Indices rational

This FOM is based on the fact that all refleetions ean be described by integer indices. If the found positions give rise to rational indices then the FOM starts to rise. A perfeet indexing gives a FOM of zero. Table 1 gives typical FOM s for different degree s N. 

Acetaminophen is one of the most important drugs used in the treatment of mild to moderate pain when an anti-inflammatory effect is not necessary. Phenacetin, a prodrug that is metabolized to acetaminophen, is more toxic than its active metabolite and has no rational indications. 

Prescribe only for a specific and rational indication. Do not prescribe omeprazole for "dyspepsia."... 

It is evident from Tigs. 9 and 10 that these planes have small indices we may therefore state that the actual faces on crystals are planes with small indices. In this form the generalization is what is known as the Taw of rational indices , which says simply that all the faces on a crystal may be described, with reference to the three axes, by three small whole numbers. It is frequently found that all the faces of even richly faceted crystals can be described by index numbers not greater than 3 numbers greater than 5 are very rare. 

The same rules apply for rational indices, as is seen in the following example ... 

This rationalization indicates that internal delivery of a hydride is not a requisite for the observed stereospecificity. Reduction of the oxonium ion with an external hydride reagent should also give equatorially oriented bicyclic ether only. Accordingly (112), reduction of tricyclic spiroketal 145 with sodium cyanoborohydride at pH =3-4 yields only the equatorial bicyclic ether alcohol (J47, CHO=CH2OH). Eliel and co-workers (113) have previously suggested that the orientation of the electron pairs of oxygen atoms influence the course of the reduction of 2-alkoxytetrahydropyran with lithium aluminium hydride-aluminium trichloride. 

In 1784, Haiiy formulated the Law of Rational Indices, which states that all faces of a crystal can be described by Miller indices (hid), and for those faces that commonly occur, h, k, and l are all small integers. The eight faces of an octahedron are (111), (111), (ill), (111), (111), (111), (III), and (III). The form symbol that represents this set of eight faces is 111. The form symbol for the six faces of a cube is 100. Some examples in the cubic system are shown in Figs. 9.1.3. and 9.1.4. 

Therefore, in compliance with the Law of Rational Indices, only n-axes with n = 1,2,3,4 and 6 are allowed in crystals. The occurrence of the inversion center means that the rotation-inversion axes I, 2(= m), 3, 4 and 6 are also possible. 

It has been recognized already in the earliest stages in the history of crystallography [8] that the most important characteristic of the outer symmetry of the crystals is not really the form itself but rather two phenomena expressed by two rules. One is the constancy of the angles made by the crystal faces. The other is the law of rational intercepts or the law of rational indices. 

Usually the crystal faces are described by the reciprocals of the multiples of the standard intercepts, hence the name the law of rational indices. In Figure 9-8 three lines are adopted as axes which may also be directions of the crystal edges. A reference face ABC makes intercepts a, b, c on these axes. Another face of the crystal, e.g., DEC, can be defined by intercepts alh, blk, dl. Here h, k, l are simple rational numbers or zero. They are called Miller indices. The intercept is infinite if a face is parallel to an axis, and horkorl will be zero. For orthogonal axes the indices of the faces of a cube are (100), (010), and (001). The indices of the face DEC in Figure 9-8 are (231). 

It is important to describe each crystal face in a numerical way if data on different crystals or from different laboratories are to be compared. The method used to describe crystal faces is derived from the Law of Rational Indices, proposed by Haiiy and Arnould Carangeot. This Law states that each face of a crystal may be described, by reference to its intercepts on three noncollinear axes, by three small whole numbers (that is, by three rational indices)/ From this law, William Whewell introduced a specific way of designating crystal faces by such indices, and William Hallowes Miller popularized it. The integers that characterize crystal faces are called Miller indices h, k, and 1. When this method is used to describe crystal faces, it is rare to find h, k, or / larger than 6, even in crystals with complicated shapes. An example of the buildup of unit cells to give crystals with different faces is shown in Figure 2.11. 

Rational Indices, Law of A rational number is an integer or the quotient of two integers. The Law of Rational Indices states that all of the faces of a crystal may be described, with respect to their intercepts on three noncolinear axes, by three small whole numbers. 

An important fact about crystal faces was known long before there was any knowledge of crystal interiors. It is expressed as the law of rational indices, which states that the indices of naturally developed crystal faces are always composed of small whole numbers, rarely exceeding 3 or 4. Thus, faces of the form 100, 111, iTOO, 210, etc., are observed but not such faces as 510, 719, etc. We know today that planes of low indices have the largest density of lattice points, and it is a law of crystal growth that such planes develop at the expense of planes with high indices and few lattice points. 

Hatiy enunciated the laws governing crystal symmetry, and paved the way for his later discovery of the law of rational indices, which, in 1801, he substantiated by a comprehensive survey of the mineral kingdom. Thus by the first year of the nineteenth century the fundamental laws of morphological crystallography had been established. 

Molecular forms bring concepts back developed during the nineteenth century in which crystal growth forms were systematically investigated. At that time, atoms were not considered to be real but only as a way of expressing chemical laws [4], and lattice periodicity an hypothesis compatible with the empirical law of rational indices with no consequence for the physical nature of crystals [5]. The present molecular situation is reversed one knows that there are atoms and where the atoms are. A molecular lattice allows an interpretation of the molecular morphology, also expressible in terms of rational indices, but without a theoretical basis, even if one can speak of molecular crystallography [6]. 

Usually, the crystal faces are described by the reciprocals of the multiples of the standard intercepts, hence the name the law of rational indices. In Figure 9-8 three lines are adopted as axes which may also be directions of the... 

Efficacy, side-effects, and compliance with AGIs strongly depend on rational indication, education of patients on how to use the drug, and good dietary advice. Even with good clinical practice, a considerable variation in response and side-effects is seen. Side-effects depend, among other things, on the... 

Nineteenth-century crystallography may be considered to be the mathematical branch of mineralogy. It is based on two empirical laws, the law of constancy of angle and the law of rational indices. These laws will be presented in the following pages after a discussion of some mathematical principles fundamental to crystallography, non-unitary coordinate systems and reciprocal coordinates. 

Cleavage of crystals, in particular of calcite CaC03, and the law of rational indices generated the idea of the periodicity of crystal structures and the theory of translational lattices ... 

The analogy between the equations representing the edges and faces of a crystal on the one hand, with lattice lines and lattice planes on the other is the foundation of the theory of the periodic nature of crystal structures. This interpretation of the law of rational indices was formulated by the French abbe Auguste Bravais (1811-1863) as follows ... 

Arsenic (As) has been reported In a variety of tissues, any of which are potentially useful as indexes to exposure. However, the organic pentavalent arsenicals are not accumulated in tissues and are rapidly excreted in urine ( - ). Therefore, urine generally is a particularly valuable index to applicator exposure. Exon et al. ( 5) reported both urine and feces were Important pathways of excretion in rabbits exposed to MSMA In their feed. They found 70 of ingested As had been excreted (54% in urine, 46% in feces) during a 17-week exposure period. Arsenic levels in liver, hair, and urine were the same as in controls after 12 weeks of MSMA exposure followed by 5 weeks of control rations. Indicating excretion was ultimately fairly complete. 

Law of rational indices The lengths of intercepts of different crystal faces on any crystallographic axis are in ratios of small integers. Rhodes G (1999) Crystallography made crystal clear a guide for users of macromolecular models. Elsevier Science and Technology Books, New York. 

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