Chapter Outline. Review of Atomic Structure Electrons, Protons, Neutrons, Quantum mechanics of atoms, Electron states, The Periodic Table

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1 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 Chapter Outline Primary Interatomic Bonds Ionic Covalent Metallic Secondary Bonding (Van der Waals) Three types of Dipole Bonds Molecules and Molecular Solids Understanding of interatomic bonding is the first step towards understanding/explaining materials properties University of Tennessee, Dept. of Materials Science and Engineering 1 Review of Atomic Structure 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. The atomic mass (A) = mass of protons + mass of neutrons # protons gives chemical identification of the element # protons = atomic number (Z) # neutrons defines isotope number University of Tennessee, Dept. of Materials Science and Engineering 2

2 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). M proton M neutron = 1.66 x g = 1 amu. The atomic mass of the 12 C 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 University of Tennessee, Dept. of Materials Science and Engineering 3 Some simple calculations The number of atoms per cm 3, n, for material of density d (g/cm 3 ) and atomic mass M (g/mol): n = N av d / M Graphite (carbon): d = 2.3 g/cm 3, M = 12 g/mol n = atoms/mol 2.3 g/cm 3 / 12 g/mol = atoms/cm 3 Diamond (carbon): d = 3.5 g/cm 3, M = 12 g/mol n = atoms/mol 3.5 g/cm 3 / 12 g/mol = atoms/cm 3 Water (H 2 O) d = 1 g/cm 3, M = 18 g/mol n = molecules/mol 1 g/cm 3 / 18 g/mol = molecules/cm 3 For material with n = atoms/cm 3 we can calculate 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 A. University of Tennessee, Dept. of Materials Science and Engineering 4

3 Electrons in Atoms (I) The electrons form a cloud around the nucleus, of radius of nm. This Bohr picture looks like a mini planetary system. But quantum mechanics tells us that this analogy is not correct: Electrons move not in circular orbits, but in odd shaped orbitals depending on their quantum numbers. Only certain orbits or shells of electron probability densities are allowed. The shells are identified by a principal quantum number n, which can be related to the size of the shell, n = 1 is the smallest; n = 2, 3.. are larger. The second quantum number l, defines subshells within each shell. Two more quantum numbers characterize states within the subshells. University of Tennessee, Dept. of Materials Science and Engineering 5 Quantum Rules n can take any positive integer value l can take any integer value between 0 and n1. Therefore there are n possible values of l for a given n m l can take any integer value between l and + l. Thus there are (2 l +1) values of m l for a given l m s can take two values: ±1/2 Thus for any given value of l (an electron subshell) there are 2(2 l +1) electrons; for any given value of n (an electron shell) there are Σ2(2 l +1) electrons (add up all the subshells) University of Tennessee, Dept. of Materials Science and Engineering 6

4 Atomic Structure Recall Isotopes C 12 where 12 = 6 Protons + 6 Neutrons C 13 where 13 = 6 Protons + 7 Neutrons (Isotope) Isotopic abundance of C % Carbon: g/mol Atoms having the same atomic number but varying numbers of neutrons are isotopes Mass of basic particles: Particle Charge Mass (amu*) (1.66x10 24 or 1/N av ) Proton (1.6734x10 24 g) Neutron (1.675x10 24 g) Electron ( x10 24 g) The atomic mass unit (amu) is the basic unit of measurement of an atom s mass, one amu = (1/12)* 12 C 6 (1 amu = x g) University of Tennessee, Dept. of Materials Science and Engineering 7 Electrons in Atoms (II) 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. The Number of Available Electron States in Some of the Electron Shells and Subshells University of Tennessee, Dept. of Materials Science and Engineering 8

5 Electrons in Atoms (III) 1s 2s sp 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 7s 7p Subshells by energy: 1s,2s,2p,3s,3p,4s,3d,4s,4p,5s,4d,5p,6s,4f, Electrons that occupy the outermost filled shell the valence electrons they are responsible for bonding. Electrons fill quantum levels in order of increasing energy (due to electron penetration) Example: Iron, Z = 26: 1s 2 2s 2 2p 6 3s 2 3p 6 3d 6 4s 2 University of Tennessee, Dept. of Materials Science and Engineering 9 University of Tennessee, Dept. of Materials Science and Engineering 10

6 Draft of the periodic table, Mendeleev, 1869 University of Tennessee, Dept. of Materials Science and Engineering 11 General Periodic Table: Metals and Non Metals Elements in the same column (Elemental Group) share similar properties. Group number indicates the number of electrons available for bonding. 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 University of Tennessee, Dept. of Materials Science and Engineering 12

7 Periodic Table Electronegativity The electronegativity values. Electronegativity a measure of how willing atoms are to accept electrons Subshells with one electron low electronegativity Subshells with one missing electron high electronegativity Electronegativity increases from left to right Metals are electropositive they can give up their few valence electrons to become positively charged ions University of Tennessee, Dept. of Materials Science and Engineering 13 Bonding Energies and Forces repulsion Potential Energy, E 0 attraction equilibrium This is typical 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. University of Tennessee, Dept. of Materials Science and Engineering 14

8 University of Tennessee, Dept. of Materials Science and Engineering 15 Bonding Behavior But what does it mean?? (a) High melting temperature, high elastic modulus, low thermal expansion coefficient (b) Low melting temperature, low elastic modulus, high thermal expansion coefficient University of Tennessee, Dept. of Materials Science and Engineering 16

9 Relevant Equations Coulombic Attraction Force Oppositely Charged Ions F c = K/ r2, r = atomic separation distance between ion centers K = k 0 (Z 1 q)(z 2 q), q = 1.6 x coulomb/unit charge Z = valence of the ion (+1,+2,+3,1,2,3 ) F c = [k 0 (Z 1 q)(z 2 q)] / r 2 Repulsive Force F R = λe a/p λ,p are constants At equilibrium: F N = 0 = F A + F R = 0, F A = F R University of Tennessee, Dept. of Materials Science and Engineering 17 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 University of Tennessee, Dept. of Materials Science and Engineering 18

10 Types of Bonding Primary bonding: e are transferred or shared Strong ( KJ/mol or 110 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 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 moleculeinduced dipole bonds (a polar molecule like induce a dipole in a nearby nonpolar atom/molecule) University of Tennessee, Dept. of Materials Science and Engineering 19 Ionic Bonding (I) Formation of ionic bond: 1. Mutual ionization occurs by electron transfer (remember electronegativity table) Ion = charged atom Anion = negatively charged atom Cation = positively charged atom 2. Ions are attracted by strong coulombic interaction Oppositely charged atoms attract An ionic bond is nondirectional (ions may be attracted to one another in any direction Example: NaCl 11 Protons Na Electron Configuration? 17 Protons Cl Electron Configuration? Na (metal) unstable Na (cation) stable electron + Coulombic Attraction Cl (nonmetal) unstable Cl (anion) stable University of Tennessee, Dept. of Materials Science and Engineering 20

11 Ionic Bonding (II) Na e Cl Na + Cl Electron transfer reduces the energy of the system of atoms, that is, electron transfer is energetically favorable Note relative sizes of ions: Na shrinks and Cl expands Ionic bonds: very strong, nondirectional bonds University of Tennessee, Dept. of Materials Science and Engineering 21 Predominant bonding in Ceramics NaCl MgO H 2.1 Li 1.0 Na 0.9 K 0.8 Be 1.5 Mg 1.2 Ca 1.0 Ti 1.5 Cr 1.6 CaF2 CsCl Fe Ni Zn 1.8 As 2.0 O F Cl 3.0 Br 2.8 He Ne Ar Kr Rb 0.8 Cs 0.7 Sr 1.0 Ba 0.9 I 2.5 At 2.2 Xe Rn Fr 0.7 Ra 0.9 Give up electrons Acquire electrons Adapted from Fig. 2.7, Callister 6e. (Fig. 2.7 is adapted from Linus Pauling, The Nature of the Chemical Bond, 3rd edition, Copyright 1939 and 1940, 3rd edition. Copyright 1960 by Cornell University. University of Tennessee, Dept. of Materials Science and Engineering 22

12 Ionic Bonding (III) Crystal Structures in Ceramics with predominantly ionic bonding Crystal structure is defined by Magnitude of the electrical charge on each ion. Charge balance dictates chemical formula (Ca 2+ and F form CaF 2 ). Relative sizes of the cations and anions. Cations wants maximum possible number of anion nearest neighbors and viceversa. Stable ceramic crystal structures: anions surrounding a cation are all in contact with that cation. For a specific coordination number there is a critical or minimum cationanion radius ratio r C /r A for which this contact can be maintained. University of Tennessee, Dept. of Materials Science and Engineering 23 Covalent Bonding (I) In covalent bonding, electrons are shared between the molecules, to saturate the valency. The simplest example is the H 2 molecule, where the electrons spend more time in between the nuclei than outside, thus producing bonding. Formation of covalent bonds: Cooperative sharing of valence electrons Can be described by orbital overlap Covalent bonds are HIGHLY directional Bonds in the direction of the greatest orbital overlap Covalent bond model: an atom can covalently bond with at most 8N, N = number of valence electrons Example: Cl 2 molecule. Z Cl =17 (1S 2 2S 2 2P 6 3S 2 3P 5 ) N = 7, 8 N = 1 can form only one covalent bond University of Tennessee, Dept. of Materials Science and Engineering 24

13 Covalent Bonding (II) Whereas the metallic and ionic CN is based on size and hard sphere Packing, covalent bonding is based on a different set of rules. Hard sphere model r/r CN (ionic, metallic) r/r<1 8 r/r = 1 12 Covalent bond model: 8N, N = number of valence electrons El. Config. X tal structure # valence e 8N C (1S) 2 2S 2 2P 2 diamond cubic 4 4 Si..3S 2 3P 2 diamond cubic 4 4 GaAs Ga..4S 2 4P 1 zinc blend 4 average 4 As.. 4S 2 4P 3 University of Tennessee, Dept. of Materials Science and Engineering 25 Covalent Bonding (III) Example: Carbon materials. Z c = 6 (1S 2 2S 2 2P 2 ) N = 4, 8 N = 4 can form up to four covalent bonds ethylene molecule: polyethylene molecule: ethylene mer diamond: (each C atom has four covalent bonds with four other carbon atoms) University of Tennessee, Dept. of Materials Science and Engineering 26

14 Covalent Bonding (IV) Example: Hybridization Diamond if covalentlybonded carbon Expected CN=12 (if ionic, equal sizes, r/r = 1) Observed CN=4 ( tetrahedral coordination) Explanation: directional bonding Outer shell electrons 2s and 2p hybridize to form 4equallyspaced orbitals Reason: greater orbital overlap possible University of Tennessee, Dept. of Materials Science and Engineering 27 EXAMPLES: COVALENT BONDING H 2.1 Li 1.0 Na 0.9 K 0.8 Rb 0.8 Cs 0.7 Fr 0.7 Be 1.5 Mg 1.2 Ca 1.0 Sr 1.0 Ba 0.9 Ra 0.9 H2 Ti 1.5 Cr 1.6 H2O C(diamond) SiC Fe Ni Zn column IVA C 2.5 Si 1.8 Ga Ge As Sn 1.8 Pb 1.8 GaAs O 2.0 F 4.0 Cl 3.0 Br 2.8 I 2.5 At 2.2 He Ne Ar Kr Xe Rn F2 Cl2 Adapted from Fig. 2.7, Callister 6e. (Fig. 2.7 is adapted from Linus Pauling, The Nature of the Chemical Bond, 3rd edition, Copyright 1939 and 1940, 3rd edition. Copyright 1960 by Cornell University. University of Tennessee, Dept. of Materials Science and Engineering 28

15 Metallic Bonding (I) Valence electrons are detached from atoms, and spread in an 'electron sea' that "glues" the ions together. A metallic bond is nondirectional (bonds form in any direction) atoms pack closely ion core Electron cloud from valence electrons University of Tennessee, Dept. of Materials Science and Engineering 29 Metallic Bonding (II) University of Tennessee, Dept. of Materials Science and Engineering 30

16 Secondary Bonding (I) Secondary = van der Waals = physical (as opposed to chemical bonding that involves e transfer) bonding results from interaction of atomic or molecular dipoles and is weak, ~0.1 ev/atom or ~10 kj/mol. Arises from interaction between dipoles Fluctuating dipoles asymmetric electron clouds + + secondary bonding H H Permanent dipolesmolecule induced general case: + + ex: liquid HCl secondary bonding ex: liquid H2 H2 H2 H H secondary bonding secondary H Cl H Cl bonding ex: polymer secondary bonding University of Tennessee, Dept. of Materials Science and Engineering 31 Secondary Bonding (II) Example: hydrogen bond in water. The H end of the molecule is positively charged and can bond to the negative side of another H 2 O molecule (the O side of the H 2 O dipole) O H H + Dipole + Hydrogen bond secondary bond formed between two permanent dipoles in adjacent water molecules. University of Tennessee, Dept. of Materials Science and Engineering 32

17 Secondary Bonding (III) Hydrogen bonding in liquid water from a molecularlevel simulation Molecules: Primary bonds inside, secondary bonds among each other University of Tennessee, Dept. of Materials Science and Engineering 33 Secondary Bonding (IV) The Crystal Structures of Ice Hexagonal Symmetry of Ice Snowflakes Figures by Paul R. Howell University of Tennessee, Dept. of Materials Science and Engineering 34

18 F F PROPERTIES FROM BONDING: T M Bond length, r Melting Temperature, Tm r Energy (r) Bond energy, Eo Energy (r) r o smaller Tm r unstretched length r o r Eo= bond energy larger Tm Tm is larger if Eo is larger. University of Tennessee, Dept. of Materials Science and Engineering PROPERTIES FROM BONDING: E Elastic modulus, E Elastic modulus F L length, Lo A = E o L o undeformed L deformed cross sectional area Ao F E ~ curvature at ro Energy unstretched length r o smaller Elastic Modulus larger Elastic Modulus r E is larger if Eo is larger. University of Tennessee, Dept. of Materials Science and Engineering 36 16

19 PROPERTIES FROM BONDING: α Coefficient of thermal expansion, α coeff. thermal expansion L Lo = α (T 2 T 1 ) length, Lo unheated, T1 L heated, T2 α ~ symmetry at ro Energy r o larger α r smaller α α is larger if Eo is smaller. University of Tennessee, Dept. of Materials Science and Engineering SUMMARY: PRIMARY BONDS Ceramics (Ionic & covalent bonding): Large bond energy large Tm large E small α Metals (Metallic bonding): Variable bond energy moderate Tm moderate E moderate α Directional Properties Polymers Secondary bonding dominates (Covalent & Secondary): small T small E large α secondary b University of Tennessee, Dept. of Materials Science and Engineering 38 18

20 Summary (II) University of Tennessee, Dept. of Materials Science and Engineering 39 Summary (III) Make sure you understand language and concepts: Atomic mass unit (amu) Atomic number Atomic weight Bonding energy Coulombic force Covalent bond Dipole (electric) Electron state Electronegative Electropositive Hydrogen bond Ionic bond Metallic bond Mole Molecule Periodic table Polar molecule Primary bonding Secondary bonding Van der Waals bond Valence electron University of Tennessee, Dept. of Materials Science and Engineering 40

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