Experimental Structure Factors Research Articles

Invalidity of deriving interparticle distance in clay–water systems using the experimental structure factor maximum obtained by small-angle scattering

Small-angle X-ray scattering (SAXS) has been widely used to investigate the organization of clay colloids in response to the particle concentration and ionic strength of the suspending medium. In such investigations, measuring the interparticle distance and/or spacing is usually attempted. In random or short-range ordered clay–water systems, the interparticle distances are often derived from the experimental structure factor maximum; however, the validity of such practice has never been theoretically or experimentally evaluated. The experimental structure factors of several clay–water systems with and without polyphosphate treatment to block the edge charges of clay particles were obtained from SAXS data in order to understand the physical meaning of this property. The results show that the polyphosphate treatment eliminated the experimental structure factor maximum and that the particle concentration effects were correlated with the depression on the curve in a random clay–water system (e.g., illite and laponite). For clay particles with greater anisotropy (i.e., montmorillonite), polyphosphate treatment enhanced the ordering of clay layers at high particle concentrations forming long-range ordered crystals showing Bragg reflections. In this ordered system, distinctive and symmetrical peaks representing the interparticle spacing were obtained by using a Fourier transform of the scattering curves. Thus, we conclude that the experimental structure factor maximum is induced by the edge–face oriented interactions, which may not be in direct contact as in a house-of-cards structure, and the position of the maximum should not be interpreted as an averaged interparticle distance in a clay–water system unless particles orient along the same direction.

Structure of the Si(113) surface studied by surface X-ray diffraction

We carried out a grazing incidence X-ray diffraction analysis of the Si(1 1 3) 3 × 1 surface using synchrotron radiation. We compared the experimental structure factors obtained from the integrated intensities of the fractional-order reflections with the calculated structure factors of the dimerized structure model of Ranke. By minimizing the R-factor, we determined the position and the size of the pentagon in the 3 × 1 dimerized structure model of Ranke. In addition, we found that a model with randomly distributed interstitial atoms at the center of the pentagon gives a smaller R-factor value.

Beyond locating the atoms towards addressing the electronic structure of crystals using advanced transmission electron microscopy

With the present focus on nanostructures, the role of the transmission electron microscope (TEM) as a research tool is becoming increasingly important. Among themajor strengths of TEM are the capability of obtaining diffraction patterns and electron energy loss spectra (EELS) from nanometer sized areas. In addition, advanced TEMmay serve as a supplement to synchrotron x-ray diffraction and absorption spectroscopy in efforts to study bonding and electronic structure of bulk materials. This is in particular the case when only small-grained polycrystalline samples are available, but TEM may also provide valuable input in studies of single crystals. For example, the near edge fine structure at EELS absorption edges was used to locate different valence states of Fe within the unit cell of a mixed valence crystal already two decades ago [1], and more recently precision convergent beam electron diffraction (CBED)was used in combination with x-ray diffraction to study the spatial distribution of valence electrons in Cu2O [2]. In this presentation, we report our recent study of the MgB2 where we use both EELS [3] and CBED [4] to gain insight into the electronic structure of this new superconductor with Tc=39K. Using angle-resolved EELS we studied the fine structure at the K-edge of boron in order to probe the empty boron pxy and pz states near the Fermi level in this anisotropic hexagonal crystal. Similar information can be obtained using polarized soft x-rays in absorption spectroscopy (XANES) if sufficiently large single crystals become available. Using quantitative CBED we determine the structure factors at short g-vectors. These structure factors at short g-vectors, which are strongly influenced by the valence electron redistribution, can be determined with very high accuracy using electron diffraction. For example, after converting to x-ray structure factors, we measure F001 of MgB2 to be 2.15±0.03 electrons while the calculated structure factor for the procrystal differs 20 standard deviations from this value (2.75 electrons).We also did DFT calculations, and found good agreement between experimental and theoretical structure factors.

Structure of the Si(1 1 3) surface studied by surface X-ray diffraction

We carried out a grazing incidence X-ray diffraction analysis of the Si(113) 3 × 1 surface using synchrotron radiation. We compared the experimental structure factors obtained from the integrated intensities of the fractional-order reflections with the calculated structure factors of the dimerized structure model of Ranke. By minimizing the R-factor, we determined the position and the size of the pentagon in the 3 × 1 dimerized structure model of Ranke. In addition, we found that a model with randomly distributed interstitial atoms at the center of the pentagon gives a smaller R-factor value.

Crystal structure of a tandem cystathionine‐β‐synthase (CBS) domain protein (TM0935) from Thermotoga maritima at 1.87 Å resolution

Crystal structure of a tandem cystathionine‐β‐synthase (CBS) domain protein (TM0935) from <i>Thermotoga maritima</i> at 1.87 Å resolution

Molecular reorientations in liquid crystals pentyloxybenzylidine hexylanilene (PBHA) and butyloxybenzylidine octylanilene (BBOA).

Molecular reorientational motions in undeuterated pentyloxybenzylidine hexylanilene (PBHA or 5O.6) and butyloxybenzylidine octylanilene (BBOA or 4O.8) as studied by the quasielastic neutron scattering (QENS) technique in their different mesophases are reported. Models are built up in stages to account for the experimental elastic incoherent structure factor (EISF). It is found that there exist simultaneous reorientational motions of the chain group and the reorientational motions of the whole molecule around its molecular axis in the smectic- G, smectic- B, and smectic- C phases. In smectic- A and nematic phases, additional body axis fluctuations are found to exist in both 5O.6 and 4O.8 systems. The average amplitude of body axis fluctuations is found to be approximately 15 degrees and 25 degrees, respectively, in the smectic- A and nematic phases of 5O.6, and approximately 14 degrees and 29 degrees, respectively, in 4O.8.

Reverse Monte Carlo modeling of amorphous silicon

An implementation of the Reverse Monte Carlo algorithm is presented for the study of amorphous tetrahedral semiconductors. By taking into account a number of constraints that describe the tetrahedral bonding geometry along with the radial distribution function, we construct a model of amorphous silicon using the reverse monte carlo technique. Starting from a completely random configuration, we generate a model of amorphous silicon containing 500 atoms closely reproducing the experimental static structure factor and bond angle distribution and in improved agreement with electronic properties. Comparison is made to existing Reverse Monte Carlo models, and the importance of suitable constraints beside experimental data is stressed.

Crystal structure of a novel Thermotoga maritima enzyme (TM1112) from the cupin family at 1.83 A resolution.

Crystal structure of a novel Thermotoga maritima enzyme (TM1112) from the cupin family at 1.83 A resolution.

Crystal structure of a novel manganese-containing cupin (TM1459) from Thermotoga maritima at 1.65 A resolution.

Crystal structure of a novel manganese-containing cupin (TM1459) from Thermotoga maritima at 1.65 A resolution.

Crystal structure of a methionine aminopeptidase (TM1478) from Thermotoga maritima at 1.9 A resolution.

Crystal structure of a methionine aminopeptidase (TM1478) from Thermotoga maritima at 1.9 A resolution.

Crystal structure of a putative oxalate decarboxylase (TM1287) from Thermotoga maritima at 1.95 A resolution.

Crystal structure of a putative oxalate decarboxylase (TM1287) from Thermotoga maritima at 1.95 A resolution.

Small bond angles in amorphous silicon: are they a new type of defect?

The reverse Monte Carlo structural modeling method and tight-binding molecular dynamics simulations were applied in order to investigate the existence of small bond angles (like those in triangles and squares) in amorphous silicon networks. The influence of small bond angles on the electronic density of states was also analyzed. It is shown that the presence of a small number of bond angles around 75° is necessary for a proper reproduction of the experimental structure factor of vapor deposited amorphous silicon.

Crystal structure of an aspartate aminotransferase (TM1255) from Thermotoga maritima at 1.90 A resolution.

Crystal structure of an aspartate aminotransferase (TM1255) from Thermotoga maritima at 1.90 A resolution.

Structure of ionic liquids of 1-alkyl-3-methylimidazolium cations: a systematic computer simulation study.

Molecular dynamics simulations of room temperature molten salts (ionic liquids) containing imidazolium cations have been performed. Ten different systems were simulated at 323 K by using united atom force fields, in which the anion size (F-, Cl-, Br-, and PF6-) and the length of the alkyl chain of 1-alkyl-3-methylimidazolium cations (1-methyl-, 1-ethyl-, 1-butyl-, and 1-octyl-) were systematically varied. It is shown that the resulting equilibrium structures account for the observed features of experimental static structure factors when available. A detailed analysis of the simultaneous effect of changing the anion and the alkyl chain on the preferential location of nearest-neighbor anions around the cations is provided. It is shown that regions above and below the imidazolium ring are the preferential ones in case of large anions. By increasing the length of the alkyl chain, nearest-neighbor anions are pushed away from the volume occupied by the flexible alkyl chain. Partial structure factors of 1-butyl- and 1-octyl- derivatives display a peak at a wave vector smaller than the main peak, indicating the occurrence of an intermediate range order in these ionic liquids due to the presence of long alkyl chains.

Development of new interatomic potentials appropriate for crystalline and liquid iron

Two procedures were developed to fit interatomic potentials of the embedded-atom method (EAM) form and applied to determine a potential which describes crystalline and liquid iron. While both procedures use perfect crystal and crystal defect data, the first procedure also employs the first-principles forces in a model liquid and the second procedure uses experimental liquid structure factor data. These additional types of information were incorporated to ensure more reasonable descriptions of atomic interactions at small separations than is provided using standard approaches, such as fitting to the universal binding energy relation. The new potentials (provided herein) are, on average, in better agreement with the experimental or first-principles lattice parameter, elastic constants, point-defect energies, bcc–fcc transformation energy, liquid density, liquid structure factor, melting temperature and other properties than other existing EAM iron potentials.

Crystal structure of an iron-containing 1,3-propanediol dehydrogenase (TM0920) from Thermotoga maritima at 1.3 A resolution.

Crystal structure of an iron-containing 1,3-propanediol dehydrogenase (TM0920) from Thermotoga maritima at 1.3 A resolution.

Influence of Ni on the structure of liquid aluminum

Total experimental structure factors for liquid Al1−xNix (x=0, 0.025, 0.05, 0.075, 0.1, 0.125) alloys were obtained by means of X-ray scattering method. The concentration dependence of the main structural parameters was analyzed. It is shown that an ideal solution model can be used for the description of these alloys within the range 0–10at.% Ni. For higher nickel contents, deviations from this model are observed due to the influence of chemical ordering.

Magnesium: Comparison of density functional theory calculations with electron and x-ray diffraction experiments

Accurate experimental structure factors for Mg have been measured and compared with density functional theory (DFT) to test some commonly used functionals and self-interaction correction (SIC) schemes. Low order structure factors, free of extinction and on absolute scale, were measured accurately by quantitative convergent beam electron diffraction. In addition, a complete set of structure factors up to sin θ/λ=1.6 Å−1 was measured by x-ray diffraction at 10 K. The DFT calculations were performed using the full potential linearized augmented plane wave method. It was found that the agreement with experiment increases when going from the local density approximation (LDA) to the generalized gradient approximation (GGA) of Perdew, Burke, and Ernzerhofer and further to the GGA of Engel and Vosko. Applying the SIC of Perdew and Zunger to the core states for LDA does not improve the agreement with theory, while applying the SIC of Lundin and Eriksson results in a significantly improved agreement. This implies that the main source of error in the LDA functional comes from the description of the core densities. Using the functional which agrees best with experiment, a non-nuclear maximum is established in the calculated electron density of beryllium but not of magnesium.

Resistivity of the liquid gallium-lead miscibility gap system

We present our electrical resistivity measurements of the gallium-lead system which shows a very large miscibility gap between 2.4 and 94.5 at. % lead with a critical temperature of $606\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$ and composition of 40 at. % lead. A small negative deviation of the experimental temperature coefficient of the resistivity (TCR) appears near the critical composition of the alloy. The resistivity of the alloys is interpreted and discussed in terms of the extended Faber-Ziman formula using the $t$-matrix formalism with hard-sphere and experimental (for pure metals only) structure factors. An approach is proposed, taking into account the information given by the experimental density of states which allowed us to explain the resistivity of pure lead and that of the liquid gallium-lead alloys. As a conclusion it was shown that two electrons in the conduction band of liquid lead better explain the experimental resistivity than four electrons.

Impact of Core Architecture on Solution Properties of Dendrimer-like Star Copolymers

We present a small-angle neutron scattering study of a series of isomeric dendrimer-like star copolymers investigated in solution. Each copolymer consists of a highly branched core with linear partially deuterated polymer chains emanating from the outermost generation to create a starlike copolymer. By studying the copolymers in solvents contrast matched to the outer starlike chains, we focus our study on the effects of the core branching architecture. In our dilute solution data analysis we use models to obtain analytical expressions for the form factor of the copolymer cores. We find the core radius of gyration and fractal dimension depend on the core branching architecture. From our semidilute data we obtain experimental structure factors and see evidence of liquidlike structuring in some copolymers. Thus, the architectural features of these isomeric copolymers have an impact on both the conformation of and interactions between these molecules in solution.