L2 - Atomic Structure and Interatomic Bonding PDF

L2 Atomic Structure and Interatomic Bonding I. Atomic Structure II. Quantum numbers III. The periodic table IV. Interatomic bonding V. Types of atomic bonds in solids Chromium Metallic Crystals Diamond Crystals Silver Metallic Crystals I- Atomic structure A. Atomic Models I- Dal...

L2 Atomic Structure and Interatomic Bonding I. Atomic Structure II. Quantum numbers III. The periodic table IV. Interatomic bonding V. Types of atomic bonds in solids Chromium Metallic Crystals Diamond Crystals Silver Metallic Crystals I- Atomic structure A. Atomic Models I- Dalton's atomic Model (1803):  Elements are made of extremely small identical particles (in size, mass and other properties) called atoms.  Atoms cannot be subdivided, created or destroyed but can combine to form chemical compounds. II- Thomson's atomic Model (1904):  Atoms are uniform spheres of positively charged matter in which electrons are embedded. III- Rutherford's atomic Model (1911):  Atom as a tiny, dense, positively charged core called a nucleus, in which nearly all the mass is concentrated, around which the electrons circulate at some distance, much like planets revolving around the Sun. IV- Bohrʼs atomic Model (1913):  Atom was consisting of a tiny positively charged heavy core, called a nucleus, surrounded by light, planetary negative electrons revolving in circular discrete orbits of arbitrary radii.  Atomic number (Z) = represents the number of protons in the nucleus or the number of electrons.  Atomic mass (A) = is expressed as the sum of the masses of protons and neutrons within the nucleus  Avogadro̓ s Number = The number of atoms in one mole of the material (NA) =6.02×1023 Bohr V- Schrodingerʼs atomic Model (1926): atomic model Quantum Model Wave-mechanical atomic model (Quantum Model).  Electrons does not have exact path but, probability predicts the location of the electron (electron cloud).  Where the cloud is most dense, the probability of finding the electron is greatest, and conversely, the electron is less likely to be in a less dense area of the cloud.  Electron exhibits both particle and wave characteristics II- Quantum numbers 1) Principal quantum number (n):  Bohr energy levels separate into electron shells and subshells.  Shells are designated by the letters K, L, M, N, O, and can also take an integral values ( n = 1, 2, 3, 4, 5,....). 2) Secondary quantum number (l):  It describes the energy levels (subshells) within each shell (l = 0, 1, 2, 3, …, n-1). n=1 ….. K l = 1-1=0 (s) n=2 ….. L l = 2-1=1 (s, p) n=3 ….. M l = 3-1=2 (s, p , d) 3) Magnetic quantum number (ml):  It specifies the orientation in space of an orbital of a given energy.  The total number of magnetic quantum numbers for each l is 2l +1.  The values for ml are given by whole Number Number numbers between -l and +l. n l ml Subshell of Orbitals of Electrons 1≡K 0 0 1s 1 2  For example: 0 0 2s 1 2 2≡L if l =0, ml=2(0)+1= 1 ml=0 ……………...…. s 1 -1, 0, +1 2p 3 6 0 0 3s 1 2 if l =1, ml=2(1)+1= 3 ml= -1,0,+1 ………..…p 3≡M 1 -1, 0, -1 3p 3 6 if l =2, ml=2(2)+1= 5 ml= -2, -1, 0, +1, +2. …d 2 -2, -1, 0, +1, +2 3d 5 10 4) Spin quantum number (ms):  Each orbital has two electrons spins opposing to each other (magnetic balance).  The values (ms) are +1/2 and -1/2, which reflect the two possible values of “spin” of an electron.  Electron Configuration Schematic representation of the relative energies of the electrons for the various shells and subshells. ─ The Aufbau Principle:  It is a graphical mean that predicts deviations from the expected ordering of the energy levels. l=0 l=1 l=2 l=3 l=4 l=5 (s) (p) (d) (f) (g) (h) n =1 (K) 2 n =2 (L) 2 6 n =3 (M) 2 6 10 n =4 (N) 2 6 10 14 n =5 (O) 2 6 10 14 18 n =6 (P) 2 6 10 14 18 22  Valence  The valence of an atom is the number of electrons in an atom that participate in bonding or chemical reactions.  Usually, the valence is the number of electrons in the outer s and p energy levels.  Examples of the valence are: Mg=12 1s2 2s2 2p6 3s2 valence=2 Al =13 1s2 2s2 2p6 3s2 3p1 valence=3 Ge=32 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p2 valence=4 III- The periodic table  Elements arrangement  All the elements have been classified according to electron configuration in the periodic table. The elements are situated, with increasing atomic number, in seven horizontal rows called periods. All elements arrayed in a given column or group have similar valence electron structures, as well as, chemical and physical properties. Groups 7 Periods  Electronegativity  It describes the “tendency of an atom to gain an electron”.  Atoms with almost completely filled outer energy levels (Cl) are strongly electronegative and readily accept electrons.  Atoms with nearly empty out levels (Na) readily give up electrons and have low electronegativity (electropositive). Electronegativity increase Electronegativity increase  Inert gases give up 1e give up 2e accept 1e accept 2e give up 3e Electropositive elements: Electronegative elements: Readily give up electrons to Readily acquire electrons to become +ve ions become -ve ions IV. Interatomic bonding Why ?!  The type of bond allows used to explain a material’s properties. For example: Carbon  May exist as both graphite and diamond. Graphite : Relatively soft and has a “greasy” feel. (Good Electrical conductor) Diamond : Is the hardest known material. (Bad electrical conductor) Diamond Graphite Materials having large bonding energies typically also have high melting temperatures. Principles of atomic bonding  The principles of atomic bonding are best illustrated by considering how two isolated atoms interact as they are brought close together from an infinite separation.  At large distances, interactions are negligible because FR the atoms are too far apart to have an influence on each other  At small distances, each atom exerts forces on the others (FA & FR). Interatomic spacing:  It is “the distance between the atoms cores caused by a balance between interatomic repulsive force (FR) and attractive force (FA)”. FA  In solid metal, the interatomic spacing is close to the atomic diameter (twice the atomic radius). Energy-distance illustration V. Types of atomic bonds in solids [A]– Primary Bonds 1- Ionic Bond (Example: NaCl) Found in compounds that are composed of both metallic and non-metallic elements. Atoms of a metallic element easily give up their valence electrons to the non-metallic atoms. Ionic bonding is termed non-directional ; that is, the magnitude of the bond is equal in all directions around an ion. Ionic materials are typically hard and brittle Electrically and thermally insulative 2- Covalent Bond : (Examples: CH4 & SiO4) Bonds that are formed by sharing of valence electrons among two or more atoms. Depending on the material, a directional relationship is formed when the bonds have specific angles, therefore, ductility is limited. Covalent bonds are very strong. As a result, covalently bonded materials are hard and have high melting temperatures. Since the valence electrons are locked in bonds between atoms and are not readily available for conduction, the electrical conductivity of many covalently bonded materials is not high. 3- Metallic Bond: (Examples: Fe, Cu, Al,..) Found in metals and their alloys. The metallic elements have electropositive atoms that donate their valence electrons to form a “sea” of electrons surrounding the atoms. Metals show good ductility since the metallic bonds are non-directional The melting points of metals are relatively high. Good conductors of both electricity and heat, due to the presence of free electrons [B]– Secondary Bonds Van der Waals] Hydrogen bonding Bonds are week in comparison to the Hydrogen bonding, a special type of primary or chemical ones. secondary bonding, is found to exist Secondary bonding exists between between some molecules that have hydrogen virtually all atoms or molecules. as one of the constituents. Molecular materials have relatively low melting and boiling temperatures. I- Atomic arrangement  Atomic arrangement plays an important role in determining the microstructure and behavior of a solid.  For example, the atomic arrangement in aluminum provides ductility, while that in iron provides strength  Neglecting the imperfections in materials, there are three levels of atomic arrangement: a) No order b)Short range order (SRO) c) Long range order (LRO) 18 Levels of atomic arrangement a) No Order :  As in case of gases, where the atoms are randomly distributed to fill up the space to which the gas is confined. Inert monoatomic gas b) Short-Range Order (SRO) [Amorphous solids]:  A material displays short-range order if the special arrangement of the atoms extends only to the atom’s nearest neighbors.  Many polymers display short-range atomic arrangements Silicate glass C) Long-Range Order (LRO) [Crystalline solids]:  As in case of metals, semi-conductors, many ceramics or even some polymers, where atoms form a grid like pattern, lattice (Polycrystalline solids). Metals/alloys order 19 II- Crystalline structure 1- Terms of crystalline structure  A crystalline material is one in which the atoms are located in a repeating or periodic array (three-dimensional pattern) over large atomic distances.  All metals, many ceramic materials, and certain polymers form crystalline structures under normal solidification conditions. Space lattice:  It is a collection of lattice points that divide space into smaller equally sized segments. Every point in this lattice has identical surroundings. Space lattice 20 Crystalline lattice:  If each space point is occupied by an atom of a certain metal, this arrangement is called crystalline lattice. Unit cell:  It is a subdivision of the crystalline lattice that still retains the overall characteristics of the entire lattice.  It is characterized by the following parameters. 3 side lengths = a , b , c Unit cell 3 angles = α , β , γ 21  2- Types of unit cells Bravais lattice: Unique three-dimensional arrangements of lattice points. [14 types]. Crystal Systems: Possible designs of Bravais lattice that can be available in materials. [7 systems]  Most of metals crystallize in one of these simple forms;  Body centered cubic (BCC)  Face centered cubic (FCC)  Hexagonal close packed (HCP) 22  3- Parameters of metallic crystal structures (1) Number of atoms per unit cell  Each unit cell contains a specific number of lattice points. A lattice point at a corner of one unit cell and the atom occupying this location are shared by seven adjacent unit cells. Thus only one-eighth of each corner belongs to one particular cell.  The number of lattice points from all corner positions in one cubic unit cell is [(1/8) ×8=1 lattice point/unit cell].  Faces points chaired between two unit cells and hence one face lattice point provide 1/2 lattice point/unit cell] 23 (2) Packing factor. Assuming that metallic atoms are hard spheres, the packing factor (PF) or atomic packing fraction (APF) can be defined as the fraction of space occupied by atoms. The general expression for the packing factor is given by the following relation 𝑵𝑨𝒕𝒐𝒎𝒔/𝑼𝒏𝒊𝒕∙𝒄𝒆𝒍𝒍 × 𝒗𝑶𝒏𝒆 𝒂𝒕𝒐𝒎 Atomic Packing Factor (APF) % = × 𝟏𝟎𝟎 𝑽𝑼𝒏𝒊𝒕∙𝒄𝒆𝒍𝒍 24 (3) Atomic radius (r) versus lattice parameter (ao).  Directions in the unit cell along which atoms are in continuous contact are close-packed directions. These directions are used to calculate the relationship between the apparent size of the atom and the size of the unit cell. (4) Coordination number:  It is the number of atoms touching a particular atom or it is the number of nearest neighbours for that particular atom. 25  4- Main types of Metallic Crystal Structures A. Simple cubic (SC) B. Body-centered cubic (BCC)  Arrangement of atoms in space: Number of atoms 1 n  8   1 atoms n 1 8 1  2 atoms 8 8 per unit cell: a  2r ao 3 Atomic radius (r): r  ao / 2 r 4 Coordination Number (C.N.) C.N. = 6 C.N. = 8 Atomic Packing factor APF = 0.52 = 52% APF = 0.68 = 68% (APF) Examples Polonium (Po) Fe(α), Ti(β), W, Mo, Nb, Ta, K, Na, V, Cr  C. Face-centered cubic D. Hexagonal closed packed (FCC) (HCP)  Arrangement of atoms in space: 1 1 Number of atoms 1 1 n  6   8   4 atoms n  3  12  6  2   6 atoms 2 2 8 per unit cell: Atomic radius (r): r ao 2 r  a o /2 4 Coordination Number (C.N.) C.N. = 12 C.N. = 12 Atomic Packing factor APF = 0.74 = 74% APF = 0.74 = 74% (APF) Examples Fe(γ), Cu, Al, Au, Ag, Pb, Ni, Pt. Ti(α), Mg, Zn, Be, Co, Zr, Cd. Further Reading Book Title Materials Science and Engineering An Introduction Jhon Wiley , William D. Callister Chapter Chapter 2: Atomic Structure and Interatomic Bonding Required subsections 2.2 FUNDAMENTAL CONCEPTS 2.4 THE PERIODIC TABLE 2.6 PRIMARY INTERATOMIC BONDS Chapter Chapter 3: The Structure of Crystalline Solids Required subsections 3.1 Introduction 3.2 Fundamental Concepts 3.3 Unit Cells 3.4 Metallic Crystal Structures 3.5 Density Computations