seem eminently suitable tools for radio frequency interference (RFI) mitigation. We describe a novel variant which works well in field trials of pulsar observations centered on an observing frequency of 675 MHz and a bandwidth of 64 MHz and with 2-bit sampling. Adaptive filters have generally received bad press for RFI mitigation in radio astronomical observations with their most serious drawback being a spectral echo of the RFI embedded in the filtered signals. Pulsar observations are intrinsically less sensitive to this as they operate in the (pulsar period) time domain. The field trials have allowed us to identify those issues which limit the effectiveness of the adaptive filter. We conclude that adaptive filters can significantly improve pulsar observations in the presence of RFI.

The high-temperature neutron diffraction measurements of UO 2 and CaF 2 made recently by Willis are examined by means of the generalized formulation of the structure factor which recognizes the antisymmetric properties of atoms occupying non-centrosymmetric lattice sites. Numerical analysis of the neutron data in terms of an anharmonic vibration formalism developed for effective one-particle potential fields of the type V j (r) = V 0 , j + ½ α j ( x 2 + y 2 + z 2 ) + β j xyz + quartic terms shows that certain unusual features of the observations are readily accounted for by the antisymmetric ( β ) components associated with the tetrahedral point symmetry of the anionic sites. Values are derived for the α j and β j parameters in both UO 2 and CaF 2 , and their ability to reproduce the experimental observations over a wide range of elevated temperature is demonstrated. The parameters derived for CaF 2 are compared with theoretical estimates obtained from an Einstein-type model of the vibrating lattice, using the various expressions for the interionic interaction in fluorite that have been proposed by Benson & Dempsey. Despite evident limitations in this model, it is possible to conclude that the Pauling radii for Ca 2+ and F - cannot reproduce the physical behaviour of this system.

In order to test recently predicted ballistic nanofriction (ultra-low drag and enhanced lubricity) of gold nanocrystals on graphite at high surface speeds, we use the quartz microbalance technique to measure the impact of deposition of gold nanocrystals on graphene. We analyze our measurements of changes in frequency and dissipation induced by nanocrystals using a framework developed for friction of adatoms on various surfaces. We find the lubricity of gold nanocrystals on graphene to be even higher than that predicted for the ballistic nanofriction, confirming the enhanced lubricity predicted at high surface speeds. Our complementary molecular dynamics simulations indicate that such high lubricity is due to the interaction strength between gold nanocrystals and graphene being lower than previously assumed for gold nanocrystals and graphite.