摘要:

AbstractIn the present paper the influence of thermal lattice vibrations on the electron diffraction intensities of polycrystalline foils is investigated. It is shown, that the distinction between Bragg‐reflections and thermal diffuse scattering is equivalent to splitting the crystal potential under influence of lattice vibrations into two terms:V= 〈V〉 +U, where 〈V〉 is the statistical average. 〈V〉 has the same periodicity as the potentialV°(r) of the lattice at rest, but the Fouriercoefficients are reduced with increasing temperature by the Debye‐Waller factor: 〈V〉h=V 0h. exp (−Mh). The temperature dependence of the Fouriercoefficients 〈V〉hdetermines the variation of the reflection intensities with temperature. The time dependent potentialUgives rise to the thermal diffuse scattering. Simple theoretical results are obtained from the kinematical approximation and from the two beam approximation of the dynamical theory. Furthermore, the influence of absorption of electrons on the temperature dependence of diffraction intensities is discussed on the basis of these approximations.Experimental investigations of the temperature dependence of Bragg‐reflections and of the diffuse scattering have been carried out mainly for aluminium, because in this case the dynamical extinction of the strong reflections can be described by the two beam approximations. The scattered electrons have been detected by a Faraday cage. In order to filter off electrons scattered inelastically with energy losses above ∼ w ev, a retarding field has been used.The experimental results concerning the influence of temperature on the intensities of various reflections can be described by introducing the temperature dependent Fouriercoefficients 〈V〉h into the relevant intensity formulae for elastic scattering.The temperature dependence of the intensities of all reflections, which behavekinematically, can be well described by the Debye‐Waller factor exp (−2Mh) within a large range of 2Mh. The mean square displacement of the lattice atoms, which was derived from the measured values of 2Mhat different temperatures, is in good agreement with results fromX‐ray measurements.For reflections, which are influenced bydynamical extinction, an effective Debye‐Waller factor exp (αhMh) has been introduced, in order to describe the temperature dependence of the intensities. The αh‐values, measured at 50 keV and for Al‐foils with crystal sizes of about 300 Å lie between 0 and 2,5 and can be interpreted by the two beam approximation of the dynamical theory.Further the thermal diffuse scattering of Al has been investigated. The measured intensity shows good agreement with the theoretical angular distribution for one‐ and two‐phonon processes.From the integrated intensities of the Debye‐Schemer rings (IR) and of the thermal diffuse scattering (ITDS) the mean free pathsARandATDSfor these scattering processes have been determined. The measured value ofARshows good agreement with the calculation based on the two beam approximation andATDSagrees fairly well with the kinematical value for the Einstein‐model of the vibrating crystal.Moreover the transmission of polycrystalline foils for fast electrons has been investigated. Besides of aluminium, also silver and gold were used, in order to study the effect of atomic number on the absorption coefficients μeland μuneldue to elastic and inelastic scattering processes respectively.The experimental results show, that μuneldecreases only slightly with temperature. On the other hand, the absorption coefficient μel, which is composed of μR = Δ R−1for Bragg‐scattering and μTDS= Δ TDS−1für thermal diffuse scattering increases with temperature. As μRand μTDSdepend on temperature in opposite sense, the resulting increase of μel= μR+ μTDSwith temperature depends on the extent, to which the temperature dependence of μRis reduced by dynamical extinction.For Al the measured temperature dependence of μelis in good agreement with the theoretical calculation of μTDSfor the Einstein‐model and of μRaccording to the two beam approximation. For Ag and Au the temperature dependence of μelis much more pronounced than for Al. This is due to the facts, that for heavy elements firstly the elastic scattering is stronger and secondly dynamical extinction effects are generally more pronounced. A quantitative interpretation however, cannot be based on the two beam approximation. In all cases studied here, the influence of anomalous absorption on the reflection intensities as well as on the tra

ISSN:0015-8208    

DOI:10.1002/prop.19680160302

出版商:WILEY‐VCH Verlag    

年代:1968

数据来源: WILEY

ISSN:0015-8208    

DOI:10.1002/prop.19680160303

出版商:WILEY‐VCH Verlag    

年代:1968

数据来源: WILEY

ISSN:0015-8208    

DOI:10.1002/prop.19680160301

出版商:WILEY‐VCH Verlag    

年代:1968

数据来源: WILEY