Thermal vibrations in convergent-beam electron diffraction

Abstract

The frozen phonon technique is introduced as a means of including the effects of thermal vibrations in multislice calculations of CBED patterns. This technique produces a thermal diffuse background, Kikuchi bands and a Debye-Waller factor, all of which are neglected in the standard multislice calculation. The frozen phonon calculations match experimental silicon (100) CBED patterns for specimen 0108-7673/91/030267-12503.00© 1991 International Union of Crystallography THERMAL VIBRATIONS IN CONVERGENT-BEAM ELECTRON DIFFRACTIONthicknesses of up to at least 550 A. The best-fit silicon r.m.s, vibration amplitude at near room temperature was determined to be 0.085(5)/~. As an independent check of validity, a comparison of calculated CBED, experimental CBED and electron energy loss spectroscopy (EELS) data was also performed. The frozen phonon technique provides an improved theoretical basis for the simulation of CBED and therefore annular dark field scanning transmission electron microscope imaging.( 1) IntroductionConvergent-beam electron diffraction (CBED) is widely used for microcharacterization (Steeds, 1983; Eades, 1988). The most common application is to identify known structures and their orientations, but CBED has also been used to determine accurate unit-cell dimensions (Jones, Rackham & Steeds, 1977), structure symmetries (Goodman, 1975;Tanaka, Saito & Sekii, 1983) and even atomic positions (Vincent, Bird & Steeds, 1984). Strain fields around defects (Fung, 1985;Carpenter & Spence, 1982), specimen thicknesses (Kelly, Jostsons, Blake & Napier, 1975;Kirkland, Loane, Xu & Silcox, 1989), ionicity (Zuo, Spence & O'Keeffe, 1988) and the phase of complex atomic structure factors (Zuo, Spence & H¢ier, 1989;Bird, James & Preston, 1987) have also been determined. The sum of the large-angle scattering in the CBED pattern produces the annular dark field (ADF) scanning transmission electron microscope (STEM) image (Langmore, Wall & Isaacson, 1973), which has recently proven capable of resolving atomic structures with Z contrast (Pennycook, 1989;Pennycook, Jesson & Chisholm, 1990) at better than 2,~ resolution (Xu, Kirkland, Silcox & Keyse, 1990; Shin, Kirkland & Silcox, 1989). Three major features of the large-angle scattering are Kikuchi bands (Kikuchi, 1928;Kainuma, 1955;Takagi, 1958), a thermal diffuse scattering (TDS) background (Hall & Hirsch, 1965) and a higher-order Laue zone (HOLZ) ring (Hirsch, Howie, Nicholson, Pashley & Whelan, 1977). Thermal vibrations generate the first two features and reduce the intensity of the third by a Debye-Waller factor (Debye, 1914). Since the intensity in the HOLZ ring may be a significant fraction of the ADF STEM signal (Spence, Zuo & Lynch, 1989), the signal may be sensitive to thermal vibration. There are suggestions that thermal vibrations can change the relative contrast of different elements in the ADF STEM signal (Wang & Cowley, 1989), which differs from the suggestion that the signal is simply related to the atomic cross sections . Accordingly, understanding the ...

Picometre-precision analysis of scanning transmission electron microscopy images of platinum nanocatalysts

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Fano resonance in atomic-resolution spectroscopic imaging of solids

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