催化剂研究方法与表征外教课件.doc

Surface enrichment The composition of the surface of most materials is different from that of the bulk and this has large consequences, not only in catalysis, but in all areas where the surface plays an important role. The reason for the surface enrichment is that atoms at the surface have a different surrounding than in the bulk and therefore thermodynamics favours some atoms to be at the surface and others to be in the bulk. We will study this with the example of alloys, but the principles are also valid for other materials, like metal oxides and sulfides. Let us take a look at the surface of a binary alloy AB. We will assume that an atom in the bulk has p direct neighbours in the plane parallel to the surface and m direct neighbours perpendicular to that plane. For an fcc metal p +m = 12 and for a bcc metal p +m = 8. An atom at the surface will have the same number (p) of neighbours in the surface plane, but only m/2 neighbours perpendicular to the plane, because the neighbours above the plane are missing. We will assume that the broken-bond model applies, which assumes that only bonds between direct neighbouring atoms contribute to the energy of the alloy, and that surface enrichment only occurs in the top surface layer. All other layers have the bulk composition, also the subsurface layer. When xs is the concentration of atom A at the surface and xb its concentration in the bulk, then the energy EAs of atom A at the surface is EAs = p[xsEAA + (1- xs)EAB] + m/2[xbEAA + (1-xb)EAB] EAs = (pxs +mxb/2) EAA + [p(1- xs) + m(1-xb)/2]EAB where EAA is the binding energy between two neighbouring A atoms and EAB is the binding energy between two neighbouring A and B atoms. The energy of an atom A in the bulk is EAb = (p + m)[xbEAA + (1-xb)EAB] Similarly, for atom B at the surface and in the bulk we get the energies EBs and Ebb, respectively: EBs = (pxs +mxb/2) EAB + [p(1- xs) + m(1-xb)/2]EBB and EBb = (p + m)[xbEAB + (1-xb)EBB] The energy difference ?E between