Different Electron-Scattering Mechanisms’ Contribution to the Formation of the Amplitude Contrast of Electron-Microscopic Images

A new method of experimental determination of the amplitude contrast value of electron-microscopic images for amorphous materials is suggested. The mathematical relations for calculating the contributions of different mechanisms of electron scattering by the object under study to the contrast on the...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Datum:2015
Hauptverfasser: Bobyk, M.Yu., Ivanitsky, V.P., Ryaboshchuk, M.M., Svatyuk, O.Ya.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут металофізики ім. Г.В. Курдюмова НАН України 2015
Schriftenreihe:Наносистеми, наноматеріали, нанотехнології
Online Zugang:http://dspace.nbuv.gov.ua/handle/123456789/87980
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:Different Electron-Scattering Mechanisms’ Contribution to the Formation of the Amplitude Contrast of Electron-Microscopic Images / M.Yu. Bobyk, V.P. Ivanitsky, M.M. Ryaboshchuk, O.Ya. Svatyuk // Наносистеми, наноматеріали, нанотехнології: Зб. наук. пр. — К.: РВВ ІМФ, 2015. — Т. 13, № 1. — С. 85–97. — Бібліогр.: 13 назв. — англ.

Institution

Digital Library of Periodicals of National Academy of Sciences of Ukraine
id irk-123456789-87980
record_format dspace
spelling irk-123456789-879802015-11-06T03:02:02Z Different Electron-Scattering Mechanisms’ Contribution to the Formation of the Amplitude Contrast of Electron-Microscopic Images Bobyk, M.Yu. Ivanitsky, V.P. Ryaboshchuk, M.M. Svatyuk, O.Ya. A new method of experimental determination of the amplitude contrast value of electron-microscopic images for amorphous materials is suggested. The mathematical relations for calculating the contributions of different mechanisms of electron scattering by the object under study to the contrast on the basis of the relevant electron-diffraction patterns are obtained. The shares of contribution of elastically coherently, elastically incoherently, and inelastically scattered electrons to the contrast are determined experimentally for the amorphous As40Se60 films. Запропоновано новий метод експериментального визначення амплітуди контрастного значення електронно-мікроскопічних зображень для аморфних матеріалів. Були одержані математичні співвідношення для розрахунку внесків різних механізмів розсіювання електронів на досліджуваному об’єкті в контраст на основі відповідних електронограм. Для аморфних плівок As40Se60 були знайдені експериментально частки внесків пружньо когерентно, пружньо некогерентно та непружньо розсіяних електронів у контраст. Предложен новый метод экспериментального определения амплитуды контрастного значения электронно-микроскопических изображений для аморфных материалов. Были получены математические соотношения для расчёта вкладов различных механизмов рассеяния электронов на изучаемом объекте в контраст на основе соответствующих электронограмм. Для аморфных плёнок As40Se60 были найдены экспериментально доли вкладов упруго когерентно, упруго некогерентно и неупруго рассеянных электронов в контраст. 2015 Article Different Electron-Scattering Mechanisms’ Contribution to the Formation of the Amplitude Contrast of Electron-Microscopic Images / M.Yu. Bobyk, V.P. Ivanitsky, M.M. Ryaboshchuk, O.Ya. Svatyuk // Наносистеми, наноматеріали, нанотехнології: Зб. наук. пр. — К.: РВВ ІМФ, 2015. — Т. 13, № 1. — С. 85–97. — Бібліогр.: 13 назв. — англ. 1816-5230 PACS numbers: 07.78.+s, 61.05.J-, 61.05.jd, 61.43.Dq, 68.37.Lp, 68.55.jd, 87.64.Ee http://dspace.nbuv.gov.ua/handle/123456789/87980 en Наносистеми, наноматеріали, нанотехнології Інститут металофізики ім. Г.В. Курдюмова НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description A new method of experimental determination of the amplitude contrast value of electron-microscopic images for amorphous materials is suggested. The mathematical relations for calculating the contributions of different mechanisms of electron scattering by the object under study to the contrast on the basis of the relevant electron-diffraction patterns are obtained. The shares of contribution of elastically coherently, elastically incoherently, and inelastically scattered electrons to the contrast are determined experimentally for the amorphous As40Se60 films.
format Article
author Bobyk, M.Yu.
Ivanitsky, V.P.
Ryaboshchuk, M.M.
Svatyuk, O.Ya.
spellingShingle Bobyk, M.Yu.
Ivanitsky, V.P.
Ryaboshchuk, M.M.
Svatyuk, O.Ya.
Different Electron-Scattering Mechanisms’ Contribution to the Formation of the Amplitude Contrast of Electron-Microscopic Images
Наносистеми, наноматеріали, нанотехнології
author_facet Bobyk, M.Yu.
Ivanitsky, V.P.
Ryaboshchuk, M.M.
Svatyuk, O.Ya.
author_sort Bobyk, M.Yu.
title Different Electron-Scattering Mechanisms’ Contribution to the Formation of the Amplitude Contrast of Electron-Microscopic Images
title_short Different Electron-Scattering Mechanisms’ Contribution to the Formation of the Amplitude Contrast of Electron-Microscopic Images
title_full Different Electron-Scattering Mechanisms’ Contribution to the Formation of the Amplitude Contrast of Electron-Microscopic Images
title_fullStr Different Electron-Scattering Mechanisms’ Contribution to the Formation of the Amplitude Contrast of Electron-Microscopic Images
title_full_unstemmed Different Electron-Scattering Mechanisms’ Contribution to the Formation of the Amplitude Contrast of Electron-Microscopic Images
title_sort different electron-scattering mechanisms’ contribution to the formation of the amplitude contrast of electron-microscopic images
publisher Інститут металофізики ім. Г.В. Курдюмова НАН України
publishDate 2015
url http://dspace.nbuv.gov.ua/handle/123456789/87980
citation_txt Different Electron-Scattering Mechanisms’ Contribution to the Formation of the Amplitude Contrast of Electron-Microscopic Images / M.Yu. Bobyk, V.P. Ivanitsky, M.M. Ryaboshchuk, O.Ya. Svatyuk // Наносистеми, наноматеріали, нанотехнології: Зб. наук. пр. — К.: РВВ ІМФ, 2015. — Т. 13, № 1. — С. 85–97. — Бібліогр.: 13 назв. — англ.
series Наносистеми, наноматеріали, нанотехнології
work_keys_str_mv AT bobykmyu differentelectronscatteringmechanismscontributiontotheformationoftheamplitudecontrastofelectronmicroscopicimages
AT ivanitskyvp differentelectronscatteringmechanismscontributiontotheformationoftheamplitudecontrastofelectronmicroscopicimages
AT ryaboshchukmm differentelectronscatteringmechanismscontributiontotheformationoftheamplitudecontrastofelectronmicroscopicimages
AT svatyukoya differentelectronscatteringmechanismscontributiontotheformationoftheamplitudecontrastofelectronmicroscopicimages
first_indexed 2025-07-06T15:39:30Z
last_indexed 2025-07-06T15:39:30Z
_version_ 1836912602295304192
fulltext 85 PACS numbers: 07.78.+s, 61.05.J-, 61.05.jd, 61.43.Dq, 68.37.Lp, 68.55.jd, 87.64.Ee Different Electron-Scattering Mechanisms’ Contribution to the Formation of the Amplitude Contrast of Electron- Microscopic Images M. Yu. Bobyk, V. P. Ivanitsky, M. M. Ryaboshchuk, and O. Ya. Svatyuk National University of Uzhhorod, Narodna Place, 3, 88000 Uzhhorod, Ukraine A new method of experimental determination of the amplitude contrast value of electron-microscopic images for amorphous materials is suggested. The mathematical relations for calculating the contributions of different mecha- nisms of electron scattering by the object under study to the contrast on the basis of the relevant electron-diffraction patterns are obtained. The shares of contribution of elastically coherently, elastically incoherently, and inelas- tically scattered electrons to the contrast are determined experimentally for the amorphous As40Se60 films. Запропоновано новий метод експериментального визначення амплітуди контрастного значення електронно-мікроскопічних зображень для амор- фних матеріалів. Були одержані математичні співвідношення для розра- хунку внесків різних механізмів розсіювання електронів на досліджува- ному об’єкті в контраст на основі відповідних електронограм. Для аморф- них плівок As40Se60 були знайдені експериментально частки внесків пру- жньо когерентно, пружньо некогерентно та непружньо розсіяних елект- ронів у контраст. Предложен новый метод экспериментального определения амплитуды контрастного значения электронно-микроскопических изображений для аморфных материалов. Были получены математические соотношения для расчёта вкладов различных механизмов рассеяния электронов на изучае- мом объекте в контраст на основе соответствующих электронограмм. Для аморфных плёнок As40Se60 были найдены экспериментально доли вкладов упруго когерентно, упруго некогерентно и неупруго рассеянных электро- нов в контраст. Key words: electron microscopy, electron diffraction, amplitude contrast, amorphous material, morphology of films, microstructure. Наносистеми, наноматеріали, нанотехнології Nanosystems, Nanomaterials, Nanotechnologies 2015, т. 13, № 1, сс. 85–97  2015 ІÌÔ (Іíñòèòóò ìåòàëîôіçèêè іì. Ã. Â. Êóðäþìîâà ÍÀÍ Óêðàїíи) Надруковано в Óкраїні. Ôотокопіювання дозволено тільки відповідно до ліöензії 86 M. Yu. BOBYK, V. P. IVANITSKY, M. M. RYABOSHCHUK, and O. Ya. SVATYUK (Received 27 February, 2015) 1. INTRODUCTION The bright field-imaging mode is the most common mode of operation in the transmission electron microscopy. The results of such electron microscopy (EM) experiments are fixed in a form of the two principal complementary sources of information: the electron diffraction pat- terns (i.e. electronograms, diffractograms, microelectronograms, nanoelectronograms) and the EM images of different areas of the ob- ject under study. In most cases, the subject of analysis of the EM images of crystalline materials is the diffraction contrast elements. They arise due to the coherently scattered electrons that interfere making the correspond- ing diffraction pattern. Therefore, when studying the crystal micro- structure, the analysis of the relevant EM images and that of the elec- tronograms are closely related [1]. The microstructure and the nanostructure of the amorphous speci- mens are studied in accordance with their EM images only. In this case, it is assumed that in such images the amplitude contrast is mainly formed [2]. It is assumed here, as a rule, that inhomogeneities of the EM images are determined mainly by the difference in the thicknesses or masses of the local areas of the specimen under study [3]. In the ex- perimental studies, such contrasts in the EM images are called the ‘mass–thickness’ contrast and describe them mainly qualitatively, i.e. determine the image homogeneity or heterogeneity, provide qualita- tive and several quantitative geometric parameters of heterogeneities. Such a theoretical approach to the analysis of the amplitude contrast of amorphous materials is very limited and does not take into account a number of factors that affect essentially the processes of the EM image formation. The principal of the above factors is the character of the spatial distribution of all the waves scattered by the specimen under study. In general, for each chemically and structurally homogeneous local area of the amorphous specimen, the electron wave (or the electron flux) intensity that forms the EM image of this area could be set by a simple relation [3]: II0exp(–Qd), (1) where Q is the parameter that characterizes the ability of this area to scatter electrons outside the aperture diaphragm. Therefore, finding the relationship between the electron beam intensity at a certain EM image point with integral scattering property Q of the relevant local ELECTRON-SCATTERING MECHANISMS’ CONTRIBUTION TO THE CONTRAST OF IMAGES 87 area of homogeneous specimen and the geometric thickness d of this area makes a ground of the amplitude contrast analysis. If one reduces the intensity I in (1) to a single atom and to the unit intensity of the incident beam I0, then the presence of variation of the scattering prop- erty of atoms for various areas of the object under study and their thicknesses will be definitive for production of the EM contrast. Scat- tering property variations could arise due to the differences in the structure of these areas, i.e. different atomic density, chemical compo- sition, structure of the short-range and medium-range order, nanopo- rosity, etc. Therefore, it is advisable to have the experimental methods of determining contribution of the differences of each of above param- eters of the amorphous material structure into the amplitude contrast. In this paper, we suggest one of the possible approaches to the solution of such problem of the applied electron microscopy. It is based on the fact that, for each amorphous material, the contrast observed in EM is formed by electrons scattered by the atoms of the specimen under study according to the three physical mechanisms, i.e. the elastic co- herent, the elastic incoherent and the inelastic ones. 2. EXPERIMENTAL TECHNIQUE Thin amorphous films were obtained by a method of discrete thermal evaporation of the As40Se60 glass with vapour condensation onto the substrate made of the NaCl single crystal. The substrates were not heated and were kept at the room temperature. Condensation rate was of 5–7 nm/s. Condensed film thickness was of 50–60 nm. The speci- mens for the EM studies were prepared according to the standard tech- nique of substrate dilution in the distilled water with film material trapping by the golden grids. As for the use of the copper grids, this resulted in the uncontrolled fast changes of the film atomic structure during the EM experiments not allowing their reliable diffractograms to be obtained. The EM studies of the amorphous As40Se60 films were carried out us- ing the transmission electron microscope JEM-2010 at the 100 kV ac- celerating voltage. The images and electronograms were detected by the Catan Ultrascan 4000SP CCD camera and processed by the comput- er software. The EM studies included several stages. 1. The general electronogram of the amorphous film was detected in the diffraction mode at one picture. Then, the aperture diaphragm was introduced ‘cutting out’ the central beam together with the adjacent area of scattered electrons and the second picture was taken fixing the diaphragm location against the electronogram background. Comparing these two pictures enabled us to determine the scattering angle value a that corresponds to the edges of the aperture diaphragm. 88 M. Yu. BOBYK, V. P. IVANITSKY, M. M. RYABOSHCHUK, and O. Ya. SVATYUK 2. The microstructure and the nanostructure of the specimens were studied in the common light field mode. Such studies allowed the local areas to be found in the amorphous film differing by their microstruc- ture. 3. The microstructurally homogeneous areas of the specimen were selected by the microdiffraction diaphragm and their microdiffraction patterns were detected. Microdiffractograms of 5–7 different areas were fixed in the same experiment for the same specimen. The data ob- tained were compared with each other and then the average micro- diffractogram of the areas under study was calculated using the com- puter program. Further computer processing of this microdiffracto- gram allowed it to be presented in a form of the intensity of electrons scattered by the local area as a function of scattering angle, I(). The function I() was determined reliably in the relative units within the range of scattering angle variation from 2 mrad to 30 mrad with the 0.3 mrad discretization step. The scattering angle () axis scale was determined with the help of the ‘embedded’ thin golden films. The normalizing factor  is a significant parameter of electrono- gram and microdiffractogram processing at the EM studies. Having found its value, one could easily transit from the relative to the abso- lute units of electron scattering intensity. This allows the correct and reliable comparison of diffractograms of the amorphous films of dif- ferent chemical compositions to be done as well as the reliable calcula- tions of electron fluxes forming the EM images of the objects under study to be carried out on their basis. We have determined the normal- izing factor and divided the total intensity I() into the elastic compo- nent and the incoherent background using the method described in [4]. The initial tabulated values of atomic scattering amplitudes F() were taken for calculations from tables quoted in [5]. 3. CONTRIBUTION OF DIFFERENT SCATTERING TYPES INTO THE CONTRAST It has been shown [6] that the contrast between the EM images of the two local areas of the object under study could be conveniently found as K(12)/112/1/1, (2) where 1 and 2 are the integral fluxes of the electron waves scattered by the two local areas outside the aperture diaphragm (it is assumed here that 12). In order to find experimentally the flux , one has to integrate the intensity І() (see Fig. 1) over the entire space beyond the aperture dia- phragm used to obtain the EM image patterns. An arrow in Figure 1 ELECTRON-SCATTERING MECHANISMS’ CONTRIBUTION TO THE CONTRAST OF IMAGES 89 indicates the scattering angle value that corresponds to the aperture diaphragm boundary. Accordingly, integration should be carried out within the scattering angle range amax, where max is the bounda- ry scattering angle value up to which the intensity І() was measured. In these conditions, one may write for each local area: max 2 ( )sin a I d         . (3) According to Figure 1, the integral intensity I() for each local area could be resolved into components, i.e. into the elastic coherent Ik(), the elastic incoherent Ie() and the inelastic In() ones. Then, relation (3) takes a form:                                max max max 2 ( ) sin 2 ( ) sin 2 ( ) sin , a a a k e n k e n I d I d I d (4) where k, e, n are the electron fluxes of the relevant electron waves scattered beyond the aperture diaphragm. Obviously, it is expedient to determine quantitatively the amplitude contrast from (2) by analysing each of the above-mentioned fluxes separately. To solve the problem of the quantitative analysis of the amplitude EM contrast on the basis of expressions (1)–(4), one has to use approx- Fig. 1. Microdiffractogram of the 60 nm thick amorphous As40Se60 film (curve 1) with selected different scattering components: the elastic coherent (2), the elastic incoherent (3) and the inelastic (4) ones. The intensities are reduced to a single scattering atom. 90 M. Yu. BOBYK, V. P. IVANITSKY, M. M. RYABOSHCHUK, and O. Ya. SVATYUK imations adequate to the real conditions. The idea of one of approximations is that the EM image is considered a result of ‘imposition’ of intensities of the electron scattering by a great number of atoms. Therefore, formation of such image could be mathematically set in a form of summating all the electron waves scat- tered by separate atoms according to the laws specific both for the co- herent and incoherent electron waves. The procedure of summation could be substantially simplified by introducing the electron scatter- ing parameters averaged over a certain macrovolume of the specimen into consideration. Obviously, this approximation confidence will be determined by the rules of averaging. Let us analyse the contribution of different types of electron scatter- ing by the object under study to the EM contrast. 4. ELASTIC INCOHERENT SCATTERING Consider the first component of the electron flux e that is due to the processes of incoherent scattering of the probing beam electrons by the atoms of the specimen under study. The intensity of this component is equal to the sum of effects of independent scattering by separate atoms from the selected local area. The spatial distribution of the intensity of the electron beam scattering by a single i-th atom is defined by its atomic factor 2 ( ) i F  , where ( ) i F  is the amplitude of electron scatter- ing by the above atom. Therefore, the intensity Ie() of elastic incoher- ent scattering by a certain local area of the specimen of the complex chemical composition could be determined via the atomic factor F 2() averaged over this area volume: Ie()NF2() 2 2 1 1 ( ) ( ) N m i j j i j F N c F       , (5) where N is the number of atoms included into the local area, m is the number of different chemical elements in the local area, сj are the rela- tive shares of different chemical elements of the local area. Thus, vari- ations of intensity of the elastic incoherent electron scattering by dif- ferent local areas will be determined by the changes in the number of atoms N and relative concentrations сj of different chemical elements in these local areas. The flux e due to the above processes could be consequently calculated from (4) as: max 2 2 ( )sin a e N F d         . (6) Let us analyse the process of formation of the flux e in more detail. To do this, we will introduce the following approximation: the whole volume of the specimen local area will be considered uniformly filled ELECTRON-SCATTERING MECHANISMS’ CONTRIBUTION TO THE CONTRAST OF IMAGES 91 with the atoms having the average atomic density 0. For the substanc- es with a complex chemical composition, this density is a sum of the partial atomic densities of different chemical elements 0і, i.e. 0 0 1 m i i    , (7) where 0ісі0. In these conditions, 0іSldx atoms of the і-th chemical element will take part in the electron scattering inside the local area volume with the thickness dx, where Sl is the cross section of the local area of the object under study. In such a case, dnі electrons will be elas- tically scattered by the atoms of a certain i-th chemical element beyond the aperture diaphragm at the electron beam transmission through this specimen area. This quantity ratio to the total number of not yet scattered electrons n will be as follows: 0 0 ei i li ei i l Sdxdn dx n S        , (8) where ei  is the cross section of the elastic electron scattering by the atoms of a certain i-th chemical element beyond the aperture dia- phragm. The further theoretical consideration of the electron scattering pro- cesses in the objects with a complex chemical composition should be carried out having introduced the elastic scattering cross section per a single atom averaged over all the chemical elements in the local area e  . In our opinion, such procedure could be correctly realized by applying the physical essence of the elastic incoherent scattering process, i.e. the total electron scattering intensity is equal to the sum of independent electron scatterings by atoms of different chemical elements. Then, taking into account (8), we have:  0 1 1 m m i ei i i i dndn dx n n        . (9) Taking into account relation (7), the derived expression could be written as follows:    0 0 1 1 m m ei i i ei i i dn c dx c dx n           . (10) It follows from the last equation that it is expedient to define the elastic scattering cross section per a single atom averaged over all the chemical elements of the specimen e  as: 1 m e i ei i c     . (11) Solving a simple differential equation (10) with the assumed defini- 92 M. Yu. BOBYK, V. P. IVANITSKY, M. M. RYABOSHCHUK, and O. Ya. SVATYUK tion (11) gives the dependence of the number of electrons not scattered beyond the aperture diaphragm on the thickness of the local area х passed by them:  0 0 exp e n n x   , (12) where n0 is the number of probing beam electrons falling onto the se- lected area. Thus, the electron beam flux retarded by the aperture diaphragm and not involved in the formation of the EM image of the local speci- men area due to elastic incoherent scattering will be determined by the quantity n0  n at the exit from this local area. Therefore, one may write down that this flux is equal to  0 0 1 exp( ) e e d      , (13) where 0 is the value of the probing beam electron flux at the object. Comparison of this relation with equation (1) shows that the scatter- ing property of the object area Q due to the elastic incoherent scatter- ing is determined by the product of the three main parameters: the av- eraged cross section of elastic electron scattering by the local area at- oms beyond the aperture diaphragm e  , the average atomic density of the specimen local area 0 and the geometric thickness of this area d. In the applied electron microscopy of amorphous substances with complex chemical composition, any of the above parameters may vary when go- ing from one local area to another, giving, thus, its own contribution to the EM image contrast. In this case, the e  variation occurs due to that of the local area chemical composition, 0 variation takes place due both to that of the chemical composition and to the presence of differ- ent continual heterogeneities in the local areas in a form of nanopores, while d variation is due to the specific features of the specimen surface topology. 5. ELASTIC COHERENT SCATTERING The elastic coherent scattering Ik is a second by its role in forming the amplitude contract of the EM images of the amorphous substances. It reflects the diffraction effects related to the interaction and interfer- ence of electron waves scattered by different atoms. The value and the spatial distribution of the elastic coherent scattering are determined by the parameters of the short-range and medium-range orders of dis- ordered atomic network. Therefore, the contribution of the coherent scattering to the EM image formation is sometimes called the ‘struc- tural’ contrast. The structural factor S() of the intensity distribution of the coher- ELECTRON-SCATTERING MECHANISMS’ CONTRIBUTION TO THE CONTRAST OF IMAGES 93 ent elastic scattering by the amorphous object beyond the aperture di- aphragm is a basic characteristic that defines its character [7]. There- fore, one may state with quite high accuracy that the amplitude con- trast of the EM images due to the elastic coherent electron scattering will be expressly determined by the S() function differences beyond the aperture diaphragm for different local specimen areas. According- ly, the variations of the short-range and medium-range order parame- ters of the amorphous substance atomic network at the transitions from one local area to other ones will be responsible for its appearance. Within the framework of the approximations assumed above, the distribution of the intensity Ik of the elastic coherent electron scatter- ing by the amorphous substance with complex chemical composition could be set as follows [8]: Ik()NF2()[S()1]. (14) As shown above, the function S() is easily determined experimen- tally by detecting electronograms from the object areas under study. From the viewpoint of contrast formation, we are interested in the dif- ference in electron scattering by different local areas of the same spec- imen. The minimal dimensions of such local areas in modern nano- materials and nanosystems are of the units of nanometres. Therefore, to use relation (14), one has to apply the electronographic methods that allow separate diffractograms to be obtained from the specimen areas with nanometric size. The electron diffraction method with strong electron beam focusing [9, 10] complies with these requirements. It allows the atomic structure of the nanoareas with size more than 5 nm to be studied. Such specimen areas could be exactly distinguished in the EM image. Having the nanoelectronograms from different local nanoareas of the object obtained in the strong focusing mode according to the tech- nique suggested above, one might calculate their structural factors S() and, accordingly, obtain the spatial distributions of the coherent elastic electron scattering from these local areas from relation (14). As a result, now, it is possible to calculate the contribution of the differ- ences in atomic structure of amorphous specimens into the EM image contrast in a form of a relevant flux k:   max 2 2 ( ) ( ) 1 sin k a N F S d           . (15) It should be noted here that the function S() must be exactly deter- mined from the nanoelectronogram in the large-angle electron scatter- ing region. In this region, the nanoelectronograms have low intensity, and this may affect considerably the result of the contrast analysis. 94 M. Yu. BOBYK, V. P. IVANITSKY, M. M. RYABOSHCHUK, and O. Ya. SVATYUK 6. INCOHERENT SCATTERING When analysing the EM image contrast one has also to take into ac- count the electron energy losses in the specimen, i.e. to take into ac- count the inelastic scattering as well. By its nature, it is incoherent and depends on the number of atoms in the area under study. Theoretical principles of the influence of inelastic electron scatter- ing on the EM image contrast formation are much more complicated as compared to those on case of elastic scattering. This is due to a number of reasons [11]. 1. Such scattering is very sensitive to the change in the state of the atomic electron orbits and electron density at large distances from atomic nuclei. Therefore, the scattering characteristics determined for certain atoms strongly differ from those for the case of the inelastic atom scattering in the condensed matter. 2. Unlike the elastic scattering, inelastic electron scattering differs drastically from the inelastic X-ray Compton scattering. 3. A share of inelastic scattering is especially large in the low s re- gion, where its intensity In may exceed that of the elastic scattering by several orders of magnitude. Only this region corresponds to the aper- ture diaphragm transmission and plays an important role in the ampli- tude EM contrast formation. Simultaneous and complex action of the above factors stipulates traditionally preferable use of experimental methods of determining the spatial intensity distribution In() in order to consider inelastic scattering in the applied electron microscopy and electronography [12]. Knowing this distribution found using the above-mentioned technique, one may calculate the electron flux that is responsible for the formation of the inelastic scattering contribution into the con- trast: max 2 ( )sin a n n N I d         . (16) Note that, in the applied electron microscopy, the In() component of intensity includes also the ‘parasite’ background electron scattering by the residual gas molecules in the microscope column, at the diaphragm edges, etc. 7. RESULTS AND THEIR ANALYSIS Figure 1 presents the distributions of the integral electron scattering intensity I (curve 1) and its components as the functions of the scatter- ing angle for the amorphous As40Se60 film. The above intensities corre- spond to the scattering by a single ‘averaged’ atom of the specimen. ELECTRON-SCATTERING MECHANISMS’ CONTRIBUTION TO THE CONTRAST OF IMAGES 95 The scattering angle value 3.8 mrad corresponds to the location of the aperture diaphragm edges when obtaining the EM pictures in our experiments. Based on these experimental data and using relations (6), (15) and (16), we have determined the relative fluxes e1, k1, n1 of electrons scattered beyond the aperture diaphragm according to dif- ferent mechanisms per a single averaged atom of the specimen under study: e1 6.610 6, k15.110 6, n1 9.110 6. These quantitative data indicate that, in the 50–60 nm amorphous thick As50Se50 films, almost a half of the scattered electrons appear to be scattered beyond the aperture diaphragm. At the same time, approximately same num- ber of electrons are scattered elastically coherently and elastically in- coherently. The above relations were obtained in the single electron-specimen scattering approximation. However, the total intensity I(s) involves a large part of multiply scattered electrons, i.e. those, for which the number of interactions with atoms during their passing the specimen exceeds a unit but is less than that necessary to describe the scattering processes by a normal Gauss distribution. The latter holds true in case of a multiple scattering. A strict account of the multiple scattering influence using known theoretical expressions is an unsolvable problem until now [11]. Com- plexity of its solution is related to the fact that in each scattering act one of the three above analysed mechanisms of electron interaction with the specimen under study could be realized. For example, triply scattered electron may take part in the elastic coherent, elastic inco- herent, and inelastic scattering in the three serial interactions with the specimen atoms. The studies of such processes and their contributions to the EM contrast are an independent problem of the theory and prac- tice of the modern electron microscopy. However, taking into account the high intensity of the multiple electron scattering by the objects with a thickness of several dozens of nanometres [13], one may state that for such specimens the fluxes k, e, and, especially, n include also a substantial part of the above multiple scattering. In our opinion, only the multiple scattering contribution stipulates such a large part of electrons being incoherently scattered by the specimens under study beyond the aperture diaphragm. If the heterogeneities of any origin are present in the specimen un- der study, then, the relevant fluxes k, e, n will differ from each other. Such differences will cause the appearance of the relevant con- trasts between the different areas of the heterogeneous object in the EM image. Using the method suggested above and the above relations, one may find on the quantitative analysis level the real nature of nano- heterogeneities present in the amorphous objects. If one takes into ac- count that the EM pictures reliably demonstrate the 2–3% contrast values, then for their appearance, the above fluxes k, e, n (or their 96 M. Yu. BOBYK, V. P. IVANITSKY, M. M. RYABOSHCHUK, and O. Ya. SVATYUK sum) from the two local areas of the heterogeneous specimen must dif- fer just by this value. 8. CONCLUSIONS The electron wave intensity distribution in the plane of formation of the EM image amplitude contrast is due to the probing electron beam scattering by the object and consists of three main parts. The first part is determined by the elastic incoherent scattering Ie(s) and equals to the sum of scattering effects related to each separate atom inde- pendently of any other atoms. The second part is the elastic coherent scattering Ik(s) that causes formation of the diffraction pattern from material. And the third intensity, In(s), results from the inelastic elec- tron scattering processes. The spatial distribution and the intensity Ie(s) are determined by the averaged cross section of electron scatter- ing by atoms of the specimen under study, its average atomic density, and geometric thickness. It seems expedient to calculate the coherent scattering contribution Ik(s) via the experimental structural factor de- fined by the short-range and medium-range orders of the atomic net- work in the object under study. The inelastic scattering component In(s) could be found from the results of the diffraction experiments in the course of normalizing the intensity of the coherent electron scat- tering by the specimen under study. Based on the intensities found, one may calculate the electron fluxes that form the EM images of dif- ferent local areas of the specimen under study and find the real physi- cal and chemical nature of its nanoheterogeneities on the quantitative level. REFERENCES 1. B. Fultz and J. Howe, Transmission Electron Microscopy and Diffractometry of Materials (Heidelberg: Springer: 2007). 2. P. Hawkes, The Beginnings of Electron Microscopy (Orlando: Academic Press: 1985). 3. D. B. Williams and C. B. Carter, Transmission Electron Microscopy: A Textbook for Materials Science (New York: Springer: 2009). 4. N. G. Nakhodkin, A. P. Bardamid, and A. I. Novoselskaya, Thin Solid Films, 112, No. 2: 267 (1984). 5. R. Herman and R. Hofstadter, High-Energy Electron Scattering Tables (Stanford: Stanford University Press: 1966). 6. M. Yu. Bobyk, E. І. Bоrkach, V. P. Ivanytskyy, and V. І. Sabov, Nanosistemi, Nanomateriali, Nanotehnologii, 10, No. 3: 423 (2012) (in Ukrainian). 7. B. E. Warren, X-Ray Diffraction (New York: Dower: 1990). 8. A. C. Wright, J. Non-Cryst. Solids, 123, No. 1: 129 (1990). 9. Y. Hirotsu, M. Ishimaru, T. Ohkubo, T. Hanada, and M. Sugiyama, J. Electron http://jmicro.oxfordjournals.org/search?author1=Manabu+Ishimaru&sortspec=date&submit=Submit http://jmicro.oxfordjournals.org/search?author1=Tadakatsu+Ohkubo&sortspec=date&submit=Submit http://jmicro.oxfordjournals.org/search?author1=Takeshi+Hanada&sortspec=date&submit=Submit http://jmicro.oxfordjournals.org/search?author1=Masaaki+Sugiyama&sortspec=date&submit=Submit ELECTRON-SCATTERING MECHANISMS’ CONTRIBUTION TO THE CONTRAST OF IMAGES 97 Microscopy, 50, No. 6: 435 (2001). 10. W. McBride, D. J. H. Cockayne, and K. Tsuda, Ultramicroscopy, 94, Nos. 3–4: 305 (2003). 11. L. Reimer and H. Kohl, Transmission Electron Microscopy: Physics of Image Formation (New York: Springer: 2008). 12. Z. L. Wang, Elastic and Inelastic Scattering in Electron Diffraction and Imaging (New York: Plenum Press: 1995). 13. H. Lipson and S. G. Lipson, J. Appl. Cryst., 5, No. 2: 239 (1972). http://scripts.iucr.org/cgi-bin/citedin?search_on=name&author_name=Lipson,%20H. http://scripts.iucr.org/cgi-bin/citedin?search_on=name&author_name=Lipson,%20S.G.