Differential quantitative analysis of background structure in energy-filtered convergent-beam electron diffraction patterns

摘要: Measurements of electronic structure in solids by quantitative convergent-beamelectrondiffraction(QCBED)willnotreachtheirultimateaccuracyorprecisionuntil the contribution background to reflections energy-filteredCBED patterns is fully accounted for. Apart from well known diffusebackground that arises thermal diffuse scattering electrons, there acomponent has a much higher angular frequency. The present work reportsexperimental evidence this component mimics distribution oftheelastically scatteredelectrons within each reflection. A differentialapproachto QCBED suggested as means quantitatively accounting for thebackground energy-filtered CBED data.1. IntroductionThe high accuracy and precision structuremeasurements inorganic with degree crystalperfection convergent-beam electron diffrac-tion (QCBED) now established (Zuo et al.,1988;BirdSZuo,1993;Deiningeretal.,1994;Holmestadetal.,1995;PengZSaundersetal.,1995,1996,1999;Zuo al.,1997,1999;TsudaTStreltsovet al.,2001, 2003; Tsuda al.,2002;Jianget al.,2003;Ogataet al.,2004; Friis, Madsen al.,2003;Friis,Jianget al.,2003;Jiangetal.,2004;Friiset al.,2004,2005;Nakashima,2005,2007).Suchmeasurements are precise enough allow meaningfulcomparisons experimentally measured structurewith different ab initio theoretical models al.,1997,1999; Saunders al.,1999;Friis,Madsenet al.,2003;Jiangetal.,2003,2004;Friiset al.,2004,2005;Nakashima,2005),including those derived density functional theory andperiodic Hartree–Fock, Dirac–Fock linear combination ofatomic orbitals calculations.QCBED originated 1940 (MacGillavry, 1940) withsporadic application until late 1980s (Goodman L Voss al.,1980)whenthedevelopmentofenergy-filtering optics transmission microscopesresulted strong revival technique al.,1988,1997, 1999; Bird & Saunders, 1992; Zuo, 1993; Holmestad etal.,1995;PengZSaunderset al.,1995,1996,1999;Tsuda Tanaka, Streltsov al.,2001,2003;Tsudaet al.,2002; Jiang al.,2004;Friis,Madsenet al.,2003; al.,2003;Jianget al.,2004;Friiset al.,2004,2005; Nakashima, 2005). ability exclude almost all ofthe inelastic signal energy filtering, coupled highdynamic range digital detection (via CCDs) thecontinuous expansion computing power, allowed unprece-dented analysis experimental data via patternmatching based on elastic theory. As result, therefinement Fourier coefficients crystal potential(structure amplitudes or factors) during pattern-matching process became sufficiently accurate tobecomparabletothemostpreciseandaccuratemeasurementsever made X-ray diffraction (Dawson, 1967; Kato, 1969;Hart Milne, 1970).Even so, not reached its full potential becauseenergy filtering does remove components CBEDpattern unaccounted theory.Thermaldiffuse (TDS) ofelectrons results energylossesoflessthan0.1 eV,wellbelowthe resolution ofthemostmodern filters also below spread energiesfrom latest monochromated sources. Argumentsagainst applying calculations incorporating treatment ofTDS because their nearly prohibitive cost computingpower time (compared purely scatteringcalculations) will eventually fade advent newsupercomputing technologies such graphics processingunits. growing number incorporateTDS (Rossouw al.,1990;Loaneet al.,1991;Wang,1992;Muller al.,2001;Omotoet al.,2002;Dwyer,2003,2005;Dwyer Etheridge, 2003), Omoto al. (2002) illus-tratinghowTDScalculationscanbeincluded(non-iteratively)in QCBED. However, very little information theliterature about associatedwith disc pattern. Most deal onlywiththetotalsignalinthepattern,withoutseparatingtheTDSand components. examined due TDS theoretically inthe absence pattern, but without comment