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COLLEGE OF ARTS AND SCIENCES DEPARTMENT OF CHEMISTRY AND EARTH SCIENCES CHEMISTRY 221: Inorganic Chemistry (I) 7 The Structures of Simple Solids Dr. Adnan S. Abu-Surrah Professor of Inorganic & Materials Chemistry Tel.: +974 4403 6839 E-mail: [email protected] The Structures of Simple Solids • The majority of inorganic compounds exist as solids and comprise ordered arrays of atoms, ions, or molecules. – Some of the simplest solids are the metals, the structures in which metal centers interact through metallic bonding, a type of bonding that can be described in two ways: ● One view is that bonding occurs in metals when each atom loses one or more electrons. The strength of the bonding results from the combined attractions between all these freely moving electrons and the resulting cations. ● An alternative view is that metals are effectively enormous molecules with a multitude of atomic orbitals that overlap to produce molecular orbitals extending throughout the sample. 2 The Structures of Simple Solids Thus, metals are malleable (easily deformed by the application of pressure) and ductile (able to be drawn into a wire) because the electrons can adjust rapidly to relocation of the metal atom nuclei and there is no directionality in the bonding. ● They are lustrous because the electrons can respond, almost freely to an incident wave of electromagnetic radiation and reflect it. 3 The description of the structures of solids ● The arrangement of atoms or ions in simple solid structures can often be represented by different arrangements of hard spheres. ● The spheres used to describe metallic solids represent neutral atoms because each cation is still surrounded by its full complement of electrons. ● The spheres used to describe ionic solids represent the cations and anions because there has been a substantial transfer of electrons from one type of atom to the other. 4 Crystal Lattices • The ‘crystal lattice’ is the pattern formed by the points and used to represent the positions of these repeating structural elements. – Lattice: a two or three dimensional array of objects with a well defined order. • Unit cells: smallest repeating unit (imaginary parallel-sided region) that through translation can recreate a lattice. (also called the asymmetric unit) Amorphous means a disordered array 5 Unit cells A two-dimensional solid and two choices of a unit cell. The entire crystal is reproduced by translational displacements of either unit cell, a b Two possible choices of repeating unit are shown but (b) would be preferred to (a) because it is smaller. Lattice and Units Cells The relationship between the lattice parameters in three dimensions as a result of the symmetry of the structure gives rise to the seven crystal systems Most common types: cubic orthorhombic monoclinic triclinic Less common types: hexagonal tetragonal trigonal 7 The angles (a, b , g) and lengths (a, b, c) used to define the size and shape of a unit cell are the unit cell parameters (the ‘lattice parameters’); Angle between b and c is a Angle between a and c is b Angle between a and b is g (or rhombohedral) Rules to determine number of lattice points in a three-dimensional unit cell 1) A lattice point in the body of, that is fully inside, a cell belongs entirely to that cell and counts as 1. 2) A lattice point on a face is shared by two cells and contributes 1/2 to the cell. 3) A lattice point on an edge is shared by four cells and contributes 1/4. 4) A lattice point at a corner is shared by eight cells that share the corner, and so contributes 1/8. The same process can be used to count the number of atoms, ions, or molecules that the unit cell contains. 9 Simple Cubic denoted by the symbol P The number of lattice points is: (8 x1/8 ) = 1. Lattice points describing the translational symmetry of a primitive cubic unit cell. Body Centered Cubic (BCC) denoted by the symbol I The number of lattice points is: (1x1) + (8 x1/8 ) = 2. Lattice points describing the translational symmetry of a cubic unit cell. Face Centered Cubic (FCC) denoted by the symbol F The number of lattice points is: (6x1/2) + (8 x 1/8) = 4 Lattice points describing the translational symmetry of a face-centred cubic unit cell. cubic: a=b=c a = b = g = 90° 13 • Usually, the smaller cations will be found in the holes in the anionic lattice, which are named after the local symmetry of the hole •i.e. six equivalent anions around the hole makes it octahedral, four equivalent anions makes the hole tetrahedral). 16 Crystal Lattices Two main types of arrays: • Open: occupies 68% of the space • Close-packed: occupies 75% of the space – Two types of close-packed arrays: hexagonal and cubic. (ABAB... versus ABCABC... ) – Close-packed structures have layers of octahedral and tetrahedral holes -- 17 Cubic Close-Packed (ccp) • ABCABC • first layer in a hexagonal arrangement of atoms or ions • second layer over depressions in the first layer, over tetrahedral holes • third layer over depressions in the second which are not over the depressions in the first that the atoms in the second occupy, over octahedral holes • fourth layer is identical to the first • fifth layer is identical to the second • sixth layer is identical to the third • face-centered-cubic, standing on its body diagonal, is camouflaged by ccp • C. N. = 12 18 Hexagonal Close-Packed (hcp) - ABABAB - first layer in a hexagonal arrangement of atoms or ions - second layer over depressions in the first layer, over tetrahedral holes - odd numbered layers identical to the first - even numbered layers identical to the second - 12 nearest neighbors, C. N. = 12 19 Examples in nature of Hexagonal Close Packing Cubic and Hexagonal Close Packing In one polytype, the spheres of the third layer lie directly above the spheres of the first. This ABAB...pattern of layers, where A denotes layers that have spheres directly above each other and likewise for B, gives a structure with a hexagonal unit cell and hence is said to be hexagonally close-packed (hcp). In the second polytype, the spheres of the third layer are placed above the gaps in the first layer. The second layer covers half the holes in the first layer and the third layer lies above the remaining holes. This arrangement results in an ABCABC...pattern. This pattern corresponds to a structure with a cubic unit cell and hence it is termed cubic closepacked (ccp). Because each ccp unit cell has a sphere at one corner and one at the centre of each face, a ccp unit cell is sometimes referred to as facecentred cubic (fcc). 21 Cubic Close Packing This pattern corresponds to a structure with a cubic unit cell and hence it is termed cubic close-packed (ccp). 22 Holes in close-packed structures Octahedral hole: rh = 0.414r Tetrahedral hole: rh = 0.225r 24 Coordination Numbers: Coordination Number: the number of nearest neighbors. Hexagonal close-packing of sphere gives a coordination number (CN) of 12 and leaves interstitial sites capable of coordination numbers 6 or 4. 25 Structures of Metals • In addition to ccp and hcp, metals also have simple cubic and body-centered cubic structures. • The CN of ccp or hcp = 12, simple or primitive cubic = 6, bodycentered cubic (bcc) = 8. • Note that bcc is favored for Group 1 and 2 metals. This is due to the weaker “electron sea” which prevents close-packing. a regular array of organized cations surrounded by delocalized sea of electrons. 26 Structures of Metals Polytypism Polytypes involving complex stacking arrangements of close-packed layers occur for some metals. a close-packed structure need not be either of the common ABAB...or ABCABC...polytypes. cobalt is an example of a metal that displays more complex polytypism above 500 0C. The structure that results is a nearly randomly stacked set ( ABACBABABC…. Nonclose-packed structures A common nonclose-packed metal structure is body-centred cubic; a primitive cubic structure is occasionally encountered. Metals that have structures more complex than those described so far can sometimes be regarded as slightly distorted versions of simple structures. One commonly adopted arrangement has the translational symmetry of the body- centred cubic lattice and is known as the body-centred cubic structure (cubic-I or bcc) in which a sphere is at the centre of a cube with spheres at each corner (See Fig). 28 Polymorphism of metals Polymorphism is a common consequence of the low directionality of metallic bonding. At high temperatures a bcc structure is common for metals that are close-packed at low temperatures on account of the increased amplitude of atomic vibrations. Iron, for example, shows several solid–solid phase transitions; a-Fe, which is bcc, occurs up to 906°C, g-Fe, which is ccp, occurs up to 1401°C, and then a-Fe occurs again up to the melting point at 1530°C. The hcp polymorph, b-Fe, is formed at high pressures and was to believed to be the form that exists at the Earth’s core. 29 Alloys • • Substitutional solid solution Interstitial solid solution substitutional Interstitial Another lattice Examples: Brass – up to 40% Zn in Cu Bronze – a metal other than Zn or Ni in Cu Stainless steel – over 12% Cr in Fe 31 Substitutional Solid Solutions -- conditions • The atomic radii of the elements are within 15% of each other • The crystal structures of the two pure metals are the same • The electropositive characteristics of the two metals are similar 32 Interstitial Solid Solutions • True compounds – simple whole number ratios of atoms • Solid solutions – small atoms distributed randomly in the available holes in the lattice Compounds with Particular Crystal Structures 34 35 The Structure of NaCl It is a fcc array of chloride ions as the packing layers. The sodium ions are in all the octahedral holes. The coordination number of both ions is 6. The unit cell has four net sodium ions and four chloride ions. Other salts with this structure are: LiX, NaX, KX, RbX where X = F, Cl, Br, I; also MgO, MgS, CaO, etc. 36 Rock Salt (NaCl) Structure Rock Salt structure (6,6) coordination Face-centered cubic (fcc) e.g. NaCl, LiCl, MgO, AgCl 37 CsCl Unit Cell--Contd-- (8,8)-coordination 38 lattice energy (Uo, Ionic Bonding: lattice energy, Uo, •The energy that holds the arrangement of ions together is called the lattice energy, Uo, and this may be determined experimentally or calculated. •A lattice energy must always be exothermic. •E.g.: Na+(g) + Cl-(g) NaCl(s) Uo = -788 kJ/mol Lattice energies are determined experimentally using a Born-Haber cycle such as this one for NaCl. This approach is based on Hess’s law and can be used to determine the unknown lattice energy from known thermodynamic values. 42 Lattice Energy, Uo DHfo = DHoie + DHosub + DHod + DHoea - Uo where DHosub => heat of sublimation - endothermic process - always positive number DHod=> bond dissociation energy - endothermic process - always positive number where DHfo => standard state enthalpy of formation - can be either endothermic or exothermic - therefore, value may be positive or negative 43 Ionic Bonding -- Born-Haber cycle DH°sub DH°ie Na(s) Na(g) Na+(g) ½ Cl2(g) Cl(g) Cl-(g) DH°d DH°ea DH°f Lattice Energy, Uo NaCl(s) DH°f = DH°sub + DH°ie + 1/2 DH°d + DH°ea - Uo -411 = 109 + 496 + 1/2 (242) + (-349) - Uo Uo = -788 kJ/mol You must use the correct stoichiometry and signs to obtain the correct lattice energy. 44 Practice Born-Haber cycle analyses at: http://chemistry2.csudh.edu/lecture_help/bornhaber.html Ionic Bonding If we can predict the lattice energy, a Born-Haber cycle analysis can tell us why certain compounds do not form. E.g. NaCl2 (DH°ie1 + DH°ie2) Na(s) Na(g) Na+2(g) DH°sub Cl2(g) 2 Cl(g) 2Cl-(g) DH°d DH°ea DH°f Lattice Energy, Uo NaCl2(s) DH°f = DH°sub + DH°ie1 + DH°ie2 + DH°d + DH°ea - Uo DH°f = 109 + 496 + 4562 + 242 + 2*(-349) + -2180 DH°f = +2531 kJ/mol This shows us that the formation of NaCl2 would be highly endothermic and very unfavourable. Being able to predict lattice energies can help us to solve many problems so we must learn some simple ways to do this. 45 K(g) + ½ Cl2(g) KCl(s) 46 Extrinsic defects are defects introduced into a solid as a result of doping with an impurity atom. Example is the introduction of As into Si to modify the latter’s semi-conducting properties. 49