Американский Научный Журнал THICKNESS OF SURFACE LAYER OF HALOGENS, METAL SULFIDES AND OXIDES

America n Scientific Journal № ( 33) / 20 20 37

мгновение, с началом расширения Вселенной
возникло и фотонное излучение [4].
Согласно общепринятой сегодня теории, в
первые моменты эволюции Вселенн ая находилась в
состоянии, которое недоступно для
экспериментального ос воения. В данной связи
проблема возникновения Вселенной является
хорошим полигоном для решения возникающих
головоломок. Р. Пенроуз выделяет «собственный
особенный Большой взрыв», а такж е его
самобытные особенности. В их числе: 1. Большой
взрыв «должен обладать абсурдно низкой
энтропией», что «следует уже из самого
существования Второго закона термодинамики». 2.
Микроволновое фоновое «излучение
действительно представляет сегодня «вспышку»
Большого взрыва, хотя и чрезвычайно
охлажденную из – за «красного смещения»,
обусловленного расширение м Вселенной». 3.
«Другим проявлением может служить
замечательно точное согласие между
предсказаниями теории и результатами
наблюдений, касающимися ядерны х процессов в
ранней Вселенной» [11, с. 609].
Выше нами предпринята попытка
приблизиться к разгадке о дной из тайн природы.
Если следовать результатам проведенного
исследования, то с учетом мнения [11, с. 609]
можно прийти и к суждению о том, ядерному
взр ыву на планковском масштабе времени
предшествовало низкоэнтропийное
высокоорганизованное многочастичное состояние
материи Вселенной.



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THICKNESS OF SURF ACE LAYER OF HALOGEN S, METAL SULFIDES AND O XIDES

Yurov V.M., Zhanabergenov T.K. , Makhanov К.М.
Karaganda State University. named after E.A Buketov

Abstract. The study of atomic -smooth surface s of solids is of fundamental and practical interest in connection
with the development of methods for the synthesis of nanostructures for electronics and photonics. Currently, there
are several methods for obtaining surfaces with a ve ry small roughness co mparable to the interatomic distance. In
this case, the question arises about the thickness of the surface layer of solids. At present, approaches based on the
use of x -ray radiation in the mode of a sliding beam are widely used and co ntinue to actively de velop. This paper
proposes methods for experimental and empirical determination of the thickness of the surface layer of halides,
sulfides and metal oxides. Experimentally, the thickness of the surface layer was determined from the siz e
dependence of the l uminescence of these compounds. The empirical determination of the thickness of the surface
layer is based on the established regularity that the thickness of this layer is determined by one parameter — the
atomic volume of the substan ce under investigatio n. In the proposed work, the surface layer is divided into two
layers — the layer h = d (I) and the layer h≈10d (II). At h≈10d (II), the size dependence of the physical properties
of solids begins. When h = d (I), a phase transition oc curs in the surface l ayer. In pure metals, the thickness of the
surface layer is significantly less than that of their compounds. For some compounds, the thickness of the surface
layer can reach micron values. At such values of the layer, the size dependen ce of the physical pr operties is still
observed.
Keywords: surface layer thickness, nanostructure, size effect.

38 American Scientific Journal № ( 33) / 20 20
Introduction
Atomically smooth surfaces of solids are
necessary both for basic research in the field of physical
chemistry of the surface, and for practical applica tions.
Only on an atomically smooth surface can nanoscale
structures be reproducibly created due to self -
organization phenomena during crystal growth or using
modern atomic probe methods [1]. Such nanostructures
are curren tly the subject of intensive resea rch and can
become the basis of nanoelectronics and nanophotonics
devices. The standard method for producing atomically
smooth surfaces is the method of chemical -mechanical
polishing [2]. Using this method, surfaces with a very
small roughness comparable t o the interatomic distance
can be obtained. In this case, the question arises of the
thickness of the surface layer of solids. Currently,
approaches based on the use of x -ray radiation are
widely used and are actively deve loping. Of the whole
complex of X -ray methods, reflectometry and X -ray
scattering under conditions of sliding incidence are
especially useful for studying surface layers [3].
Gibbs [4] considered the surface layer as a
geometric surface without thickness. This is
characteristic of classica l thermodynamics. For
thermodynamics of surface phenomena, the approach
of Van der Wals, Guggenheim, Rusanov is used, in
which the surface layer is considered as a layer of finite
thickness [5].
According to modern concept s [6, 7], the surface
layer is und erstood to mean an ultrathin film in
thermodynamic equilibrium with a crystalline
substrate, the properties, structure and composition of
which are different from bulk. However, the question
of the "thickness" of this film for various substances is
still o pen. In [8, 9], we proposed a method for
determining the surface tension of solids from the size
dependence of a certain physical property.
In this paper, we propose a methodology for
experimentally determining the thickne ss of the surface
layer for atomic ally smooth metals and their
compounds, based on size effects in the physical
properties of solids.
Experimental technique
For the dimensional dependence of some physical
property of a solid body A(r), we obtained the rela tions
[8, 9]:
������(�)= ������0⋅(1−�
������),�>> �
������(�)= ������0⋅(1− �
�+������),�≤ �., (1)
where A 0 is the physical property of a massive
sample, the parameter d is determined by the formula
[8]:
�= 2�������
�� , (2)
where σ is the surface tension of the sample, υ is
the molar volume of the sample, R is the gas constant,
and T is the temperature.
Most of the experiments were carried out
according to the methodology of [8]. The dependence
of the X -ray luminescence intensity of halides, sulfides
and metal oxides on the grain size of the phosphor was
studied. The X -ray luminescenc e intensity of the
samples was determined by the standard photoelectric
method. The grain size of the sample was determined
using an Epiquant metallogra phic microscope. As an
example, the dependence of I / I0 on the grain size of
alkaline earth metal halid es is shown in Fig. 1.

Figure 1 - Dependence of the relative luminescence intensity
on the grain size of the phosphor
r

In coordinates, the experimental curve is
straightened in accordance with (1), giving the value of
d in accordance with (2). This situa tion is presented in
fig. 2 and in [10]. A layer of thickness h = d is called

America n Scientific Journal № ( 33) / 20 20 39

layer (I), and a layer at h≈10 d is called layer (II) of an
ato mically smooth crystal. At h≈10 d, the size
dependence of the physical properties of the material
begins to appear and this structure is called a
nanostructure. At h = d, a phase transition occurs in the
surface layer. It is accompanied by sharp changes in
physical properties, for example, the direct Hall -Petch
effect is reversed [11].
Below are the values of the thick ness of the
surface layer (II), determined by the dependence (1)
and formula (2). Part of the results obtained by the
empirical formula :
�= 0,17 ⋅�, , (3)
where υ is the atomic volume of the material.

Figure 2 - Schematic representation of th e surface layer

Formula (3) with great accuracy (at least 5%) will
coincide with the experimental data. The thickness of
the surface layer of pure metals was determined by us
in [11].
Table 1
The thickness of the surface layer d (II) of pure metals
M d(I I), nm M d(II) , nm M d(II) , nm M d(II) , nm
Li 22 Sr 59 Sn 28 Cd 34
Na 45 Ba 66 Pb 31 Hg 18
K 77 Al 16 Se 28 Cr 12
Rb 100 Ga 20 Te 35 Mo 18
Cs 121 In 27 Cu 12 W 16
Be 8 Tl 21 Ag 17 Mn 11
Mg 24 Si 20 Au 17 Tc 14
Ca 44 Ge 24 Zn 16 Re 15

Table 2
Th e thickness of the surface layer of metal halides (M)
M d(II) ,
nm M d(II) ,
nm M d(II) ,
nm M d(II) ,
nm M d(II) ,
nm M d(II) ,
nm
LiCl 35 SrCl 2 88 SnCl 2 39 CdCl 2 77 FeCl 3 95 GdCl 3 99
NaCl 46 BaCl 2 92 PbCl 2 81 HgCl 2 85 CoCl 2 66 TbCl 3 98
KCl 64 AlCl 3 54 Se2Cl2 140 CrCl 3 94 NiCl 2 62 DyCl 3 125
RbCl 73 GaCl 2 121 TeCl 2 141 MoCl 2 76 CeCl 3 106 HoCl 3 125
CsCl 72 InCl 110 CuCl 41 WCl 6 192 PrCl 3 105 ErCl 3 113
BeCl 2 72 TlCl 58 AgCl 44 MnCl 2 72 NdCl 3 103 TmCl 3 118
MgCl 2 70 SiCl 4 195 AuCl 110 TcCl 4 123 SmCl 3 98 YbCl 3 83
CaCl 2 88 GeCl 4 194 ZnCl 2 80 ReCl 5 155 EuCl 3 98 LuCl 3 120

40 American Scientific Journal № ( 33) / 20 20
Table 3
The thickness of the surface layer of metal sulfides (M)
M d(II) ,
nm M d(II) ,
nm M d(II) ,
nm M d(II) ,
nm M d(II) ,
nm M d(II) ,
nm
Li2S 47 SrS 50 SnS 48 CdS 51 FeS 31 GdS 45
Na 2S 71 BaS 68 PbS 54 HgS 49 CoS 28 Tb 2S3 111
K2S 104 Al2S3 110 SeS 62 Cr2S3 90 NiS 29 DyS 45
Rb 2S 119 Ga 2S3 107 TeS 35 MoS 2 54 CeS 50 HoS 42
Cs 2S - In2S3 116 CuS 34 WS 2 56 Pr2S3 128 ErS 41
BeS - Tl2S3 53 Ag 2S3 58 MnS 37 NdS 48 TmS 41
MgS 36 SiS 2 - Au 2S3 95 Tc 2S7 - SmS 55 YbS 52
CaS 47 GeS 2 - ZnS 40 Re 2S7 208 EuS 55 LuS 39

Table 4
The thickness of the surface layer of metal oxides (M)
M d(II) ,
nm M d(II) ,
nm M d(II) ,
nm M d(II) ,
nm M d(II) ,
nm M d(II) ,
nm
Li2O 25 SrO 38 SnO 36 CdO 18 Fe2O3 52 Gd 2O3 34
Na 2O 46 BaO 46 PbO 40 HgO 33 CoO 20 Tb 2O3 33
K2O 68 Al2O3 44 SeO 48 Cr2O3 50 NiO 20 Dy 2O3 81
Rb 2O 79 Ga 2O3 50 TeO 48 MoO 2 34 CeO 2 41 Ho 2O3 77
Cs 2O 103 In2O3 66 CuO 22 WO 3 55 Pr2O3 81 Er2O3 75
BeO 14 Tl2O3 76 Ag 2O 56 MnO 2 30 Nd 2O3 79 Tm 2O3 76
MgO 19 SiO 2 39 Au 2O3 66 Tc 2O7 15 Sm 2O3 71 Yb 2O3 73
CaO 28 GeO 2 42 ZnO 25 Re 2O7 23 Eu 2O3 81 Lu 2O3 72

Discussion of the experimental results
The thickness of the surface layer of metal
compounds is much greater than that of atomically
smooth metals.
For compounds su ch as GaCl 2 (121 nm), InCl (110
nm), DyCl 3 (125 nm), Ga 2S3 (107 nm), In 2S3 (116 nm),
TmCl 3 (118 nm), Re 2S7 (20 8 nm) and a number of
others, the surface thickness layer exceeds 100 nm.
In all manuals and textbooks (see, for example,
[11]), the nanometer ran ge of sizes 1 –100 nm is the
“calling card” of nanostructures. It is with these sizes
that size effects begin. However, our results show that
size effects can also be observed at 208 nm (Re 2S7).
Scientific research of nano -objects began in the 19th
century, when M. Faraday (1856 -1857) obtained and
studied the properties of colloidal solutions of highly
dispersed gold and thin films based on it. The color
change noted by M. Faraday depending on the size of
the particles is perhaps the first example of the stu dy of
size effects in nano -objects. It follows from Fig. 2 that,
at h=d, an orientation phase tran sition of the λ type (Fig.
3) occurs in the nanostructure, which is associated with
the processes of reconstruction and surface relaxation
[6]. Here, the role of the temperature T, K begins to
play the size of the nanoparticle [10, 12].

Figure 3 - Schema tic representation of the λ – transition

Experimental studies of the mechanical properties
of nanomaterials have shown that the tensile strength
and hardness of many metals (Pd, Cu, Ag, Ni, etc.) are
significantly higher than in the corresponding massive

America n Scientific Journal № ( 33) / 20 20 41

analogues. An increase in hardness and strength with a
decrease in grain size to a certain critical size is
practically characteristic of all crystals. This fo llows
from the well -known Hall -Petch equation:
�������= ������М+��−1/2, (4)
где σМ – предел прочно сти монокристалла , k –
коэффициент пропорциональности .
For h=d, in particular, the Hall –Petch law is
reversed [13] and other phenomena. This is primarily
due to the size dependence of surface tension at h To describe the phase tra nsitions in
nanostructures, various models have been proposed,
among which the Landau mean field method, in which
the order parameter is used [14], can be noted. From a
thermodynamic point of view, the order parameter is
one of the parameters of the thermo dynamic syst em,
which along with parameters such as temperature T,
pressure P, volume V, etc. describe the state of the
thermodynamic system. Work in this direction is
ongoing.
However, beyond the phase transition point at h ≤
d, (with a further decrease i n the charac teristic size of
the nanostructure), the thermodynamic method
becomes inapplicable. In this size range, new physical
properties of nanostructures are observed, for e xample,
the effect of magic numbers affects [15]. Electrons
placed in a potential well at h ≤ d are not free, but
interact with each other. Therefore, the average
potential acting on a single electron differs from the
potential created only by a positive n ucleus. Taking
into account the electron – electron interaction leads to
a change in the el ectronic spectrum, however, as in the
case of atoms, the energies of single -particle states can
be approximately characterized by the same quantum
numbers if the clu ster sphericity remains sufficiently
high.
Conclusion
Based on the results of the studies, the following
conclusions can be drawn:
- the dimensional dependence of the physical
properties of crystals at sizes above 100 nm shows that
the concept of nanostruc tures may need to be changed;
- the situation is most likely similar to the situation
with macroscopic quantum effects.
The work was carried out under the program
of the Ministry of Education and Science of the
Republic of Kazakhstan. Grants No. 0118РК0000 63
and No. Ф.0781.

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