Unit-cell parameters

Crystal system Triclinic Orthorhombic stable monoclinic Orthorhombic Monoclinic, metastable 

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Zeohte type Designation Cation Effective pore diameter, E Unit cell parameter, E... 

Step 3. The computer collects about 45 frames of data. The crystal is rotated about the vertical axis for 0.3 degree for each frame. Usually the crystal is exposed to x-rays for about 5 seconds for each frame. The computer finds the centers of many reflections (typically 25 to several hundred) and determines indices for these reflections. It then determines the unit cell parameters and the orientation of the unit cells with respect to the diffractometer. 

Step 4. The user may then search for a match of the measured unit cell parameters against all unit cell parameters that have been pubUshed. 

Currently, there are about 197,500 entries in the National Institute of Standards and Technology (NIST) Crystal Data File. An exhaustive search takes about one minute. Unit cell parameters are very definitive. Usually only one or a few hits are found and the appropriate Hterature reference(s) are Hsted. If no hits are found, the stmcture has not been previously reported. 

The time for these four steps is typically about 15—20 min. It takes 1—2 h with the older single-reflection detector instmments. Because all reflections with weak, as well as moderate to strong intensities, are measured with the SMART system, the probabiUty of obtaining incorrect unit cell parameters is less than for conventional instmments. 

For small crystals, the 5 s per frame must be increased, but because so many reflections can be measured in a short period of time, it is possible to determine the unit cell parameters and identify crystals considerably smaller than was possible with conventional instmments. Currently (1996), the smallest sample for which this method has been used had dimensions of approximately 0.01 mm x 0.01 mm x 0.01 mm (about 2 n). As a result the SMART system is one of the most powerful tools for determining the identity of very small samples. 

Indexings and Lattice Parameter Determination. From a powder pattern of a single component it is possible to determine the indices of many reflections. From this information and the 20-values for the reflections, it is possible to determine the unit cell parameters. As with single crystals this information can then be used to identify the material by searching the NIST Crystal Data File (see "SmaU Molecule Single Stmcture Determination" above). 

Fig. 102 shows the temperature dependence of K5Nb30Fi8 and Rb5Nb30Flg unit cell parameters [438]. Parameter a increases with the increase in temperature, while parameter c displays a maximum at a temperature of about 490-500K. The changes in parameter values with respect to the temperature are reversible. 

Fig. 102. Temperature dependence of unit cell parameters a and c ratio of parameters - c/a volume - V. Figure (a) - KsNb3OFi8, figure (b) -RbsNb3OFi8 (after Agulyansky and Ravez [438]).

Vector notation is being used here because this is the easiest way to define the unit-cell. The reason for using both unit lattice vectors and translation vectors lies in the fact that we can now specify unit-cell parameters in terms of a, b, and c (which are the intercepts of the translation vectors on the lattice). These cell parameters are very useful since they specify the actual length eind size of the unit cell, usually in A., as we shall see. 

The SAD patterns were Indexed to a [101] zone axis, as described In reference ( ). The unit cell parameters of the mineral and synthetic aurlchalclte are given In Table I together with the Cu/Zn ratios. 

Since the values of the unit cell parameter of the acidic salts were not intermediate between those of the neutral salts and of the parent acid (ao = 1.216 and 1.217 nm, respectively, for H3PWX2O40 and H4SiWi204o), one may propose that there is no formation of solid solutions but rather a mixture of the neutral salt and of the acid highly dispersed on the neutral salt. 

The information stored in the specimen database is sufficient to identify the particular specimen and the material from which it is made. Other parameters provide information on the orientation of the specimen and on its unit cell parameters. These latter parameters are used by the data collection tasks and the crystal geometry calculation function to determine diffraction angles, the angles between crystal planes, etc. The user can store information on several specimens in the specimen database, thus permitting him to easily remount and rerun a specimen after looking at the collected data. 

The 28 scan and layer line scan functions are provided as an aid to obtaining better estimates of the unit cell parameters for the substance being studied and in assessing contributions from background scattering and overlapping diffraction maxima. 

With lower-molecular-weight polymers unit cell parameters may also vary with the molecular mass distribution. For poly(ethylene terephthalate) the history of reported unit cell parameters reflects the progress of chemical processing technology [105]. 

US patent 6,677,373, Polymorphic B form of 3-(cyclopropylmethoxy)-4-[4-(methylsulfonyl)phenyl]-5,5-dimethyl-5H-furan-2-one [96]. This invention concerns Form B of the title compound, crystallizing in the hexagonal R-3 space group, and which was characterized by its unit cell parameters. For this form, a = 18.183 A, b = 18.183 A, c = 26.950 A, a = jS = 90°, and y = 120°. The unit-cell volume was found to be 7716.5 A3, and there were 18 molecules per unit cell. 

Table 2. Characteristics of the silica templates and the corresponding carbon materials a unit cell parameter Sbet- specific surface area Vp total pore volume (at P/Po=0.95) Pore size determined according to the BJH method - Maximum value of the BJH pore size distribution peak calculated from the adsorption branch of the N2 isotherm.

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