Engineering Physics of High-Temperature Materials. Nirmal K. Sinha

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СКАЧАТЬ knowledge, even at the rudimentary level, of minerals is also necessary for materials scientists and engineers, including geologists, metallurgists, chemists, and physicists. A “mineral” may simply be defined as a naturally occurring inorganic substance that is chemically homogeneous and has an ordered internal structure. Common mineral groups include silicates, oxides, sulfates, sulfides, carbonates, halides, and the native elements. The rocks of Earth's crust, lithosphere, and – to some extent – asthenosphere consist of units that are essentially minerals with wide‐ranging chemical and physical properties.

      While the basic trinity of classification is one of the primary ways in which materials classification is accomplished, other methods of grouping materials have evolved to support research and development in specific fields. For example, although not generally explored in the traditional basic trinity of materials classification, “semiconductors” are an important classification in our modern age. As the name implies, semiconductors are classified largely based on their electronic properties. In a semiconducting material, the electrical conductivity falls between that of a conductor (metal) and an insulator. Semiconductors are typically characterized as having covalent bonding. Traditional semiconductors include elements (also termed metalloids) like silicon and compounds like gallium arsenide, but semiconducting properties are also being designed into polymers and ceramics.

      Trinity of States

      GAS

      LIQUID

      SOLID

      Materials consisting of single elements or compounds can exist in three well‐defined physical states: gas, liquid, and solid. These states depend on temperature and pressure.

A “gas” is a state of matter in which the atoms or molecules are separated by a large distance. Molecules in the gaseous state vibrate and move freely to occupy the volume made available. A related term is “vapor,” which technically refers to a material that is in the gaseous state at conditions in which it can also exist in the liquid or solid state (i.e. below its critical temperature, described further later in the text). Often, the terms “vapor” and “gas” are used synonymously.

      A “liquid” is, in general, a condensed state of matter in which the particles are irregularly spaced (or, in other words, there is no long‐range order); that is, they are amorphous in nature. Unlike gases, liquids are generally not easily compressible; however, they flow easily.

      On the other hand, under such basic classification schemes, “solids” are materials in which the particles are regularly spaced and form repeating structures in three dimensions; that is, they are crystalline in nature. Solids generally retain a fixed volume and shape and do not flow easily.

      The outcome of such classification leads to some interesting areas to consider. For example, amorphous materials, such as traditional glasses, which are usually considered solid materials in everyday use, are classified as supercooled liquids (albeit this is debatable), and materials like liquid crystals, amorphous metals, and supercritical gases fall somewhat between the phase definitions. In addition, a fourth state, i.e. “plasma,” is introduced to describe matter at very high temperatures and pressures where the atoms start to break down resulting in a mixture of neutral atoms, free electrons, and charged ions. The sun, lightning, and beautifully colored auroras are examples of plasmas in nature.

      Significant progress has been made in understanding the states and their boundaries, particularly for metals, metallic alloys, and ceramics (Reed‐Hill and Abbaschian 1992; chapter 10). The fluid states (liquid, gas, and plasma), though particularly important for process industries and for specific applications, are often not discussed when dealing with the compositions, physical metallurgy, and engineering mechanics revolving around microstructure–property relationships. Understanding the solid state is, however, of the utmost practical importance for all engineering applications for metals, alloys, and ceramics.

      Due to the complex nature of materials, the modern‐day classification of states often relies on a more sophisticated system that focuses on the elastic response of the material. At a high level, in this scheme, solids respond to shear stress by the momentary relative motion of adjacent layers of particles whereas fluids undergo continuous relative motion or flow (DeVoe n.d.; chapter 2). This difference between states depends not only on temperature and pressure, but also on the timescale of observation. Time dependency will be a critical aspect explored throughout this text.

2.2 Solid‐state Materials

      As materials, solids can largely be grouped into crystalline and amorphous materials. Crystalline solids are those in which the atoms are regularly spaced and form repeating structures in three dimensions. This definition of solids applies to the traditional classification of phases. Amorphous materials do not have any long‐range order in their structures, but they have demonstrated unique properties of interest to engineers.

2.2.1 Structure of Crystalline Solids

      The three‐dimensional structure or arrangement of atoms is called the crystal structure of the solid. The unit cells are the repeating structures in the crystal, and the smallest repeating unit is called the primitive unit cell. The Bravais lattice concept is generally used to define the structure. There are 14 Bravais lattices that define arrangements that can fill three‐dimensional space. Lattice constants refer to the physical dimensions of the unit cells and are generally denoted by a, b, and c.

      To describe crystallography, points, direction, and planes are given indices that are used in conjunction with the lattice constants. Points are given labels, like points in a Cartesian coordinate system so that the point represented by coordinate ua, vb, and wc is u, v, and w units along the corresponding lattice direction. A direction is denoted with square brackets such that [uvw] represents a direction parallel to the direction of the origin with the point at coordinates ua, vb, and wc. A family of directions represents all directions in the lattice that are similar by symmetry and are denoted as <uvw>. In crystallography, planes are defined by their Miller indices. Miller indices rely on the reciprocal lattice vectors rather than the direct Bravais lattice. For simplicity, a plane with Miller index (hkl) represents the plane that passes through the points (a/h, 0, 0), (0, b/k, 0), and (0, 0, c/l). A family of planes represents all planes in the lattice that are similar by symmetry and are denoted as {hkl}. For more information on crystallography, there are several resources available, such as Vainshtein et al. (1982) and Mak and Gong‐Du (1992).

      Trinity of Crystal Structure

      BODY‐CENTERED CUBIC

      FACE‐CENTERED CUBIC

      HEXAGONAL CLOSE‐PACKED

Nature's efficiency in packing leads to the abundance of three main crystal structures. While these structures do not describe all materials, their prevalence makes them important to dive into and enables understanding of similar structures. Two of these structures are based on a simple cubic arrangement. The simple cubic structure consists of atoms placed on each corner of a cube. The simple cubic unit cell is thus a cube containing 1/8 of each corner atom for a total of one atom per unit cell. The distance between the corners of the cube is called the unit cell dimension, which is commonly denoted as the lattice constant, “a.” Assuming the highest packing efficiency in the simple cube and the model of an atom as incompressible spheres of radius “r” we have a = 2r. Three of the most common crystal structures in nature are the body‐centered СКАЧАТЬ