Isotropic temperature factor

Isotropic temperature factors (B) are in A standard deviations are given in parentheses. 

Refinement takes place by adjusting the model to find closer agreement between the calculated and observed structure factors. For proteins the refinements can yield R-factors in the range of 10-20%. An example taken from reference 10 is instructive. In a refinement of a papain crystal at 1.65-A resolution, 25,000 independent X-ray reflections were measured. Parameters to be refined were the positional parameters (x, y, and z) and one isotropic temperature factor parameter... 

Reflection intensity in the SAED negatives was measured with a microdensitometer. The refinement of the structure analysis was performed by the least square method over the intensity data (25 reflections) thus obtained. A PPX single-crystal is a mosaic crystal which gives an "N-pattem". Therefore we used the 1/d hko as the Lorentz correction factor [28], where d hko is the (hkO) spacing of the crystal. In this case, the reliability factor R was 31%, and the isotropic temperature factor B was 0.076nm. The molecular conformation of the P-form took after that of the P-form since R was minimized with this conformation benzene rings are perpendicular to the trans-zigzag plane of -CH2-CH2-. 

For vanadium, the ratios are smaller, and the dynamic density maps do not show a distinct maximum in the cube direction. The difference is attributed to anharmonicity of the thermal motion. Thermal displacement amplitudes are larger in V than in Cr, as indicated by the values of the isotropic temperature factors, which are 0.007 58 and 0.00407 A2 respectively. As in silicon, the anharmonic displacements are larger in the directions away from the nearest neighbors, and therefore tend to cancel the asphericity of the electron density due to bonding effects. 

Evaluate the bias in the isotropic temperature factor of the hydrogen atom of problem 1.1 as a function of the true k value, if k is arbitrarily set to 1 in a refinement. 

An interesting fact is that in the case of K Cu[Fei cCo c(CN)6], the potassium ions occupy statistically one-half of the eight cubes of one unit cell, but with a high value of the isotropic temperature factor indicating a smudgy position of the potassium ions. In the compound K Ni[Fei xCox(CN)6], an eccentric position of potassium ions was found. Such an eccentric position of the countercation was also described by Bo-carsly et al. for sodium-containing nickel hexacyanoferrate(II) [34]. 

Isotropic temperature factors were used for 0(2) through 0(9) This compound Is a superconductor with Tc 40 K. 

TABLE 4.5 Fractional atomic coordinates and equivalent isotropic temperature factors (A2) for non-H atoms with e.s.d. s in parentheses [21]... 

The refinement procedures for hydrogen atoms also vary. Isotropic temperature factors are assigned to the hydrogen atoms, but are generally not refined. They are fixed at the isotropic equivalent values of the anisotropic factors for the atom to which the hydrogen is covalently bonded, or, more appropriately, twice those values. 

Parameters and Ujj, like the isotropic temperature factor, are expressed in A, while are dimensionless. The accepted standard now is to report U for the isotropic model (Uiso) and Uij for the anisotropic one. ... 

Temperature factor An exponential expression by which the scattering of an atom is reduced as a consequence of vibration (or a simulated vibration resulting from static disorder). For isotropic motion the exponential factor is exp(—5iso sin 0/A ), where Biso is the isotropic temperature factor. It equals 87r (ti ), where (ti ) is the mean-square displacement of the atom from its equilibrium position. For anisotropic motion the exponential expression usually contains six parameters, the anisotropic vibration or displacement parameters, which describe ellipsoidal rather than isotropic (spherically symmetrical) motion or average static displacements. 

Hamilton, W. C. On the isotropic temperature factor equivalent to a given anisotropic temperature factor. Ada Cryst. 12, 609-610 (1959). 

Atomic Coordinates and Equivalent Isotropic Temperature Factors ... 

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