7 Key excerpts on "Crystalline Solids"

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  eBook - ePub

  General Chemistry for Engineers

  • Jeffrey Gaffney, Nancy Marley(Authors)
  • 2017(Publication Date)
  • Elsevier

    (Publisher)

  Fig. 11.1 Classification of solid materials according to their structure and properties.

  11.1 Crystalline Solids

  Some examples of Crystalline Solids are shown in Fig. 11.2 . The process by which a crystalline solid is formed is known as crystallization. Crystals can be formed by precipitating from a highly concentrated solution, by freezing of a liquid mixture, or by deposition from a gas phase. Crystallization is a chemical separation technique commonly used in industrial process that will be further discussed in Chapter 12 .

  Fig. 11.2 Some examples of Crystalline Solids.

  From Rob Lavinsky, iRocks.com , Wikimedia Commons.

  As described in Chapter 1 , a crystalline solid is a solid material with the constituent species (atoms, ions, or molecules) arranged in a highly ordered microscopic structure that extends in all directions. Because Crystalline Solids have a highly ordered internal structure that extends throughout the material, the geometric shape of the macroscopic form of a crystalline solid is dependent on the microscopic structure. The geometric shapes of these macroscopic crystals consist of flat surfaces, or faces, with sharp angles oriented in different directions. The faces intersect at angles that reflect the internal arrangement of the component species. When a crystalline solid is exposed to X-rays, the constituent species inside the crystal cause the X-ray beam to diffract into many directions. A three-dimensional picture of the microscopic arrangement of the crystalline solid can be obtained by measuring the angles and intensities of the diffracted X-ray beams, called a diffraction pattern. By using this technique, called X-ray crystallography

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  Materials Science of Thin Films

  • Milton Ohring(Author)
  • 2001(Publication Date)
  • Academic Press

    (Publisher)

  Similar divisions occur with respect to structure of solids. Solids are either internally crystalline or noncrystalline. Those that are crystalline can be further subdivided according to one of 14 different geometric arrays or lattices depending on the placement of the atoms. When properties are considered, there are similar descriptors and simplifying categorizations. Thus, materials are either good, intermediate, or poor conductors of electricity, they are either mechanically brittle or can easily be stretched without fracture, they are either optically reflective or transparent, etc. It is, of course, easier to recognize that property differences exist than to understand why they exist. Nevertheless, much progress has been made in this subject as a result of the research of the past century. Basically, the richness in the diversity of materials properties occurs because countless combinations of the admixture of chemical compositions, bonding types, crystal structures, and morphologies either occur naturally or can be synthesized.

  This chapter reviews various aspects of the structure, bonding, and properties of solids with the purpose of providing the background to better understand the remainder of the book. Additional topics dealing with thermodynamics and kinetics of atomic motion in materials are also included. These will later have relevance to aspects of the formation, stability, and solid-state reactions in thin films. This review ends with a discussion of mechanical properties, a subject of significance in phenomena ranging from film deposition to adhesion. Although much of this chapter is a condensed adaptation of standard treatments of bulk materials, it is largely applicable to thin films as well. Nevertheless, many distinctions between bulk materials and films exist and they will be stressed in the ensuing discussion. Readers already familiar with concepts of materials science may wish to skip this chapter. However, it is recommended that those who seek deeper and broader coverage of this background material should consult the general overview texts in the list of references.

  1.2 STRUCTURE

  1.2.1 Crystalline Solids

  Many solid materials possess an ordered internal crystal structure despite external appearances which are not what we associate with the term crystalline, i.e., clear, transparent, faceted, etc. Actual crystal structures can be imagined to arise from a three-dimensional array of points geometrically and repetitively distributed in space such that each point has identical surroundings. There are only fourteen ways to arrange points in space having this property and the resulting point arrays are known as Bravais lattices. They are shown in Fig. 1-1

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  An Introduction to Nuclear Materials

  Fundamentals and Applications

  • K. Linga Murty, Indrajit Charit(Authors)
  • 2013(Publication Date)
  • Wiley-VCH

    (Publisher)

  2 Fundamental Nature of Materials “FORTUNATELY crystals are seldom, if ever, perfect.”

  —Anonymous

  2.1 Crystal Structure

  Engineering materials (metals and alloys and ceramics) used in nuclear applications are almost always crystalline. That is why the understanding of crystal structure basics is very important in the context of nuclear materials. As a matter of fact, an overwhelming majority of materials crystallize when they solidify, that is, atoms get arranged in a periodic three-dimensional pattern leading to a long-range order and symmetry, while minimizing the overall free energy of the solid. However, before we start discussing the details of a crystal structure, let us assess broadly what are the different length scales in a material system. It has long been established that only a single length scale cannot adequately describe all the behaviors of a material, and that is why multiscale methodologies (Figure 2.1 ) are being increasingly implemented in modeling various materials systems, including nuclear materials. For instance, subatomic scale involves the interaction between the subatomic particles (neutrons, protons, and electrons). On the other hand, a single crystal entails an ensemble of several atoms (the smallest unit being called a unit cell ), while several such single crystals can create a polycrystalline material (microscale), and, finally, the macrostructure (basically the components, machines, etc.) can be seen by our bare eyes at the top of the length scale. Hence, to describe the behavior of a material, one needs to rely on several length scales, not just one.

  Figure 2.1 Different length scales present in a material.

  An underlying theme of the materials science and engineering (MSE) field is to understand the interrelationships of processing–structure–property , which gives one greater opportunity for predicting to a reasonable degree the materials performance under real service conditions. This is exemplified by the materials science tetrahedron, as depicted in Figure 2.2

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  Developing Solid Oral Dosage Forms

  Pharmaceutical Theory and Practice

  • Yihong Qiu, Yisheng Chen, Geoff G.Z. Zhang, Lawrence Yu, Rao V. Mantri, Yihong Qiu, Yisheng Chen, Geoff G.Z. Zhang, Lawrence Yu, Rao V. Mantri(Authors)
  • 2016(Publication Date)
  • Academic Press

    (Publisher)

  Amorphous phases are those solids that do not exhibit long-range order in any of the three physical dimensions. However, short-range order could exist for amorphous solids. Because of the importance of this class of solids to pharmaceutical development, it is discussed in detail in Section 2.7 of this chapter. If materials have long-range order in only one or two dimensions, they are liquid crystalline in nature. Liquid crystalline materials can be further categorized based on the number of components contained therein, as is the case for Crystalline Solids. Since liquid crystals, with properties intermediate to conventional liquids and three-dimensional solids, are not frequently encountered, they will not be discussed in detail. The vast majority of pharmaceutical solids fall into the category of Crystalline Solids because they exhibit long-range order in all three dimensions. Crystalline Solids can be further categorized into various subtypes based on the number of components that make up the solid internally, in a homogeneous fashion. The solid could be composed of the drug alone, or as adducts with one (binary), two (ternary), three (quaternary), other chemical species. Although the number of other chemical species, apart from the drug itself, can increase without limit, it usually is a relatively low integer. When the overall chemical composition of solids is the same, they can be different in internal structures. The ability of a substance to exist as two or more crystalline phases that have different arrangements or conformations of the molecules in a crystalline lattice is called polymorphism, and these different solids are termed polymorphs. One point to emphasize is that, according to the strict definition of this term, different polymorphs are only different physically, not chemically. When these solids are melted or dissolved in solutions, they are exactly the same, both physically and chemically

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  X-Ray Diffraction Imaging

  Technology and Applications

  • Joel Greenberg, Joel Greenberg(Authors)
  • 2018(Publication Date)
  • CRC Press

    (Publisher)

  A commonsensical approach to the discussion of X-ray coherent scatter for differentiating materials type is by considering the degree of structural order within a substance. The extremes in such cases are those materials that are crystalline and those that are either disordered Crystalline Solids or amorphous substances, exhibiting high to no structural order, respectively. We will begin by considering materials that are crystalline in nature characterized by atoms or molecules configured in a pattern periodic in three dimensions. Spectral attributes of amorphous solids and liquids will be considered in the next section.

  5.2.1 Crystallinity and Long-Range Order

  Born out of advances in X-ray structural characterization, crystallography is a field of science used to determine atomic arrangements in Crystalline Solids and forms its geometrical basis through the work of Nicolaus Steno and René-Just Haüy [16 ]. Steno’s law of constancy of angles states that angles between similar crystal facets and associated planes are constant and repeatable throughout crystalline materials. The law of rational indices was deduced by Haüy reporting that crystalline planes intersect crystallographic axes in whole number ratios.

  One of the foundational studies applied to the field of crystallography was performed in the mid-19th century by Auguste Bravais and was purely mathematical in origin. Bravais considered symmetric arrays of points to define 14 types of discrete lattices [4 ]. A three-dimensional array of lattice points is formed at the intersection of lattice planes due to long-range periodicity, as illustrated in Figure 5.3 for the generation of a single lattice point shown at the corner of a cubic lattice. As shown in Figure 5.4

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  Elements of Structures and Defects of Crystalline Materials

  • Tsang-Tse Fang(Author)
  • 2018(Publication Date)
  • Elsevier

    (Publisher)

  From the viewpoint of thermodynamics, the equilibrium structural state of a system is considered to be the minimization of the free energy under some constrains, such as constant temperature, pressure, and composition. For a solid, the related free energy can be approximated as internal energy. Thus the free energy is minimized by minimizing internal energy with reference to the lattice energy that is relevant to the interatomic potentials. Since the interatomic potential usually decreases with decreasing separation distance, most materials would adopt a very densely packed structure at low temperature. Such low-temperature, densely packed states can be said to be “internal energy stabilized” or to have a “high degree of order.”

  At sufficiently high temperatures, entropy would become dominant. Thus if the system possesses high entropy, namely, it adopts less well-ordered atomic/molecular arrangements, the free energy would be minimized. The high-temperature, more disordered equilibrium states can be referred to be “entropically stabilized” or as having a “low degree of order.” Note that for the metal iron, in addition to spatial locations of the iron atoms, the free energy depends on the structural order of magnetic spins, leading to the more open structure (BCC) at low temperatures.

  3.1 Arrangements of Atoms and Ions in Crystalline Solids: Space Lattice

  The essential characteristic of the crystalline state is the regularity in the arrangement of atoms. While the ways to describe the crystal structures are considerable, the science of crystallography has established a convenient system of classifying these structures. The structure is defined as a periodic array of lattice points associated with the pattern possessing translation symmetry, in which the surroundings viewed from an arbitrary origin are identical to the surroundings viewed from a point separated from the origin by a translation vector. The set of lattice points construct a lattice. Thus the simple way to describe the crystalline structure is to consider that it consists of a three-dimensional arrangement of lattice points in space, shown in Fig. 3.1 , where a , b , and c

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  eBook - ePub

  Materials for Engineers and Technicians

  • W. Bolton, R.A. Higgins(Authors)
  • 2014(Publication Date)
  • Routledge

    (Publisher)

  Chapter 22 .
• Electronic materials, e.g. semiconductors and ferrites.
Even some metallic materials which can be cooled quickly enough from the molten state form glasses; speeds of about 106 °C/second are necessary to prevent them from crystallising. At the other extreme, plastics materials are either completely 'glassy' or contain both crystalline and glass regions (see Figure 20.1 ) because they are composed of very large and cumbersome linear molecules which can 'wriggle' into position only with difficulty so that the process is overtaken by a fall in temperature.

21.2 Silicate-based ceramics

Those ceramic materials derived from sand, clay or cement contain the elements silicon and oxygen (the two most abundant elements on planet Earth) in the form of silicates, which also contain one or more of the metals sodium, potassium, calcium, magnesium and iron. The most simple silicon-oxygen unit in these compounds is the group in which a small silicon atom is covalently bonded to four oxygen atoms (Figure 21.1 ), the -4 indicating, as will be seen in Figure 21.1B , that each oxygen atom in this unit has an 'unused' valency bond. Thus, these units can link up, rather like the 'mers' in a polymer structure, to form a continuous structure. A number of different basic structures can be formed in this way, but two of the more important are described here.
Figure 21.1 (A) The structure of the
unit in silicates. (B) The small central silicon atom surrounded by and covalently bonded to four oxygen atoms. (C) Here, the silicon atom is omitted to simplify the diagram of the unit. (D) A 'plan' view of the
unit, i.e. with the 'apex' oxygen atom A on 'top', again with the silicon atom omitted.