Gases, Liquids, and Solids - Types of Solids (PDF)

Solids Solids have a definite volume and shape. The particles are tightly packed and hardly move. Solids can be: crystalline amorphous NaC si...

Solids Solids have a definite volume and shape. The particles are tightly packed and hardly move. Solids can be: crystalline amorphous NaC si H20 plastic ordered - arrangement of atoms/molecules random arrangment of atoms 70 © L. Pei, H. Taha, A, Mar, Department of Chemistry, University of Alberta (2024)  Types of Crystalline Solids: Discrete (molecular) Structures solids can be classified according to the structural entities (particles) present and the interparticle forces between them. Structural model Dominant Type Physical properties Examples (Structural be particles) interparticle forces formed atoms or single dispersion Soft CHyls)-182 ° C Non-polar Low mp COLs)-78 ° Csubvert Poor thermal and 1890 electrical conductors Arcss - molecule non polar , dipole-dipot H20(s)0 % Polar Fairly soft Hydrogen- CH-bonding Low to moderate mp CHCls (s) - 64° bonded Poor thermal and electrical conductors polar molecules 71 © L. Pei, H. Taha, A, Mar, Department of Chemistry, University of Alberta (2024)  Types of Crystalline Solids: Extended Structures Structural model Dominant Type (Structural Physical properties Examples interparticle forces particles) ionicbording Cs2lis 645 % Ist Hard and brittle , Cl High mp Ionic Good thermal and (when molten) 2800" electrical conductors MgOcs anic bindry fore excrete cation covalent Cldiamond) >3300 Very hard Covalent Very high mp 1600: network Usually poor thermal and electrical S: 02 (quarte conductors atoms metallic Soft to hard Nas 98 % Usually high mp Metallic bonding Lustrous Wass 3400c Ductile, malleable Excellent thermal and electrical conductors cations and delodized e 72 © L. Pei, H. Taha, A, Mar, Department of Chemistry, University of Alberta (2024)  Example Match these solids with their properties: Pb(s), P4S3(s), BN(s), CaCl2(s). Ph(ss mp 327 ºC, shiny solid, conducts electricity _____ metallic CaCle(S) _____ mp 772 ºC, white solid, conducts electricity when molten ioni ______ mp 172 ºC, yellow-green solid molecular solid ______ mp 3000 ºC, very hard solid covalent network sold 73 © L. Pei, H. Taha, A, Mar, Department of Chemistry, University of Alberta (2024)  Structures of Crystals The highly symmetrical external shapes of crystals suggests a regular ordered arrangement of atoms. There are a very large number of atoms, so we need a compact way to describe their arrangement. We do this by defining: – unit cell: _______________ smallest report unit (consistent with _________________________) highest symmetry of structur which, when translated, ________________________________. structure reproduces the entire crystal In general, to describe a crystal structure, we specify a pattern, and the atoms that belong to the pattern: – lattice: a set of points such that an observer _____________________________ at one point sees exactly __________________________________________________________. the same environment as other point any – unit cell contents: set of _____ atoms whose positions are defined _______________________, relective to lattice pointy which serve as __________________________________. orgins of coordinate system A lattice is imaginary. The crystal structure is what is real. Complete lesson on “Structures of Crystals” 74 © L. Pei, H. Taha, A, Mar, Department of Chemistry, University of Alberta (2024)  Lattice and Unit Cell Contents Consider the crystal structure shown consisting of Fe (blue) and P (red) atoms. A crystal structure is an infinite, 3D periodic arrangement of atoms. How can we find a repeat unit in this structure? O 80 environ goo j 8 Pick a point, any point. Find other points with exactly the same environment. This set of points is called the lattice.* ] ↓/notsin see 75 © L. Pei, H. Taha, A, Mar, Department of Chemistry, University of Alberta (2024)  Lattice and Unit Cell Contents ↳ A possible unit cell can be outlined. O ⑭En ⑯ 10 und % & ⑳ 100 % z Ou What are the unit cell contents? 2Fe + 8 - Fe = 6 Fe 2p + 44p = 3P FebPy or Sunit of FeP *Do not confuse the lattice (which is this set of mathematical points, an imaginary construct, and thus having no physical reality) with the crystal structure (which is the arrangement of real objects, namely the atoms). Do not use the term “lattice structure,” which is nonsensical and betrays a confusion between the lattice and crystal structure. 76 © L. Pei, H. Taha, A, Mar, Department of Chemistry, University of Alberta (2024)  Lattice and Unit Cell Contents Identify the lattice and unit cell contents for cesium chloride. - · i 77 © L. Pei, H. Taha, A, Mar, Department of Chemistry, University of Alberta (2024)  Lattice and Unit Cell Contents In a primitive (“simple”) cubic lattice, the lattice points lie at the corners of a cubic unit cell. (There are multiple choices of lattice and unit cell.) lattice Centers of 8 identical particles define the corners of a cube. 78 © L. Pei, H. Taha, A, Mar, Department of Chemistry, University of Alberta (2024)  Cubic Lattices Atoms located at boundaries of a unit cell are shared with adjacent unit Cs ? cells, so count only the portions that lie within the given unit cell. Cl- What fraction of each atom contributes to the contents of the unit cell? I 12 In " centre face edge corner How many corners, faces, and edges does a cube have? 8612 79 © L. Pei, H. Taha, A, Mar, Department of Chemistry, University of Alberta (2024)  Simple Cubic Lattice Identify the lattice and unit cell contents for elemental tungsten. In a body-centred cubic lattice, the lattice points lie at the corners and centre of a cubic unit cell. 80 © L. Pei, H. Taha, A, Mar, Department of Chemistry, University of Alberta (2024)  Lattice and Unit Cell Contents We focus on three types of cubic lattices (although keep in mind that there are also other types of lattices with lower symmetry not described in introductory textbooks): b f(C primitive (simple) cubic body-centred cubic face-centred cubic %o 06 - O. corner corner and Caltica corners the and centr certre of faces at point Then, we associate atoms with respect to the lattice points. (Atoms do not always have to coincide with lattice points, despite what many textbooks say.) 81 © L. Pei, H. Taha, A, Mar, Department of Chemistry, University of Alberta (2024)  Examples What are the lattices for these crystal structures? C60 Fe Cu face face fore face I2 body-centered tetragonal side-centered orthorhombic 82 © L. Pei, H. Taha, A, Mar, Department of Chemistry, University of Alberta (2024)  Examples What are the formulas and lattices of these solids? Cs O Cl Re Cs1 · (1) = 8. 8 - 5 = 9 CsCl 83 © L. Pei, H. Taha, A, Mar, Department of Chemistry, University of Alberta (2024)  Examples The structure of Cu(s) has atoms at points of an fcc lattice. The density of Cu(s) is 8.93 g/cm3. (a) Calculate the length of a unit cell edge (in Å). Co is at 10 , 0 , 0) == a d 1a + 6 6x1063 53 m= 8. +. = 84 © L. Pei, H. Taha, A, Mar, Department of Chemistry, University of Alberta (2024)  Examples (b) Calculate the radius of a Cu atom (4r) ↳ a2+ az = r ag -as These diagrams help you figure out the trigonometry. 85 © L. Pei, H. Taha, A, Mar, Department of Chemistry, University of Alberta (2024)  Try @ Home The crystal structure of MgO is similar to that of NaCl (shown below). The ionic radius of Mg2+ is 72 pm and that of O2— is 140 pm. a. Determine the number of formula units in the unit cell b. Determine the edge and volume of the unit cell set s c. Determine the density of MgO problem 86 © L. Pei, H. Taha, A, Mar, Department of Chemistry, University of Alberta (2024)  X-Ray Diffraction The detailed arrangement of atoms in crystal structures is determined by X-ray diffraction. Because atoms are arranged with regular spacings of a few Å, crystals act as diffraction gratings when electromagnetic radiation with similar wavelength, namely X-rays, impinge on them. The resulting diffraction pattern consists of many spots. These spots are then analyzed to infer the crystal structure. – In early 2020, crystallographers were able to determine the protein crystal structure of the novel coronavirus SARS-CoV-2 within five weeks (!), so that their mechanism of infection can be understood in detail to enable the rapid design of appropriate drug or vaccine treatments. 87 © L. Pei, H. Taha, A, Mar, Department of Chemistry, University of Alberta (2024)  Structures of Metallic Solids Because metallic bonding is nondirectional (“sea of electrons”), the atoms pack tightly to fill space. If atoms are rigid and non-interacting, the most efficient packing of equal-sized spheres in 2D gives a closest-packed layer. DD A DY There remain interstitial spaces (or voids or holes) between the spheres, having roughly triangular shape. 88 © L. Pei, H. Taha, A, Mar, Department of Chemistry, University of Alberta (2024)  Stacking Sequences In 3D, these closest-packed layers can be arranged in different stacking sequences. = t A A 2 A C i B A B face cented & cubic HCG CCP Calte (0 , 0 , 0) What are the lattices that correspond to these two types of stacking sequences? - primilive nexagnal lattice with atom 10 001 , & ( % 3 , 5 2) , © L. Pei, H. Taha, A, Mar, Department of Chemistry, University of Alberta (2024) 89  Packing Efficiency #05 chara surondet & What are the coordination numbers (CN) and geometries around each sphere? A C B B A N en = R CN-12 anticobochchedral cubactaedra Many metallic elements crystallize in hcp or ccp (also called fcc) structures. In both cases, the packing efficiency is _________. 74 % A third common type adopted is a body-centred cubic (bcc) structure, which is not based on closest packing of spheres. But the packing efficiency 68% for bcc (____________) is still pretty good. v * & x x X BodeyCentred. Cubic x Y Fe 90 © L. Pei, H. Taha, A, Mar, Department of Chemistry, University of Alberta (2024)  Metallic Solids The three common types of structures found for metallic elements are: structure type stacking sequence lattice hcp primitive hexagonal L A BABAB ccp ABCABC faced centered cohich bcc body centred cubic h 91 © L. Pei, H. Taha, A, Mar, Department of Chemistry, University of Alberta (2024)  Metallic Alloys Combinations of two or more metals (alloys and intermetallic compounds) can give improved physical properties (strength, hardness, resistance to corrosion). For example, pure Fe(s) is soft and corrodes easily, but its properties change dramatically when combined with other elements: – substitutional alloy 16 % subsituting ~ Cr , ~890 Ni for Es metal gives statainless steel resistant to corrosion , – interstitial alloy of small Adding - % Catoms which are , into the interties of Fe givessted which is strong and hand 92 © L. Pei, H. Taha, A, Mar, Department of Chemistry, University of Alberta (2024)  Structures of Ionic Solids Ionic bonding (based on electrostatic forces) is also non-directional, but the structures now contain two types of spheres: larger anions are often found in close-packing arrangements smaller cations are found in holes (“interstices”) Octahedral sites are sandwiched Tetrahedral sites are sandwiched between three spheres of one layer and between three spheres of one layer and three spheres of another layer. one sphere of another layer. 93 © L. Pei, H. Taha, A, Mar, Department of Chemistry, University of Alberta (2024)  Structures of Ionic Solids Suppose anions are placed at points of an fcc lattice. Locate the octahedral and tetrahedral sites: ux G * # U & G Y Z X Xy q > - g ul xc V anions 000 anions at (0 , 0 , %) tet sites octhedral sites at (Eizit It ) (a). 94 © L. Pei, H. Taha, A, Mar, Department of Chemistry, University of Alberta (2024)  Structures of Ionic Solids Two common structure types for ionic solids are derived by placing cations in octahedral or tetrahedral sites within a ccp arrangement of anions. NaCl-type (rocksalt) Li2O-type(antifluorite) Cl There are many other possibilities of arrangements of anions and cations that lead to the structures of other ionic solids. 95 © L. Pei, H. Taha, A, Mar, Department of Chemistry, University of Alberta (2024)  Examples (Silberberg 11.92) Zinc selenide (with the structure shown) has a density of 5.42 g/cm3. a. What is the formula? b. Calculate the length of a unit cell edge (in Å). 96 © L. Pei, H. Taha, A, Mar, Department of Chemistry, University of Alberta (2024)  Examples c. Calculate the Zn–Se bond length (in Å). 97 © L. Pei, H. Taha, A, Mar, Department of Chemistry, University of Alberta (2024)