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Periodic table 0 IA IIA transition metals IIIB IVB VB VIBVIIB VIIIB postIIIA IVA VA VIA VIIA transition metals IB IIB Bonding in Solids e repulsive Coulomb interaction between ions e repulsive Coulomb interaction between electrons attractive Coulomb interaction between ions and electrons Stable Solids : EK EP energy of neutral atoms kinetic energy of electrons 2 EK ~ 2m( x)2 Molecular (van der Waals) bond Crystals of “inert” gases of group 0: Ar, Kr, Xe, Rn e e m1 m2 Electric field in the visinity of the second atom : E ~ 2 m1 40 R 3 Induced dipole moment in the second atom : m2 ~ E R 2m1 40 R 3 Potential energy between two dipoles : 2 2 m12 C 2 : V ( R ) ~ - m2 E E 6 R6 40 R Van-der Waals, London or fluctuating dipole interaction Molecular (van der Waals) bond atom1 atom2 electron charge distribution Electron charge distributi on overlaps. Repulsive interactio n arises due to Pauli exclusion principle : VRepalsive( R ) ~ Lennard - Jones potential : V ( R ) ~ - C B R 6 R12 B ,B0 12 R V (R ) 4 12 6 4 , 4 6 C , 4 12 B R R 6 -1/4 2 R IONIC bond Crystals: NaCl, CsCl, CaCl2 Na + Na+ Cl Cl- cohesive energy + 7.9eV Na 5.1eV Na free electron Energy balance Cl free electron Cl 3.6eV Coulomb interactio n between Na and Cl : V ( R) e2 40 R 5eV , R 2.81 IONIC bond: Madelung constant Vi V ji i j i j 40 Rij R Rij pij R , where R nearest 40 R A, A i j separation in the crystal then Vi q2 for like charge for unlike charge q2 pij Madelung constant A 1 1 1 2 ...... R R 2 R 3R 2 ln 2 R IONIC bond: Madelung constant Rij pij R , where R nearest separation in the crystal then Vi q2 40 R Madelung constant A, A i j pij NaCl~ 1.75 CsCl~1.76 ZnS (cubic)~1.64 For 2 N ions ( N pairs of ions) Nq2 V NVi A 40 R Covalent bond Crystals: C, Si, Ge, H Covalent bond is formed by two electrons, one from each atom, localised in the region between the atoms (spins of electrons are anti-parallel ) Example: Carbon 1S2 2S2 2p2 C C 3D Diamond: tetrahedron, cohesive energy 7.3eV 2D Covalent bond Energy Hydrogen molecule H4 1S 1S H atom Methane molecule H atom H2 molecule C H1 H3 H2 Covalent bond Atoms in group III, IV,V,&VI tend to form covalent bond Filling factor T. :0.34 F.C.C :0.74 Metallic bond Atoms in group IA-IIB let electrons to roam in a crystal. Free electrons glue the crystal Attract eAttract Repel Repel Na+ Na+ Attract Attract e- Additional binding due to interaction of partially filled d – electron shells takes place in transitional metals: IIIB - VIIIB The Hydrogen bond Hydrogen bond is formed between the most electronegative atoms: F,O and N. Bonding energy is ~ 0.1ev Bonding in DNA molecule F- N H+ C N sugar N C H C H C H C N C C H adenine O C N N H C C H H H F- N sugar thymine Bonding in Solids Melting point (K) Molecular crystals Metals Ionic crystals W(3683) C(<3500) BN(3270) 3000 Mo(2883) Pt(2034) Fe(1808) 2000 1000 organic crystals 0 Covalent crystals Cu(1336) Al(933) Pb(600) Na(371) Hg(234) SiO2(2001) LiF(1143) KCl(1063) Si(1683) Ge(1240)