X-ray Absorption Fine Structure in Embedded Atoms

Oscillatory structure is found in the atomic background absorption in x-ray-absorption fine structure (XAFS). This atomic-XAFS or AXAFS arises from scattering within an embedded atom, and is analogous to the Ramsauer-Townsend effect. Calculations and measurements confirm the existence of AXAFS and show that it can dominate contributions such as multi-electron excitations. The structure is sensitive to chemical effects and thus provides a new probe of bonding and exchange effects on the scattering potential.Comment: 4 pages plus 2 postscript figures, REVTEX 3.

Critical Point Field Mixing in an Asymmetric Lattice Gas Model

The field mixing that manifests broken particle-hole symmetry is studied for a 2-D asymmetric lattice gas model having tunable field mixing properties. Monte Carlo simulations within the grand canonical ensemble are used to obtain the critical density distribution for different degrees of particle-hole asymmetry. Except in the special case when this asymmetry vanishes, the density distributions exhibit an antisymmetric correction to the limiting scale-invariant form. The presence of this correction reflects the mixing of the critical energy density into the ordering operator. Its functional form is found to be in excellent agreement with that predicted by the mixed-field finite-size-scaling theory of Bruce and Wilding. A computational procedure for measuring the significant field mixing parameter is also described, and its accuracy gauged by comparing the results with exact values obtained analytically.Comment: 10 Pages, LaTeX + 8 figures available from author on request, To appear in Z. Phys.

Deconvolving Instrumental and Intrinsic Broadening in Excited State X-ray Spectroscopies

Intrinsic and experimental mechanisms frequently lead to broadening of spectral features in excited-state spectroscopies. For example, intrinsic broadening occurs in x-ray absorption spectroscopy (XAS) measurements of heavy elements where the core-hole lifetime is very short. On the other hand, nonresonant x-ray Raman scattering (XRS) and other energy loss measurements are more limited by instrumental resolution. Here, we demonstrate that the Richardson-Lucy (RL) iterative algorithm provides a robust method for deconvolving instrumental and intrinsic resolutions from typical XAS and XRS data. For the K-edge XAS of Ag, we find nearly complete removal of ~9.3 eV FWHM broadening from the combined effects of the short core-hole lifetime and instrumental resolution. We are also able to remove nearly all instrumental broadening in an XRS measurement of diamond, with the resulting improved spectrum comparing favorably with prior soft x-ray XAS measurements. We present a practical methodology for implementing the RL algorithm to these problems, emphasizing the importance of testing for stability of the deconvolution process against noise amplification, perturbations in the initial spectra, and uncertainties in the core-hole lifetime.Comment: 35 pages, 13 figure

Experimental mathematics on the magnetic susceptibility of the square lattice Ising model

We calculate very long low- and high-temperature series for the susceptibility $\chi$ of the square lattice Ising model as well as very long series for the five-particle contribution $\chi^{(5)}$ and six-particle contribution $\chi^{(6)}$. These calculations have been made possible by the use of highly optimized polynomial time modular algorithms and a total of more than 150000 CPU hours on computer clusters. For $\chi^{(5)}$ 10000 terms of the series are calculated {\it modulo} a single prime, and have been used to find the linear ODE satisfied by $\chi^{(5)}$ {\it modulo} a prime. A diff-Pad\'e analysis of 2000 terms series for $\chi^{(5)}$ and $\chi^{(6)}$ confirms to a very high degree of confidence previous conjectures about the location and strength of the singularities of the $n$-particle components of the susceptibility, up to a small set of ``additional'' singularities. We find the presence of singularities at $w=1/2$ for the linear ODE of $\chi^{(5)}$, and $w^2= 1/8$ for the ODE of $\chi^{(6)}$, which are {\it not} singularities of the ``physical'' $\chi^{(5)}$ and $\chi^{(6)},$ that is to say the series-solutions of the ODE's which are analytic at $w =0$. Furthermore, analysis of the long series for $\chi^{(5)}$ (and $\chi^{(6)}$) combined with the corresponding long series for the full susceptibility $\chi$ yields previously conjectured singularities in some $\chi^{(n)}$, $n \ge 7$. We also present a mechanism of resummation of the logarithmic singularities of the $\chi^{(n)}$ leading to the known power-law critical behaviour occurring in the full $\chi$, and perform a power spectrum analysis giving strong arguments in favor of the existence of a natural boundary for the full susceptibility $\chi$.Comment: 54 pages, 2 figure

Studies of Vibrational Properties in Ga Stabilized d-Pu by Extended X-ray Absorption Fine Structure

Temperature dependent extended x-ray absorption fine structure (EXAFS) spectra were measured for a 3.3 at% Ga stabilized Pu alloy over the range T= 20 - 300 K at both the Ga K-edge and the Pu L_III-edge. The temperature dependence of the pair-distance distribution widths, \sigma(T) was accurately modeled using a correlated-Debye model for the lattice vibrational properties, suggesting Debye-like behavior in this material. We obtain pair- specific correlated-Debye temperatures, \Theta_cD, of 110.7 +/- 1.7 K and 202.6 +/- 3.7 K, for the Pu-Pu and Ga-Pu pairs, respectively. These results represent the first unambiguous determination of Ga-specific vibrational properties in PuGa alloys, and indicate the Ga-Pu bonds are significantly stronger than the Pu-Pu bonds. This effect has important implications for lattice stabilization mechanisms in these alloys.Comment: 7 pages, 4 figures, Phys. Rev. B in pres

Space-time evolution of electron cascades in diamond

Here we describe model calculations to follow the spatio-temporal evolution of secondary electron cascades in diamond. The band structure of the insulator has been explicitly incorporated into the calculations as it affects ionizations from the valence band. A Monte-Carlo model was constructed to describe the path of electrons following the impact of a single electron of energy E 250 eV. The results show the evolution of the secondary electron cascades in terms of the number of electrons liberated, the spatial distribution of these electrons, and the energy distribution among the electrons as a function of time. The predicted ionization rates (5-13 electrons in 100 fs) lie within the limits given by experiments and phenomenological models. Calculation of the local electron density and the corresponding Debye length shows that the latter is systematically larger than the radius of the electron cloud. This means that the electron gas generated does not represent a plasma in a single impact cascade triggered by an electron of E 250 eV energy. This is important as it justifies the independent-electron approximation used in the model. At 1 fs, the (average) spatial distribution of secondary electrons is anisotropic with the electron cloud elongated in the direction of the primary impact. The maximal radius of the cascade is about 50 A at this time. As the system cools, energy is distributed more equally, and the spatial distribution of the electron cloud becomes isotropic. At 90 fs maximal radius is about 150 A. The Monte-Carlo model described here could be adopted for the investigation of radiation damage in other insulators and has implications for planned experiments with intense femtosecond X-ray sources.Comment: 26 pages, latex, 13 figure

Optical to UV spectra and birefringence of SiO2_2 and TiO2_2: First-principles calculations with excitonic effects

A first principles approach is presented for calculations of optical -- ultraviolet (UV) spectra including excitonic effects. The approach is based on Bethe-Salpeter equation calculations using the \textsc{NBSE} code combined with ground-state density-functional theory calculations from the electronic structure code \textsc{ABINIT}. Test calculations for bulk Si are presented, and the approach is illustrated with calculations of the optical spectra and birefringence of $\alpha$-phase SiO$_2$ and the rutile and anatase phases of TiO$_2$. An interpretation of the strong birefringence in TiO$_2$ is presented.Comment: 8 figure

Correlated local distortions of the TlO layers in Tl2_2Ba2_2CuOy_{y}: An x-ray absorption study

We have used the XAFS (x-ray-absorption fine structure) technique to investigate the local structure about the Cu, Ba, and Tl atoms in orthorhombic Tl-2201 with a superconducting transition temperature T$_c$=60 K. Our results clearly show that the O(1), O(2), Cu, and Ba atoms are at their ideal sites as given by the diffraction measurements, while the Tl and O(3) atoms are more disordered than suggested by the average crystal structure. The Tl-Tl distance at 3.5 \AA{ } between the TlO layers does not change, but the Tl-Tl distance at 3.9 \AA{ } within the TlO layer is not observed and the Tl-Ba and Ba-Tl peaks are very broad. The shorter Tl-O(3) distance in the TlO layer is about 2.33 \AA, significantly shorter than the distance calculated with both the Tl and O(3) atoms at their ideal $4e$ sites ( $x=y=$0 or $\frac{1}{2}$). A model based on these results shows that the Tl atom is displaced along the directions from its ideal site by about 0.11 \AA; the displacements of neighboring Tl atoms are correlated. The O(3) atom is shifted from the $4e$ site by about 0.53 \AA{ } roughly along the directions. A comparison of the Tl L$_{III}$-edge XAFS spectra from three samples, with T$_c$=60 K, 76 K, and 89 K, shows that the O environment around the Tl atom is sensitive to T$_c$ while the Tl local displacement is insensitive to T$_c$ and the structural symmetry. These conclusions are compared with other experimental results and the implications for charge transfer and superconductivity are discussed. This paper has been submitted to Phys. Rev. B.Comment: 20 pages plus 14 ps figures, REVTEX 3.