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PHYSICS FOR ENGINEERING Sub-topics 1 Structure of atom Bonding in materials Bonding and properties WHY TO STUDY ATOMIC STRUCTURE? The structure of atoms is important to engineers because it influences the way atoms are bonded together which helps us to categorize the materials that they form. The atomic structure and bonding also allows us to formulate some general conclusions on the mechanical and physical properties of the material. 2 WHY STUDY BONDING? Because the properties of materials (strength, hardness, conductivity, etc..) are determined by the manner in which atoms are connected. What determines the nature of the chemical bond between atoms? Electronic structure (distribution of electrons in atomic orbitals) Number of electrons and electronegativity (tendency for an atom to attract an electron) 3 INTERATOMIC BONDING All of the mechanisms which cause bonding between the atoms derive from electrostatic interaction between nuclei and electrons. The differing strengths and differing types of bond are determined by the particular electronic structures of the atoms involved. The existence of a stable bonding arrangement implies that the spatial configuration of positive ion cores and outer electrons has less total energy than any other configuration (including infinite separation of the respective atoms). The energy deficience of the configuration compared with isolated atoms is known as a cohesive energy, and ranges in value from 0.1 eV/atom for solids which can muster only the weak van der Waals to 7ev/atom or more in some covalent and ionic compounds and some metals. 4 WHAT IS THE STRUCTURE OF ATOM? It well known that the material properties are structure-sensitive. neutron Subatomic <1A ● ● ● ● ● nucleus ● proton ● ● electron ● ● ● ● Atoms are made by massive, point-like nuclei (protons + neutrons) - Electron structure dictates how •Surrounded by tightly bound, rigid shells of core electrons bonding occurs - The nature of the bond, in turn, dictates many material properties •Bound together by a glue of valence electrons (gas vs. atomic orbitals) 5 STRUCTURE OF ATOM A normal atom has equal numbers of protons and electrons. The Atomic Number of an atom is the number of protons it has in it’s nucleus. 6 ATOMIC MASS 7 BOHR ATOM The energies of electrons are quantized; electrons are permitted to have only specific values of energy. May e change its energy? The simplified Bohr atomic model, in which electrons are assumed to revolve around the atomic nucleus in discrete orbitals, and the position of any particular electron is more or less well defined in terms of its orbital. 8 ELECTRON ENERGY STAGES n – principal quantum number Pauli exclusion principal states that no two identical 9 fermions may occupy the same quantum state simultaneously. QUANTUM PHYSICS MILESTONES Between 1900 and 1925 Quantum Physics was developed by a number of physicists, including Planck, Einstein, Bohr and de Broglie. From 1925 onwards a more mathematical approach was developed by Schrödinger (wave mechanics), Heisenberg (matrix mechanics) and Dirac (who developed a more general formulation). 10 If you are not confused by Quantum Physics then you haven't really understood it. N.Bohr WHAT IS QUANTUM MECHANICS GOOD FOR? Quantum mechanics does not explain how a quantum particle behaves. Instead, it gives a recipe for determining the probability of the measurement of the value of a physical variable (e.g. energy, position or momentum). This information enables us to calculate the average value of the measurement of a physical variable. Quantum mechanics is the study of mechanical systems whose dimensions are close to the atomic scale. Quantum mechanics is a fundamental branch of physics with wide applications. Quantum theory generalizes classical mechanics to provide accurate descriptions for many previously unexplained phenomena such as black body radiation and stable electron orbits. The effects of quantum mechanics become evident at the atomic and subatomic level, and they are typically not observable on macroscopic scales. - Wikipedia 11 WAVE-PARTICLE DUALITY In physics and chemistry, wave–particle duality is the concept that all matter and energy exhibits both wave-like and particle-like properties. Particles are waves, waves are particles. In quantum mechanics, the motion of particles is described with probabilities. Probability distribution of the Bohr atom – Wikipedia 12 HOW MANY QUANTUM NUMBERS? Using wave mechanics, every electron in an atom is characterized by four parameters called quantum numbers. The Bohr model was a one-dimensional model that used one quantum number to describe the distribution of electrons in the atom. The only information that was important was the size of the orbit, which was described by the n quantum number. Schrödinger's model allowed the electron to occupy three-dimensional space. It therefore required three coordinates, or three quantum numbers, to describe the orbitals in which electrons can be found. The three coordinates that come from Schrödinger's wave equations are the principal (n), angular (l), and magnetic (m) quantum numbers. 13 These quantum numbers describe the size, shape, and orientation in space of the orbitals on an atom. QUANTUM NUMBERS The principal quantum number (n) describes the size (distance of an electron from the nucleus) of the orbital. Orbitals for which n = 2 are larger than those for which n = 1. The principal quantum number therefore indirectly describes the energy of an orbital. The angular quantum number (l) describes the shape of the orbital. Orbitals have shapes that are best described as spherical (l = 0), polar (l = 1), or cloverleaf (l = 2). They can even take on more complex shapes as the value of the angular quantum number becomes larger. A third quantum number, known as the magnetic quantum number (m), describes the orientation in space of a particular orbital and shows the energy states in sub-shells. 14 SHELLS AND SUB-SHELLS OF ORBITALS Orbitals that have the same value of the principal quantum number form a shell. Orbitals within a shell are divided into subshells that have the same value of the angular quantum number. Bohr and (b) wavemechanical atom models in terms of electron distribution. 15 SUB-SHELLS •s, p, d and f signify the subshells which the electrons occupy. • Different types of subshells have different numbers of energy states •Within each energy state there are two possible spin orientations Schematic representation of the relative energies of the electrons for the various shells and subshells 16 ELECTRON STATES What is electron configuration for C? Na and Cl (is it easy to create sodium chloride molecule?) 17 ELECTRON CONFIGURATIONS 18 CHEMICAL BONDING BETWEEN ATOMS • Electron states is controlling factor for atomic bonding • Types of primary (strong) bonds: ionic, covalent, metallic • Types of secondary (weak) bonds: van der Waals, hydrogen • Properties that are controlled by interatomic potentials: melting point, bond stiffness, thermal expansion coefficient 19 BONDING FORCES Many properties of materials are determined by the interatomic forces that bind the atoms together. Equilibrium spacing These forces are of two types, attractive and repulsive, and the magnitude 20 of each is a function of the separation or interatomic distance. ENERGY OF BONDING Bonding energy Once in this position, the two atoms will counteract any attempt to separate them by an attractive force, or to push them together by21 a repulsive action. This typical curve has a minimum at equilibrium distance R0 R > R0 ; the potential increases gradually, approaching 0 as R ∞ the force is attractive R < R0; the potential increases very rapidly, approaching ∞ at small separation. the force is repulsive V(R) Repulsive 0 R0 R Attractive r R Force between the atoms is the negative of the slope of this curve. At equlibrium, repulsive force becomes equals to the attractive part. 22 IS IT DIFFICULT TO SEPARATE ATOMS? represents the energy that would be required to separate The magnitude of this bonding energy and the these two atoms to an infinite shape of the energy versus interatomic separation distance 23 curve vary from material to material, and they both depend on the type of atomic bonding. ATOMIC INTERACTIONS 24 THE POTENTIAL ENERGY OF ATOM V= decrease in potential energy+increase in potential energy (due to attraction) (due to repulsion) −a b V (r ) = m + n r r V(r): the net potential energy of interaction as function of r r : the distance between atoms, ions, or molecules a,b: proportionality constant of attraction and repulsion, respectively m, n: constant characteristics of each type of bond and type of structure 25 MODULUS AND BONDING ENERGY The magnitude of the modulus of elasticity is proportional to the slope of each curve at the equilibrium interatomic separation r0 26 ELASTIC MODULUS 27 COHESIVE ENERGY Atoms are held together by bonds that behave like springs Cohesive energy is a measure of the strength of the bonds Bond Stiffness 28 TYPES OF BONDING It is conventional to classify the bonds between atoms into different types as Ionic, Covalent, Metallic, Van der Waals, Hydrogen. All bonding is a consequence of the electrostatic interaction between nuclei and electrons obeying Schrödinger’s equation. 29 IONIC BONDING • Occurs between strongly electronegative and strongly electropositive atoms • Electron(s) are transferred from electropostive atom to electronegative atom, thereby forming a cation (positively charged) and an anion (negatively charged) 30 NACL When sodium loses its one valence electron it gets smaller in size, while chlorine grows larger when it gains an additional valance electron. After the reaction takes place, the charged Na+ and Cl- ions are held together by electrostatic forces, thus forming an ionic bond. 31 IONIC BONDING When the Na+ and Cl- ions approach each other closely enough so that the orbits of the electron in the ions begin the overlap each other, then the electron begins to repel each other by virtue of the repulsive electrostatic coulomb force. The closer together the ions are, the grater the repulsive force. Pauli exclusion principle has an important role in repulsive force. To prevent a violation of the exclusion principle, the potential energy of the system increases very rapidly. 32 Property Explanation Melting point and boiling point The melting and boiling points of ionic compounds are high because a large amount of thermal energy is required to separate the ions which are bound by strong electrical forces. Electrical conductivity Solid ionic compounds do not conduct electricity when a potential is applied because there are no mobile charged particles. No free electrons causes the ions to be firmly bound and cannot carry charge by moving. Hardness Most ionic compounds are hard; the surfaces of their crystals are not easily scratches. This is because the ions are bound strongly to the lattice and aren't easily displaced. Brittleness Most ionic compounds are brittle; a crystal will shatter if we try to distort it. This happens because distortion cause ions of like charges to 33 come close together then sharply repel. EXAMPLES OF IONIC BONDING 34 COVALENT BONDING 35 COVALENT BONDING Covalent bonding takes place between atoms with small differences in electronegativity which are close to each other in periodic table (between nonmetals and non-metals). The covalent bonding is formed by sharing of outer shell electrons (i.e., s and p electrons) between atoms rather than by electron transfer. This bonding can be attained if the two atoms each share one of the other’s electrons. So the noble gas electron configuration can be attained. 36 COVALENT BONDING Atoms form stable electron structures, i.e. those of inert gases, by sharing of electrons with other atoms • Resulting bonds are strongly directional 37 Property Melting point and boiling point Electrical conductivity Hardness Brittleness Explanation Very high melting points because each atom is bound by strong covalent bonds. Many covalent bonds must be broken if the solid is to be melted and a large amount of thermal energy is required for this. Poor conductors because electrons are held either on the atoms or within covalent bonds. They cannot move through the lattice. They are hard because the atoms are strongly bound in the lattice, and are not easily displaced. Covalent network substances are brittle.If sufficient force is applied to a crystal, covalent bond are broken as the lattice is distorted. Shattering occurs rather than deformation of a38 shape. COMPARISON OF IONIC AND COVALENT BONDING 39 METAL BONDING Valence electrons ( in outer shell) leave atoms and form a “sea” of free electrons Positively charged ion cores are shielded from one another by the free electrons Free electron acts as the “glue” that hold positive cores together Non-directional High thermal and electrical conductivity 40 HOW STRONG IS METAL BONDING? Valance electrons are relatively bound to the nucleus and therefore they move freely through the metal and they are spread out among the atoms in the form of a lowdensity electron cloud. A metallic bond result from the sharing of a variable number of electrons by a variable number of atoms. A metal may be described as a cloud of free electrons. Therefore, metals have high electrical and thermal conductivity. + + + + + + + + + 41 METAL BONDING - SUMMARY All valence electrons in a metal combine to form a “sea” of electrons that move freely between the atom cores. The more electrons, the stronger the attraction. This means the melting and boiling points are higher, and the metal is stronger and harder. The positively charged cores are held together by these negatively charged electrons. The free electrons act as the bond (or as a “glue”) between the positively charged ions. This type of bonding is non-directional and is rather insensitive to structure. As a result we have a high ductility of metals - the “bonds” do not “break” when atoms are rearranged – metals can experience a significant degree of plastic deformation. 42 VAN DER WAALS BONDING It is a weak bond, with a typical strength of 0.2 eV/atom. It occurs between neutral atoms and molecules. The explanation of these weak forces of attraction is that there are natural fluctuation in the electron density of all molecules and these cause small temporary dipoles within the molecules. It is these temporary dipoles that attract one molecule to another. They are called van der Waals' forces. The bigger a molecule is, the easier it is to polarize (to form a dipole), and so the van der Waal's forces get stronger, so bigger molecules exist as liquids or solids rather than gases. 43 THE WAY TO CREATE VAN DER WAALS BOND (1) The shape of a molecule influences its ability to form temporary dipoles. Long thin molecules can pack closer to each other than molecules that are more spherical. The bigger the 'surface area' of a molecule, the greater the van der Waal's forces will be and the higher the melting and boiling points of the compound will be. Van der Waal's forces are of the order of 1% of the strength of a covalent bond. Homonuclear molecules, such as iodine, develop temporary dipoles due to natural fluctuations of electron density within the molecule Heteronuclear molecules, such as H-Cl have permanent dipoles that attract the opposite pole in other molecules. 44 THE WAY TO CREATE VAN DER WAALS BOND (2) The dipoles can be formed as a result of unbalanced distribution of electrons in asymettrical molecules. This is caused by the instantaneous location of a few more electrons on one side of the nucleus than on the other. symmetric asymmetric Therefore atoms or molecules containing dipoles are attracted to each other by electrostatic forces. Display a marked attractive forces 45 No attraction is produced THE WAY TO CREATE VAN DER WAALS BOND (3) These forces are due to the electrostatic attraction between the nucleus of one atom and the electrons of the other. In polyvinyl chloride (PVC), the chlorine atoms attached to the polymer chain have a negative charge and the hydrogen atoms are positively charged. The 46 chains are weakly bonded by van der Waals bonds. This additional bonding makes PVC stiffer. VAN DER WAALS BONDING • Dipole moment produced by instantaneous asymmetry of electron charge distribution • Coulombic attraction occurs between positive end of one dipole and negatively charged end of another 47 SECONDARY BONDING The bonding results from the coulombic attraction between the positive end of one dipole and the negative region of an adjacent one 48 HYDROGEN BONDING 49 HYDROGEN BONDING A hydrogen atom, having one electron, can be covalently bonded to only one atom. However, the hydrogen atom can involve itself in an additional electrostatic bond with a second atom of highly electronegative character such as fluorine or oxygen. This second bond permits a hydrogen bond between two atoms or strucures. The strength of hydrogen bonding varies from 0.1 to 0.5 ev/atom. Hydrogen bonds connect water molecules in ordinary ice. Hydrogen bonding is also very important in proteins and nucleic acids and therefore in life processes. 50 BOND STIFFNESS AND MODULUS Bond stiffness largely determines the value of the modulus - E 51 SUMMARY 52 MELTING TEMPERATURE 53 BONDING ENERGIES AND MELTING TEMPERATURES 54