Quantum-Mechanical Model of Interconsistent Amplitude and Dispersion Influences of Structure Imperfections on the Multiple Scattering Pattern for Mapping and Characterization of Strains and Defects in Ion-Implanted Garnet Films

Quantum-Mechanical Model of Interconsistent Amplitude and Dispersion Influences of Structure Imperfections on the Multiple Scattering Pattern for Mapping and Characterization of Strains and Defects in Ion-Implanted Garnet Films

Numerical simulation of the reciprocal-space maps for ion-implanted single-crystal yttrium—iron garnet films on gadolinium—gallium garnet substrates is carried out and based on the theoretical model of the triple-axes dynamical diffractometry of multilayer crystalline systems with inhomogeneous stra...

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Datum:2015
Hauptverfasser: Molodkin, V.B., Olikhovskii, S.I., Skakunova, E.S., Len, E.G., Kislovskii, E.N., Reshetnyk, O.V., Vladimirova, T.P., Lizunov, V.V., Skapa, L.N., Lizunova, S.V., Fuzik, E.V., Tolmachev, N.G., Ostafiychuk, B.K., Pylypiv, V.M., Garpul’, O.Z.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут металофізики ім. Г.В. Курдюмова НАН України 2015
Schriftenreihe:Металлофизика и новейшие технологии
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Взаимодействия излучения и частиц с конденсированным веществом
Online Zugang:http://dspace.nbuv.gov.ua/handle/123456789/112280
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Zitieren:Quantum-Mechanical Model of Interconsistent Amplitude and Dispersion Influences of Structure Imperfections on the Multiple Scattering Pattern for Mapping and Characterization of Strains and Defects in Ion-Implanted Garnet Films / V. B. Molodkin, S. I. Olikhovskii, E. S. Skakunova, E. G. Len, E. N. Kislovskii, O. V. Reshetnyk, T. P. Vladimirova, V. V. Lizunov, L. N. Skapa, S. V. Lizunova, E. V. Fuzik, N. G. Tolmachev, B. K. Ostafiychuk, V. M. Pylypiv, and O. Z. Garpul’ // Металлофизика и новейшие технологии. — 2015. — Т. 37, № 8. — С. 1017-1026. — Бібліогр.: 7 назв. — англ.

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spelling irk-123456789-1122802017-01-20T03:02:22Z Quantum-Mechanical Model of Interconsistent Amplitude and Dispersion Influences of Structure Imperfections on the Multiple Scattering Pattern for Mapping and Characterization of Strains and Defects in Ion-Implanted Garnet Films Molodkin, V.B. Olikhovskii, S.I. Skakunova, E.S. Len, E.G. Kislovskii, E.N. Reshetnyk, O.V. Vladimirova, T.P. Lizunov, V.V. Skapa, L.N. Lizunova, S.V. Fuzik, E.V. Tolmachev, N.G. Ostafiychuk, B.K. Pylypiv, V.M. Garpul’, O.Z. Взаимодействия излучения и частиц с конденсированным веществом Numerical simulation of the reciprocal-space maps for ion-implanted single-crystal yttrium—iron garnet films on gadolinium—gallium garnet substrates is carried out and based on the theoretical model of the triple-axes dynamical diffractometry of multilayer crystalline systems with inhomogeneous strain distributions and randomly distributed defects. In this model, the amplitude and dispersion mechanisms of influence of the structure imperfections on diffraction or refraction, absorption and extinction of radiation, respectively, for the coherent and diffuse scattering intensities are interconsistently taken into account for all the layers of the system, using derived recurrent relations between the coherent-scattering amplitudes. The presence of growth defects in both the film and the substrate as well as radiation defects created in subsurface layer of nanometre-scale thickness after 90 keV F⁺ ion implantation are taken into account in the proposed model of the multilayer systems. Using this model, the rocking curves measured from as-grown and ion-implanted samples are also treated for determination of realistic strain-profile parameters and structural-defect characteristics in both implanted films and substrates with the aim of numerical reconstruction of the diffraction patterns from multilayer imperfect single-crystal systems. Чисельне моделювання карт оберненого простору для йонно-імплантованих монокристалічних залізо-ітрійових плівок ферит-ґранатів на підложжях з ґадоліній-ґалійового ґранату здійснено на основі теоретичного моделю тривісної динамічної дифрактометрії для багатошарових кристалічних систем із неоднорідними розподілами деформації та випадково розподіленими дефектами. В цьому моделі амплітудний і дисперсійний механізми впливу недосконалостей структури відповідно на дифракцію чи на заломлення, поглинання й екстинкцію випромінення в інтенсивності когерентного та дифузного розсіяння взаємоузгоджено враховувалися для всіх шарів системи за допомогою одержаних рекурентних співвідношень між амплітудами когерентного розсіяння. В запропонованому моделі багатошарових систем враховано наявність ростових дефектів, як у плівці, так і в підложжі, а також радіяційних дефектів у приповерхневому шарі нанометрової товщини, утворених після імплантації йонів F⁺ з енергією у 90 кеВ. З використанням зазначеного моделю також оброблялися криві хитання вихідного та йонно-імплантованого зразків для визначення реалістичних параметрів профілів деформації та структурних характеристик дефектів у підложжях та імплантованих плівках з метою чисельної реконструкції картин динамічної дифракції від монокристалічних багатошарових зразків. Численное моделирование карт обратного пространства для ионно-имплантированных монокристаллических железо-иттриевых плёнок феррит-гранатов на подложках из гадолиний-галлиевого граната осуществлено на основе теоретической модели трёхосной динамической дифрактометрии для многослойных кристаллических систем с неоднородными распределениями деформации и случайно распределёнными дефектами. В этой модели амплитудный и дисперсионный механизмы влияния несовершенств структуры соответственно на дифракцию или на преломление, поглощение и экстинкцию излучений в интенсивности когерентного и диффузного рассеяния взаимосогласованно учитывались для всех слоёв системы с помощью полученных рекуррентных соотношений между амплитудами когерентного рассеяния. В предлагаемой модели многослойных систем учтено наличие ростовых дефектов, как в плёнке, так и в подложке, а также радиационных дефектов в приповерхностном слое нанометровой толщины, образованных после имплантации ионов F⁺ с энергией 90 кэВ. С использованием упомянутой модели также обрабатывались кривые качания исходного и ионно-имплантированного образцов для реалистичного определения параметров профилей деформации и структурных характеристик дефектов в подложках и имплантированных плёнках с целью численной реконструкции картин динамической дифракции от монокристаллических многослойных образцов. 2015 Article Quantum-Mechanical Model of Interconsistent Amplitude and Dispersion Influences of Structure Imperfections on the Multiple Scattering Pattern for Mapping and Characterization of Strains and Defects in Ion-Implanted Garnet Films / V. B. Molodkin, S. I. Olikhovskii, E. S. Skakunova, E. G. Len, E. N. Kislovskii, O. V. Reshetnyk, T. P. Vladimirova, V. V. Lizunov, L. N. Skapa, S. V. Lizunova, E. V. Fuzik, N. G. Tolmachev, B. K. Ostafiychuk, V. M. Pylypiv, and O. Z. Garpul’ // Металлофизика и новейшие технологии. — 2015. — Т. 37, № 8. — С. 1017-1026. — Бібліогр.: 7 назв. — англ. 1024-1809 PACS: 61.05.cc, 61.05.cf, 61.72.Dd, 61.72.up, 61.80.Jh, 61.82.Ms, 68.55.Ln http://dspace.nbuv.gov.ua/handle/123456789/112280 en Металлофизика и новейшие технологии 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
topic Взаимодействия излучения и частиц с конденсированным веществом
Взаимодействия излучения и частиц с конденсированным веществом
spellingShingle Взаимодействия излучения и частиц с конденсированным веществом
Взаимодействия излучения и частиц с конденсированным веществом
Molodkin, V.B.
Olikhovskii, S.I.
Skakunova, E.S.
Len, E.G.
Kislovskii, E.N.
Reshetnyk, O.V.
Vladimirova, T.P.
Lizunov, V.V.
Skapa, L.N.
Lizunova, S.V.
Fuzik, E.V.
Tolmachev, N.G.
Ostafiychuk, B.K.
Pylypiv, V.M.
Garpul’, O.Z.
Quantum-Mechanical Model of Interconsistent Amplitude and Dispersion Influences of Structure Imperfections on the Multiple Scattering Pattern for Mapping and Characterization of Strains and Defects in Ion-Implanted Garnet Films
Металлофизика и новейшие технологии
description Numerical simulation of the reciprocal-space maps for ion-implanted single-crystal yttrium—iron garnet films on gadolinium—gallium garnet substrates is carried out and based on the theoretical model of the triple-axes dynamical diffractometry of multilayer crystalline systems with inhomogeneous strain distributions and randomly distributed defects. In this model, the amplitude and dispersion mechanisms of influence of the structure imperfections on diffraction or refraction, absorption and extinction of radiation, respectively, for the coherent and diffuse scattering intensities are interconsistently taken into account for all the layers of the system, using derived recurrent relations between the coherent-scattering amplitudes. The presence of growth defects in both the film and the substrate as well as radiation defects created in subsurface layer of nanometre-scale thickness after 90 keV F⁺ ion implantation are taken into account in the proposed model of the multilayer systems. Using this model, the rocking curves measured from as-grown and ion-implanted samples are also treated for determination of realistic strain-profile parameters and structural-defect characteristics in both implanted films and substrates with the aim of numerical reconstruction of the diffraction patterns from multilayer imperfect single-crystal systems.
format Article
author Molodkin, V.B.
Olikhovskii, S.I.
Skakunova, E.S.
Len, E.G.
Kislovskii, E.N.
Reshetnyk, O.V.
Vladimirova, T.P.
Lizunov, V.V.
Skapa, L.N.
Lizunova, S.V.
Fuzik, E.V.
Tolmachev, N.G.
Ostafiychuk, B.K.
Pylypiv, V.M.
Garpul’, O.Z.
author_facet Molodkin, V.B.
Olikhovskii, S.I.
Skakunova, E.S.
Len, E.G.
Kislovskii, E.N.
Reshetnyk, O.V.
Vladimirova, T.P.
Lizunov, V.V.
Skapa, L.N.
Lizunova, S.V.
Fuzik, E.V.
Tolmachev, N.G.
Ostafiychuk, B.K.
Pylypiv, V.M.
Garpul’, O.Z.
author_sort Molodkin, V.B.
title Quantum-Mechanical Model of Interconsistent Amplitude and Dispersion Influences of Structure Imperfections on the Multiple Scattering Pattern for Mapping and Characterization of Strains and Defects in Ion-Implanted Garnet Films
title_short Quantum-Mechanical Model of Interconsistent Amplitude and Dispersion Influences of Structure Imperfections on the Multiple Scattering Pattern for Mapping and Characterization of Strains and Defects in Ion-Implanted Garnet Films
title_full Quantum-Mechanical Model of Interconsistent Amplitude and Dispersion Influences of Structure Imperfections on the Multiple Scattering Pattern for Mapping and Characterization of Strains and Defects in Ion-Implanted Garnet Films
title_fullStr Quantum-Mechanical Model of Interconsistent Amplitude and Dispersion Influences of Structure Imperfections on the Multiple Scattering Pattern for Mapping and Characterization of Strains and Defects in Ion-Implanted Garnet Films
title_full_unstemmed Quantum-Mechanical Model of Interconsistent Amplitude and Dispersion Influences of Structure Imperfections on the Multiple Scattering Pattern for Mapping and Characterization of Strains and Defects in Ion-Implanted Garnet Films
title_sort quantum-mechanical model of interconsistent amplitude and dispersion influences of structure imperfections on the multiple scattering pattern for mapping and characterization of strains and defects in ion-implanted garnet films
publisher Інститут металофізики ім. Г.В. Курдюмова НАН України
publishDate 2015
topic_facet Взаимодействия излучения и частиц с конденсированным веществом
url http://dspace.nbuv.gov.ua/handle/123456789/112280
citation_txt Quantum-Mechanical Model of Interconsistent Amplitude and Dispersion Influences of Structure Imperfections on the Multiple Scattering Pattern for Mapping and Characterization of Strains and Defects in Ion-Implanted Garnet Films / V. B. Molodkin, S. I. Olikhovskii, E. S. Skakunova, E. G. Len, E. N. Kislovskii, O. V. Reshetnyk, T. P. Vladimirova, V. V. Lizunov, L. N. Skapa, S. V. Lizunova, E. V. Fuzik, N. G. Tolmachev, B. K. Ostafiychuk, V. M. Pylypiv, and O. Z. Garpul’ // Металлофизика и новейшие технологии. — 2015. — Т. 37, № 8. — С. 1017-1026. — Бібліогр.: 7 назв. — англ.
series Металлофизика и новейшие технологии
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fulltext 1017 PACS numbers:61.05.cc, 61.05.cf,61.72.Dd,61.72.up,61.80.Jh,61.82.Ms, 68.55.Ln Quantum-Mechanical Model of Interсonsistent Amplitude and Dispersion Influences of Structure Imperfections on the Multiple- Scattering Pattern for Mapping and Characterization of Strains and Defects in Ion-Implanted Garnet Films V. B. Molodkin, S. I. Olikhovskii, E. S. Skakunova, E. G. Len, E. N. Kislovskii, O. V. Reshetnyk, T. P. Vladimirova, V. V. Lizunov, L. N. Skapa, S. V. Lizunova, E. V. Fuzik, N. G. Tolmachev, B. K. Ostafiychuk*, V. M. Pylypiv*, and O. Z. Garpul’* G. V. Kurdyumov Institute for Metal Physics, N.A.S. of Ukraine, 36 Academician Vernadsky Blvd., UA-03680 Kyiv, Ukraine *Vasyl Stefanyk Precarpathian National University, 57 Shevchenko Str., UA-76025 Ivano-Frankivsk, Ukraine Numerical simulation of the reciprocal-space maps for ion-implanted single- crystal yttrium—iron garnet films on gadolinium—gallium garnet substrates is carried out and based on the theoretical model of the triple-axes dynamical dif- fractometry of multilayer crystalline systems with inhomogeneous strain dis- tributions and randomly distributed defects. In this model, the amplitude and dispersion mechanisms of influence of the structure imperfections on diffrac- tion or refraction, absorption and extinction of radiation, respectively, for the coherent and diffuse scattering intensities are interconsistently taken into ac- count for all the layers of the system, using derived recurrent relations be- tween the coherent-scattering amplitudes. The presence of growth defects in both the film and the substrate as well as radiation defects created in subsur- face layer of nanometre-scale thickness after 90 keV F  ion implantation are taken into account in the proposed model of the multilayer systems. Using this model, the rocking curves measured from as-grown and ion-implanted samples are also treated for determination of realistic strain-profile parameters and structural-defect characteristics in both implanted films and substrates with the aim of numerical reconstruction of the diffraction patterns from multi- layer imperfect single-crystal systems. Чисельне моделювання карт оберненого простору для йонно-імпланто- ваних монокристалічних залізо-ітрійових плівок ферит-ґранатів на під- ложжях з ґадоліній-ґалійового ґранату здійснено на основі теоретичного Металлофиз. новейшие технол. / Metallofiz. Noveishie Tekhnol. 2015, т. 37, № 8, сс. 1017—1026 Оттиски доступны непосредственно от издателя Фотокопирование разрешено только в соответствии с лицензией 2015 ИМФ (Институт металлофизики им. Г. В. Курдюмова НАН Украины) Напечатано в Украине. 1018 V. B. MOLODKIN, S. I. OLIKHOVSKII, E. S. SKAKUNOVA et al. моделю тривісної динамічної дифрактометрії для багатошарових кристалі- чних систем із неоднорідними розподілами деформації та випадково розпо- діленими дефектами. В цьому моделі амплітудний і дисперсійний механіз- ми впливу недосконалостей структури відповідно на дифракцію чи на за- ломлення, поглинання й екстинкцію випромінення в інтенсивності когере- нтного та дифузного розсіяння взаємоузгоджено враховувалися для всіх шарів системи за допомогою одержаних рекурентних співвідношень між амплітудами когерентного розсіяння. В запропонованому моделі багато- шарових систем враховано наявність ростових дефектів, як у плівці, так і в підложжі, а також радіяційних дефектів у приповерхневому шарі наноме- трової товщини, утворених після імплантації йонів F  з енергією у 90 кеВ. З використанням зазначеного моделю також оброблялися криві хитання ви- хідного та йонно-імплантованого зразків для визначення реалістичних па- раметрів профілів деформації та структурних характеристик дефектів у підложжях та імплантованих плівках з метою чисельної реконструкції ка- ртин динамічної дифракції від монокристалічних багатошарових зразків. Численное моделирование карт обратного пространства для ионно- имплантированных монокристаллических железо-иттриевых плёнок фер- рит-гранатов на подложках из гадолиний-галлиевого граната осуществле- но на основе теоретической модели трёхосной динамической дифрактомет- рии для многослойных кристаллических систем с неоднородными распре- делениями деформации и случайно распределёнными дефектами. В этой модели амплитудный и дисперсионный механизмы влияния несовер- шенств структуры соответственно на дифракцию или на преломление, по- глощение и экстинкцию излучений в интенсивности когерентного и диф- фузного рассеяния взаимосогласованно учитывались для всех слоёв систе- мы с помощью полученных рекуррентных соотношений между амплиту- дами когерентного рассеяния. В предлагаемой модели многослойных си- стем учтено наличие ростовых дефектов, как в плёнке, так и в подложке, а также радиационных дефектов в приповерхностном слое нанометровой толщины, образованных после имплантации ионов F  с энергией 90 кэВ. С использованием упомянутой модели также обрабатывались кривые кача- ния исходного и ионно-имплантированного образцов для реалистичного определения параметров профилей деформации и структурных характери- стик дефектов в подложках и имплантированных плёнках с целью числен- ной реконструкции картин динамической дифракции от монокристалли- ческих многослойных образцов. Key words: dynamical diffraction theory, thin films, yttrium—iron garnet, ion implantation, radiation defects, strain distribution, growth defects. (Received May 17, 2015) 1. INTRODUCTION Modern technologies allow to grow almost perfect multilayer crystal- line systems and to influence purposefully on their physical properties by the controlled introduction of various structural defects. In partic- INFLUENCES OF IMPERFECTIONS ON THE MULTIPLE-SCATTERING PATTERN 1019 ular, epitaxial single-crystal yttrium—iron garnet (YIG) Y3Fe5О12 films grown on gadolinium—gallium garnet (GGG) Gd3Ga5O12 substrate are widely used in energy-independent magnetic-memory devices, magnet- ic microelectronics, and integral magnetooptics, etc. (see, e.g., Ref. [1]). Modification of physical properties of their functional layers with sizes, which are often of nanometre scale, is carried out, in particular, by ion implantation. X-ray diffraction methods are most widely used to characterize structural defects and strains in the modified crystal layers. In partic- ular, the measurements by high-resolution double-crystal diffractome- ter (DCD) and triple-crystal one (TCD) were carried out to characterize inhomogeneous strain distributions and structure imperfections in implanted garnet crystals [2, 3]. These methods are highly informative if the analytical formulae, which give the adequate description of measured diffraction-intensity distributions, are available and used in interconsistent combination for both components of intensity (i.e., for Bragg and diffuse scattering) and different dynamical diffraction conditions or measurements methods (i.e., commonly integral, DCD, and TCD diffractometry). The purpose of this work is demonstration of diagnostic possibilities offered by the theoretical method for interpretation of results of high- resolution X-ray diffraction mapping of the real film and multilayer systems with defects [4]. This method of structural diagnostics will be applied to the simulation of the influence of nanometre-size defects and inhomogeneous strain distributions in the epitaxial YIG films grown on GGG substrate, which were implanted with 90 keV F  ions, on the form of the coherent and diffuse components of diffraction inten- sity distributions on reciprocal-lattice maps measured by TCD. 2. COHERENT AND DIFFUSE COMPONENTS OF RECIPROCAL- LATTICE MAPS Differential X-ray diffraction intensity distributions measured by TCD from multilayer crystalline systems with inhomogeneous strain distributions and randomly distributed defects can be represented as a sum of coherent (Icoh) and diffuse (Idiff) components. If Bragg angles for monochromator, analyser, and crystal under in- vestigation are nearly equal, it is possible to ignore the dispersion ef- fects and the coherent component of the two-dimensional intensity dis- tribution can be calculated approximately in the case of quasi- nondispersive geometry (m, n, m) as follows [5, 6]: m m 1 coh 0 S M coh A S SM( , ) ( ) ( ) [ (1 ) ], x x I I b dzR b z R z R b z b             (1) 1020 V. B. MOLODKIN, S. I. OLIKHOVSKII, E. S. SKAKUNOVA et al. where I0 is an intensity of incident X-ray beam, RM and RA are the re- flection coefficients of monochromator and analyser crystals,  and  are the angular deviations of the crystal under investigation and analyser crystal, bM and bS are asymmetry parameters of monochroma- tor and sample crystals, respectively. The expression for the coherent component of the reflection coefficient Rcoh() for imperfect crystal has been derived elsewhere earlier [7] and takes into account all the dy- namical scattering effects including the extinction of Bragg waves due to diffuse scattering by defects as well as dispersion mechanism of in- fluence of a sample structure on multiple-scattering pattern. Particularly, the dynamical consideration is necessary in the case of X-ray diffraction by the implanted YIG films of thickness, which is of the order of an extinction length. The coherent component of reflec- tion coefficient of such inhomogeneous crystalline system with chaoti- cally distributed defects can be calculated in so called ‘layer approxi- mation’ using the recurrence relations between coherent components of amplitude reflection coefficients of adjacent layers for Bragg dif- fraction geometry [5]: 1 2 1 2 1 1 1 ( ) , 1 j j j j j j j j jj r R e t r R r R            (2) where rj and tj are amplitudes of reflectivity and transmissivity of j th layer, respectively, ej is the phase factor, and j  1. The diffuse component of the diffraction intensity measured by TCD can be represented approximately by the following expression [5, 6]: diff 0 iM iA diff( , ) ( ),I I R R r   k (3) where RiM and RiA are the integrated reflectivities of monochromator and analyser crystals, respectively, and components kx and kz of two- dimensional vector k describe a deviation from the reciprocal-lattice point H in the coherent-scattering plane. Function rdiff(k) in Eq. (3) represents the diffuse component of the differential reflection coefficient of the multilayer sample (containing M layers) after integration over vertical divergence [7]: diff ext abs diff 0 ( ) ( ), M j j j j r F F r  k k (4) where ext jF is the extinction factor describing the influence of redistri- bution of X-ray intensity between the transmitted and diffracted co- herent waves in j th layer, the factor abs jF describes photoelectric absorp- tion and absorption caused by diffuse scattering in layers lying above jth layer, and diff ( )jr k is the diffuse component of the differential reflec- tion coefficient of j th layer. INFLUENCES OF IMPERFECTIONS ON THE MULTIPLE-SCATTERING PATTERN 1021 Thus, the formulae presented above provide the possibilities for the effective, i.e., with minimization of required calculation time expens- es, and self-consistent quantitative analysis of the coherent and dif- fuse components of reciprocal-lattice maps, which are measured from crystalline film or multilayer systems, including those with inhomo- geneous strain distributions, large strain gradients at layer interfaces, and randomly distributed defects of different types in all the layers and substrate. 3. MODEL OF THE DEFECT STRUCTURE IN ION-IMPLANTED YIG FILM The sample of the epitaxial YIG film with 5.33 m thickness, which was grown on GGG substrate and implanted with F  ions of the 90 keV energy at dose D  61013 cm 2, has been chosen as a model object for simulation. To determine realistic strain-profiles’ parameters and structural- defects’ characteristics, this sample was investigated using the high- resolution double-crystal X-ray diffractometer (see, for example, Fig. 1). As has been established by simultaneous treatment of the rocking curves (RC) measured for symmetric (444) and (888) reflections, the strain profile in YIG film implanted with F  ions has the shape shown Fig. 1. Measured (markers) and calculated (solid line) RCs for (444) reflection of CuK1-radiation from YIG/GGG film system implanted with F  ions (E  90 keV) at doses D  61013 cm 2. The coherent and diffuse RC components are shown by dashed and dot-dashed lines, respectively. 1022 V. B. MOLODKIN, S. I. OLIKHOVSKII, E. S. SKAKUNOVA et al. in Fig. 2. This strain profile is formed due to the radiation defects, which are distributed inhomogeneously in depth and cause the corre- sponding ‘in average’ inhomogeneous strain. The depth profile of the strain caused by ion implantation is calculated, using the determined characteristics of spherical amorphous clusters in implanted layer, namely, concentration of 51020 cm 3, radius of 0.75 nm, and volume misfit strain at the boundary between cluster and crystal matrix  0.0375. Besides, in the model of defect structure of the implanted epitaxial single-crystalline system of YIG film grown on GGG substrate, the presence of two types of growth microdefects, namely, spherical clus- ters and circular prismatic dislocation loops is taken into account. Their characteristics are also determined by the DCD-profiles’ treat- ment; namely, for spherical clusters in YIG film and GGG substrate, we put cluster radii of 10 and 8 nm, respectively, concentration of 1014 cm 3, and volume misfit strain at the boundary between cluster and crystal matrix of 0.03. Similarly, for dislocation loops of <110>- type within the YIG film, we put dislocation loop radius of 5 nm and concentration of 1015 cm 3, whereas, within the GGG substrate, we put dislocation loop radii of 5 and 90 nm, and concentrations of 1015 and 1,21012 cm 3, respectively. The YIG/GGG film system as a whole is considered as a multilayer system in each layer of which the strain is consisted of sum of average and fluctuating components. At modelling, the average strain distri- bution, the implanted layer is subdivided into 10 nm thick laminae, Fig. 2. Strain profile in YIG film implanted with F  ions (E  90 keV) at dose D  61013 cm 2. INFLUENCES OF IMPERFECTIONS ON THE MULTIPLE-SCATTERING PATTERN 1023 whereas the transition layer between film and substrate is subdivided into layers with thicknesses of order of few hundreds of nanometres. 4. SIMULATION OF RECIPROCAL-LATTICE MAPS FOR ION-IMPLANTED YIG FILMS WITH DEFECTS The results of numeral simulation of reciprocal-lattice maps are de- scribed below for the YIG film, which was implanted with F  ions of the energy of 90 keV at dose D  61013 cm 2. The maps were simulated for the case of measurements by the high-resolution PANalytical X’Pert Pro MRD XL diffractometer for (444) reflection of characteristic CuK1-radiation in the symmetrical Bragg diffraction geometry at the sample under investigation. As far as the Bragg angle for Ge (220) re- flection used in monochromator and analyser crystals of the diffrac- tometer is nearly equal to Bragg angles for (444) reflection of YIG film and GGG substrate, the influence of dispersion effects can be neglect- ed, and for calculation of the coherent and diffuse components of re- ciprocal-lattice maps, the simplified formulae (1) and (3) can be used. To elucidate the role of microdefects growth in YIG film and GGG substrate in the formation of diffraction patterns, we first calculated the reciprocal-lattice map for the symmetrical (444) reflection of CuK1-radiation from as-grown YIG/GGG film system (Fig. 3). As is Fig. 3. Reciprocal-lattice map (middle), its coherent component (left), and longitudinal cross section (right) for (444) reflection of CuK1-radiation from as-grown YIG/GGG film system. 1024 V. B. MOLODKIN, S. I. OLIKHOVSKII, E. S. SKAKUNOVA et al. evident from comparison between the total reciprocal-lattice map and its coherent component, the diffuse scattering intensity from microde- fects in both the YIG film and the GGG substrate give a substantial contribution to the formation of observed diffraction-intensity distri- butions. The reciprocal-lattice map simulated for the symmetrical (444) re- flection of CuK1-radiation from the YIG/GGG film system implanted with F  ions of 90 keV energy at dose D  61013 cm 2 is shown in Fig. 4. As can be seen by comparing Figs. 3 and 4, the irregularly shaped diffuse scattering intensity distribution from spherical clusters in im- planted YIG layer appears additionally to the diffuse scattering inten- sity distributions from microdefects in both YIG film and GGG sub- strate around corresponding reciprocal-lattice points. It should be not- ed that the irregular shape of diffuse scattering intensity distribution from spherical clusters in implanted layer is caused by the inhomoge- neous ‘in-average’ strain distribution in this layer, which leads to smoothing and deformation of the double-drop form known for iso- diffuse lines from spherical clusters. It should be especially emphasized that longitudinal cross sections of the simulated reciprocal-lattice maps in Figs. 3 and 4 closely coin- cide in form with the rocking curves, which were measured using the high-resolution double-crystal X-ray diffractometer for the corre- Fig. 4. Reciprocal-lattice map (middle), its coherent component (left), and longitudinal cross section (right) for (444) reflection of CuK1-radiation from YIG/GGG film system implanted with F  ions (E  90 keV) at dose D  61013 cm 2. INFLUENCES OF IMPERFECTIONS ON THE MULTIPLE-SCATTERING PATTERN 1025 sponding as-grown and implanted epitaxial YIG films (Fig. 1). The on- ly distinction consists in that the oscillations at the tail of the rocking curve measured from implanted epitaxial YIG film are something smoothed as compared with longitudinal cross section of the simulated reciprocal-lattice map in Fig. 4, which is explained by an additional contribution of diffuse scattering intensity from defects in implanted YIG layer due to integration over vertical divergence. 5. RESUME AND CONCLUSIONS On the basis of the created theoretical model of the triple-crystal X-ray dynamical diffractometry of the multilayer crystalline systems with inhomogeneous strain profile and randomly distributed defects, the numerical simulation of reciprocal-lattice maps for the ion-implanted single-crystal YIG films on GGG substrate has been carried out. The presence of growth defects in both the film and the substrate as well as radiation defects created in subsurface layer are taken into account. It is established that, as a result of superposition of coherent and diffuse-scattering intensities from defects of various types in differ- ent layers with heterogeneous strain, the reciprocal-lattice maps take the form, which substantially differs from that characteristic for crys- tals with homogeneous strain and one type of defects. Self-consistent description of the coherent and diffuse components of dynamical X-ray scattering with account for amplitude and disper- sion mechanisms of influence of structure imperfections on multiple- scattering pattern as well as instrumental factors of TCD makes possi- ble the correct quantitative analysis of complete reciprocal-lattice maps measured from inhomogeneous imperfect crystal structures with defects. REFERENCES 1. T. Wehlus, T. Körner, S. Leitenmeier, A. Heinrich, and B. Stritzker, phys. status solidi (a), 208: 252 (2011). 2. B. K. Ostafiychuk, I. P. Yaremiy, S. I. Yaremiy, V. D. Fedoriv, U. O. Tomyn, M. M. Umantsiva, I. M. Fodchuk, and V. P. Kladko, Crystallography Reports, 58: 1017 (2013). 3. I. M. Fodchuk, V. V. Dovganiuk, I. I. Gutsuliak, I. P. Yaremiy, A. Y. Bonchyk, G. V. Savytsky, I. M. Syvorotka, and O. S. Skakunova, Metallofiz. Noveishie Tekhnol., 35, No. 9: 1209 (2013) (in Russian). 4. O. S. Skakunova, S. I. Olikhovskii, V. B. Molodkin, E. G. Len, E. M. Kislovskii, O. V. Reshetnyk, T. P. Vladimirova, E. V. Kochelab, V. V. Lizunov, S. V. Lizunova, V. L. Makivs’ka, M. G. Tolmachov, L. M. Skapa, Ya. V. Vasylyk, and K. V. Fuzik, Metallofiz. Noveishie Tekhnol., 37: No. 3: 409 (2015) (in Ukrainian). 1026 V. B. MOLODKIN, S. I. OLIKHOVSKII, E. S. SKAKUNOVA et al. 5. V. B. Molodkin, S. I. Olikhovskii, E. G. Len, E. N. Kislovskii, V. P. Kladko, O. V. Reshetnyk, T. P. Vladimirova, and B. V. Sheludchenko, phys. status solidi (а), 206: 1761 (2009). 6. E. N. Kislovskii, V. B. Molodkin, S. I. Olikhovskii, E. G. Len, B. V. Sheludchenko, S. V. Lizunova, T. P. Vladimirova, E. V. Kochelab, O. V. Reshetnik, V. V. Dovganyuk, I. M. Fodchuk, T. V. Litvinchuk, and V. P. Klad’ko, J. Surf. Investigation. X-Ray, Synchrotron, and Neutron Techniques, 7: 523 (2013). 7. V. B. Molodkin, S. I. Olikhovskii, Ye. M. Kyslovskyy, I. M. Fodchuk, E. S. Skakunova, E. V. Pervak, and V. V. 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