LECTURE 14 Dr. Teres D. Golden University of North Texs Deprtment of Chemistry
Quntittive Methods A. Quntittive Phse Anlysis Qulittive D phses by comprison with stndrd ptterns. Estimte of proportions of phses by compring pek intensities ttributed to the identified phses with stndrd intensity rtios Quntittive Determintion of mounts of different phses in multi-phse smples bsed on precise determintion of diffrction intensity nd/or determintion of the fit of the pttern of ech phse to the chrcteristics of tht phse i.e., mount, crystl structure, crystllite size nd shpe.
Quntittive Methods A. Quntittive Phse Anlysis Quntittive Cn be difficult need to do complete clibrtion of instrument, creful prepping of stndrds, nd repetitive mesurements. For quntittive nlysis, must equte concentrtion of given phse or phses with line intensities. Line intensities re ffected by vriety of fctors.
Quntittive Methods
hkl Quntittive Methods A. Quntittive Phse Anlysis The intensity eqution from lecture 6, ex: structure fctor, multiplicity, Lorenz-polriztion fctor, temperture fctor, bsorption fctor describes the dependence of intensity of the diffrction line for phse. 3 ol e 64r mec M V hkl F hkl 1 cos sin q cos q m q cosq r X m / r s hkl = ntensity of reflection of hkl in phse r = distnce from specimen to detector ndterm = squre of clssicl electron rdius 0 = incident bem intensity l = X-ry wvelength M hkl = multiplicity of reflection hkl of phse Next to lst term on right = Lorentz-polriztion nd monochromtor correction for hkl n tht term, qm = diffrction ngle of the monochromtor V = volume of the unit cell of phse Fhkl = structure fctor for reflection hkl of phse X weight frction of r density of phse m/r s mss ttenution coefficient of smple.
Quntittive Methods A. Quntittive Phse Anlysis The entire eqution shown here cn be reduced, since the 1 st nd nd terms in brckets re constnt for the prticulr setup. X weight frction of r density of phse m/r s mss ttenution coefficient of smple. s m hkl hkl e o hkl X F V M m c e r r m r q q q q l / cos sin cos cos 1 64 3
Quntittive Methods A. Quntittive Phse Anlysis Therefore the totl dsorption of the smple is sum of the products of the individul ttenution coefficients nd weight fctions two unknowns So need to use vrious methods to solve eqution.
Quntittive Methods A. Quntittive Phse Anlysis Wht is the RR? RR is n intensity rtio of pek re in determined phse to tht of stndrd phse usully corundum t is rtio of the integrted intensity of the strongest pek of the phse in question to the strongest pek of corundum /crrcoris published for mny phses in the CDD PDF dtbse t my be experimentlly determined for prticulr systems nd used in spiked specimens Common internl stndrds in use include: -Al O 3 corundum, Qurtz SiO, ZnO
Quntittive Methods A. Quntittive Phse Anlysis Methods - bsorption-diffrction - stndrd dditions - internl stndrds
Quntittive Methods A. Quntittive Phse Anlysis Absorption-Diffrction Method hkl o hkl m / r m / r s X where hkl intensity of phse of unknown o hkl intensity of pure smple of phse
Quntittive Methods A. Quntittive Phse Anlysis For binry mixture: Since X + Xb = 1, cn simplify eqution to the Klug eqution: b b r m r m r m / / / X X X o hkl hkl b b r m r m r m r m / / / / / / o hkl hkl o hkl hkl X
Quntittive Methods A. Quntittive Phse Anlysis X m / r hkl hkl / / o hkl o hkl m / r m / r b m / r b Exmple: SiO in SiO /CSiO 3 m/r for SiO is 35.9 nd m/r b for CSiO 3 is 74.1 for SiO phse is 470 counts nd for pure SiO is 10,000 counts then X 0.4774.1 35.9 0.4735.9 74.1 60.6%
Quntittive Methods A. Quntittive Phse Anlysis Stndrd Addition Method or spiking method Method used to determine phse in mixture, s long s one other phse, b, hs diffrction line tht does not overlp with ny line. b does not even hve to be identified.
Quntittive Methods A. Quntittive Phse Anlysis With this method, some of the pure phse is dded to the mixture contining the unknown concentrtion of. hkl hkl' b K X Y where X is the initil weight frction of phse Xb is the initil weight frction of phse b Y is the number of grms of pure phse dded per grm of the originl smple.
Quntittive Methods A. Quntittive Phse Anlysis After severl dditions of Y grms of the phse, plot of / b versus Y cn be constructed.
Quntittive Methods A. Quntittive Phse Anlysis nternl Stndrd Method Most common Plot clibrtion curve of hkl / hkl b versus X /X b with k s the slope. hkl hkl' b k X X b
Quntittive Methods A. Quntittive Phse Anlysis n this method, known mount, X b, of n internl stndrd is dded to mixture of phses. The ddition of this new phse increses the complexity of the pttern, so must be creful in choosing the stndrd. Usully, F-centered cubic mterils with smll unit cells re used becuse of their simple ptterns.
Quntittive Methods A. Quntittive Phse Anlysis Rietveld Method Quntittive method bsed on the use of the totl pttern. nvolves fitting the entire diffrction pttern with synthetic diffrction pttern, which is either produced or clculted stndrd pttern. The full-pttern pproch pioneered by Dr. Hugo M. Rietveld ttempts to ccount for ll of the contributions to the diffrction pttern to discern ll of the component prts by mens of lestsqures fit of the diffrction pttern. The method is mde possible by the power of digitl dt processing nd very complicted softwre.
Quntittive Methods A. Quntittive Phse Anlysis Rietveld Method Quntittive method bsed on the use of the totl pttern. The method is mde possible by the power of digitl dt processing nd very complicted softwre Originlly conceived only for use with extremely clen neutron diffrction dt, the method hs evolved to del with the reltively poor-qulity of dt from conventionlly-sourced diffrctometers. Rietveld refinement is conducted by minimizing the sum of the weighted, squred differences between observed nd clculted intensities t ech step.
Quntittive Methods A. Quntittive Phse Anlysis Rietveld Method nput dt needed includes spce group symmetry, tomic positions, site occupncies, lttice prmeters for ech phse, profile shpe, bckground function, nd scle fctor. Cn set certin dt nd let others vry, i.e. scle fctor, profile, bckground, nd lttice prmeter.
Quntittive Methods A. Quntittive Phse Anlysis Rietveld Method The method is cpble of much greter ccurcy in quntifying XRD dt thn ny pek-intensity-bsed method becuse of the systemic wholepttern pproch The initil primry use of the method ws nd still is to mke precise refinements of crystl structures bsed on fitting the experimentl diffrction pttern to precise structure Though it generlly hs firly steep lerning curve, very sophisticted softwre is vilble t no cost to do the refinements: Mjor pckges include GSAS nd FullPROF Reitveld s 1969 pper is recommended for further reding http://crystl.tu.c.il/xtl/pper/pper.html
Quntittive Methods A. Quntittive Phse Anlysis FULLPAT: A Full Pttern Qunt System Developed by Steve Chipernd Dve Bisht LANL primrily for use in nlysis of Yucc Mountin Tuff smples. s full pttern fitting system but unlike Reitveld does not do detiled structure determintion. Uses the built-in Solver functions of Microsoft Excel. Will work on virtully ny computer tht hs MS Excel on it s long s the correct extensions re instlled. Softwre is free nd in the public domin your tx dollrs t work; vilble on ftp://eps.unm.edu/pub/xrd Bsiclly, the progrm mkes use of the fct tht the totl diffrction pttern is the sum of the diffrction ptterns of the constituent phses, nd does lest-squres fit on the observed smple pttern to the pproprite stndrd ptterns.
Reding Assignment: Red Chpter 13 from: -ntroduction to X-ry powder Diffrctometry by Jenkins nd Synder Red Chpter 13 nd 14 from: -Elements of X-ry Diffrction, 3 rd edition, by Cullity nd Stock