Factor displacement

One at fundamental frequency. Its displacement with the fundamental voltage is termed the displacement factor, and for a linear voltage and linear load will define the p.f of the load, i.e. 

Definitive proof of the structure of porphine in the solid state awaits a variable-temperature crystallographic (X-ray or neutron diffraction) study the analysis of the anisotropic displacement factors (ADP) should disclose any rotational motion or its absence as well as determine the positions of the inner hydrogens. A search in the September 1998 version of the Cambridge Structural Database [CSD (91MI187)] showed that the only structures of porphine (codename PORPIN) were obtained in 1965 and 1972. 

Mehl, E., Riither, E., and Redemann, J. (1977) Endogenous ligands of a putative LSD-serotonin receptor in the cerebrospinal fluid Higher level of LSD-displacing factors (LDF) in unmedicated psychotic patients. Psychopharmacology, 54 9-16. 

Reference cites the literature from which the crystal data, atomic coordinates, and displacement factors were obtained. In many cases there are multiple refinements of the same zeolitic material, but because of space limitations not all refinements could be included. We would be appreciative if authors and users would inform us of any errors or omissions. A listing of the references for isotypic species can be found in the Atlas of Zeolite Framework Types (Baerlocher, McCusker and Olson (2007)). A list of references to structure analyses of zeolites with different cations, up to 1982, is given in the Compilation of Extra Framework Sites in Zeolites, Mortier (1982). 

Table 4. Anistropic displacement parameters (Angstroms2) for [Cu(imidazole)4Cl]Cl. The anistropic displacement factor exponent takes the form -2% [h a U +. ..+ Ihkd b U ]...

Table 2 Atomic coordinates of a TDAE-C60 at room temperature and isotropic displacement factors.The atoms assigned with a prime belong to the TDAE molecule whilethe others belong to the C60 molecule...

The C60 molecules were found to be executing large amplitude reorientations at room temperature, so that large anisotropic thermal displacement factors of the C60 carbon atoms were found. The thermal displacement parameters for some of the C60 carbon atoms at room temperature are, in fact, so large that the C60 atomic coordinates may well represent only an average over one or more disordered structures involving fractional atomic occupancy. On the other hand, the TDAE N and C atomic coordinates are well-defined already at room temperature. 

Estimated standard deviation given in brackets to same significance level as parameter. x,y,z given as decimal fraction of cell edge. Anisotropic displacement factor given as 103 exp - 2tt. a a h.h. Fixed to define origin. J J J... 

FIGURE 6.22. Isotropic displacement factors for oxygen, atomic number 8. Note that the larger the value of B, the greater the falloff in intensity as a function of sinO/X. but that the values of / when sin = 0 is always 8.0. 

Difference maps also allow adjustments to be made to displacement parameters. If the displacement parameter of an atom in the model is too large, it will be spread over more space than necessary, and its peak height will be lower than it should be. As a result, there will be a positive peak at the atomic center in the difference map if the displacement factor is too small, a negative valley will appear in that position [Figure 9.8(b)]. The final difference Fourier map is generally not completely flat because it contains indications of both errors in the data ( Ft, 1) and inadequacies in the model ( Fc ), including, of course, the relative phase angle, a hkl)c-... 

Atoms in crystals seldom have isotropic environments, and a better approximation (but still an approximation) is to describe the atomic motion in terms of an ellipsoid, with larger amplitudes of vibration in some directions than in others. Six parameters, the anisotropic vibration or displacement parameters, are introduced for each atom. Three of these parameters per atom give the orientations of the principal axes of the ellipsoid with respect to the unit cell axes. One of these principal axes is the direction of maximum displacement and the other two are perpendicular to this and also to each other. The other three parameters per atom represent the amounts of displacement along these three ellipsoidal axes. Some equations used to express anisotropic displacement parameters, which may be reported as 71, Uij, or jdjj, axe listed in Table 13.1. Most crystal structure determinations of all but the largest molecules include anisotropic temperature parameters for all atoms, except hydrogen, in the least-squares refinement. Usually, for brevity, the equivalent isotropic displacement factor Ueq, is published. This is expressed as ... 

FIGURE 16.4 (cont d). Portions of an output file from the Protein Data Bank, (b) The end of the amino-acid sequence, the presence of metal ions, and orthogonal coordinates of each atom together with its displacement factor. Courtesy the Protein Data Bank. 

We require only three parameters not available through the model, the root mean square thermal displacement amplitude and estimates of and cop, in order to recreate the entire fiber diffractogram. For our universal isotropic thermal displacement factor we employed the B value used successfully by Noitholt (1) for the experimental analysis of scattering from PPTA ... 

Notably, the anisotropic thermal displacement factors form the elements of a 3x3 symmetric matrix. The physically meaningful form of this matrix when it is positive-definite is that of an ellipsoidal probability surface centered at the equilibrium atom position. An alternative form for Equation (22) frequently used in crystallography ... 

B coefficient consisting of inverted Maxwell-Stefan diffusivities s/m ) B displacement factor ( —)... 

Mehl, E. Riither, E. Redemann, J. Endogenous Ligands of a Putative LSD-Serotonin Receptor in the Cerebrospinal Fluid Higher Level of LSD-Displacing Factors (LDF) in Unmedicated Psychotic Patients Psychopharmacology (1977) 54 9-16... 

The distribution function P(A) may describe not only the dynamic displacements of the atom due to thermal vibrations, but also static displacements. In this latter case a disordered atom can occupy different sites at random which are themselves periodic. The average structure is then a spatial average taken over a large number of unit cells. For this reason T(S) is called the displacement factor thus avoiding the use of the more traditional term of temperature factor. 

The creep anisotropy of polypropylene when formed into wheels by the solid-phase forming, or forging, process has been studied by Abrahams et A displacement factor was defined as (to—ti)Ao>< 100. where to was the original billet thickness and ti the final thickness of the wheel web. Specimens were cut parallel (0 = 0°) and perpendicular (0 =s 90°) to the radial direction. Isochronous creep tests showed little change in stiffness at 90° to the radial direction for a range of displacement factors from 0 to 58%. However, significant increases in stiffness were found at 0°, above a displacement factor of 50%. Creep tests on... 

In Fig. 18, all data Ig ( o- ), adduced in Table 4 matching with usage of the two estimated above displacement factors—and —is shown. 

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