DOCSLIB.ORG

APS104S – Introduction to Materials & Chemistry

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
APS104S – Introduction to Materials & Chemistry APS104S – Introduction to Materials & Chemistry Lecture 4 January 12, 2016 Instructor: Gisele Azimi 1) Bonding energy 2) Ionic bonding (Madelung constant) Bonding energy, attractive, repulsive - A + B EN = EA + ER = n r r A3rac5ve Repulsive energy energy A, B, n = constants At r = r0 ! dE/dr = 0 & E = E0 r0 = equilibrium separaon distance (bond distance) E0 = Bond energy r0 = rcaon + ranion Example 2 • The potential energy between Mg2+ and O2- ions in a MgO crystal can be estimated as • where A = 1.61 x 10-27 J m, B = 3.87×10-96 J m8, r is the separation (between ion centers) in m, and E is the potential energy in J. • Calculate the equilibrium separation between the ion centers. • Calculate the bonding energy between the Mg and O ions at this equilibrium distance. • If the ionic radius of Mg2+ is 0.072 nm, what is the ionic radius of O2- ? Example 2-solution Ionic. Bonding (example NaCl) Bonding is described as electrostatic attraction between point charges. Na+ Cl- Ionic. Bonding (example NaCl) 6 nearest neighbours @ r = a (+ -) Let’s call this “a” a = r0 Ionic. Bonding (example NaCl) 12 nearest neighbours @ r = √2 a (+ +) √2 a Let’s call this “a” a = r0 Ionic. Bonding (example NaCl) 8 nearest neighbours @ r = √3 a (+ -) √3 a !! 8 ! = − ( ) 4!!! 3! Let’s call this “a” a = r0 Ionic. Bonding (example NaCl) e2 " 6 12 8 % E = − $ − + −!' 4πεo # a a 2 a 3 & e2 1 E = −M 4πεo a 12 8 Let’s call this “a” M = 6 − + −... M: Madelung constant a = r0 2 3 M depends on the geometry; for rock salt = 1.748 1 eV = 1.60 x 10-19 J e = 1.602 × 10-19 C a = r0 = 0.28 nm -12 2 2 ε0 = 8.854 x 10 C /(Nm ) E = -8.97 eV/atom (only 10% of the real value) Madelung. constant for CsCl 8 nearest neighbours @ r = √3/2 a (+ -) √3/2 a Let’s call this “a” Madelung. constant for CsCl 6 nearest neighbours @ r = a (+ +) Madelung. constant for CsCl e2 1 E = −M 4πεo a Let’s call this “a” the crystalline solid state CHAPTER 3_C topics: unit cell metallic crystal structures density computaons metallic/ceramic ceramic crystal structures direc/ons planes & densies 5.2 & 5.3 Light & the Electromagne/c Spectrum 5.4 The Plank Equa/on 5.5 The de Broglie Equaon 5.6 Heisenberg Uncertainty Principle 5.7 & 5.10 Quantum Numbers 5.8 Shapes of Orbitals 5.9 Quantum Mechanics & Atomic Spectra 5.11-14 Mul/electron Atoms 5.15 Periodic Properes Subjects we will study • What are crystals • Crystal systems • Crystal structure in metals (with a focus on cubic systems) Why study crystal structure? Many properties of materials are directly related to their crystallinty and crystal structure Crystallographic - points Crystalline Crystal structure Unit cell - Direcons - planes Non-crystalline Classification of solids by atomic arrangement " Has a well-defined ordered structure in 3D (over large range). Atoms self-organize in a periodic Dense, array. ORDERED packing " Well defined shaped due to well- ordered par5cles. • metals • many ceramics • some polymers " Has a disordered structure, lacking a systemac atomic arrangement. " Poorly defined shapes because they don’t have extensive ordering of Non dense, par5cles. RANDOM packing • complex structures • rapid cooling Some crystals (well-defined ordered structure; well-defined shape) Au Cu Cr PbS FeS2 NiSO4 NaCl Some amorphous solids (disordered structure, poorly defined shapes) Gummite amorphous solid Obsidian, a volcanic glass Gummite: a yellow, amorphous mineral, a mixture of oxides and silicates of uranium, formed by weathering of pitchblende (a mineral used as a source of uranium). Stacking objects in 2-D with no voids square rectangle NO trapezoid Unit cell: the repeating group – 7 ways to stack crystals in 3D with no voids Unit cell: the repeating group A unit cell is the most basic and least volume consuming repeang structure of any solid. Unit cell: where atoms sit: Bravais Lattices Let us look at “cubic” crystal structure Note: for metals, all atoms are iden5cal; the FCC and BCC atoms are shaded 1 differently only for ease of viewing. ½ ¼ An ion in the body of a cell belongs en5rely to that cell and counts as 1. An ion on a face is shared by two cells and contributes ½. An ion on an edge is shared by four cells and hence contributes ¼. ⅛ An ion at a vertex is shared by eight cells, and so contributes ⅛. Crystal structure in metals Metallic bonds (such as Au, Ag, Cu) Can be pictured as an array of positive ions in a “sea of electrons". Cu (FCC) Tend to be densely packed. REASONS FOR DENSE PACKING - Typically, only one element is present, so all atomic radii are the same. - Nearest neighbor distances tend to be small in order to lower bond energy. - Electron cloud shields cores from each other. - Metallic bonding is not directional • Have the simplest crystal structures. Lattice points per cell: how many atoms we have in each unit cell 2 4 1 The relation between unit cell length (a) and radius of atom (r) BCC SC FCC r a 2a = 4r 3a= 4r a = 2r Coordination #: the number of nearest neighbors SC 6 BCC 8 FCC 12 Atomic packing factor (APF) volume of atoms in unit cell APF = volume of unit cell Example 1: for FCC APF=(4x(4/3)Πr3/a3 4r = √2 x a APF=0.74 a= unit cell length r= atoms radii Example: Atomic packing factor (APF) for BCC volume of atoms in unit cell APF = volume of unit cell 3 a 4r = 3 a r = a/4 3 a 2 a R Volume of each atom a atoms / unit cell 2 (4/3)π(r)3 APF = a3 volume / unit cell APF = 0.68 Summary Face centered cubic (fcc) Body centered cubic (bcc) Simple Cubic FCC BCC Al, Cu Cr, Fe, Au, Pt Mo r = radius of atom a = length of unit cell FCC BCC SC # of atoms in cell 4 2 1 Coordina>on # 12 8 6 Filling Fracon 74 % 68% 52% Rela>on 2a = 4r 3a= 4r a = 2r Calculating theoretical density of metals Example: Calculate the density of iron, which has a body-centered cubic unit cell with an edge length of 286.6 pm. The molar mass of iron is 55.85 g/ mol. Measured (literature) value for iron density: 7.874 g/cm3 Calculating theoretical density of metals Theoretical density formula atomic mass (g / mol) #atoms / unit cell n A ρ = VC NA volume / unit cell Avogadro’s number 23 (cm3 / unit cell) 6.02 × 10 atoms / mol Characteristics of selected elements at 20°C At. Weight Density Atomic radius Element Symbol (amu) (g/cm3) (nm) Aluminum Al 26.98 2.71 0.143 Argon Ar 39.95 ------ ------ Barium Ba 137.33 3.5 0.217 Beryllium Be 9.012 1.85 0.114 Boron B 10.81 2.34 ------ Bromine Br 79.90 ------ ------ Cadmium Cd 112.41 8.65 0.149 Calcium Ca 40.08 1.55 0.197 Carbon C 12.011 2.25 0.071 Cesium Cs 132.91 1.87 0.265 Chlorine Cl 35.45 ------ ------ Chromium Cr 52.00 7.19 0.125 Cobalt Co 58.93 8.9 0.125 Copper Cu 63.55 8.94 0.128 Flourine F 19.00 ------ ------ Gallium Ga 69.72 5.90 0.122 Germanium Ge 72.59 5.32 0.122 Gold Au 196.97 19.32 0.144 Helium He 4.003 ------ ------ Hydrogen H 1.008 ------ ------ Example Nickel crystallizes in a fcc lattice. Its density is 8.90 g/cm3. What is the atomic radius of nickel in pm? 1 m = 1012 pm 1 cm = 1010 pm Example - Solution .
Load more

Recommended publications
  • In Kapustinskii Equation
    III-1 1 PART THREE: Ionic Bonding In . Molecules And Solids So far we have defined several energies of interaction between charged particles. - Ionization Energy - Electron Affinity - Coulombic (Electrostatic) Attraction & Repulsion. We now use these to look at further bonding properties: Mostly solids. Why are solids important? Catalysts Ad & Ab – Sorbents Lasers Fibre Optics Magnetic Memories Optical Switching (Computers) Batteries Fluorescent Lights Superconductors LED’s ………. III-2 2 We Need To Start At The Beginning One of the simplest ionic solids is sodium chloride (NaCl). Various depictions of the rocksalt structure. Not all will be met in this course. III-3 3 Discrete NaCl molecules can exist in the gas phase. NaCl(g) → Na(g) + Cl(g) ∆H for this reaction is called the Bond Dissociation Energy (409 kJ mol-1) • We can judge the stability of solids whether they form or not by looking at the free energy change for: M+(g) + X-(g) → MX(s) ∆G = ∆H - T∆S • If ∆G is –ve then spontaneous. • Note: Process of Lattice formation (solid ) is very exothermic at room temperature (∆S may be neglected). III-4 4 • We will use ∆H’s (enthalpy). Born Haber Cycle + - Na (g) + Cl (g) IP EA Electrostatic (U) _1 Attraction Na(g) + 2 Cl2(g) NaCl(g) ∆H f ( NaCl ) We can calculate U from this cycle Can You Do It ?: watch the signs However: NaCl(g) is NOT NaCl(s) III-5 5 - We want to get an idea of how stable different solids are. - Then U is more complicated. WHY? Sodium Chloride Lattice Cubic Na Cl + Cl Each Na has 2r - 3r Na 6 near neighbour Cl Cl Na Each Cl- has Na + r Cl 6 near neighbour Na • The attractive energy between a Na+ and its 6 near neighbour Cl- is offset by repulsion from 12 next near neighbour Na+.
    [Show full text]
  • Pauling's Rules: Goldschmidt's Structural Principles for Ionic Crystals Were Summarized by Linus Pauling in a Set of 5 Rules
    CRYSTALS THAT CANNOT BE DESCRIBED IN TERMS OF INTERSTITIAL FILLING OF A CLOSE-PACKED STRUCTURE 154 CsCl STRUCTURE → → → Adoption by chlorides, bromides and iodides of larger cations 155 MoS2 STRUCTURE • layered structure → → → 156 •both MoS2 and CdI2 are LAYERED structures •MoS2 layers are edge-linked MoS6 trigonal prisms •CdI2 layers are edge-linked CdI6 octahedra 157 MoS6 trigonal prisms AsNi6 trigonal prisms 158 COVALENT NETWORK STRUCTURES Concept of CONNECTEDNESS (P) of a network connecting structural units (atoms or groups) e.g. Structures of Non-Metallic Elements The "8-N Rule“ connectedness = 8 – # valence electrons P = 8 – N P = 1 e.g. I2 dimers Space group: Cmca orthorhombic 159 STRUCTURES OF THE ELEMENTS P = 1 e.g. I2 DIMERS FCC metal 160 P = 2 e.g. S8 RINGS • the packing approximates a distorted close-packing arrangement • apparently 11-coordinate (3 left + 5 in-plane + 3 right) 161 P = 2 e.g. gray selenium HELICAL CHAINS Chains form a 3-fold Helix down c • this allotrope of Se is an excellent photoconductor 162 ALLOTROPY A polymorph is a distinct crystalline form of a substance (e.g., zinc blende & wurtzite). Polymorphs of elements are known as allotropes. 163 P = 3 e.g. gray As, Bi LAYERS Interlinked 6-membered rings 164 165 P = 3 e.g. sp2 carbon LAYERS and CAGES 166 P = 4 e.g. sp3 carbon DIAMOND FRAMEWORK 167 P = 4 Networks Structures with the Diamond FRAMEWORK 168 Cristobalite: a high- temperature polymorph of quartz cuprite: a cubic semiconductor CNCu : 2 CNO : 4 O Cu 169 SILICATE MINERALS 4- Networks of corner-sharing tetrahedral SiO4 Units Chemical formula hints at network structure: • terminal oxygens count as 1 • bridging oxygens count as 1/2 170 Si:O = 1:4 4- P = 0, Orthosilicate, SiO4 e.g.
    [Show full text]
  • Solids Close-Packing
    Solids Solid State Chemistry, a subdiscipline of Inorganic Chemistry, primarily involves the study of extended solids. •Except for helium*, all substances form a solid if sufficiently cooled at 1 atm. •The vast majority of solids form one or more crystalline phases – where the atoms, molecules, or ions form a regular repeating array (unit cell). •The primary focus will be on the structures of metals, ionic solids, and extended covalent structures, where extended bonding arrangements dominate. •The properties of solids are related to its structure and bonding. •In order to understand or modify the properties of a solid, we need to know the structure of the material. •Crystal structures are usually determined by the technique of X-ray crystallography. •Structures of many inorganic compounds may be initially described in terms of simple packing of spheres. Close-Packing Square array of circles Close-packed array of circles Considering the packing of circles in two dimensions, how efficiently do the circles pack for the square array? in a close packed array? 1 Layer A Layer B ccp cubic close packed hcp hexagonal close packed 2 Layer B (dark lines) CCP HCP In ionic crystals, ions pack themselves so as to maximize the attractions and minimize repulsions between the ions. •A more efficient packing improves these interactions. •Placing a sphere in the crevice or depression between two others gives improved packing efficiency. hexagonal close packed (hcp) ABABAB Space Group: P63/mmc cubic close packed (ccp) ABCABC Space Group: Fm3m 3 Face centered cubic (fcc) has cubic symmetry. Atom is in contact with three atoms above in layer A, six around it in layer C, and three atoms in layer B.
    [Show full text]
  • Madelung Constant, A
    SolidSolid StateState TheoryTheory PhysicsPhysics 545545 Structure of Matter • Properties of materials are a function of their: Atomic Structure Bonding Structure Crystal Structure Imperfections • If these various structures are known then the properties of the material can be determined. • We can tailor these properties to achieve the material needed for a particular product. ¾¾ PropertiesProperties ofof aa materialmaterial z DependsDepends onon bondingbonding ofof atomsatoms thatthat formform thethe materialmaterial z DictatesDictates howhow itit interactsinteracts andand respondsresponds toto thethe worldworld aroundaround it.it. TheseThese include:include: • Physical Properties z Form (Gas, Liquid, Solid) ,Hardness (Rigid, Ductile, Strength), Reactivity • Thermal Properties z Heat capacity, Thermal conductivity, • Electrical Properties z Conductivity, Dielectric Strength, Polarizability • Magnetic Properties z Magnetic permittivity, • Optical Properties z Spectral absorption, Refractive index, Birefringence, Polarization, Atomic Theory • Nucleus of the atom is made up of protons (+) and neutrons (-) • Number of electrons surrounding the nucleus must equal the number of protons (free state-electrically neutral). • Atomic Number - the number of protons in the nucleus • Atomic Number determines the properties and characteristics of materials Atomic Structures And Atomic Bonding • gives chemical identification Nucleus • consists of protons and neutrons • # of protons = atomic number • # of neutrons gives isotope number Electrons • participate
    [Show full text]
  • Solutions of Alkali Halides in Water Conduct Electricity
    Chapter 7 The Crystalline Solid State 97 CHAPTER 7: THE CRYSTALLINE SOLID STATE 7.1 a. Oh b. D4h c. Oh d. Td e. The image in Figure 7.10, which has D3d symmetry, actually consists of three unit cells. For an image of a single unit cell, which has point group C2h, see page 556 in the Greenwood and Earnshaw reference in the “General References” section. 7.2 The unit-cell dimension is 2r, the volume is 8r3. Since this cell contains one molecule 4/3r 3 whose volume is 4/3 π r3, the fraction occupied is 0.524 52.4%. 8r 3 7.3 The unit-cell length for a primitive cubic cell is 2r. Using the Pythagorean theorem, we 2 2 can calculate the face diagonal as 2r 2r 2.828rand the body diagonal as 2 2 2.828r 2r 3.464r . Each corner atom contributes r to this distance, so the diameter of the body center is 1.464 r and the radius is 0.732 r, 73.2% of the corner atom size. 7.4 a. A face-centered cubic cell is shown preceding Exercise 7.1 in Section 7.1.1. The cell contains 6 × 1 = 3 atoms at the centers of the faces and 8 × 1 = 1 atom at the corners, a 2 8 4 16 total of 4 atoms. The total volume of these 4 atoms 4 r 3 r 3, where r is the 3 3 radius of each atom (treated as a sphere). As can be seen in the diagram, the diagonal of a face of the cube = 4r.
    [Show full text]
  • Structures of Solids
    Structures of solids LATTICE ≣ An infinite array of points in space, in which each point has identical surroundings to all others. CRYSTAL STRUCTURE ≣ The periodic arrangement of atoms in the crystal. It can be described by associating with each lattice point a group of atoms called the basis (motif). Lattice + Basis = Crystal Structure • Don't mix up atoms with lattice points • Lattice points are infinitesimal points in space • Atoms are physical objects • Lattice Points do not necessarily lie at the centre of atoms UNIT CELL ≣ The smallest component of the crystal, which when stacked together with pure translational repetition reproduces the whole crystal. Primitive (P)unit cells contain only a single lattice point Hexagonal pattern of a single layer of GRAPHITE Counting Lattice Points/Atoms in 2D Lattices •Unit cell is Primitive (1 lattice point) but contains TWO atoms in the basis 1 •Atoms at the corner of the 2D unit cell contribute only /4 to unit cell count 1 •Atoms at the edge of the 2D unit cell contribute only /2 to unit cell count •Atoms within the 2D unit cell contribute 1 (i.e. uniquely) to that unit cell The 14 possible BRAVAIS LATTICES Close-Packed Structures (Coordination Number = 12; 74% of space is occupied) Hexagonal Close-Packing (HCP): ABABAB.... 2 lattice points in the unit 2 1 1 cell: (0, 0, 0) ( /3, /3, /2) Cubic Close-Packing (CCP): ABCABC.... 4 lattice points in the unit 1 1 cell: (0, 0, 0) (0, /2, /2) 1 1 1 1 ( /2, 0, /2) ( /2, /2, 0) A non-closed-packed structure adopted by some metals • Two lattice points
    [Show full text]
  • E12 UNDERSTANDING CRYSTAL STRUCTURES 1 Introduction in This
    E12 UNDERSTANDING CRYSTAL STRUCTURES 1 Introduction In this experiment, the structures of many elements and compounds are rationalized using simple packing models. The pre-work revises and extends the material presented in the lecture course. 2 The Lattice Energy of Ionic Compounds The compounds formed between elements of very different electronegativities are usually ionic in character. Ionic compounds are usually solids at room temperature, although ionic liquids also exist. They are held together in three-dimensional arrangements by the attractive forces between every pair of oppositely charged ions – not just by the interaction between neighbouring ions. The energy that is required to completely separate the ions is called the lattice energy. The figures opposite show part of the structure of NaCl and the cubic unit cell which generates the whole lattice when repeated infinitely in all directions. The distance between the ions is determined by the balance of the attractive force between cation and anion and the repulsive forces between both the core electrons of the ions and their nuclei. The simplest model imagines that the ions are hard spheres with fixed radii. The ions touch but do not overlap. We first use this model to calculate the lattice energy and then show how the model is improved by including the compressibility of the ions. If the charges on the cation and anion are q1 and q2, the attractive interaction between a pair is: 2 ⎛⎞1 qq12 e Eelectrostatic =−⎜⎟ ⎝⎠4πε0 r where e is the charge on an electron, ε0 is the permittivity of a vacuum and r is the distance between the centres of the ions.
    [Show full text]
  • The Electronic Structure of F-Centres in Alkali Halide Crystals
    Revista Brasileira de Física, Vol. 12, nP 1, 1982 The Electronic Structure of F-Centres in Alkali Halide Crystals ZELEK S. HERMAN Quantum Chemistry Group, University of Uppsala, Box 518, 75120 Uppsala 1, Sweden and GENE BARNETT Division of Research National lnstitute on Drug Abuse Rockville, Maryland 20852 USA Recebido em 10 de Outubro de 1981 A method is presented for estimating the number of bound sta- tes of different orbital angular momentum quantum number for an F-cen- tre residing in an alkali halide crystal through the introduction of a spherically symmetric potential well of finite depth. The method is il- lustrated through its application to the F-centre in sodium chloride,and the resul ts for F-centres in various a1 kal i hal ide lattices are tabula- ted. The results provide a good account of the experimental features of the F-centre including the K-band which we suggest is due to transi- tions from the 2p to excited levels. Values for the effective range of penetration of the defect electron with the neighbouring cation in dif- ferent crystals are determined by requiring that the well depth be in- dependent of orbital angular momentum quantum number. The technique is applied to estimate the Madelung constant nd Madelung potential for the host crystal. Apresenta-se um método para est mar o número de estados 1 i- gados de diferente momento angular orbital para um F-centro residente em um cristal de haleto alcal ino, pela introdução de um polo de poten- cial esfer icamente simétrico de profundidade infinita.
    [Show full text]
  • Computation of Madelung Energies for Ionic Crystals of Variable Stoichiometries and Mixed Valencies and Their Application in Lithium-Ion Battery Voltage Modelling
    Computation of Madelung Energies for Ionic Crystals of Variable Stoichiometries and Mixed Valencies and their application in Lithium-ion battery voltage modelling K. Ragavendran, D. Vasudevan, A. Veluchamy and Bosco Emmanuel* Central Electrochemical Research Institute, Karaikudi-630 006, India Abstract Electrostatic energy (Madelung energy) is a major constituent of the cohesive energy of ionic crystals. Several physicochemical properties of these materials depend on the response of their electrostatic energy to a variety of applied thermal, electrical and mechanical stresses. In the present study, a method has been developed based on Ewald’s technique, to compute the electrostatic energy arising from ion-ion interactions in ionic crystals like LixMn2O4 with variable stoichiometries and mixed valencies. An interesting application of this method in computing the voltages of lithium ion batteries employing spinel cathodes is presented for the first time. The advantages of the present method of computation over existing methods are also discussed. __________________________ * author for correspondence Introduction Electrostatic energy of ionic crystals [1-3] is an important constituent of the cohesive energy [4] of these crystals. Various physicochemical properties such as melting points, heats of fusion and evaporation and activation energies for formation and diffusion of electronic and atomic point defects are related to the solid-state cohesion [5]. Response of the lattice energy towards a variety of applied thermal, electrical and mechanical stresses lead to piezoelectric, ferroelectric and electrochromic properties of these materials. Madelung energy computations have also recently generated much interest [6-9]. A Madelung model has been used to predict the dependence of lattice parameter on the nanocrystal size [6].
    [Show full text]
  • Ionic Bonding, an Introduction to Materials and to Spreadsheets
    Ionic Bonding, An Introduction to Materials and to Spreadsheets Mike L. Meier Department of Chemical Engineering and Materials Science University of California, Davis Davis, CA 95616 Keywords Ionic bonding, NaCl-type structure, halite, interatomic spacing, bulk modulus, shear modulus, Young’s modulus, Poisson’s ratio. Prerequisite Knowledge The student should be familiar with the basics of ionic bonding, including the attractive and repulsive energy terms, their relationship to interatomic forces, the relationships between bulk, shear and Young’s elastic moduli and the effect of temperature on lattice energy. They should also be familiar with the basics of simple crystal structures, particularly the halite structure. Objective In this experiment the energies and forces involved in ionic bonding plus selected physical properties will be computed. The energy-spacing and force-spacing results will be graphed and the calculated properties will be compared to the values available in the literature. All calculations plus the graphing will be done using a spreadsheet. This spreadsheet program will be constructed using a logical, progressive approach which allows one to carefully examine each aspect of the program as it is being built. This spreadsheet will also be somewhat generalized, allowing one to calculate the bonding energies and forces for a number of ionic substances. This exercise will involve first performing these calculations for KCl and, when you are sure your program works correctly, repeating the calculations for at least one of the other compounds listed in tables 1 and 2. The results will be compared to those compiled in table 2. Equipment and Materials 1. Personal computers, at least one for every two students, running a spreadsheet program such as Quattro Pro, Excel, etc., and a printer 2.
    [Show full text]
  • Ionic Radii with Coordination Number
    Basic Structural Chemistry Crystalline state Structure types Degree of Crystallinity Crystalline – 3D long range order Single-crystalline Polycrystalline - many crystallites of different sizes and orientations (random, oriented) Paracrystalline - short and medium range order, lacking long range order Amorphous – no order, random Degree of Crystallinity z Single Crystalline z Polycrystalline z Semicrystalline z Amorphous Grain boundaries Crystal Structure •The building blocks of these two are identical, but different crystal faces are developed • Cleaving a crystal of rocksalt Crystals • Crystal consist of a periodic arrangement of structural motifs = building blocks • Building block is called a basis: an atom, a molecule, or a group of atoms or molecules • Such a periodic arrangement must have translational symmetry such that if you move a building block by a distance: T = n1a + n2b + n3c where n1, n2 , and n3 are integers, and a, b, c are vectors. then it falls on another identical building block with the same orientation. • If we remove the building blocks and replace them with points, then we have a point lattice or Bravais lattice. Planar Lattice 2D Five Planar Lattices Unit Cell: An „imaginary“ parallel sided region of a structure from which the entire crystal can be constructed by purely translational displacements Contents of unit cell represents chemical composition Space Lattice: A pattern that is formed by the lattice points that have identical environment. Coordination Number (CN): Number of direct neighbours of a given atom (first coordination sphere) Crystal = Periodic Arrays of Atoms Translation Vectors c a,b,c b Lattice point (Atom, molecule, group of molecules,…) a Primitive Cell: • Smallest building block for the crystal lattice.
    [Show full text]
  • Crystal Structure
    Crystalline State Basic Structural Chemistry Structure Types Lattice Energy Pauling Rules 1 Degree of Crystallinity Crystalline – 3D long range order Single-crystalline Polycrystalline - many crystallites of different sizes and orientations (random, oriented) Paracrystalline - short and medium range order, lacking long range order 2 Amorphous – no order, random Degree of Crystallinity Single Crystalline Polycrystalline Semicrystalline Amorphous Grain boundaries 3 Degree of Crystallinity A crystalline solid: HRTEM image of strontium titanate. Brighter atoms are Sr and darker are Ti. A TEM image of amorphous interlayer at the Ti/(001)Si interface in an as-deposited sample. 4 Crystal Structure The building blocks of these two are identical, but different crystal faces are developed Conchoidal fracture in chalcedony Cleaving a crystal of rocksalt 5 X-ray structure analysis with single crystals 6 Single crystal X-ray diffraction structure analysis a four circle X-ray diffractometer 7 CAD4 (Kappa Axis Diffractometer) 8 IPDS (Imaging Plate Diffraction System) 9 Crystals • Crystal consist of a periodic arrangement of structural motifs = building blocks • Building block is called a basis: an atom, a molecule, or a group of atoms or molecules • Such a periodic arrangement must have translational symmetry such that if you move a building block by a distance: T n1a n2b n3c where n1, n2 , and n3 are integers, and a, b, c are vectors. then it falls on another identical building block with the same orientation. • If we remove the building blocks and replace them with points, then we have a point lattice or Bravais lattice. 10 Planar Lattice 2D LATTICE A lattice is the geometrical pattern formed by points representing the locations of these basis or motifs.
    [Show full text]