DSpace at VNU: Generalized Xafs Cumulant Theory and a new Procedure for Structural Determination

VNU JOURNAL OF SCIENCE Mathematics - Physics T XVIII N()2 - 2002 G E N E R A L IZ E D X A F S C U M U L A N T T H E O R Y A N D A N E W P R O C E D U R E F O R S T R U C T U R A L D E T E R M IN A T IO N Nguyen Van Hung D cịìcìi ' men I o f Physics, C olleg e o f Science ‘ V N Ư Abstract: /1 n.('ii) yc.ncrulizcd X A F S cum ulant theory has l)('£* — a D ( 15 — -Ị- - — aa 1/2 M aMs » - m TTm ? /' \ and the corrolated Einstein température (7) 1/2 1‘ ( s + ) - ệ ™ ) (8 Kb where A/ is mass of absorber, A/ is mass o f backscatterer, and k-B is B oltzm ann's co n sta n t Thi' cum ulants are díTÌved hv averaging the value o f V [5,7,10] A tom ic vibration is quantized as phonon and anharm onicity is the result of phonon interaction Therefore, to evaluate the* m atrix elem ents we express y in terms o f creation a w l annihilation operators and i e., H = ơo(ơ + ò ); ƠQ = ựh/2fj.u>E- (9) U sing oscillator state 17/ > as eigen state with eigenvalue E n — nhujE (ignoring tlie zero-point energy for convenience) and the m ethod o f d en sity m atrix [10 ] we derived the second cum ulant or DH>ye-Waller factor: == - Y c- ' - n h ^ / k u T < „ | y |n > z« r zo = 1 _ e - 0E / T ' which by using IJ from Eq (9) to calculate the matrix elements is changed into: "’ ■ ỵ i t o K t (10) Evaluating the traces in the density m atrix m ethod, th e rem aining odd m om ents are given by: Ị _—^ ,t E nt /k liT < ym > = V z - F - „ < "I