Physical and Non-Physical Methods of Solving Crystal Structures

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QR Code. A negative diamagnetic anistropy is observed for purely cycloaliphatic LCs. The diffuse peak at small angles condense into sharp quasi-Bragg peaks. The peak intensity distribution at large angles is not very sharp because molecules within the smectic planes are randomly arranged. This tilt can easily be seen in the diffraction pattern as the diffuse peaks at smaller and larger angles are no longer orthogonal to each other. In general, X-ray scattering measurements of liquid crystal samples are considered more difficult to perform than those of crystalline samples.

The following steps should be performed for diffraction measurement of liquid crystal samples:. Identification of the phase of a liquid crystal sample is critical in predicting its physical properties. It is also critical to determine the orientational order of a liquid crystal.

This is important to characterize the extent of sample alignment. For simplicity, the rest of the discussion focuses on nematic liquid crystal phases. In an unaligned sample, there isn't any specific macroscopic order in the system. In the micrometer size domains, molecules are all oriented in a specific direction, called a local director.

Because there is no positional order in nematic liquid crystals, this local director varies in space and assumes all possible orientations. For example, in a perfectly aligned sample of nematic liquid crystals, all the local directors will be oriented in the same direction. The specific alignment of molecules in one preferred direction in liquid crystals makes their physical properties such as refractive index, viscosity, diamagnetic susceptibility, directionally dependent.

When a liquid crystal sample is oriented using external fields, local directors preferentially align globally along the field director. This globally preferred direction is referred to as the director and is denoted by unit vector n. For isotropic samples, the value of S is zero, and for perfectly aligned samples it is 1.

Physical and Non-Physical Methods of Solving Crystal Structures

This gives a uniformly aligned sample with the nematic director n oriented along the magnetic field. The sample to detector distance was mm. The glass capillary can just be seen between the sides of the holder. Through the course of our structural characterization of various tetrafluoroborate salts, the complex cation has nominally been the primary subject of interest; however, we observed that the tetrafluoroborate anion BF 4 - anions were commonly disordered 13 out of 23 structures investigated.

Furthermore, a consideration of the Cambridge Structural Database as of 14 th December yielded 8, structures in which the tetrafluoroborate anion is present; of these, Several different methods have been reported for the treatment of these disorders, but the majority was refined as a non-crystallographic rotation along the axis of one of the B-F bonds. Unfortunately, the very property that makes fluoro-anions such good candidates for non-coordinating counter-ions i. In other words, the appearance of disorder is intensified with the presence of a weakly coordinating spherical anion e.

Essentially, these weakly coordinating anions are loosely defined electron-rich spheres. All considered it seems that fluoro-anions, in general, have a propensity to exhibit apparently large atomic displacement parameters ADP's , and thus, are appropriately refined as having fractional site-occupancies. In crystallography the observed atomic displacement parameters are an average of millions of unit cells throughout entire volume of the crystal, and thermally induced motion over the time used for data collection.

Such cases of disorder are usually the result of either thermally induced motion during data collection i. The latter is defined as the situation in which certain atoms, or groups of atoms, occupy slightly different orientations from molecule to molecule over the large volume relatively speaking covered by the crystal lattice.

This static displacement of atoms can simulate the effect of thermal vibration on the scattering power of the "average" atom. Consequently, differentiation between thermal motion and static disorder can be ambiguous, unless data collection is performed at low temperature which would negate much of the thermal motion observed at room temperature.

In most cases, this disorder is easily resolved as some non-crystallographic symmetry elements acting locally on the weakly coordinating anion.

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This is accomplished by replacing For instance, the "NAME. Note that for more heavily disordered structures, i.

Physical and non-physical methods of solving crystal structures

These are designated in FVAR as the second, third, and fourth terms. INS" file for treatment of disordered tetrafluoroborate. In small molecule refinement, the case will inevitably arise in which some kind of restraints or constraints must be used to achieve convergence of the data. A restraint is any additional information concerning a given structural feature, i. For example, aromatic systems are essentially flat, so for refinement purposes, a troublesome ring system could be restrained to lie in one plane.

Restraints are not exact, i. Restraints can be regarded as falling into one of several general types:. Adapted from P. The disorder is a rotation about the axis of the B 1 -F 1 bond. Restraints were lifted for final refinement cycles. Adapted from J. Allen, C. Hamilton, and A.

Barron, Dalton Trans. All restraints, with the exception of SIMU, were lifted for final refinement cycles. Allen and A. Barron, J. Crys t. Tilt angles range from 6. The disordered BF 4 - anion present in the crystal structure of [Cu Ph-dpa styrene ]BF 4 was refined having fractional site occupancies for all four fluorine atoms about a rotation slightly tilted off the B 1 -F 2A bond. Adapted from S. Martinez-Vargas, R. Toscano, and J. Valdez-Martinez, Acta Cryst. Although a wide range of tilt angles are possible, in some systems the angle is constrained by the presence of hydrogen bonding.

By crystallographic symmetry, the carbon atom from methanol and the boron atom from the BF 4 - anion lie on a C 2 -axis. MeOH between anion and solvent of crystallization, both disordered about a crystallographic C 2 -rotation axis running through the B 1 … C 1S vector.


Multiple disorders can be observed with a single crystal unit cell. For example, the two BF 4 - anions in [Cu Mes-dpa styrene ]BF 4 both exhibited site occupancy disorders, the first is a C 2 -rotation tilted off one of the B-F bonds, while the second is disordered about an inversion centered on the boron atom. Another instance in which the BF 4 - anion is disordered about a crystallographic symmetry element is that of [Cu H-dpa 1,5-cyclooctadiene ]BF 4. In this instance fluorine atoms F 1 through F 4 are present in the asymmetric unit of the complex.

Restraints were lifted for final refinement cycles, in which the boron atom lies on a crystallographic mirror plane, and all four fluorine atoms are reflected across. Mague and S. Hawbaker, J. In fact, some disorders of the latter types must be refined isotropically, or as a last-resort, not at all, to prevent one or more atoms from turning non-positive definite. Szklarz, M. Owczarek, G. Bator, T.

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Lis, K. Gatner, and R. Jakubas, J. Principles of X-Ray Diffraction XRD The simplest definition of diffraction is the irregularities caused when waves encounter an object. Evolution of Powder XRD Over time, XRD analysis has evolved from a very narrow and specific field to something that encompasses a much wider branch of the scientific arena. There are two main methods for interpreting diffraction data: The first is known as the traditional method, which is very straightforward, and bears resemblance to single crystal data analysis. This method involves a two step process: 1 the intensities and diffraction patterns from the sample is collected, and 2 the data is analyzed to produce a crystalline structure.

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As mentioned before, however, data from a powdered sample is often obscured by multiple diffraction patterns, which decreases the chance that the generated structure is correct. The second method is called the direct-space approach. This method takes advantage of the fact that with current technology, diffraction data can be calculated for any molecule, whether or not it is the molecule in question.

Even before the actual diffraction data is collected, a large number of theoretical patterns of suspect molecules are generated by computer, and compared to experimental data.

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  • Based on correlation and how well the theoretical pattern fits the experimental data best, a guess is formulated to which compound is under question. This method has been taken a step further to mimic social interactions in a community. For example, first generation theoretical trial molecules, after comparison with the experimental data, are allowed to evolve within parameters set by researchers. Furthermore, if appropriate, molecules are produce offspring with other molecules, giving rise to a second generation of molecules, which fit the experimental data even better.

    Just like a natural environment, genetic mutations and natural selection are all introduced into the picture, ultimately giving rise a molecular structure that represents data collected from XRD analysis.