Chapter Outline Understanding of interatomic bonding is the first step towards understanding/explaining materials properties Review of Atomic

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1 Chapter Outline Understanding of interatomic bonding is the first step towards understanding/explaining materials properties Review of Atomic Structure: Electrons, Protons, Neutrons, Quantum mechanics of atoms, Electron states, The Periodic Table Atomic Bonding in Solids: Bonding Energies and Forces Periodic Table Primary Interatomic Bonds: Ionic, Covalent, Metallic Secondary Bonding (Van der Waals): Three types of Dipole Bonds Molecules and Molecular Solids

2 Review : Atomic Structure and Bonding The atom consists of neutral neutrons and positively charged protons (which form a dense nucleus) surrounded by negatively charged electrons. Atoms = nucleus (protons and neutrons) + electrons Charges: Electrons and protons have negative and positive charges of the same magnitude, Coulombs. Neutrons are electrically neutral. Masses: Protons and Neutrons have the same mass, kg. Mass of an electron is much smaller, kg and can be neglected in calculation of atomic mass. # protons gives chemical identification of the element # protons = atomic number (Z) # neutrons defines isotope number The atomic mass (A) = mass of protons + mass of neutrons

3 Atomic mass units. Atomic weight. The atomic mass unit (amu) is often used to express atomic weight. 1 amu is defined as 1/12 of the atomic mass of the most common isotope of carbon atom that has 6 protons (Z=6) and six neutrons (N=6). Mproton Mneutron = 1.66 x g = 1 amu. The atomic mass of the 12C atom is 12 amu. The atomic weight of an element = weighted average of the atomic masses of the atoms naturally occurring isotopes. Atomic weight of carbon is amu. The atomic weight is often specified in mass per mole. A mole is the amount of matter that has a mass in grams equal to the atomic mass in amu of the atoms (A mole of carbon has a mass of 12 grams). The number of atoms in a mole is called the Avogadro number, N av = N av = 1 gram/1 amu. Example: Atomic weight of iron = amu/atom = g/mol

4 Some simple calculations The number of atoms per cm 3, n, for material of density ρ(g/cm 3 ) and atomic mass A(g/mol): N ρ n = av A Graphite (carbon): ρ = 2.3 g/cm 3, A = 12 g/mol n = atoms/mol 2.3 g/cm 3 / 12 g/mol = atoms/cm 3 Diamond (carbon): ρ = 3.5 g/cm 3, A = 12 g/mol n = atoms/mol 3.5 g/cm 3 / 12 g/mol = atoms/cm 3 Water (H 2 O) ρ = 1 g/cm 3, A = 18 g/mol n = molecules/mol 1g/cm 3 / 18g/mol = molecules/cm 3 For material with n = atoms/cm 3 we can calculate the mean distance between atoms L = (1/n) 1/3 = 0.25 nm.! the scale of atomic structures in solids a fraction of 1 nm or a few Angstroms.

5 nucleus protons & neutrons electrons Example: Calculate the number of atoms in 100g of silver. (From the periodic table: the atomic mass of Ag = g/mol) Solution: # of 100 g Ag atoms = (100g) ( atom/mol)/( g/mol) = atoms

6 Example 1 : The cladding (outside layer coating) of the U.S. quarter coin consists of an alloy of 75wt%Cu and 25wt%Ni. What are the atomic percent Cu and atomic percent Ni contents of this material? Cu (A = 63.54g/mol) Ni (A = 58.69g/mol) Clad : Composite coinage metal strip composed of a core, usually of a base metal such as copper, and surface layers of more valuable metal, silver (or sometimes copper-nickel). Cladding is a cost-saving measure, making coins cheaper to produce while maintaining a desired appearance. Solution: In 100g of the75wt%cu-25wt%ni alloy, there are 75g of Cu and 25g of Ni. Number of gram-mol of Cu = 75g / 63.54g/mol = mol Number of gram-mol of Ni = 25g / 58.69g/mol = mol Total gram-moles = mol Cu at% = (1.1803mol / mol)(100%) = 73.5at% Ni at% = (0.4260mol / mol)(100%) = 26.5at%

7 Example 2 : An intermetallic compound has the general chemical formula Ni X Al Y, where X and Y are simple integers, and consists of 42.04wt%Ni and 57.96wt%Al. What is the simplest formula of this nickel aluminide? Ni (A = 58.69g/mol) Al (A = 26.98g/mol) Solution In 100g of the 42.04wt%Ni-57.96wt%Al alloy, there are 42.04g Ni and 57.96g Al. Number of gram-mol of Ni = 42.04g / 58.69g/mol = mol Number of gram-mol of Al = 57.96g / 26.98g/mol = mol Total gram-moles = mol Ni gram-mol fraction = mol / mol = 0.25 Al gram-mol fraction = mol / mol = 0.75 Next, we replace the X and Y in the Ni X Al Y compound with 0.25 and 0.75 respectively, to give Ni 0.25 Al 0.75 which is the simplest chemical formula. On an integral basis we need to multiply times four to give NiAl 3 for the simplest chemical formula of this nickel aluminide.

8 The Electronic Structure of Atoms Electrons move not in circular orbits, but in 'fuzzy orbits. Actually, we can only say what is the probability of finding it at some distance from the nucleus. In other words, the exact position of an electron can not be specified when the energy is known (Heisenberg Uncertainty Principle) x is the uncertainty in the position of the electron, p is the uncertainty in the momentum (mass x velocity) and h is the Planck s constant. x p h 4π Only certain orbits or shells of electron probability densities are allowed. The shells are identified by a principal quantum number (n)

9 The principal quantum number n defines the energy of the electrons: Where A is a constant equal to 2.179x10-18 J (or 13.6eV) and Z is the positive charge of the nucleus. The negative sign of the equation indicates that the energy of the electron is chosen as zero when n is infinite (the electron is not longer bound to the nucleus). E = AZ 2 n The principal quantum number n is not sufficient to determine the location of the electron. Two other independent quantum numbers are needed l and m l

10 Principal quantum number n: shell - 1,2,3, shells can also be designated by the letters K, L, M, N,O, 2nd quantum number l: subshell - denoted by s, p, d or f. It is related to the shape of the electron sub-shell. 3rd quantum number m l : the number of energy states for each subshell. s - 1 state; p - 3; d - 5; & f - 7. The above quantum numbers are needed to indicate the orbital of the electrons. A fourth quantum number (m s ) is needed to explain some chemical and physical properties of the atoms. 4th quantum number m s : the spin moment (+1/2 or -1/2) one for each of the spin orientation. The quantum numbers arise from solution of Schrodinger s equation Pauli Exclusion Principle: only one electron can have a given set of the four quantum numbers Or No more than two electrons can occupy a single orbital and when two electrons occupy a single orbital their spins must be different

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12 C (Z= 6) 1s 2 2s 2 2p x1 2p 1 y Si (Z = 14) 1s 2 2s 2 2p x2 2p 2 y 2p z2 3s 2 3p 1 x 3p 1 y Mg (Z = 12) 1s 2 2s 2 2p x2 2p 2 y 2p z2 3s 2 F (Z = 9) 1s 2 2s 2 2p x2 2p 2 y 2p 1 z

13 Electrons that occupy the outermost filled shell the valence electrons they are responsible for bonding. Electrons fill quantum levels in order of increasing energy (only n, l make a significant difference). Example: Iron, Z = 26: 1s 2 2s 2 2p 6 3s 2 3p 6 3d 6 4s 2 f d Energy p s d p s p s s Principle Quantum Number, n

14 Electronic Structure and Chemical Reactivity The chemical properties of the atoms of the elements depend principally on the reactivity of the outer electrons. Noble gases Most stable (He 1s 2, all others s 2 p 6 configuration) Valence electrons: occupy the outermost filled shell. [Valence of an atom = No. of electrons that the atom loses, gains or shares to attain an octet] Example: Sodium atom: Na: 1s 2 2s 2 2p 6 3s 1 Na + +11e Only 1 electron in the 3 rd shell, it is readily released. Once this electron is released, it becomes Sodium ion (Na + ). Cation: positive charge (usually a small atom) Anion: negative charge (usually a large atom)

15 Electronic Configuration Valence (a) C 1s 2 2s 2 2p 2 4 (b) Li 1s 2 2s 1 1 (c) Be 1s 2 2s 2 2 (d) Mg 1s 2 2s 2 2p 6 3s 2 2 (e) P 1s 2 2s 2 2p 6 3s 2 3p 3 3 (f) S 1s 2 2s 2 2p 6 3s 2 3p 4 2 Electronegativity: Electronegativity is defined as the degree to which an atom attracts electrons to itself. Electronegativity is measured in a scale from 0 to 4.1 Atomic Size: Each atom can be considered as a sphere with a definite radius. The radius of the atomic sphere is not constant but depend on its environment.

16 The Periodic Table Elements in the same column (Elemental Group) share similar properties. Group number indicates the number of electrons available for bonding.

17 0: Inert gases (He, Ne, Ar...) have filled subshells: chem. inactive IA: Alkali metals (Li, Na, K ) have one electron in outermost occupied s subshell - eager to give up electron chem. active VIIA: Halogens (F, Br, Cl...) missing one electron in outermost occupied p shell - want to gain electron - chem. active In general: within a horizontal row in the periodic table, the more electropositive elements are those farthest left, and the more electronegative elements are those farthest right. within a vertical column in the periodic table, the more electropositive elements are those towards the bottom, and the more electronegative elements are those towards the top.

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19 Different types of atomic radii (!! atoms can be treated as hard spheres!!) element or compounds compounds only elements or compounds ( alloys )

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21 Bonding Energy and Forces There is a potential well for two interacting atoms The repulsion between atoms, when they are brought close to each other, is related to the Pauli principle: when the electronic clouds surrounding the atoms starts to overlap, the energy of the system increases abruptly. The origin of the attractive part, dominating at large distances, depends on the particular type of bonding.

22 The electron volt (ev) energy unit convenient for description of atomic bonding Electron volt the energy lost / gained by an electron when it is taken through a potential difference of one volt. E = q V For q = 1.6 x Coulombs V = 1 volt 1 ev = 1.6 x J

23 Types of Bonding Primary bonding: e- are transferred or shared Strong ( KJ/mol or 1-10 ev/atom) Ionic: Strong Coulomb interaction among negative atoms (have an extra electron each) and positive atoms (lost an electron). Example - Na + Cl - Covalent: electrons are shared between the molecules, to saturate the valency. Example - H 2 Metallic: the atoms are ionized, loosing some electrons from the valence band. Those electrons form a electron sea, which binds the charged nuclei in place.

24 Secondary Bonding: no e- transferred or shared. Interaction of atomic/molecular dipoles Weak (< 100 KJ/mol or < 1 ev/atom) Fluctuating Induced Dipole (inert gases, H 2, Cl 2 ) Permanent dipole bonds (polar molecules - H 2 O, HCl...) Polar molecule-induced dipole bonds (a polar molecule like induce a dipole in a nearby nonpolar atom/molecule)