Chapter III Solids PDF

 Solids We can think of solids as falling into two groups: – Crystalline—particles are in highly ordered arrangement. – All ionic solids are crystals at room temp (& much higher temps too!) Solids – Amorphous—no particular order...

 Solids We can think of solids as falling into two groups: – Crystalline—particles are in highly ordered arrangement. – All ionic solids are crystals at room temp (& much higher temps too!) Solids – Amorphous—no particular order in the arrangement of particles. – Can be from- Mix of molecules that do not fit together well Large molecules with shapes that don’t stack well Molecules that were cooled to quickly to form a crystal. Crystalline solids melt at a specific temperature BECAUSE their internal structure is regular. The intermolecular forces holding the solid particles in position are identical so they are overcome at the same temp. Amorphous ones tend to melt over a temperature range BECAUSE their internal structure is varied. Intermolecular attractions vary throughout the solid because particles are positioned differently throughout the solid. Crystalline Solids Because of the order in a crystal, we can focus on the repeating pattern of arrangement called the unit cell.  Crystalline Solids There are several types of basic arrangements in crystals, such as the ones shown above. Crystalline Solids We can determine the empirical formula of an ionic solid by determining how many ions of each element fall within the unit cell. Types and Properties of Solids 8  Ionic Solids What are the empirical formulas for these compounds? (a) Green: chlorine; Gray: cesium (b) Yellow: sulfur; Gray: zinc (c) Green: calcium; Gray: fluorine (a) (b) (c) CsCl ZnS CaF2 Ionic Bonds Three Types of Holes in Closest Packed Structures 1) Trigonal holes are formed by three spheres in the same layer. 11 Three Types of Holes in Closest Packed Structures 2) Tetrahedral holes are formed when a sphere sits in the dimple of three spheres in an adjacent layer. 12 Three Types of Holes in Closest Packed Structures 3) Octahedral holes are formed between two sets of three spheres in adjoining layers of the closest packed structures. 13  For spheres of a given diameter, the holes increase in size in the order: trigonal < tetrahedral < octahedral 14 2 = one whole atom & eight 1/8 atoms There are two ways to define the unit cell NaCl unit cell representing appropriate ion sizes The coordination number tells the number of particles surrounding a particular particle in a crystal. For ionic compounds & alloys there can be multiple coordination numbers. The coordination number tells the number of particles surrounding a particular particle in a crystal. For ionic compounds & alloys there can be multiple coordination numbers.  Covalent-Network and Molecular Solids Diamonds are an example of a covalent-network solid in which atoms are covalently bonded to each other. – They tend to be hard and have high melting points.  Covalent-Network and Molecular Solids Graphite is an example of a molecular solid in which atoms are held together with van der Waals forces. – They tend to be softer and have lower melting points. CONDUCTS electricity C6H6  Metallic Solids Metals are not covalently bonded, but the attractions between atoms are too strong to be van der Waals forces. In metals, valence electrons are delocalized throughout the solid.  Metallic Crystal Structures How can we stack metal atoms to minimize empty space? 2-dimensions vs. Now stack these 2-D layers to make 3-D structures 23  Metallic Crystal Structures Tend to be densely packed. Reasons for dense packing: - Typically, only one element is present, so all atomic radii are the same. - Metallic bonding is not directional. - Nearest neighbor distances tend to be small in order to lower bond energy. - Electron cloud shields cores from each other Have the simplest crystal structures. We will examine three such structures... 24  Simple Cubic Structure (SC) Rare due to low packing density (only Po has this structure) Close-packed directions are cube edges. Coordination # = 6 (# nearest neighbors) Click once on image to start animation (Courtesy P.M. Anderson) 25  Atomic Packing Factor (APF) Volume of atoms in unit cell* APF = Volume of unit cell *assume hard spheres APF for a simple cubic structure = 0.52 volume atoms atom a 4 unit cell p (0.5a) 3 1 3 R=0.5a APF = a3 volume close-packed directions unit cell contains 8 x 1/8 = 1 atom/unit cell Adapted from Fig. 3.24, Callister & Rethwisch 8e. 26  Body Centered Cubic Structure (BCC) Atoms touch each other along cube diagonals. --Note: All atoms are identical; the center atom is shaded differently only for ease of viewing. ex: Cr, W, Fe (), Tantalum, Molybdenum Coordination # = 8 Adapted from Fig. 3.2, Click once on image to start animation Callister & Rethwisch 8e. (Courtesy P.M. Anderson) 2 atoms/unit cell: 1 center + 8 corners x 1/8 27  Atomic Packing Factor: APF for a body-centered cubic structure = 0.68 BCC 3a a 2a Close-packed directions: Adapted from R length = 4R = 3a Fig. 3.2(a), Callister & a Rethwisch 8e. atoms 4 volume unit cell 2 p ( 3 a/4 ) 3 3 atom APF = volume a3 unit cell 28  Face Centered Cubic Structure (FCC) Atoms touch each other along face diagonals. --Note: All atoms are identical; the face-centered atoms are shaded differently only for ease of viewing. ex: Al, Cu, Au, Pb, Ni, Pt, Ag Coordination # = 12 Adapted from Fig. 3.1, Callister & Rethwisch 8e. Click once on image to start animation (Courtesy P.M. Anderson) 4 atoms/unit cell: 6 face x 1/2 + 8 corners x 1/8 29  Atomic Packing APF for a face-centered cubic structure = 0.74 Factor: FCC maximum achievable APF Close-packed directions: length = 4R = 2a 2a Unit cell contains: 6 x 1/2 + 8 x 1/8 = 4 atoms/unit cell a Adapted from Fig. 3.1(a), Callister & Rethwisch atoms 4 volume p ( 2 a/4 ) 3 8e. unit cell 4 3 atom APF = volume a3 unit cell 30  FCC Stacking Sequence ABCABC... Stacking Sequence 2D Projection B B C A A sites B B B C C B sites B B C sites A FCC Unit Cell B C 31  Hexagonal Close-Packed Structure (HCP) ABAB... Stacking Sequence 3D Projection 2D Projection A sites Top layer c B sites Middle layer A sites Bottom layer a Adapted from Fig. 3.3(a), Callister & Rethwisch 8e. Coordination # = 12 6 atoms/unit cell APF = 0.74 ex: Cd, Mg, Ti, Zn c/a = 1.633 32  Theoretical Density, r Mass of Atoms in Unit Cell Density = r = Total Volume of Unit Cell r = nA VC NA where n = number of atoms/unit cell A = atomic weight VC = Volume of unit cell = a3 for cubic NA = Avogadro’s number = 6.022 x 1023 atoms/mol 33  Theoretical Density, r Ex: Cr (BCC) A = 52.00 g/mol R = 0.125 nm n = 2 atoms/unit cell R a a = 4R/ 3 = 0.2887 nm atoms g unit cell 2 52.00 mol rtheoretical = 7.18 g/cm3 r= ractual = 7.19 g/cm3 a3 6.022 x 1023 volume atoms unit cell mol 34  Closest Packing Model Closest Packing: – Assumes that metal atoms are uniform, hard spheres. – Spheres are packed in layers. 35  The Closest Packing Arrangement of Uniform Spheres abab packing – the 2nd layer is like the 1st but it is displaced so that each sphere in the 2nd layer occupies a dimple in the 1st layer. The spheres in the 3rd layer occupy dimples in the 2nd layer so that the spheres in the 3rd layer lie directly over those in the 1st layer. 36  The Closest Packing Arrangement of Uniform Spheres abca packing – the spheres in the 3rd layer occupy dimples in the 2nd layer so that no spheres in the 3rd layer lie above any in the 1st layer. The 4th layer is like the 1st. 37 Hexagonal Closest Packing 38 Cubic Closest Packing 39  The Indicated Sphere Has 12 Nearest Neighbors Each sphere in both ccp and hcp has 12 equivalent nearest neighbors. 40 The Net Number of Spheres in a Face-Centered Cubic Unit Cell 41  Metal Alloys Substitutional Alloy – some of the host metal atoms are replaced by other metal atoms of similar size. Interstitial Alloy – some of the holes in the closest packed metal structure are occupied by small atoms. Brass is a substitutional alloy. Steel is an interstitial alloy. 42  CONCEPT CHECK! Determine the number of metal atoms in a unit cell if the packing is: a) Simple cubic b) Cubic closest packing a) 1 metal atom b) 4 metal atoms 43 CONCEPT CHECK! A metal crystallizes in a face-centered cubic structure. Determine the relationship between the radius of the metal atom and the length of an edge of the unit cell. Length of edge = r  8 44 CONCEPT CHECK! Silver metal crystallizes in a cubic closest packed structure. The face centered cubic unit cell edge is 409 pm. Calculate the density of the silver metal. Density = 10.5 g/cm3 45 Molecular solids are made of discrete covalent molecules. Examples: Iodine, naphthalene, phosphorus, sulphur, etc. The physical properties of molecular solids are governed by van der Waals forces. The individual units of these solids are discrete molecules.  Molecular solids are weak crystalline lattices made of atoms or molecules held together by weak intermolecular forces (i.e., van der Waals forces)  Crystalline lattices are an ordered, repeating arrangement of atoms/molecules.  Van der Waals forces are weak forces that exist between atom/molecules. These forces are electrostatic, meaning they are caused by the attraction/repulsion of electrical charges  consist of either atoms or molecules formed by non- polar covalent bonds (London dispersion forces), Ar, He, H2, Cl2, I2, Naphthalene.  London dispersion forces are the electrostatic forces between a non- polar species with an instantaneous dipole and a non-polar species with an induced dipole. consist of polar covalent molecules are held together by dipole-dipole interactions, Solid SO2, solid HCl.  Dipole-dipole interactions are the electrostatic forces between two polar molecules. are held together by hydrogen bonding When hydrogen is bonded to a very electronegative atom (usually N, O, or F), it will have a large, partial positive charge. Because of this, the hydrogen will be attracted to the non-bonded electrons of a nearby electronegative atom (again N, O, or F). This attraction is referred to as hydrogen bonding Weakest: London dispersion forces Dipole-dipole Strongest: Hydrogen bonding The properties of molecular solids are:  Soft Weak forces --> easy to deform  Low melting point Weak forces --> easy to overcome  Low density Density is a measure of mass per volume. The intermolecular “bonds” are long, so the space between molecules is great  Poor conductors of electricity Structure prevents electron movement  Poor thermal conductors Structure is too far apart