Indexing tetragonal crystal system

The x-ray diffraction powder pattern for Mg2NiH4 was indexed on the basis of a tetragonal crystal system with unit cell dimensions of a = 6.464 A and c = 7.033 A. The measured density was 2.57 g/cm3, compatible with four formula units of Mg2NiH4 per unit cell. 

We will begin with the cubic crystal system, where the assignment of indices is nearly transparent and then consider the theory behind the ab initio indexing in crystal systems with tetragonal and hexagonal symmetry. Indeed, as with any kind of experimental work, experience is paramount, and we hope that the contents of this section may help the reader to achieve accurate solutions of real life indexing tasks successfully. 

Unfortunately, the X-ray diffraction patterns for different UZM-5 preparations showed broad peaks (due to the very small crystalhte size and anisotropic morphology) and were not of sufficient quality for ah initio structure solution. However, indexing the patterns did provide the crystal system (tetragonal) and approximate... 

For powder photographs, the use of the charts described on p. 143 and in Appendix 3 will show whether the substance is cubic, tetragonal, or hexagonal if it is not, the numerical methods of indexing the patterns of crystals of low symmetry may be tried or, if it is. possible to pick out single crystals, or if the specimen can be recrystallized to give suitable crystals, the unit cell dimensions may be determined by the methods described earlier. A search may then be made in the tables of Donnay and Nowacki (1954), in which, for each crystal system, the species are arranged in order of the axial ratios. 

Porter, M. W. and Spiller, R. C. (1951). Crystals of the tetragonal, hexagonal, trigonal and orthorhombic systems. In The Barker index of crystals. A method for the identification of crystalline substances, Vol. 1, W. Heffer Sons, Cambridge. [14, 95] Porter, M. W. and Spiller, R. C. (1956). Crystals of monoclinic system. In The Barker index of crystals. A method for the identification of crystalline substances, Vol. 2, W. Heffer Sons, Cambridge. [14]... 

At this point (or after the whole pattern has been indexed) the analysis of the observed values of A enables one to establish whether we deal with the tetragonal or hexagonal crystal systems. As seen in Table 5.19, the whole multipliers of a are 1 and 3, and 3 is only possible in the hexagonal crystal system for A =, k= 1. After a simple calculation using the average values of a and c listed in Table 5.19 we find approximate values of a and c as 5.046 and 4.015 A, respectively. A least squares refinement of the lattice parameters using the entire array of indexed Bragg peaks obviously yields the same lattice parameters as were established before (see Table 5.6). 

Compounds belonging to the cubic crystal system have only a single refractive index value, but other systems are anisotropic, so that the crystal is characterized by two or three unique indexes. Hexagonal, rhombohedral, and tetragonal crystals have two unique indexes which are traditionally labeled and for ordinary ray and extraordinary ray . Orthorhombic, monoclinic, and triclinic crystals are characterized by three indexes which are here called n, and n. The table indicates the crystal system for each entry in order to identify the material uniquely. 

Fortunately, but also evidently, many simplifications arise when considering the uniaxial indicatrix of crystals belonging to the trigonal, tetragonal, and hexagonal crystal systems. First, there is only one optic axis which, by convention, always lies along the z crystallographic axis hence, X, Y, and Z disappear, as z suffices to define this direction. The refractive index associated with this direction is called or n. The plane perpendicular to the optic axis is necessarily a circular section whose diameters all have the same refractive index denoted or n. Thus, and Hy disappear. Optically positive means... 

Optically uniaxial crystals may be tetragonal, hexagonal, or trigonal. If it is possible to recognize a shape characteristic of a particular system this information is useful supplementary evidence but it must be emphasized that the refractive index values by themselves are usually sufficient for identification. 

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