Crystallography

8 Key excerpts on "Crystallography"

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  Nanoparticles in Nanotechnology

  • (Author)
  • 2014(Publication Date)
  • The English Press

    (Publisher)

  X-ray Crystallography is still the chief method for characterizing the atomic structure of new materials and in discerning materials that appear similar by other experiments. X-ray crystal structures can also account for unusual electronic or elastic properties of a material, shed light on chemical interactions and processes, or serve as the basis for designing pharmaceuticals against diseases. In an X-ray diffraction measurement, a crystal is mounted on a goniometer and gradually rotated while being bombarded with X-rays, producing a diffraction pattern of regularly spaced spots known as reflections . The two-dimensional images taken at different rotations are converted into a three-dimensional model of the density of electrons within the crystal using the mathematical method of Fourier transforms, combined with chemical data known for the sample. Poor resolution (fuzziness) or even errors may result if the crystals are too small, or not uniform enough in their internal makeup. X-ray Crystallography is related to several other methods for determining atomic structures. Similar diffraction patterns can be produced by scattering electrons or neutrons, which are likewise interpreted as a Fourier transform. If single crystals of sufficient size cannot be obtained, various other X-ray methods can be applied to obtain less detailed information; such methods include fiber diffraction, powder diffraction and small-angle X-ray scattering (SAXS). If the material under investigation is only available in the form of nanocrystalline powders or suffers from poor crystallinity, the methods of electron Crystallography can be applied for determining the atomic structure. For all above mentioned X-ray diffraction methods, the scattering is elastic; the scattered X-rays have the same wavelength as the incoming X-ray. By contrast, inelastic X-ray scattering methods are useful in studying excitations of the sample, rather than the distribution of its atoms.

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  Solid State Characterization of Pharmaceuticals

  • Richard A. Storey, Ingvar Ymén, Richard A. Storey, Ingvar Ymén(Authors)
  • 2011(Publication Date)
  • Wiley-Blackwell

    (Publisher)

  Chapter 2 X-Ray Diffraction Chris J. Gilmore University of Glasgow, Scotland 2.1 Introduction

  X-ray diffraction and X-ray Crystallography have been described as the gold standard in the characterization of pharmaceutical materials in the solid state. Certainly its importance cannot be overstressed. It is the source of much of our knowledge of the three-dimensional structure of matter; it is also used for fingerprinting and quantitative analysis because it is so sensitive to small chemical changes. A crystal structure is a source of a wealth of information of great pharmaceutical importance: it is the major source of our knowledge of crystal packing, hydrogen bonding and structural conformation, and it acts as a source for understanding the physical properties of the solid state.

  In this chapter we will first describe some basic theory relating to X-rays, crystals and their interactions, and then examine the information that can be obtained in the context of the characterization of pharmaceutical materials. To begin we need to understand the nature of X-rays and crystals and the way they interact.

  2.2 Generation and Properties of X-Rays

  X-rays occupy that part of the electromagnetic spectrum with wavelengths between 10−7 and 10−11  m. Crystallography, in general, works in units of Å where 1 Å = 10−10  m, so this range is usually expressed as 1000–0.1 Å. The higher, soft X-ray, end of this range is not useful in a crystallographic context and we will focus on the hard X-ray region between ca. 0.5–2.0 Å. These X-rays are generated in two ways:

  • the rapid deceleration of high energy electrons;
  • the emission of radiation when an electron decays from an M or L-level atomic energy level to a K-level in a metal atom.

  In practice, this is quite simply achieved in a sealed laboratory tube by using a heated filament (the cathode) as a source of electrons, which are then accelerated though a voltage of 40–50 kV and strike a target (the anode) that is usually Cu, Mo, Cr or Ag. Each of these targets produces a characteristic X-ray spectrum. Figure 2.1 shows an example for Cu. There is a smooth background with a sharp, low wavelength cut off (called the ‘Bremsstrahlung’ radiation) caused by decelerated electrons and sharp peaks caused by electronic transitions from the L to K levels (the Kα1 and Kα2 radiation) and from the M to K levels (the Kβ

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  Crystallography

  An Introduction for Earth Science (and other Solid State) Students

  • E. J. W. Whittaker(Author)
  • 2013(Publication Date)
  • Pergamon

    (Publisher)

  PART II This page intentionally left blank CHAPTER 8 The Basis of X-ray Crystallography THE use of X-rays in Crystallography is largely unrelated to their property of penetrating through material objects with which they are often primarily associated; it is dependent on the fact that they have a wave-like nature with a wavelength that is of the same order of magnitude as the distances between neighbouring atoms in chemical structures. In fact, as we shall see later, X-rays that have the most useful wavelengths in Crystallography have a very restricted ability to penetrate material objects, as compared with the X-rays that are used for medical and industrial purposes. The generation of X-rays suitable for use in Crystallography, and their particular properties, will be discussed later in this chapter; in order to introduce their use we need to know merely that they are electromagnetic radiation, like light but with very much shorter wavelength. By suitable experimental arrangements we may obtain X-rays having either a wide range of wavelengths, or a very narrow range (and virtually a specific wavelength), and by analogy with light we describe these as white X-rays and monochromatic X-rays respectively. X-rays are scattered in all directions when they hit electrons, and they are therefore scattered in their passage through matter by the electrons present in the atoms. However, if the matter concerned is a crystal then the scattering takes place only in specific directions that depend on the repeating pattern of the crystal structure. The direction in which scattering occurs can therefore be used as a means of investigating the nature of the repeating pattern that we were led to postulate in Chapter 2 in order to account for crystal morphology. A crystal structure is a three-dimensional repeating pattern of atoms in which we can define a lattice of similar, similarly situated, points which define the repetitive character of the pattern.

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  Semiconductor Silicon Crystal Technology

  • Fumio Shimura(Author)
  • 2012(Publication Date)
  • Academic Press

    (Publisher)

  Chapter 3 Basic Crystallography Classic Crystallography was established during the seventeenth to nineteenth centuries. T h e aims were to classify natural crystal morphologies based on observation a n d to study their macroscopic physical properties. However, it was the discovery of X-ray diffraction by the a t o m s of solids by Laue, Friedrich, a n d K n i p p i n g in 1912, proving for the first time the regular a n d periodic a r r a n g e m e n t of the a t o m s in a crystal structure, that enabled the investigation of the a t o m i c structure of materials. T h e aims of crystallogra-phy as developed by von L a u e et al. a n d later by W. H. Bragg a n d W. L. Bragg have been to investigate the microscopic structure of materials a n d their d y n a m i c behavior due to external a n d internal stimulation. M o d e r n Crystallography has contributed to wide academic areas, such as physics, chemistry, a n d biology. In these days, particularly, m o d e r n Crystallography as technological Crystallography has greatly contributed to marvelous progress of the electronics technology that is based mainly o n semiconductor crystals. In this chapter, c r y s t a l is defined first a n d then the structure of crystals determined by X-ray analyses is introduced. A basic idea of crystal lattice defects, which greatly affect the performance of electronic devices, is also discussed. Finally, the structure of the silicon crystal is presented. T h e knowledge of crystal structures a n d crystal defects surely helps in under-standing the subjects that will be dealt with in the following chapters. 3.1 Solid-State Structure 3.1.1 Crystalline and Noncrystalline Materials In Section 2.2.1, the three states of aggregation were described: the solid state, the liquid state, a n d the gaseous state. T h e solid state m a y be classified into 2 2 3.1 Solid-State Structure 2 3 polycrystalline o OQQ ^^iraDqQpoa TTXI amorphous polycrystalline single-crystalline Fig.

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  Recent Advances in Crystallography

  • Jason B. Benedict(Author)
  • 2012(Publication Date)
  • IntechOpen

    (Publisher)

  Subsequently, the growth of crystals became a part of problem solving in metallurgy, physics, chemistry, and pharmacology, connecting Crystallography with many branches of pure and applied science. This prevented Crystallography from coalescing as an independent science for a long time. Crystallography was variously considered as a part physics, chemistry, mathematics, or especially mineralogy. In the 19 th Century, Crystallography was “preparatory mineralogy”. Young Fedorov called Crystallography “geometrical mineralogy”. Even after having placed the capstone on the science of classical Crystallography with the derivation of the space groups, Fedorov wrote at the end of his life: “[Crystallography] plays an essential role at the heart of mineralogy and as part of mining science whose primary purpose is utilization of natural resources” (Fedorov, 1955). Only recently has the characterization of Crystallography as a “servant of mineralogy” faded. Today even cell biologists, and biomedical researchers embrace Crystallography although this aspect of the history of Crystallography is not covered herein. Metzger, it her doctoral dissertation Genèse de la Science d’Cristaux (1918), previously considered Crystallography’s emergence from other sciences. Nevertheless, there is backflow; advances in the aforementioned disciplines draw Crystallography back in. For instance, according to Vernadsky, “Crystallography has not been separated from mineralogy. It embraced mineralogy in a new way, entered its foundations and changed it radically…Mineralogy does not need to free itself from the physical sciences. Rather we must build new relationships between Crystallography and mineralogy so as to transform the latter” (Vernadsky, 1928). Similar things have been said about the relationship of Crystallography to chemistry (Engels, 1954) and to pharmacy (Fabian, 1967).

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  X-Ray Fluorescence Spectrometry

  • Ron Jenkins(Author)
  • 2012(Publication Date)
  • Wiley-Interscience

    (Publisher)

  CHAPTER 3

  X-RAY DIFFRACTION

  3.1. USE OF X-RAY DIFFRACTION TO STUDY THE CRYSTALLINE STATE

  A crystal consists of atoms or molecules arranged in patterns that are repeated regularly in three dimensions. The smallest repeat unit, the unit cell, of this three-dimensional unit may consist of one or many atoms. In a given crystal, all of the individual unit cells must be identical in orientation and composition. While the term crystallinity is commonly used to explain diffraction phenomena, it is not an ideal term since it is generally related to physical characteristics, such as shape and luster, observable by eye or with the optical microscope. In practice, there are many cases of materials giving diffraction patterns, where such physical properties are not visibly apparent, because the size of the particles is so small. In fact, the property that gives rise to the interference of coherently scattered X-rays, and hence to the diffraction pattern, is order. Almost all solid materials exhibit some degree of regular order and, as shown in Section 1.6, under certain experimental circumstances, this order will give rise to an X-ray diffraction pattern. The X-ray pattern is characteristic of the material from which it was derived, because each unique compound is made up of a similarly unique combination and arrangement of atoms. X-ray diffraction patterns can thus be used to characterize materials. This is the basis of the X-ray powder method.

  X-ray patterns are recorded with an almost monochromatic X-ray source and each diffraction peak angle corresponds to one or more d-spacings. Bragg’s law, Equation 3.1 , is used to convert each observed peak maximum measured in degrees 2θ to d-spacing. When using Bragg’s law for powder diffraction, it is customary to write it in a form in which the n does not appear explicitly. That is

  (3.1)

  The d/n term is the d-value that is almost invariably used in powder diffraction. It should be noted that d/n is a submultiple of the separation between adjacent planes that pass through lattice points. The value of λ is known to a few parts per million. Thus measurements of angles at which diffraction occurs make the determination of the d-values possible, with relative ease and with high precision. Bragg’s law also shows that since the maximum value of θ is 90°, and hence the maximum value of sin θ is unity, the minimum detectable value of d will be equal to λ/2. The maximum value of d

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  Structural and Resonance Techniques in Biological Research

  • Denis Rousseau(Author)
  • 2012(Publication Date)
  • Academic Press

    (Publisher)

  The theory underlying x-ray Crystallography is dealt with briefly (Section III and Appendix A), largely to introduce the terminology, as this theory is treated extensively in numerous textbooks (see Appendix D). Its extension to phase determination in macromolecules (Section IV and V) is also straightforward. Since the subject is still evolving, some important new developments are considered in Section VII. Experimental details are considered only briefly except for the all-important area of crystallization (Section II). Crystallization of macromolecules is often viewed as a black art, in which muttering appropriate incantations at the critical moment plays a major role. While divine or other assistance should not be rejected, the general chemical procedures for crystallization are well understood and easy to conduct quickly. With hope of encouraging more scientists to at-tempt crystallization of their favorite macromolecule, an explicit experi-mental protocol, based on the general principles outlined in Section II, is given in Appendix B. Finally, Appendix C poses key questions which should be applied to any crystallographic results. Like all other techniques, macromolecular Crystallography is fallible; its limitations, and possible sources of error, should not be ignored. II. Crystallization of Macromolecules A. Strategies The procedures necessary to grow crystals of macromolecules are straight-forward, simple to execute, and do not require large amounts of time or complicated apparatus. An extensive and valuable review article and a recent book by McPherson (1976a, 1982) are devoted to the procedures necessary to grow crystals of macromolecules; much of what follows is based on a shorter article, aimed at biologists and other noncrystallographers, by Moffat (1980).

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  Metals and Materials

  Science, Processes, Applications

  • R. E. Smallman, R J Bishop(Authors)
  • 2013(Publication Date)
  • Butterworth-Heinemann

    (Publisher)

  This filtered radia-tion is sufficiently monochromatic for many X-ray techniques, but for more specialized studies when a pure monochromatic beam is required, crystal monochromators are used. The X-ray beam is then reflected from a crystal, such as quartz or lithium fluoride, which is oriented so that only the desired wavelength is reflected according to the Bragg law (see below). 5.3.2 Diffraction of X-rays by crystals The phenomena of interference and diffraction are commonplace in the field of light. The standard school physics laboratory experiment is to deter-mine the spacing of a grating, knowing the wavelength of the light impinging on it, by measur-ing the angles of the diffracted beam. The only conditions imposed on the experiment are that (1) the grating be periodic, and (2) the wavelength of the light is of the same order of magnitude as the spacing to be determined. This experiment immedi-ately points to the application of X-rays in deter-mining the spacing and inter-atomic distances in crystals, since both are about 0.1-0.4 nm in dimen-sion. Rigorous consideration of diffraction from a crystal in terms of a three-dimensional diffraction grating is complex, but Bragg simplified the problem by showing that diffraction is equivalent to symmetrical reflection from the various crystal planes, provided certain conditions are fulfilled. Figure 5.9a shows a beam of X-rays of wavelength λ, impinging at an angle öona set of crystal planes of spacing d. The beam reflected at the angle Θ can be real only if the rays from each successive plane (a) Incident >-(b) I Reflected rays ^ 0

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