Integrated diffractometry: achieved progress and new performance capabilities
This review provides a brief overview and a discussion of dynamical integrated diffractometry and its functional capabilities. It is demonstrated that the combined use of measurements of integrated diffraction parameters on different diffraction conditions allows determining the parameters of severa...
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Інститут металофізики ім. Г.В. Курдюмова НАН України
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| Zitieren: | Integrated diffractometry: achieved progress and new performance capabilities / V.V. Lizunov, I.M. Zabolotnyy, Ya.V. Vasylyk, I.E. Golentus, M.V. Ushakov // Progress in Physics of Metals. — 2019. — Vol. 20, No 1. — P. 75-95. — Bibliog.: 49 titles. — eng. |
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nasplib_isofts_kiev_ua-123456789-1679232025-02-09T16:34:00Z Integrated diffractometry: achieved progress and new performance capabilities Інтегральна дифрактометрія: досягнуті успіхи та нові можливості Интегральная дифрактометрия: достигнутые успехи и новые возможности Lizunov, V.V. Zabolotnyy, I.M. Vasylyk, Ya.V. Golentus, I.E. Ushakov, M.V. This review provides a brief overview and a discussion of dynamical integrated diffractometry and its functional capabilities. It is demonstrated that the combined use of measurements of integrated diffraction parameters on different diffraction conditions allows determining the parameters of several types of microdefects, which are simultaneously present in a single crystal. These parameters are the total integrated intensity of dynamical diffraction, the contribution of its diffuse component, and their dependences on different diffraction conditions. Examples of the use of integrated diffraction parameters for non-destructive express diagnostics of the characteristics of the defects’ structure of single crystals are discussed. Статтю присвячено обговоренню динамічної інтегральної дифрактометрії та її функціональних можливостей. Показано, що комбіноване використання вимірювань інтегральних дифракційних параметрів за різних умов дифракції уможливлює визначення параметрів мікродефектів декількох типів, одночасно присутніх у монокристалі. Обговорюються приклади використання вимірювання повної інтегральної інтенсивності динамічної дифракції, внеску її дифузійної складової та їхніх залежностей від різних умов динамічної дифракції для неруйнівної експресної діагностики характеристик дефектної структури монокристалічних систем. Статья посвящена обсуждению динамической интегральной дифрактометрии и её функциональных возможностей. Показано, что комбинированное использование измерений интегральных дифракционных параметров при различных условиях дифракции позволяет определять параметры микродефектов нескольких типов, одновременно присутствующих в монокристалле. Обсуждаются примеры использования измерения полной интегральной интенсивности динамической дифракции, вклада её диффузной составляющей и их зависимостей от различных условий динамической дифракции для неразрушающей экспрессной диагностики характеристик дефектной структуры монокристаллических систем. The authors are grateful to the Corresponding Member of the National Academy of Sciences of Ukraine V. B. Molodkin for the support in their work and useful discussion of the article. This paper was supported by the National Academy of Sciences of Ukraine (contract no. 43Г/51-18). 2019 Article Integrated diffractometry: achieved progress and new performance capabilities / V.V. Lizunov, I.M. Zabolotnyy, Ya.V. Vasylyk, I.E. Golentus, M.V. Ushakov // Progress in Physics of Metals. — 2019. — Vol. 20, No 1. — P. 75-95. — Bibliog.: 49 titles. — eng. 1608-1021 DOI: https://doi.org/10.15407/ufm.20.01.075 https://nasplib.isofts.kiev.ua/handle/123456789/167923 en Успехи физики металлов application/pdf Інститут металофізики ім. Г.В. Курдюмова НАН України |
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This review provides a brief overview and a discussion of dynamical integrated diffractometry and its functional capabilities. It is demonstrated that the combined use of measurements of integrated diffraction parameters on different diffraction conditions allows determining the parameters of several types of microdefects, which are simultaneously present in a single crystal. These parameters are the total integrated intensity of dynamical diffraction, the contribution of its diffuse component, and their dependences on different diffraction conditions. Examples of the use of integrated diffraction parameters for non-destructive express diagnostics of the characteristics of the defects’ structure of single crystals are discussed. |
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Article |
| author |
Lizunov, V.V. Zabolotnyy, I.M. Vasylyk, Ya.V. Golentus, I.E. Ushakov, M.V. |
| spellingShingle |
Lizunov, V.V. Zabolotnyy, I.M. Vasylyk, Ya.V. Golentus, I.E. Ushakov, M.V. Integrated diffractometry: achieved progress and new performance capabilities Успехи физики металлов |
| author_facet |
Lizunov, V.V. Zabolotnyy, I.M. Vasylyk, Ya.V. Golentus, I.E. Ushakov, M.V. |
| author_sort |
Lizunov, V.V. |
| title |
Integrated diffractometry: achieved progress and new performance capabilities |
| title_short |
Integrated diffractometry: achieved progress and new performance capabilities |
| title_full |
Integrated diffractometry: achieved progress and new performance capabilities |
| title_fullStr |
Integrated diffractometry: achieved progress and new performance capabilities |
| title_full_unstemmed |
Integrated diffractometry: achieved progress and new performance capabilities |
| title_sort |
integrated diffractometry: achieved progress and new performance capabilities |
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Інститут металофізики ім. Г.В. Курдюмова НАН України |
| publishDate |
2019 |
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https://nasplib.isofts.kiev.ua/handle/123456789/167923 |
| citation_txt |
Integrated diffractometry: achieved progress and new performance capabilities / V.V. Lizunov, I.M. Zabolotnyy, Ya.V. Vasylyk, I.E. Golentus, M.V. Ushakov // Progress in Physics of Metals. — 2019. — Vol. 20, No 1. — P. 75-95. — Bibliog.: 49 titles. — eng. |
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Успехи физики металлов |
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ISSN 1608-1021. Usp. Fiz. Met., 2019, Vol. 20, No. 1 75
© V.V. lIZUNoV, I.M. ZABolotNyy, ya.V. VASylyK,
I.e. GoleNtUS, M.V. UShAKoV, 2019
https://doi.org/10.15407/ufm.20.01.075
v.v. lIZuNOv, I.M. ZaBOlOTNyy,
ya.v. vasylyk, I.e. GOleNTus, and M.v. ushakOv
G.V. Kurdyumov Institute for Metal Physics of the N.A.S. of Ukraine,
36 Academician Vernadsky Blvd., UA-03142 Kyiv, Ukraine
integrated diffractoMetry:
achieved Progress and new
PerforMance caPabilities
this review provides a brief overview and a discussion of dynamical integrated dif-
fractometry and its functional capabilities. It is demonstrated that the combined use
of measurements of integrated diffraction parameters on different diffraction con-
ditions allows determining the parameters of several types of microdefects, which
are simultaneously present in a single crystal. these parameters are the total inte-
grated intensity of dynamical diffraction, the contribution of its diffuse component,
and their dependences on different diffraction conditions. examples of the use of
integrated diffraction parameters for non-destructive express diagnostics of the
characteristics of the defects’ structure of single crystals are discussed.
Keywords: dynamical diffraction, diffuse scattering, integrated diffractometry, mi-
crodefects.
1. Introduction
the development of materials with new, necessary for practical appli-
cation properties, is often achieved by forming unique structural and
phase states. It means that the corresponding advance of func tional ca-
pabilities of the diagnostic equipment for controlling the structural
perfection of the materials should be achieved. the diffrac tometry
methods play the most important role in solve this problem and allow
conducting non-destructive diagnostics of materials.
In addition, the important requirement (especially for practical ap pli-
cations) for diagnostic methods is short-term of the measurement. the
reduction of the measurement time did the diagnostic method is more
convenient, allowing more samples to be investigated for a fixed time.
76 ISSN 1608-1021. Prog. Phys. Met., 2019, Vol. 20, No. 1
V.V. Lizunov, I.M. Zabolotnyy, Ya.V. Vasylyk, I.E. Golentus, and M.V. Ushakov
Modern diffractometry methods chiefly use triple-axis and less com-
monly double-axis schemes. the use of triple-axis diffractometry makes
possible to measure distributions of the diffracted radiation in ten sity in
the reciprocal lattice space and, therefore, to determine the structure of
the objects under study. however, with the advantages of the mentioned
techniques, they also have disadvantages, which are long-term measu-
rements, expensive radiation sources and comp lex equipment. Duration
of the exposure time is associated primarily with problem of measuring
too low values of the diffracted radiation intensity at each point of the
reciprocal space. In other words, the problem is registration a small
num ber of counts per unit time. An alternative to this would be to
measu re some integral parameters, which would increase the number of
recorded counts per unit of time and thus significantly decrease the
time of diagnostics. the develop ment of similar integrated diffractometry
methods began almost immediately after the discovery of the phenomenon
of radiation diffraction on crystal structures about 100 years ago.
the first results were obtained for the integrated intensities, i.e.
for the sum of intensities in all diffracted waves, including the ener gy
distribution near the Bragg reflection. For describing the diffrac tion
processes on crystals, the kinematical (single-scattering appro ximation)
theory and rigorous dynamical theory (taking into account multiple
scat tering) were developed [1–6]. As a result, formu las that relate the
magnitudes of the integrated intensities with the structural factors of
the crystals were obtained. this allowed determining the structure of
crystalline objects by simple non-destructive methods.
Most natural crystals are poly- and mosaic crystals, and no single
crystals. So, for a long time there was a paradoxical situation: the for-
mulas obtained within the framework of the approximate kinematical
theory described the experiment much more accurately than the rigorous
dynamical theory. thus, the formulas of the kinematical theory of dif-
frac tion were sufficiently for the study of crystal structures. the effects
of multiple scattering can be observed only when the coherence length
of the scattering and the size of the crystals exceed the extinction
length, i.e. in crystals close to perfect single crystals.
however, since 1960s, methods for growing almost perfect single
crystals with a low concentration of microdefects have been developed.
these crystals have been required in industry that stimulated a rapid
growth in the number of studies related to dynamical diffraction.
In addition, later it found out that the properties of modern materials
are determined not so much by the structure and parameters of their
ideal periodic lattices, as by the statistical characteristics of the micro-
defects and parameters of substructure. therefore, the theo ries of ra-
diation diffraction on perfect crystals that existed at that time required
generalization to the case of single crystals with microdefects.
ISSN 1608-1021. Usp. Fiz. Met., 2019, Vol. 20, No. 1 77
Integrated Diffractometry: Achieved Progress and New Performance Capabilities
A similar generalization was carried out in the works of M.A. Kri-
voglaz (systematic description of his results presents in the mono graphs
[7, 8]), where a statistical averaging of the crystal susceptibi lity over
the distribution of defects have been performed. As a result, periodical
‘average’ functions with new periods and effective atomic factors, as
well as the fluctuation waves of deviations from this periodicity of the
crystal susceptibility were introduced. In addition, relations between
these new parameters and the characteristics of the defects were deter-
mined. As a result, the coherent (Bragg) and diffuse components of
scattering radiation in the kinematical appro ximation were determined.
Based on the obtained results, M.A. Kri voglaz classified microdefects
according to their influence on the kinematical scattering pattern. Until
today, Krivoglaz’s classification is used in almost all structural labora-
tories in the world for characterizing crystals with microdefects.
however, the use of the kinematical theory of scattering for cha-
racterization of imperfect crystals significantly limited the appli cability
of the integrated intensities methods. As shown, the total (the Bragg +
+ diffuse components) integrated intensity does not de pend on the dis-
tortion of the crystal lattice at kinematical diffraction. thus, the me-
thods for characterizing structure, based on measuring the total integ-
rated scattering intensities, are inapplicable for kine matically scattering
crystals with microdefects.
the situation changes due to the use of the dynamical scattering
pattern instead of the kinematical one. It was shown that the dyna mical
pattern of scattering is sensitive to structure imperfections of crystals
due to the dispersion mechanism. this mechanism also pro vides the
sensitivity to structure imperfections in individual integral characteristics
of scattering pattern (see, for example, [9, 10]). thus, the measurement
of the total integrated intensity of dynamical diffraction (tIIDD) allows
quantifying the characteristics of the defect structure of single
crystals.
In this article, we illustrate the use of dynamical diffraction methods
to determine the parameters of structural imperfections of single crys-
tals on examples of semiconductor materials. however, the appropriateness
of using dynamical methods for characterization of metallic single
crystals with microdefects is perhaps even higher than for semiconductors.
the fact is that without taking into account the effects of dynamical
scattering of radiation in metallic single crystals the description of the
defect structure can be not only qua ntitatively but also qualitatively
incorrect. For example, the kine matical description of single crystals
with dislocations predicts a complete absence of a coherent component
of intensity. At the same time, the use of the dynamical approach with
taking into account the effects of multiple scattering leads to an effective
cutoff of the con tribution of distant dislocations to the scattering
78 ISSN 1608-1021. Prog. Phys. Met., 2019, Vol. 20, No. 1
V.V. Lizunov, I.M. Zabolotnyy, Ya.V. Vasylyk, I.E. Golentus, and M.V. Ushakov
characteristics. As a result, even at high concentration of dislocations
in the crystal, coherent peaks can be preserved. the same scattering
pattern is ob served experimentally.
the article has following structure. In Section 2, some of the classical
results of the integrated intensity theory for mosaic and perfect crystals
are briefly described. In Section 3, the problems of the statistical scat-
tering theories related with interpreting scattering patterns for crystals
with several types of microdefects are presented. the main results of
the statistical theory of tIIDD in crystals with microdefects, which
allow solving these problems, are described in Section 4.
2. The Intensity of Integrated
Reflection of X-Ray by crystals
2.1. The Integrated Reflection from Mosaic Crystals
the majority of nature crystals are not single crystals. In fact, crystal
which appeared one whole consists of a number of independent crystalline
regions. each such region is a small single crystal block in which the
atomic planes are regular and parallel. the whole crystal consists in
very large number of such blocks; their atomic planes are almost parallel,
but the orientations are distributed in a certain range of angles, although
small, but still larger than the angular region of reflection from a single
block. Such composite crystals on the proposal of ewald are called mosaic
crystals.
For simplicity, we assume that the individual blocks are small
enough and the absorption in them can be neglected. the intensity of
the scattering radiation by a single crystal block is described by the
expression [5, 11]:
2
0
02
( , , )J I
R
Φ
= ξ η ζ , (1)
where
22 2
31 2
0 2 2 2
sin ( )sin ( ) sin ( )
( , , )
sin ( ) sin ( ) sin ( )
NN N
I
π ζπ ξ π η
ξ η ζ =
πξ πη πζ
(2)
is laue interference function; Φ0 is the amplitude of the scattered wave
at unit distance from the scattering point (lattice-point); N1, N2, N3 are
the numbers of lattice-points in the block in the directions of the basis
lattice vectors; ξ, η, ζ are the integers coordinates of the diffraction
vector in reciprocal space, R is the distance from the crystal to the
observation point.
For calculation the intensity scattered from the whole crystal it is
necessary to sum the intensities scattered from each of the blocks. Since
the blocks are disoriented, it is need to sum up exactly the intensities,
not the amplitudes of the scattered waves.
ISSN 1608-1021. Usp. Fiz. Met., 2019, Vol. 20, No. 1 79
Integrated Diffractometry: Achieved Progress and New Performance Capabilities
the reflection intensity has a sufficiently large value in the small
range of the incidence angles. the maximum value of the reflected
intensity corresponds to the incident radiation by the Bragg angle θB.
Usually, under measuring integrated reflections the crystal is rota ted
with a constant angular velocity ω around an axis parallel to the ref-
lecting planes and perpendicular to the direction of incidence [11].
let I is the total diffracted intensity recorded during crystal rotation
over the entire reflection region and I0 is the intensity of the incident
beam, then I/I0 is called the integrated reflection from the crystal
element. As shown in [11]:
22 3 2
2 B
2
B
1 cos 2
sin2 2
N e
F v Q v
mc
+ θλ
ρ = ∆ = ∆ θ
, (3)
where ∆v is the volume of the irradiated crystal element, N is the number
of atoms per unit volume, F is the structural factor, λ is the radiation
wavelength, e and m are the electron charge and mass, c is the speed of
light. the parameter Q characterizes the scattering intensity by a unit
volume of the crystal. thus, the measurement of the integrated reflection
allows determining the structural factor of the crystal, and, consequently,
its atomic structure.
the scattering patterns from different blocks of the mosaic crystal
displace relative to each other that lead to some blurring of the resulting
scattering pattern. In addition, the finite size of the x-ray source also
leads to a blurring of the measured scattering pattern. thus, there is an
additional appropriateness of measuring of the integrated intensity, since
the redistribution of the scattered energy does not change its total value.
2.2. The Integrated Reflection from Perfect Crystals
Now we consider the scattering of radiation by perfect single crystals.
In according the kinematical theory for calculating the intensity
scattered by the whole crystal the intensities (not amplitudes) scattered
by individual blocks are summed. therefore, the calculation of the
intensity is reduced to calculation of the intensity of the radiation
scattered by one block. the amplitude of the wave scattered by one block
is small compared with the amplitude of the incident wave, so the
interaction between this waves can be neglected. however, when the size
of the crystal is large and it is a single crystal, this statement becomes
incorrect.
For x-rays, the ratio q of the amplitudes of a wave scattered by a
single atomic plane to the amplitude of the incident wave is about 10−5;
so for a large number of atomic planes the amplitude of the scattered
wave becomes comparable to the amplitude of the incident wave and its
interaction cannot be neglected.
80 ISSN 1608-1021. Prog. Phys. Met., 2019, Vol. 20, No. 1
V.V. Lizunov, I.M. Zabolotnyy, Ya.V. Vasylyk, I.E. Golentus, and M.V. Ushakov
Dynamical theory was developed in
two forms: Darwin theory and ewald–
laue theory. Darwin’s dynamical theory
was constructed by analogy with the
kinematical theory. each atom in the
crystal lattice is characterized by an
atomic scattering function, and waves
scattered by atoms are added, taking into
account the phases and scattering ampli-
tudes. Darwin’s theory takes into account the interaction of the crystal
not only with the incident, but also with the scattered waves, as well as
absorption. In the ewald–laue theory, the propagation of elec tromagnetic
waves in a medium with taking into account the continuous distribution
of electron density was considered.
Both of these approaches are equivalents, in whole, and in many
cases give the same results. however, the ewald–laue theory was deve-
loped much more intensively because it allows solving a much wider
range of problems. here we present only formulas describing the integ-
rated reflection from a perfect single crystal.
We consider a non-absorbing perfect single crystal. let us note T0
and S0 the amplitudes of the incident and reflected waves. It was shown
(see, e.g., [11]) that:
0
2 2
0
S q
T q
−
=
ε ± ε −
, (4)
where q determines the amplitude of the wave scattered by an atomic
plane in the direction of the reflected beam, and ε is a small value con-
nec ted with the deviation of the incidence angle of radiation θ from the
exact Bragg angle.
the corresponding reflection curve is presented in Fig. 1. A charac-
teristic property of this curve is the presence of a region of total
reflection: in the interval −q < ε < q, the ratio S0/T0 = 1.
the integrated reflection will be determined by the area under the
curve in Fig. 1:
2
0 0( ) /R d S T d
∞ ∞
−∞ −∞
ρ = θ θ = θ∫ ∫ . (5)
By the integration for nonpolarized radiation can be obtained [11]:
2
B
dyn
B
1 cos28
(2 )
3 sin2 2
N
F
+ θλ
ρ = θ
π θ
. (6)
this formula in essence is different from formula (3) for the
integrated intensity of a mosaic crystal. It can be seen from formulas
Fig. 1. reflection curve of a perfect single crystal
ISSN 1608-1021. Usp. Fiz. Met., 2019, Vol. 20, No. 1 81
Integrated Diffractometry: Achieved Progress and New Performance Capabilities
that ρkin ∼ ∝ F2 and ρdyn ∝ F. the difference between ρdyn and ρkin can
reach 30–40 times, and the dynamical integrated intensity is less than
kinematical despite the presence of a region of total reflection. one of
the reasons for this is that the width of the reflection curve of perfect
single crystal is very small (several angular seconds), and for a mosaic
crystal the width of the reflection curve is much larger.
It should be noted that when radiation is incident on a crystal at the
Bragg angle, only the upper layers of the crystal take part in the ref-
lection. this is because the waves twice reflected from the crystal planes,
which propagate in the direction of the primary wave, differ from the
primary wave in phase by π and as a result, the primary wave is quickly
extinguished. this phenomenon is called the primary extinction. the
primary extinction can be formally interpreted as an effective increase
of the absorption coefficient around the reflection region. In this angle
range, the intensity of the incident beam is attenuated not only by ordi-
nary absorption, but also by transfer to the reflected wave.
Formula (6) was obtained for an infinite single crystal. It is necessary
to consider the interaction of radiation with a single crystal of finite
size with correct boundary conditions for the practical use of integrated
intensity.
If the blocks of the mosaic crystal are large enough, then it is
necessary to take into account the extinction for each of them. the
formula for a mosaic crystal with taking into account primary extinction
can be written [1, 2]:
th( )pq
Q v
pq
ρ = ∆ , (7)
where p is the number of atomic crystal planes. this formula allows
determining the size of coherent blocks in a mosaic crystal.
thus, the use of integrated intensity methods allows determining
the structural characteristics of ideal mosaic crystals, as well as perfect
single crystals.
3. Integrated Intensity of Reflection
for crystals with Microdefects
Any real single crystal contains microdefects, the statistical charac te-
ristics of which determine its properties. For describing the radiation
diffraction on single crystals with microdefects M. A. Krivoglaz created
the statistical kinematical theory of scattering in the 1950s. this theory
gives the following formulas for the total integrated intensity (tII) Ri
[8, 17, 18]:
Ri = RiB + RiD, (8)
RiB = Ripe
−2L, (9)
82 ISSN 1608-1021. Prog. Phys. Met., 2019, Vol. 20, No. 1
V.V. Lizunov, I.M. Zabolotnyy, Ya.V. Vasylyk, I.E. Golentus, and M.V. Ushakov
RiD = Rip(1 − e−2L), (10)
Rip = C2Qt/γ0, (11)
Q = (π|χHr|)
2/[λsin(2θB)]. (12)
here Rip is the integrated scattering intensity in the perfect crystals
(without microdefects), χHr is the real part of the Fourier component of
the polarizability of the crystal, t is the crystal thickness, C is the
polarization factor.
It should be noted that in expressions (9) and (10) for Bragg (RiB)
and diffuse (RiD) components of tII, only the factor Rip is dependent on
diffraction conditions. In addition, factor Rip does not depend on the
defects structure of the crystal. only the factors that include the
Krivoglaz factor (static Debye–Waller factor E = e−L) depend on the
characteristics of the defects structure of crystal lattice. the Krivo glaz
factor is independent on the diffraction conditions for each reflex.
From formulas (8)–(12), it follows that the integrated intensity in
crystals with microdefects can be characterized by two integral para-
meters. the first parameter is the total brightness of the scattering
pattern, i.e. the total integrated reflection intensity Ri, equal to the sum
of the Bragg and diffuse components (see eq. (9)). For convenience this
parameter should be normalized to the total brightness of the scattering
pattern of an perfect crystal (Rip). the second parameter is the specific
contribution of the diffuse component or the ratio of the diffuse and
Bragg components (RiD/RiB). From formulas (8)–(12) it follows that in
the kinematical theory of non-ideal crystals:
Ri = Rip or Ri/Rip = 1, (13)
RiD/RiB = (1 − e−2L)/e−2L ≈ 2L, (14)
thus, for fixed reflex the total integrated intensity does not depend on
the distortions of the crystal lattice, and the only structurally sensitive
factor is the second parameter (RiD/RiB), which is not depend on diffrac-
tion conditions.
From the expressions (13) and (14) two conservation laws of the
kinematical theory is followed. the first conservation law is the inde-
pendence of the total integrated intensity Ri from the characteristics of
crystal defects. therefore, in kinematical theory Ri for a crystal with
defects remains the same as in a perfect crystal (Rip) and depends only
on diffraction conditions. however, the normalization of this parameter
to Rip leads to a loss of dependence on diffraction conditions and makes
it a universal constant equal to unity in the kinematical theory, i.e.
completely uninformative. the second law of conservation of the kine-
matical theory is the independence of the contribution of the diffuse
component from the diffraction conditions for each reflex. thus, in the
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Integrated Diffractometry: Achieved Progress and New Performance Capabilities
kinematical case, there is only this structurally sensitive parameter for
any diffraction conditions. As a result, the use of integrated methods
for kinematical scattering is practically meaningless.
the Kato’s statistical dynamical theory of diffraction [19, 20] and
its improved modifications [21–26] were also widely known. however,
measurements for imperfect crystals showed a discrepancy between
experimental data and Kato’s theory. For example, in [27] the integrated
intensity in the Bragg diffraction geometry for silicon crystals with
defects was measured. It was found that in most cases Kato’s theory
does not correctly describe obtained experimental data. this is due to
the fact that Kato’s theory is based on solving the takagi equations
[28], which are valid only for smooth displacement fields. For this reason
Kato’s theory is generally not applicable or not sufficiently correct
quantitatively for single crystals with microdefects.
In addition, this approximation is closely related with the concept
of a single optical path in the scattering plane and does not allow to
correctly describing the processes of multiple diffuse scattering near
Bragg reflection, which also include waves with diffraction vectors
beyond the coherent scattering plane. this disadvantage was noted in
[24], in which calculations based on the Green function method in real
space are given with taking into account the second derivative with
respect to the spatial coordinate corresponding to the vertical divergence.
Kato also noted this problem in ref. [29], where his previous appro-
ximation [19, 20] was reformulated without using the takagi appro-
ximation.
Another problem in mentioned statistical dynamical theories is that
they are aimed at solving the problem of secondary extinction and are
based on the imperfect crystal model, which consists of mosaic blocks.
As a result, the formulas for the integrated diffraction intensity include
as parameters of imperfection the Krivoglaz factor and correlation
lengths, which are related, in particular, to the block sizes. however,
correlation lengths cannot be directly associated with the characteristics
of microdefects (concentration, radius, etc.) when considering the imper-
fect single crystals. therefore, in this case a completely different prob-
lem should be solved and completely different methods.
4. Methods of Total Integrated Intensity of Dynamical
Diffraction in single crystals with Microdefects
In the case of dynamical scattering both integral parameters, defined in
the previous section, are depended on the characteristics of the defect
crystal structure. this allows us to determine the parameters of the
defect crystal structure by measuring the dependences of tIIDD on
different diffraction conditions and their combined processing using the
84 ISSN 1608-1021. Prog. Phys. Met., 2019, Vol. 20, No. 1
V.V. Lizunov, I.M. Zabolotnyy, Ya.V. Vasylyk, I.E. Golentus, and M.V. Ushakov
formulas of Molodkin dynamical theory [12–18]. Methods based on this
approach are express and have the highest sensitivity compared to other
diffraction methods. Measurements can be made under all possible
diffraction conditions (laue and Bragg geometries, cases of ‘thin’ and
‘thick’ crystals, spectral, azimuthal, deformation dependencies, etc.).
let us consider these cases in more detail.
4.1. The Method of Thickness Dependences of TIIDD
one of the primary methods of tIIDD is the method of the measuring of
thickness dependences [18, 30–36]. As shown, the diffracted integrated
intensities are significantly depended on the crystal thickness and the
radiation energy. two limiting cases of dynamical diffraction exist.
they correspond to the so-called approximations of ‘thin’ (µ0t < 1) and
‘thick’ (µ0t >> 1) crystals [17], where µ0 is the coefficient of linear pho-
toelectric absorption and t is the thickness of the crystal. the impor tant
advantage of this method, as well as others methods, based on the
measurement of tIIDD, is the possibility of a significant increase of the
diffuse component compared to the coherent component.
Figure 2 presents the results of an experimental measurement of
the thickness dependence of the contribution of diffuse scattering and
violation of the first conservation law. Markers show the experimentally
Impurities composition and conditions
of heat treatment of samples of dislocation-free silicon
No.
orientation of the large
sample surface
Impurities
composition
conditions of heat
treatment
1 Plane (110) parallel
to the direction
of growing ingot 001
o2 — 8.2 ⋅ 1017 cm−3
Ge — 1020 см−3
Annealing for 2 hours at
1523 K in Ar atmosphere
2 — o2 — 8.2 ⋅ 1017 cm−3
Ge — 1019 cm−3
Annealing for 2 hours at
1523 K in Ar atmosphere
3 — o2 — 8.2 ⋅ 1017 cm−3
Ge — 1020 cm−3
Annealing for 2 hours at
1523 K in Ar atmosphere,
cu diffusion for 1 hour at
1173 K in N2 atmosphere
4 — o2 — 8.2 ⋅ 1017 cm−3
Ge — 1019 cm−3
—
5 — o2 — 8.2 ⋅ 1017 cm−3
Ge — 1020 cm−3
cu diffusion for 1 hour at
1173 K in N2 atmosphere
6 — o2 — 8.2 ⋅ 1017 cm−3
Ge — 1019 cm−3
—
7 Plane (111) perpendicular
to the direction of growth
of the ingot 111
o2 — 8.2 ⋅ 1017 cm−3 cu diffusion for 3 hours at
1173 K in N2 atmosphere
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Integrated Diffractometry: Achieved Progress and New Performance Capabilities
measured thickness dependences of tIIDD, and the solid lines show the
results of theoretical calculations.
Samples were cut from Si ingot without dislocations, grown by the
czochralski method (see table). tIIDD were determined using a unia xial
diffractometer for symmetric (220) laue reflexes using FeKα-, cuKα-
and MoKα-radiation. the thickness of the samples was varied by bleeding
from 1000 to 300 µm. For FeKα- and cuKα-radiations the approximation
of ‘thick’ crystal was realized and for MoKα-radiation the approximation
of ‘thin’ crystal was realized.
According to the kinematical theory, the ratio ρ = Ri/Rip should be
a constant equal to unity in all range of µ0t, regardless of the degree of
distortion of the crystal lattice.
As can see, the deviations of the real experimental dependencies
from the kinematical line (ρ = 1) are an order of magnitude greater
than the experimental error (∼10%) even for weakly disturbed single
crystals. the deviations sharply increase with increasing degree of dis-
tor tion of the crystals, demonstrating a high sensitivity of the propo -
sed method.
It should be noted that, in accordance with the developed physical
concepts [17, 30], the obtained curves deviate from the kinematical line
in opposite directions in approximations of ‘thin’ and ‘thick’ crystals. A
change in the heat treatment conditions leads to a change in the defect
structure of the crystals under study and, accordingly, to a significant
difference in the thickness dependences of tIIDD among themselves.
thus, the use of the thickness dependence method allows us to determine
the parameters of the defect structure of a single crystals.
Fig. 2. tIIDD normalized to Rip vs. value of µ0t for samples 1–4 (a) and 5–7 (b),
the heat treatment conditions are listed in table
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V.V. Lizunov, I.M. Zabolotnyy, Ya.V. Vasylyk, I.E. Golentus, and M.V. Ushakov
4.2. The Method of Energy-Dispersion Dependences of TIIDD
the method of the energy-dispersion dependences of tIIDD is closely
related with the method of the thickness dependences of tIIDD. the
difference of the method of the energy-dispersion dependences is changing
the effective thickness of the crystal by changing the wavelength.
In the work [37], tIIDD were measured for different wavelengths
and reflexes from dislocation-free Si single crystals of varying degrees
of structural perfection. Samples of dislocation-free silicon single
crys tals were cut from czochralski-grown ingot (p-type conductivity,
ρ ∼ 10 ohm/cm, the growth axis was directed along the 〈111〉, oxygen
and carbon concentrations were 1 ⋅ 1018 cm−3 and 1016 cm−3, respectively).
the samples were prepared in the form of plates parallel to the (111)
plane, which made an angle ψ = (2.0 ± 0.1)° with the surface. Disruptions
of the surface structure because of mechanical processing were removed
by chemical-mechanical polishing and next chemical etching to a depth
of ∼10 µm. Samples no. 1 and no. 2 were annealed in air and sample no.
3 was annealed in a nitrogen atmosphere for 4, 6, and 7 hours at 1000
°c, 1080 °c, and 1250 °c, respectively. Sample thicknesses were
controlled with an accuracy of 1 µm and were equal to 490 µm, 488 µm,
and 487 µm for samples nos. 1, 2 and 3, respectively.
Figure 3 shows the spectral dependences of tIIDD for mentioned
non-ideal crystals, which are experimental confirmation of the difference
between dependences of tIIDD in the approximations of ‘thin’ and
‘thick’ crystals in the case of Bragg diffraction.
As follows from the presented results, in the considered case the
high sensitivity of the dynamical scattering pattern to the defect struc-
ture of single crystals is observed.
4.3. The Method of Azimuthal Dependences of TIIDD
It was considered that the azimuthal dependences (AD) of the normalized
tIIDD for different types of lattice distortions are symmetric about an
angle of 90°. For study the mentioned symmetry of AD were measured
for a crystal with defects (see refs. [31, 32, 38]). the objects of study
were the same as described in the previous section. the sample was
made in the form of a plate parallel to the (111) plane, with a thickness
of t = 4000 µm. Disruptions of the surface structure because of mecha-
nical processing were removed by chemical-mechanical polishing and
next chemical etching to a depth of ∼10 µm.
It was experimentally established that as a result of the presence of
large-size defects in this crystal (dislocation loops with a radius of
15 µm) AD of the normalized tIIDD is asymmetric (see Fig. 4, a, mar-
kers). the calculation also gives the asymmetry of AD of the normalized
tIIDD and practically coincides with the experiment (Fig. 4, a, solid line).
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Fig. 3. tIIDD normalized to Rip vs. radiation
wavelength for single crystals Si with micro-
defects in the case of Bragg diffraction ge-
ometry. the results of the calculation show
solid lines, the experiment show markers
Integrated Diffractometry: Achieved Progress and New Performance Capabilities
Analysis of the causes of the asymmetry of AD showed that this
effect is explained by the behaviour of the diffuse component of tIIDD.
It has been established that the presence of large-sized defects in a
single crystal causes the symmetry of non-normalized diffuse component
of AD (which asymmetric in the case of small defects), while AD of
cohe rent component remains asymmetric (as in the case of a perfect
crystal). It is shown in Figs. 4, b, c.
thus, by normalizing AD of tIIDD of single crystal with defects on
similar AD of perfect crystal, we obtain a symmetric dependence in the
case of small defects and asymmetric in the case of large defects. thus,
due to the different character of AD in cases of small and large defects,
Fig. 4. experimental (markers) and
calculated AD of tIIDD at the values
of the average radius of the disloca-
tion loops R = 15 µm (solid line) and
R = 0.02 µm (dash line) (a); the calcu-
lated AD of tIIDD for an ideal crystal
(solid line) as well as the calculated AD
of diffuse component of tIIDD RiD (b)
and coherent components of tIIDD Ric
(dashed and dotted lines) (c)
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V.V. Lizunov, I.M. Zabolotnyy, Ya.V. Vasylyk, I.E. Golentus, and M.V. Ushakov
and selective sensitivity of AD to large defects, it becomes possible to
determine their parameters. the parameters of small defects can be
determined using other diffraction conditions for the same sample.
4.4. The Method of Deformation Dependences (DD) of TIIDD
the methods of tIIDD described in the previous sections have disad-
vantages: when using the method of thickness dependences, it is not
always possible to conserve the integrity of the original sample, and for
all three methods it is impossible to exclude stochastic crystal defor-
mations that influence to the measurement results. research of the
effect of macroscopic elastic deformation on the tIIDD not only made it
possible to control its influence, but also formed the method for diag-
nostics of microdefects [18, 31–35, 39–42].
Figure 5 illustrates a significant change of the character of the
defects effect on the integrated scattering intensity (first parameter)
Fig. 5. theoretical and experimental values of DD of tIIDD (a is a ‘thin’ crystal, b
is a ‘thick’ crystal) and normalized DD of tIIDD (c is a ‘thin’ crystal, d is a ‘thick’
crystal) are shown with solid lines and markers, respectively. the dashed lines are
the calculated DD of the coherent component of tIIDD, the dashed lines are the dif-
fuse component, and the solid thin lines are DD of tIIDD crystal without defects
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Integrated Diffractometry: Achieved Progress and New Performance Capabilities
depending on the radius r of curvature of the macroscopic elastic bending
of a silicon crystal, as well as the change of the character of the defects
effect on these DD depending on other diffraction conditions. Figure 5
shows mentioned change at the transition from the case of a ‘thin’ crys-
tal (a) to the case of a ‘thick’ crystal (b). the total brightness of the
dynamical scattering pattern, normalized to the brightness of the pattern
for the perfect crystal, and its DD become sensitive to the characteristics
of the defects.
In the next papers [43, 44], the use of DD of tIIDD to determine the
parameters of the defect structure of silicon crystals with thicknesses
significantly smaller than the absorption length and containing a rela-
tively small number of defects was considered. In this case, the diffuse
component has a small value and, accordingly, small value has the effect
of its anomalous growth. In the work [45], the diagnostic capabilities of
the method of DD of tIIDD for single crystals containing a larger num-
ber of defects were experimentally considered. In this case, the diffuse
component of tIIDD is commensurate with its coherent component or
significantly exceeds it. It was shown that in such cases DD of tIIDD
are sensitive to the characteristics of microdefects in single crystals.
4.5. The Method of DD of TIIDD at Violation
of the Friedel Law
this method is based on the influence of the defect structure of the
crystal on the ratio of tIIDD for reflections (hkl) and : .hkl hklhkl Y I I=
For example, the change of Y at the K-absorption edge is sensitive to
large defects [46]. As can be seen from Fig. 6, for a crystal with defects,
due to the contribution of the diffuse component, the thickness
dependence of Y is different from the similar dependence for a perfect
crystal. the characteristics of defects can be determined by the degree
of this difference. Similarly, it is possible to determine via deviations of
Fig. 6. the ratio of the change
of parameter Y of a real Ge
single crystal (the parameters
of defects are shown in the fig-
ure) to the change of the para-
meter of an ideal perfect crys-
tal vs. the thickness of crystal.
the calculations were perfor-
med with the radius of curva-
ture of the elastic bend r =
= ±2.4 m
90 ISSN 1608-1021. Prog. Phys. Met., 2019, Vol. 20, No. 1
V.V. Lizunov, I.M. Zabolotnyy, Ya.V. Vasylyk, I.E. Golentus, and M.V. Ushakov
Fig. 7. the methods of separation of coherent (a) and diffuse (b) components of the
total integrated intensity. here M is a slit monochromator with three consecutive
reflections, S is a sample crystal, A is an analyzer crystal, D is a detector
Fig. 8. thickness dependences of tIIDD (•) and its coherent component (▲), meas-
ured by the slope method. here solid lines are the result of theoretical calculations
for the determined defects parameters, dashed line is the calculations for an ideal
crystal, dash-dotted line is the separated true values of the diffuse component of
tIIDD, and dotted line is the contribution of the diffuse component in the measured
coherent component
Fig. 9. thickness dependences of tIIDD (•) and its duffuse component (▲), meas-
ured by the slope method. here solid lines are the result of theoretical calculations
for the determined defects parameters, dashed line is the lost part of the diffuse
component, dotted line is the calculations for an ideal crystal, and dash-dotted line
is the separated true values of the diffuse component of tIIDD
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Integrated Diffractometry: Achieved Progress and New Performance Capabilities
the parameter Y for a single crystal with defects from the parameter
Yperf for a perfect crystal and their variations with thickness, both below
and above the K-absorption edge.
4.6. The Method of Integrated
Triple-Axis Diffractometry
In addition to measuring the dependences of the tIIDD (the first para-
meter) on diffraction conditions, similar dependences of the relative con-
tribution of the diffuse component of the tIIDD (the second para meter)
can be measured [47–49]. the scheme that is used is shown in Fig. 7.
experimental measurements were carried out on a sample of Si cut
along (111) surface perpendicular to the growth axis from an ingot
grown according to czochralski. A p-type conductivity sample (alloying
element B, ρ = 10 Ω ⋅ cm) with an oxygen atom concentration of about
1.1 ⋅ 1018 cm−3 and carbon atoms 1016 cm−3 was heat treated in air at
1080 °c for 6 hours.
the experimental results of diagnostics using the method of integral
triple-axis diffractometry [47–49] are presented in Figs. 8 and 9. the
method of separation of the true contribution of the diffuse component
developed in [48] was used.
thus, the proposed measuring method makes it possible to increase
the accuracy of determining the second structurally sensitive integrated
parameter in comparison with the conventional methods. In addition, it
should be noted that the redistributing of the contributions of the
coherent and diffuse components to the measured intensity is feasible.
this effect can be obtained by a choice of the width of the total reflection
region of the analyzer crystal due to the asymmetry parameter or the
reflection order. the redistribution can provide an optimization of
measurements with respect to sensitivity to parameters of structural
perfection, which affect the coherent and diffuse components of diffrac-
tion intensity in different ways.
5. conclusions
the integrated diffractometric methods have a long and difficult history.
For a long time the integrated reflectivity was the main measured
parameter in most experiments for determination of the structural para-
meters of crystalline materials. however, since the 1980s the integrated
methods were practically refused by the scientific community as uninfor-
mative and, therefore, useless in practice. however, the measu rement
of the total integrated intensity of dynamical diffraction can be extremely
useful for determining the parameters of microdefects of several types
that can simultaneously be in a single crystal. At the same time, the loss
of informativity is compensated by the combined use of different dif-
92 ISSN 1608-1021. Prog. Phys. Met., 2019, Vol. 20, No. 1
V.V. Lizunov, I.M. Zabolotnyy, Ya.V. Vasylyk, I.E. Golentus, and M.V. Ushakov
fract ion conditions and different methods, if they provide experimental
measurements of both main integrated parameters of the dynamical
scattering pattern (i.e., measurements of the corresponding parameters
for both the full scattering pattern and its diffuse component) for the
same sample. this approach may allow us to solve the problem of multi-
parameterical diagnostics of single-crystal systems with microdefects.
Acknowledgements. the authors are grateful to the corresponding
Member of the National Academy of Sciences of Ukraine V. B. Molodkin
for the support in their work and useful discussion of the article. this
paper was supported by the National Academy of Sciences of Ukraine
(contract no. 43Г/51-18).
reFereNceS
c.G. Darwin, 1. Phil. Mag., 27: 315 (1914).
c.G. Darwin, 2. Phil. Mag., 27: 675 (1914).
A.h. compton, 3. Phys. Rev., 9: 29 (1917). https://doi.org/10.1103/Physrev.9.29
W.l. Bragg, r. W. James, and c.h. Bosanquet, 4. Phil. Mag., 41: 309 (1921).
W. Friedrich, P. Knipping, and M. von laue, 5. Sitzungsberichte der Kgl. Bayer.
Akad. Der Wiss.: 303 (1912); reprinted Ann. Phys., 41: 971 (1913).
M. von laue, Sitzungsberichte der Kgl. Bayer. Akad. Der Wiss.: 363 (1912); 6.
reprinted Ann. Phys., 41: 989 (1913).
M.A. Krivoglaz, 7. Teoriya Rasseyaniya Rentgenovskikh Luchey i Teplo vykh Neyt-
ronov Real’nymi Kristallami [theory of X-ray and thermal Neutrons Scattering
by Nonideal crystals] (Moscow: Nauka: 1967) (in russian).
M.A. Krivoglaz, 8. X-Ray and Neutron Diffraction in Nonideal Crystals (Berlin,
heidelberg: Springer-Verlag: 1996). https://doi.org/10.1007/978-3-642-74291-0
V.V. lizunov, V.B. Molodkin, S.V. lizunova, N.G. tolmachev, e.S. Ska kunova, 9.
S.V. Dmit riev, B.V. Sheludchenko, S.M. Brovchuk, l.N. Ska pa, r.V. lekhnyak,
and e.V. Fuzik, Metallofiz. Noveishie Tekhnol., 36, No. 7: 857 (2014) (in
russian). https://doi.org/10.15407/mfint.36.07.0857
l.N. Skapa, V.V. lizunov, V.B. Molodkin, e.G. len’, B.V. Sheludchenko, S.V. li-10.
zunova, e.S. Skakunova, N.G. tolmachev, S.V. Dmitriev, r.V. lek hnyak, G.o. Ve-
likhovskiy, V.V. Molodkin, I.N. Zabolotnyy, e.V. Fu zik, and o.P. Vas’kevich,
Metallofiz. Noveishie Tekhnol., 37, No. 11: 1567 (2015) (in russian). https://
doi.org/10.15407/mfint.37.11.1567
r.W. James, 11. The Optical Principles of the Diffraction of X-Ray (lon don: 1950).
V.B. Molodkin and e.A. tikhonova, 12. Fiz. Met. Metalloved., 24, No. 3: 385 (1967)
(in russian).
V.B. Molodkin, 13. Fiz. Met. Metalloved., 25, No. 3: 410 (1968) (in rus sian).
V.B. Molodkin, 14. Fiz. Met. Metalloved., 27, No. 4: 582 (1969) (in russian).
V.B. Molodkin, 15. Metallofizika, 2, No. 1: 3 (1980) (in russian).
V.B. Molodkin, 16. Phys. Metals, 3: 615 (1981).
l.I. Datsenko, V.B. Molodkin, and M.e. osinovskiy, 17. Dinamicheskoe Rasseyanie
Rentgenovskikh Luchey Real’nymi Kristallami [Dynamical X-ray Scattering of
Nonideal crystals] (Kyiv: Naukova Dumka: 1988) (in russian).
V.B Molodkin, A.I. Nizkova, A.P. Shpak, V.F. Machulin, V.P. Klad’ko, I.V. Pro-18.
kopenko, r.N. Kyutt, e.N. Kislovskiy, S.I. olikhovskiy, e.V. Pervak, I.M. Fod-
chuk, A.A. Dyshekov, and yu.P. Khapachev, Dif rak tometriya Nanorazmernykh
ISSN 1608-1021. Usp. Fiz. Met., 2019, Vol. 20, No. 1 93
Integrated Diffractometry: Achieved Progress and New Performance Capabilities
De fektov i Geterosloev Kristallov [Diffractometry of Nanoscale Defects and hete-
ro geneous layers of crystals] (Kyiv: Akademperiodika: 2005) (in russian).
N. Kato, 19. Acta Crystallogr. A, 36: 763 (1980). https://doi.org/10.1107/
S0567739480001544
N. Kato, 20. Acta Crystallogr. A, 36: 770 (1980). https://doi.org/10.1107/
S0567739480001556
M. Al haddad and P. Becker, 21. Acta Crystallogr. A, 44: 262 (1988). https://doi.
org/10.1107/S0108767387011681
P. Becker and M. Al haddad, 22. Acta Crystallogr. A, 45: 333 (1989). https://doi.
org/10.1107/S0108767388014692
P. Becker and M. Al haddad, 23. Acta Crystallogr. A, 48: 121 (1992). https://doi.
org/10.1107/S0108767391009376
A.M. Polyakov, F.N. chukhovskiy, and D.I. Piskunov, 24. ZhETF, 99, No. 2: 589
(1991) (in russian).
J.P. Guigay and F.N. chukhovskii, 25. Acta Crystallogr. A, 48: 819 (1992). https://
doi.org/10.1107/S0108767392003830
J.P. Guigay and F.N. chukhovskii, 26. Acta Crystallogr. A, 51: 288 (1995). https://
doi.org/10.1107/S0108767394010895
J.r. Schneider, h.A. Graf, and o. Goncalves, 27. J. Crystal Growth, 80: 225 (1987).
https://doi.org/10.1016/0022-0248(87)90067-4
S. takagi, 28. Acta Crystallogr., 15, No. 12: 1311 (1962). https://doi.org/10.1107/
S0365110X62003473
N. Kato, 29. Acta Crystallogr. A, 47: 1 (1991). https://doi.org/10.1107/
S0108767390008790
V.V. Nemoshkalenko, V.B. Molodkin, S.I. olikhovskii, M.V. Koval chuk, yu.M. lit-30.
vinov, e.N. Kislovskii, and A.I. Nizkova, Nucl. Instr. Phys. Res. A, 308, Nos. 1– 2:
294 (1991). https://doi.org/10.1016/0168-9002(91)90651-6
A.P. Shpak, M.V. Koval’chuk, I.M. Karnaukhov, V.V. Molodkin, e.G. len, 31.
A.I. Nizkova, S.I. olikhovskiy, B.V. Sheludchenko, G.e. Ice, and r.I. Barabash,
Usp. Fiz. Met., 9, No. 3: 305 (2008) (in russian). https://doi.org/10.15407/
ufm.09.03.305
A.P. Shpak, M.V. Koval’chuk, V.B. Molodkin, V.l. Nosik, S.V. Dmitriev, e.G. len, 32.
S.I. olikhovskiy, A.I. Nizkova, V.V. Molodkin, e.V. Pervak, A.A. Katasonov,
l.I. Ninichuk, and A.V. Mel’nik, Usp. Fiz. Met., 10, No. 3: 229 (2009) (in
russian). https://doi.org/10.15407/ufm.10.03.229
A.P. Shpak, M.V. Koval’chuk, V.l. Nosik, V.B. Molodkin, V.F. Machulin, I.M. Kar-33.
naukhov, V.V. Molodkin, e.G. len, G.e. Ice, r.I. Barabash, and e.V. Pervak,
Metallofiz. Noveishie Tekhnol., 31, No. 5: 615 (2009) (in russian).
A.P. Shpak, M.V. Koval’chuk, V.B. Molodkin, A.I. Nizkova, I.V. hin’ko, S.I. oli-34.
khovskiy, e.N. Kislovskii, e.G. len, A.o. Bilots’ka, K.V. Pervak, and V.V. Mo-
lodkin, Sposib Bahatoparametrychnoyi Strukturnoyi Diahnostyky Monokrystaliv
z Dekil’koma Typamy Defektiv [Method of Multiparameterical Structural Diag-
nostics of Single crystals with Several types of Sefects], Patent of Ukraine
No. 36075 (Published october, 2008) (in Ukrainian).
A.P. Shpak, M.V. Koval’chuk, V.B. Molodkin, V.l. Nosik, V.yu. Storizhko, 35.
l.A. Bulavin, I.M. Karnaukhov, r.I. Barabash, G.e. Ice, A.I. Nizkova, I.V. hin’ko,
S.I. olikhovskiy, e.N. Kislovskii, V.A. tatarenko, e.G. len, A.o. Bilots’ka,
K.V. Pervak, and V.V. Molodkin, Sposib Bahatoparametrychnoyi Strukturnoyi
Diahnostyky Monokrystaliv z Dekil’koma Typamy Defektiv [Method of Multi pa-
rameterical Structural Diagnostics of Single crystals with Several types of Se-
fects], Patent of Ukraine No. 89594 (Published February, 2010) (in Ukrainian).
94 ISSN 1608-1021. Prog. Phys. Met., 2019, Vol. 20, No. 1
V.V. Lizunov, I.M. Zabolotnyy, Ya.V. Vasylyk, I.E. Golentus, and M.V. Ushakov
V.V. Nemoshkalenko, V.B. Molodkin, A.I. Nizkova, S.I. olikhovskiy, A.P. Shpak, 36.
M.t. Kogut, and o.l. Shkol’nikov, Metallofizika, 14, No. 8: 79 (1992) (in russian).
V.V. Nemoshkalenko, V.B. Molodkin, e.N. Kislovskii, M.t. Kogut, A.I. Nizkova, 37.
e.N. Gavrilova, S.I. olikhovskii, and o.V. Sul’zhenko, Metallofiz. Noveishie
Tekhnol., 16, № 2: 48 (1994).
V.B. Molodkin, S.V. Dmitriev, e.V. Pervak, A.A. Belotskaya, A.I. Nizkova, and 38.
A.V. Mel’nik, Metallofiz. Noveishie Tekhnol., 28, No. 8: 1055 (2006) (in russian).
A.P. Shpak, V.B. Molodkin, S.V. Dmitriev, e.V. Pervak, I.I. rudnitskaya, yu.A. Di-39.
naev, A.I. Nizkova, e.G. len, A.A. Belotskaya, A.I. Grankina, M.t. Kogut, o.S. Ko-
nonenko, A.A. Katasonov, I.N. Zabolotnyy, ya.V. Vasilik, l.I. Ninichuk, and
I.V. Prokopenko, Metallofiz. Noveishie Tekhnol., 30, No. 7: 873 (2008) (in russian).
A.P. Shpak, V.B. Molodkin, S.V. Dmitriev, e.V. Pervak, e.G. len, A.A. Be-40.
lotskaya, ya.V. Vasilik, A.I. Grankina, I.N. Zabolotnyy, A.A. Katasonov, M.t. Ko-
gut, o.S. Kononenko, V.V. Molodkin, A.I. Nizkova, l.I. Ninichuk, I.V. Pro-
kopenko, and I.I. rudnitskaya, Metallofiz. Noveishie Tekhnol., 30, No. 9: 1189
(2008) (in russian).
A.N. Bagov, yu.A. Dinaev, A.A. Dyshekov, t.I. oranova, yu.P. Khapachev, 41.
r.N. Kyutt, e.G. len, V.V. Molodkin, A.I. Nizkova, A.P. Shpak, and V.A. elyukhin,
Rentgenodifraktsionnaya Diagnostika Uprugo-Napryazhennogo Sostoyaniya Nano-
geterostruktur [X-ray Diffraction Diagnostics of the elastic-Stressed State of
heterogeneous Nanostructures] (eds. B. S. Karamurzov and yu. P. Khapachev)
(Nal’chik: Kabardino-Balkarskiy Universitet: 2008) (in russian).
A.P. Shpak, V.B. Molodkin, M.V. Koval’chuk, V.l. Nosik, A.I. Nizkova, V.F. Ma-42.
chulin, I.V. Prokopenko, e.N. Kislovskiy, V.P. Klad’ko, S.V. Dmitriev, e.V. Per-
vak, e.G. len, A.A. Belotskaya, ya.V. Vasilik, A.I. Grankina, I.N. Zabolotnyy,
A.A. Katasonov, M.t. Kogut, o.S. Kononenko, A.V. Mel’nik, V.V. Molodkin,
l.I. Ninichuk, I.I. rudnitskaya, and B.F. Zhuravlev, Metallofiz. Noveishie
Tekhnol., 31, No. 8: 1041 (2009) (in russian).
S.M. Brovchuk, V.B. Molodkin, A.I. Nizkova, I.I. rudnytska, G.I. Grankina, 43.
V.V. lizunov, S.V. lizunova, B.V. Sheludchenko, e.S. Skakunova, S.V. Dmitriev,
I.N. Zabolotnyi, A.A. Katasonov, B.F. Zhuravlev, r.V. lekhnyak, l.N. Skapa,
and N.P. Irha, Metallofiz. Noveishie Tekhnol., 36, No. 8: 1035 (2014). https://
doi.org/10.15407/mfint.36.08.1035
V.V. lizunov, S.M. Brovchuk, A.I. Nizkova, V.B. Molodkin, S.V. lizunova, B.V. She-44.
ludchenko, A.I. Grankina, I.I. rudnitskaya, S.V. Dmitriev, N.G. tolmachev,
r.V. lekhnyak, l.N. Skapa, N.P. Irkha, Metallofiz. Noveishie Tekhnol., 36,
No. 9: 1271 (2014) (in russian). https://doi.org/10.15407/mfint.36.09.1271
V.B. Molodkin, A.I. Nizkova, V.V. lizunov, V.V. Molodkin, e.N. Kislovskiy, 45.
ya.V. Vasilik, o.V. reshetnik, t.P. Vladimirova, A.A. Belotskaya, and N.V. Bar-
vinok, Metallofiz. Noveishie Tekhnol., 40, No. 8: 1123 (2018) (in russian).
https://doi.org/10.15407/mfint.40.08.1123
A.P. Shpak, V.B. Molodkin, M.V. Koval’chuk, V.l. Nosik, A.I. Nizkova, V.F. Ma-46.
chulin, I.V. Prokopenko, e.N. Kislovskiy, V.P. Klad’ko, S.V. Dmitriev, e.V. Per-
vak, e.G. len, A.A. Belotskaya, ya.V. Vasilik, A.I. Grankina, I.N. Zabolotnyy,
A.A. Katasonov, M.t. Kogut, o.S. Kononenko, A.V. Mel’nik, V.V. Molodkin,
l.I. Ninichuk, and I.I. rudnitskaya, Metallofiz. Noveishie Tekhnol., 31, No. 7:
927 (2009) (in russian).
V.B. Molodkin, h.I. Nizkova, ye.I. Bogdanov, S.I. olikhovskii, S.V. Dmitriev, 47.
M.G. tolmachev, V.V. lizunov, ya.V. Vasylyk, A.G. Karpov, and o.G. Voytok,
Usp. Fiz. Met., 18, No. 2: 177 (2017) (in Ukrainian). https://doi.org/10.15407/
ufm.18.02.177
ISSN 1608-1021. Usp. Fiz. Met., 2019, Vol. 20, No. 1 95
Integrated Diffractometry: Achieved Progress and New Performance Capabilities
V.V. Nemoshkalenko, V.B. Molodkin, e.N. Kislovskiy, S.I. olikhovskiy, t.A. Gri-48.
shchenko, M.t. Kogut, and e.V. Pervak, Metallofiz. Noveishie Tekhnol., 22,
No. 2: 42 (2000) (in russian).
V.V. Nemoshkalenko, V.B. Molodkin, S.I. olikhovskiy, e.N. Kislovskiy, M.t. Ko-49.
gut, l.M. Sheludchenko, and e.V. Pervak, Metallofiz. Noveishie Tekhnol., 22,
No. 2: 51 (2000) (in russian).
received September 14, 2018;
in final version, December 3, 2018
В.В. Лізунов, І.М. Заболотний,
Я.В. Василик, І.Е. Голентус, М.В. Ушаков
Інститут металофізики ім. Г.в. Курдюмова нан україни,
бульв. акад. вернадського, 36, 03142 Київ, україна
ІнтеГраЛьна ДИФраКтОметрІя:
ДОсяГнутІ усПІХИ та нОвІ мОЖЛИвОстІ
статтю присвячено обговоренню динамічної інтегральної дифрактометрії та її
функціональних можливостей. Показано, що комбіноване використання вимі-
рю вань інтегральних дифракційних параметрів за різних умов дифракції умож-
ливлює визначення параметрыв мікродефектів декількох типів, одночасно при-
сут ніх у монокристалі. Обговорюються приклади використання вимірювання
пов ної ін тегральної інтенсивности динамічної дифракції, внеску її дифузійної
складової та їхніх залежностей від різних умов динамічної дифракції для не-
руйнівної експресної діагностики характеристик дефектної структури монокрис-
талічних систем.
Ключові слова: динамічна дифракція, дифузне розсіяння, інтегральна дифракто-
метрія, мікродефекти.
В.В. Лизунов, И.Н. Заболотный,
Я.В. Василик, И.Э. Голентус, Н.В. Ушаков
Институт металлофизики им. Г.в. Курдюмова нан украины,
бульв. акад. вернадского, 36, 03142 Киев, украина
ИнтеГраЛьная ДИФраКтОметрИя:
ДОстИГнутые усПеХИ И нОвые вОзмОЖнОстИ
статья посвящена обсуждению динамической интегральной дифрактометрии и
её функциональных возможностей. Показано, что комбинированное использование
измерений интегральных дифракционных параметров при различных условиях
дифракции позволяет определять параметры микродефектов нескольких типов,
одновременно присутствующих в монокристалле. Обсуждаются примеры исполь-
зования измерения полной интегральной интенсивности динамической дифрак-
ции, вклада её диффузной составляющей и их зависимостей от различных ус-
ловий динамической дифракции для неразрушающей экспрессной диагностики
характеристик дефектной структуры монокристалличе-ских систем.
Ключевые слова: динамическая дифракция, диффузное рассеяние, интегральная
дифрактометрия, микродефекты.
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