Bloch wave symmetries in electron diffraction: applications to Friedels law, Gjonnes-Moodie lines and refraction at interfaces.

We classify the point symmetries at the different points in the Brillouin zone for the 17 two-dimensional space groups and the symmetries of the Bloch waves for the 10 two-dimensional crystallographic point groups. Simple examples involving breakdown of Friedels law, Gjonnes-Moodie lines, and reflection and refraction at interfaces are presented.

Comparison of the electronic structure of a thermoelectric skutterudite before and after adding rattlers: an electron energy loss study.

Skutterudites, with rattler atoms introduced in voids in the crystal unit cell, are promising thermoelectric materials. We modify the binary skutterudite with atomic content Co(8)P(24) in the cubic crystal unit cell by adding La as rattlers in all available voids and replacing Co by Fe to maintain charge balance, resulting in La(2)Fe(8)P(24). The intention is to leave the electronic structure unaltered while decreasing the thermal conductivity due to the presence of the rattlers. We compare the electronic structure of these two compounds by studying the L-edges of P and of the transition elements Co and Fe using electron energy loss spectroscopy (EELS). Our studies of the transition metal white lines show that the 3d electron count is similar for Co and Fe in these compounds. As elemental Fe has one electron less than Co, this supports the notion that each La atom donates three electrons. The L-edges of P in these two skutterudites are quite similar, signalling only minor differences in electronic structure. This is in reasonable agreement with density functional theory (DFT) calculations, and with our multiple scattering FEFF calculations of the near edge structure. However, our experimental plasmon energies and dielectric functions deviate considerably from predictions based on DFT calculations.

A quantitative study of valence electron transfer in the skutterudite compound CoP(3) by combining x-ray induced Auger and photoelectron spectroscopy.

We use the sum of the ionization and Auger energy, the so-called Auger parameter, measured from the x-ray photoelectron spectrum, to study the valence electron distribution in the skutterudite CoP(3). The electron transfer between Co and P was estimated using models relating changes in Auger parameter values to charge transfer. It was found that each P atom gains 0.24 e(-), and considering the unit formula CoP(3) this is equivalent to a donation of 0.72 e(-) per Co atom. This is in agreement with a recent electron energy-loss spectroscopy study, which indicates a charge transfer of 0.77 e(-)/atom from Co to P.

A unique determination of boundary condition in quantitative electron diffraction: Application to accurate measurements of mean inner potentials.

We combine off-axis electron holography and electron shadow imaging to accurately determine the specimen thickness and the incident electron beam direction over the illuminated area of a crystal. We, furthermore, quantify the variations in diffraction intensity with position over the same area. This unique solution to the experimental boundary condition problem enables us to make precise measurements of mean inner electrostatic potentials and structure factors that are sensitive to the bonding characteristics of materials. In this paper, we present the results of mean-inner potential determination from silicon and the newly discovered magnesiumdiboride superconductor.

Determination of the crystal structure of the pi-AlFeMgSi phase using symmetry- and site-sensitive electron microscope techniques.

The crystal structure of the complex pi-AlFeMgSi phase, which was previously thought to have the composition Al(8)FeMg(3)Si(6), has been investigated. Microprobe analysis revealed that the phase has a different composition, Al(9)FeMg(3)Si(5). The space group was determined and confirmed to be P62m with the use of parallel-beam electron diffraction (SAD) and convergent-beam electron diffraction (CBED). Owing to symmetry considerations the elements within the unit cell had to be rearranged. The rearrangement was confirmed using electron channelling. The z parameters of the elements were refined by examining the intensities from high-angle convergent-beam electron diffraction. Finally, the x parameters were adjusted slightly to arrive at acceptable interatomic distances.

Accurate measurements of valence electron distribution and interfacial lattice displacement using quantitative electron diffraction.

We developed a novel electron-diffraction technique by focusing a small probe above (or below) the sample in an electron microscope to measure charge density and lattice displacement in technologically important materials. The method features the simultaneous acquisition of shadow images within many Bragg reflections, resulting in parallel recording of dark-field images (PARODI). Because it couples diffraction with images, it is thus suitable for studying crystals as well as their defects. We used this technique to accurately locate the charge-carrying holes in superconducting crystals, and to determine displacement vectors across planar faults by comparing the experiments with calculations, and by using fitting and error analyses. Examples are given for complex YBa2Cu3O7 and Bi2Sr2CaCu2O8+delta oxides and the newly discovered MgB2 superconductor.

Unraveling the symmetry of the hole states near the Fermi level in the MgB2 superconductor.

We use x-ray absorption spectroscopy (XAS) and electron energy loss spectroscopy (EELS) to study the fine structure at the K edge of boron in MgB(2). We observe in XAS a peak of width 0.7 eV at the edge threshold, signaling a narrow energy region with empty boron p states near the Fermi level. The changes in the near edge structure observed in EELS with direction of the momentum transfer imply that these states have p(x)p(y) symmetry. Our observations are consistent with electronic structure calculations indicating a narrow energy window of empty p(x)p(y) states that falls to zero at 0.8 eV above the Fermi level. The disappearance of the p(x)p(y) feature in EELS at grain boundaries suggests that this signature may become powerful in probing superconductivity at nanoscale.

A novel shadow-imaging technique to measure charge distribution and lattice displacement.

We developed a novel shadow-imaging diffraction technique, using both non-coherent and coherent sources, based on parallel recording of diffraction intensity of many reflections to measure charge distribution and lattice displacement in crystals and in defects. Applying the method to Bi2Sr2CaCu2O8 superconductors demonstrated its unprecedented sensitivity and accuracy.

Picometer accuracy in measuring lattice displacements across planar faults by interferometry in coherent electron diffraction

We calculate the shadow image in far field below a thin crystal when a coherent electron source is placed at micrometer distances above the specimen, and note that the presence of a planar fault results in very strong oscillatory contrast. We realize these predictions experimentally using a field-emission electron source in a microscope. With this technique, we determine displacement vectors at planar faults with an accuracy down to 1 pm in studies of the Bi2Sr2CaCu2O8 superconductor containing thin intercalated layers.

A study of charge distribution in Bi2Sr2CaCu2O8+delta superconductors using novel electron-diffraction and imaging techniques.

We report our study of the distribution of valence electrons in Bi2Sr2CaCu2O8+delta high-temperature superconductors using novel electron-diffraction and imaging techniques. The former method was based on quantitative analyses of the diffraction intensity of many reflections as a function of crystal thickness to determine, with an unprecedented accuracy, the Fourier components of the electron distribution in Bi2Sr2CaCu2O8+delta. The latter was based on examining the effect of charge transfer on many-beam imaging by comparing the observed and calculated low- and high-resolution images of long-period displacive and charge modulation of the cuprate. Our study demonstrates that fast electrons have greater sensitivity than X-rays to valence electrons distribution at small scattering angles, and that electron microscopy is a powerful tool in revealing charge distribution in materials.

Crystal site location of iron and trace elements in a magnesium-iron olivine by a new crystallographic technique.

A new crysallographic technique has been developed, which has been applied to the problem of locating the cations in a natural olivine crystal with the composition (Mg(0.90)Fe(0.10)Ni(0.004)Mn(0.002))(2)SiO(4). The method uses the variation of characteristic x-ray emission with the direction of an exciting electron beam in an analytical transmission electron microscope. It may be applied to nanometer-sized areas and to concentrations as low as 0.1 atomic percent, is capable of distinguishing neighbors in the periodic table, and does not require external standards. The iron atoms in this crystal are evenly distributed between the two available crystal sites M1 and M2 (49.6 +/- 1 percent on M1), whereas the trace elements nickel and manganese occupy the M1 and M2 positions, respectively (97 +/- 5 percent nickel on M1 and 1 +/- 5 percent manganese on M1).