Properties of solids. Properties of Solids As you should remember from the kinetic molecular theory, the molecules in solids are not moving in the same manner as those in liquids or gases. Solid molecules simply vibrate and rotate in place rather than move about.
Solids are generally held together by ionic or strong covalent bonding, and the attractive forces between the atoms, ions, or molecules in solids are very strong. In fact, these forces are so strong that particles in a solid are held in fixed positions and have very little freedom of movement. Solids have definite shapes and definite volumes and are not compressible to any extent. There are two main categories of solids—crystalline solids and amorphous solids. Download as Powerpoint Presentation (.ppt /.pps), PDF File (.pdf), Text. 2.Since different covalent solids have very much different bond strengths.Crystalline solids are those in which the atoms, ions, or molecules that make up the solid exist in a regular, well- defined arrangement. The other main type of solids are called the amorphous solids. Amorphous solids do not have much order in their structures. Though their molecules are close together and have little freedom to move, they are not arranged in a regular order as are those in crystalline solids. Common examples of this type of solid are glass and plastics. There are four types of crystalline solids: Ionic solids—Made up of positive and negative ions and held together by electrostatic attractions. Valence bond theory; Generalized valence bond Modern valence bond. Electronic band structure; Nearly free electron model. Band theory has been successfully used to explain many physical properties of solids. Valence Bond (VB) theory. The theory that once charted the mental map of chemists has been abandoned since the mid 1960s for reasons that are discussed in Chapter 1. They’re characterized by very high melting points and brittleness and are poor conductors in the solid state. An example of a molecular solid is sucrose. Covalent- network (also called atomic) solids—Made up of atoms connected by covalent bonds; the intermolecular forces are covalent bonds as well. Characterized as being very hard with very high melting points and being poor conductors. Examples of this type of solid are diamond and graphite, and the fullerenes. As you can see below, graphite has only 2- D hexagonal structure and therefore is not hard like diamond. The sheets of graphite are held together by only weak London forces! Metallic solids—Made up of metal atoms that are held together by metallic bonds. Characterized by high melting points, can range from soft and malleable to very hard, and are good conductors of electricity. CRYSTAL STRUCTURES WITH CUBIC UNIT CELLS (From https: //eee. RDGcrystalstruct. Crystalline solids are a three dimensional collection of individual atoms, ions, or whole molecules organized in repeating patterns. These atoms, ions, or molecules are called lattice points and are typically visualized as round spheres. The two dimensional layers of a solid are created by packing the lattice point “spheres” into square or closed packed arrays. Figure 1: Two possible arrangements for identical atoms in a 2- D structure. Stacking the two dimensional layers on top of each other creates a three dimensional lattice point arrangement represented by a unit cell. A unit cell is the smallest collectionof lattice points that can be repeated to create the crystalline solid. The solid can be envisioned as the result of the stacking a great number of unit cells together. The unit cell of a solid is determined by the type of layer (square or close packed), the way each successive layer is placed on the layer below, and the coordination number for each lattice point (the number of “spheres” touching the “sphere” of interest.)Primitive (Simple) Cubic Structure. Placing a second square array layer directly over a first square array layer forms a . The simple “cube” appearance of the resulting unit cell (Figure 3a) is the basis for the name of this three dimensional structure. This packing arrangement is often symbolized as . The coordination number of each lattice point is six. This becomes apparent when inspecting part of an adjacent unit cell (Figure 3b). The unit cell in Figure 3a appears to contain eight corner spheres, however, the total number of spheres within the unit cell is 1 (only 1/8th of each sphere is actually inside the unit cell). The remaining 7/8ths of each corner sphere resides in 7 adjacent unit cells. The considerable space shown between the spheres in Figures 3b is misleading: lattice points in solids touch as shown in Figure 3c. For example, the distance between the centers of two adjacent metal atoms is equal to the sum of their radii. Refer again to Figure 3b and imagine the adjacent atoms are touching. The edge of the unit cell is then equal to 2r (where r = radius of the atom or ion) and the value of the face diagonal as a function of r can be found by applying Pythagorean’s theorem (a. Figure 4a). Reapplication of the theorem to another right triangle created by an edge, a face diagonal, and the body diagonal allows for the determination of the body diagonal as a function of r (Figure 4b). Few metals adopt the simple cubic structure because of inefficient use of space. The density of a crystalline solid is related to its . The packing efficiency of a simple cubic structure is only about 5. The first layer of a square array is expanded slightly in all directions. Then, the second layer is shifted so its spheres nestle in the spaces of the first layer (Figures 5a, b). This repeating order of the layers is often symbolized as . Like Figure 3b, the considerable space shown between the spheres in Figure 5b is misleading: spheres are closely packed in bcc solids and touch along the body diagonal. The packing efficiency of the bcc structure is about 6. The coordination number for an atom in the bcc structure is eight. How many total atoms are there in the unit cell for a bcc structure? Draw a diagonal line connecting the three atoms marked with an . Assuming the atoms marked ? Find the edge and volume of the cell as a function of r. Cubic Closest Packed (ccp)A cubic closest packed (ccp) structure is created by layering close packed arrays. The spheres of the second layer nestle in half of the spaces of the first layer. The spheres of the third layer directly overlay the other half of the first layer spaces while nestling in half the spaces of the second layer. The repeating order of the layers is . The coordination number of an atom in the ccp structure is twelve (six nearest neighbors plus three atoms in layers above and below) and the packing efficiency is 7. Figure 6: Close packed Array Layering. The 1st and 3rd layers are represented by lightspheres; the 2nd layer, dark spheres. The 2nd layer spheres nestle in the spaces of the 1stlayer marked with an “x”. The 3rd layer spheres nestle in the spaces of the 2nd layer thatdirectly overlay the spaces marked with a “. The fcc unit cell contains 8 corner atoms and an atom in each face. The face atoms are shared with an adjacent unit cell so each unit cell contains . Atoms of the face centered cubic (fcc) unit cell touch across the face diagonal (Figure 9). What is the edge, face diagonal, body diagonal, and volume of a face centered cubic unit cell as a function of the radius? Figure 8: The face centered cubic unit cell is drawn by cutting a diagonal plane throughan ABCA packing arrangement of the ccp structure. The unit cell has 4 atoms (1/8 ofeach corner atom and . Figure 9b: The face of fcc. Face diagonal = 4r. Ionic Solids. In ionic compounds, the larger ions become the lattice point “spheres” that are the framework of the unit cell. The smaller ions nestle into the depressions (the “holes”) between the larger ions. There are three types of holes: . Cubic and octahedral holes occur in square array structures; tetrahedral and octahedral holes appear in close- packed array structures (Figure 1. Which is usually the larger ion – the cation or the anion? How can the periodic table be used to predict ion size? What is the coordination number of an ion in a tetrahedral hole? Holes in ionic crystals are more like . Small ions can fit into these holes and are surrounded by larger ionsof opposite charge. The type of hole formed in an ionic solid largely depends on the ratio of the smaller ion’s radius the larger ion’s radius (rsmaller/rlarger). Table 2 lists types of atoms and the fraction contained in the unit cell. The number of each ion in the unit cell is determined: 1/8 of each of the 8 corner X ions and 1/4 of each of the 1. Y ions are found within a single unit cell. Therefore, the cell contains 1 X ion (8/8 = 1) for every 3 Y ions (1. XY3. When writing the formula of ionic solids, which comes first? Second Method: The second method is less reliable and requires the examination of the crystal structure to determine the number of cations surrounding an anion and vice versa. The structure must be expanded to include more unit cells. Figure 1. 2 shows the same solid in Figure 1. Examination of the structure shows that there are 2 X ions coordinated to every Y ion and 6 Y ions surrounding every X ion. A 2 to 6 ratio gives the same empirical formula, XY3. Summary: Simple Cubic: 1 total atom per cell (1/8 each corner)Body Centered Cubic: 2 atoms per cell (1 in center and 1/8 for each corner) Face Centered Cubic: 4 atoms per cell (1/2 per face and 1/8 for each corner).
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