Angstroms

MEAN RADIUS OF GYRATION, ANGSTROMS DIPCLF MOMENT, DEBYES... 

Angstrom unit, A A unit of length equivalent to 10" cm, (10 °m). Used to describe molecular and lattice dimensions and wavelengths of visible light. 

D. Royer and E. Dieulesaint, Optical detection of sub-angstrom transient mechanical displacements , IEEE Ultrasonics Symposium Proceedings, 1986. 

Reference 3 gives the equation log (a/ao) = l6/x, where a is the solubility activity of a crystal, ao is the normal value, and x is the crystal size measured in angstroms. Derive this equation. 

A special case of adsorption in cavities is that of clatherate compounds. Here, cages are present, but without access windows, so for adsorption to occur the solid usually must be crystallized in the presence of the adsorbate. Thus quinol crystallizes in such a manner that holes several angstroms in diameter occur and, if crystallization takes place in the presence of solvent or gas... 

Scaiming probe microscopies have become the most conspicuous surface analysis tecimiques since their invention in the mid-1980s and the awarding of the 1986 Nobel Prize in Physics [71, 72]- The basic idea behind these tecimiques is to move an extremely fine tip close to a surface and to monitor a signal as a fiinction of the tip s position above the surface. The tip is moved with the use of piezoelectric materials, which can control the position of a tip to a sub-Angstrom accuracy, while a signal is measured that is indicative of the surface topography. These tecimiques are described in detail in section BI.20. 

In order to describe the second-order nonlinear response from the interface of two centrosynnnetric media, the material system may be divided into tlnee regions the interface and the two bulk media. The interface is defined to be the transitional zone where the material properties—such as the electronic structure or molecular orientation of adsorbates—or the electromagnetic fields differ appreciably from the two bulk media. For most systems, this region occurs over a length scale of only a few Angstroms. With respect to the optical radiation, we can thus treat the nonlinearity of the interface as localized to a sheet of polarization. Fonnally, we can describe this sheet by a nonlinear dipole moment per unit area, -P ", which is related to a second-order bulk polarization by hy P - lx, y,r) = y. Flere z is the surface nonnal direction, and the... 

Dadap J I, Doris B, Deng Q, Downer M C, Lowell J Kand Diebold A C 1994 Randomly oriented Angstrom-scale... 

The field of corrected microscopes has just begun with the instruments discussed above. The progress in this field is very rapid and proposals for a sub-Angstrom TEM (SATEM) or even the combination of this instrument with a corrected energy filter to fonn a sub-electronvolt/sub-Angstrom TEM (SESAM) are underway. 

Figure B3.4.1. The potential surfaee for the eollinear D + H2 DH + H reaetion (this potential is the same as for H + H2 — H2 + H, but to make the produets and reaetants identifieation elearer the isotopieally substituted reaetion is used). The D + H2 reaetant arrangement and the DH + H produet arrangement are denoted. The eoordinates are r, the H2 distanee, and R, the distanee between the D and the H2 eentre of mass. Distanees are measured in angstroms the potential eontours shown are 4.7 eV-4.55 eV,.. ., -3.8 eV. (The potential energy is zero when the partieles are far from eaeh other. Only the first few eontours are shown.) For referenee, the zero-point energy for H2 is -4.47 eV, i.e. 0.27 eV above the H2 potential minimum (-4.74 eV) the room-temperature thennal kinetie energy is approximately 0.03 eV. The graph uses the aeeiirate Liu-Seigbalm-Triihlar-Horowitz (LSTH) potential surfaee [195].

Figure B3.5.2. Example Z matrix for fliioroethylene. Notation for example, line 4 of the Z matrix means that a H atom is bonded to earbon atom Cl with bond length L3 (angstroms), making an angle with earbon atom...

Zenhausern F, Martin Y and Wiekramasinghe H K 1995 Seanning interferometrie apertureless mieroseopy optioal imaging at 10 Angstrom resolution Science 269 1083-5... 

Goldstein A N, Colvin V L and Alivisatos A P 1991 Qbservation of melting in 30 angstrom diameter CdS nanocrystals Mater. Res. Soc. Symp. Proc. 206 271... 

Tsukihara T, Aoyama H, Yamashita E, Tomizaki T, Yamaguchi H, Shinzawaitoh K, Nakashima R, Yaono R and Yoshikawa S 1995 Structures of metai sites of oxidized bovine heart cytochrome c oxidase at 2.8 angstrom Science 269 1069-74... 

Abstract. A smooth empirical potential is constructed for use in off-lattice protein folding studies. Our potential is a function of the amino acid labels and of the distances between the Ca atoms of a protein. The potential is a sum of smooth surface potential terms that model solvent interactions and of pair potentials that are functions of a distance, with a smooth cutoff at 12 Angstrom. Techniques include the use of a fully automatic and reliable estimator for smooth densities, of cluster analysis to group together amino acid pairs with similar distance distributions, and of quadratic progrmnming to find appropriate weights with which the various terms enter the total potential. For nine small test proteins, the new potential has local minima within 1.3-4.7A of the PDB geometry, with one exception that has an error of S.SA. 

The chaotic nature of individual MD trajectories has been well appreciated. A small change in initial conditions (e.g., a fraction of an Angstrom difference in Cartesian coordinates) can lead to exponentially-diverging trajectories in a relatively short time. The larger the initial difference and/or the timestep, the more rapid this Lyapunov instability. Fig. 1 reports observed behavior for the dynamics of a butane molecule. The governing Newtonian model is the following set of two first-order differential equations ... 

C- cutoff radius method - all non-bonded forces between particles within angstroms of each other are computed explicitly... 

The CIF format not only defines its dictionary of available data names, but restricts the STAR file syntax as well. For example, lines may not exceed 80 characters and data names can contain a maximum of 32 characters. Furthermore, the CIF dictionaiy specifies default units for numeric fields that represent numeric values with units. If the data item is not stored in the default units, then the units code is appended to the data name. Thus cell length a and cell length a pm represent the dimensions ofthe unit cell in Angstrom (the default units conforming to the SI Standard) and picomclcrs, respectively. 

---