2. InteratomicForce Models Topic 2.1 -Origins, Mie potential, van derW - PDF document

2. InteratomicForce Models Topic 2.1 -Origins, Mie potential, van derWaals -�= gases-�= liquids-�= solids (with different crystal structures)Repulsive force has shorter range than attractive force.Forces decrease with increasiIn solids and liquids the atoms are almost touching; 2. InteratomicForce Models� 2.1 Origins and potentials metallic and van derWaals2. InteratomicForce Models� 2.1 Origins and potentials (e.g. Na+)In ionic materials there is a complete transfer of electrons between atoms ………Coulomb force F ~ Na Attraction of …Na Repulsion: 2. InteratomicForce Models� 2.1 Origins and potentials (e.g. Na)……(not unlike covalent bonds but electron are shared between many atoms)�= (e.g. diamond)In covalent materials atoms share electrons.… each atom touches 8 others. Electrons + 4 Attractive force cont.VAN DER WAALS occur between all types of atoms or molecules, (*when, although it is a weak foattractive forces are absent)2. InteratomicForce Models� 2.1 Origins and potentialsVdWforces arise from an attraction permanent or instantaneous) of one atom (molecule) and that (either permanent or induced) of another + - + - -+ -+ Example of Van derWaals’forces•Van derWaals’forces give a gecko an ability to climb!2. InteratomicForce Models� 2.1 Origins and potentials K. Autumn et al., PNAS 2002, Has both ELECTROSTATICand QUANTUM-MECHANICALorigins.(i) +venuclear charges no longer �screened = Coulomb repulsion(ii) Electrons near to each-other canor more convenientlywhere n = 10 2. InteratomicForce Models� 2.1 Origins and potentials Interatomicforces: Representationmolecule) at the origin andanother a distance r away.repulsive force + ve; attractive force F0rmrepulsive force FR=+const=+A( a)m rattractive force FA=+const.Õ=-A(a)n 2. InteratomicForce Models� 2.1 Origins and potentials repulsionRF attractionAF Interatomicpotential energies2. InteratomicForce Models� 2.1 Origins and potentials 2. InteratomicForce Models� 2.1 Origins and potentials V(r) equilibrium potential energy less steepvery steep derWaals solid)A good approximation to the potential energy.(equivalent to Mie potential with m=12, n=6, A=The L-J 6-12 potential describes the interaction between two isolated atoms 2. InteratomicForce Models� 2.1 Origins and potentials V(r) to a good approximation, the number of NEAREST NEIGHBOURS of any particular molecule2. InteratomicForce Models� 2.1 Origins and potentials 12Consequences of L-J potential:•Many properties of macroscopic assemblies (liquids and solids) of neutral atoms/molecules can be derived from the •We will consider density, critical temperature, latent heat, mechanical properties (compressibility) and V(r) High energy collision cross-section thermal expansion, compressibility Critical temperature Latent heat Surface energy 2. InteratomicForce Models� 2.1 Origins and potentials VdWterm is negligible compared with Coulomb term (~0.01 -0.1eV 2 InteratomicForce Models2.2. Interatomicpotential for an ionic crystal2. InteratomicForce Models� 2.2 Interatomicpotential for ionic crystalBetween ions there are repulsive forces, van derWaals forces (as for Coulomb forcespotential energy between an isolated pair of ions ,, Ionic interatomicpotential in solids2. InteratomicForce Models� 2.2 Interatomicpotential for ionic crystalTwo important differences (complications) compared with neutral molecules r like chargesUnlike charges Madelungconstant for ionic crystalsConsider a line of ions: ...+ -+ -+ -+ -+ 2. InteratomicForce Models� 2.2 Interatomicpotential for ionic crystal Madelungconstant )1ln(3232xxxx .02ln...1413121 II Interatomicforce mo�dels II.2 Potential for ionic crystal which depends on the particular arrangement of ions. (typicaly1-2)= 1.38; for 3D NaClstructure Interatomicpotential for ionic crystals2. InteratomicForce Models� 2.2 Interatomicpotential for ionic crystal multiplied by the Madelungconstant Interatomicpotential of ionic crystals2. InteratomicForce Models� 2.2 Interatomicpotential for ionic crystal