Американский Научный Журнал EXPERIMENTAL DETERMINATION OF THE THICKNESS OF THE SURFACE LAYER IN THE PHYSICS OF NANOSTRUCTURES (32-36)

Atomically smooth surfaces of solids, especially semiconductors, are urgently needed to study the fundamental nature of surface phenomena. They are also needed in the manufacture of modern semiconductor devices. It is believed that only on atomically smooth surfaces can nanostructures be created that undergo crystal self-organization during crystal growth. In this paper, we consider methods for experimental determination of the thickness of the surface layer, surface tension, and the melting temperature of nanostructures of dielectrics, magnetic materials, metals, and alloys. The X-ray luminescence intensity of dielectrics was determined by the standard photoelectric method. Specific magnetization was measured using a vibrating magnetometer. The electrical conductivity of a metal or alloy film was determined using a standard three-electrode circuit. The use of Patents and utility model descriptions for patents provides simple formulas for calculating or experimentally determining the thickness of the surface layer, surface tension and the melting temperature of American Scientific Journal № (39) / 2020 33 nanostructures of dielectrics, magnetic materials, metals and alloys. The experimental determination of these values will allow you to control the technological processes of obtaining nanomaterials from any materials with desired properties. Скачать в формате PDF
32 American Scientific Journal № ( 39 ) / 2020
Candidate of Sciences in Physics and Mathemat ics
V.A. Rantsev - Kartinov.
Conclusion
And, of course, I would like to express my sincere
gratitude and deep appreciation to my teachers,
outstanding scientists, senior fellows, and colleagues at
my previous job who have already passed away, to
Academicia n A.P. Aleksandrov and Academician,
Nobel Laureate in physics A.M. Prokhorov, who not
only explained to me the scale of what I have
discovered in physics and what to do next, but also
the peculiarities of my
future fate: they told me: “Keep in mind, a pers on
ahead of his time, waiting for its arrival in
uncomfortable conditions and remember for life the
following prophetic words of the great Russian scientist
V.I. Vernadsky: “The whole history of science at every
step shows that individuals were more right in their
statements than entire corporations of scientists or
hundreds and thousands of researchers adhering to
prevailing views... Undoubtedly, in our time the most
true, most correct, and deepest scientific worldview lies
among some individual scientists or small groups of
researchers whose opinions do not attract our attention
or excite our dissatisfaction or denial." These
instructions allowed me to withstand the blows of
scientific fate and continue my scientific work.
In my heart, a memory will always be kept off my
friend, a wonderful scientist, and just a wise man, PhD
in Physics & Mathematics - Rumiantsev A. A.
Finally, I would like to express my heartfelt
gratitude to PhD in Engineering V.M. Tiutiunnik and
Candidate of Sciences in Physics and Mathe matics
V.A. Rantsev - Kartinov for the joint work on universal
industrial modules of disintegrators/activators.

References
1. A.V. Kulakov, A.A. Rumiantsev.
Spontaneous magnetization of plasma of quantum
origin, Journ al of Technical Physics, 1988, Volume 58,
Issue 4, p. 657 - 660.
2. A.V. Kulakov, E.V. Orlenko, A.A.
Rumiantsev. Quantum exchange forces in condensed
matter, Moscow, Nauka Publishing House, 1990.
3. A.V. Kulakov, A.A. Rumiantsev. Ball
lightning as a quantum condensate, Reports of the
Academy of Sciences of USSR, Physics, 1991. Volume
320, No. 5, p. 103 -1106.
4. A.V. Kulakov, V.M. Tiutiunnik. Solid phase
plasma ultraviolet laser, International Journal of
Advanced Research, 2017, Vol. 5(4), pp.271 -273.
5. A.V . Kulakov, V.A. Rantsev -Kartinov.
Experimental confirma tion of the existence of plasma
quantum condensate, Izvestia RAS. Energetics, 2015,
No.1, p. 46-61.
6. A.V. Kulakov, A.A. Rumiantsev. Generation
of high -energy particles by MPD shock turbulence,
Journal of Technical Physics, 1979. Volume 49, Issue
10, p. 2127 -2132
7. A.V. Kulakov. Quantum plasma condensate as
a new source of electric energy. MHD - generator with
plasma separation. International Journal of Advanced
Research -2017 - Res. 5(8).2004 -2011.
8. A.V. Kulakov. Quantum non -ideal plasma as
a source of heat ener gy. Plasma fuel combustion
International Journal of Current Research. - 2017. -Vol.
9. P.6. P.53361 -53365.
9. V.A. Rantsev -Kartinov, A.V. Kulakov.
Universal mod ule of industrial
disintegrators/activators, Utility Model Patent No.
161751, Bulletin of the Federa l Service for Intellectual
Property, Patents, and Trademarks No. 13, dated
05/10/2016
10. A.V. Kulakov, V.A. Rantsev -Kartinov.
Eurasian patent for invention No. 029979 Device for a
universal module of industrial disintegrators/activators
June 29, 2018.
11. P.L. Ka pitsa. Why is fame needed?, Priroda
Magazine, 1994, No. 4 (944)
12. А.V. Kulakov, V.A. Rantsev -Kartinov, and
V.M. Tiutiunnik. Application of universal
multipurpose modules of industrial disintegrator -
activators for the processing of cereals and potatoes into
starch products International Journal of Advanced
Researc.2017 Res 5(5).1759 -1762
13. A.V. Kulakov. Quantum plasma condensate.
Cold nuclear fu sion. New nano - technologies.
LAMBERT Academic Publishing. 2019

EXPERIMENTAL DETERMINATION OF THE THICKNESS OF THE SU RFACE LAYER
IN THE PHYSICS OF NANOSTRUCTURES

Yurov V.M.
Karaganda State University. named after E.A Buketov

Abstract . Atomically smooth surfaces of solids, especially semiconductors, are urgently needed to study the
fundamental nature of surface phenomen a. They are also needed in the manufacture of modern semiconductor
devices. It is believed that only on atomically smooth surfaces can nanostructures be created that undergo crystal
self -organization during crystal growth.
In this paper, we consider method s for experimental determination of the thickn ess of the surface layer,
surface tension, and the melting temperature of nanostructures of dielectrics, magnetic materials, metals, and
alloys.
The X -ray luminescence intensity of dielectrics was determined by the standard photoelectric method.
Specific m agnetization was measured using a vibrating magnetometer. The electrical conductivity of a metal or
alloy film was determined using a standard three -electrode circuit.
The use of Patents and utility model descr iptions for patents provides simple formulas f or calculating or
experimentally determining the thickness of the surface layer, surface tension and the melting temperature of

American Scientific Journal № ( 39 ) / 2020 33

nanostructures of dielectrics, magnetic materials, metals and alloys. The experime ntal determination of these
values will allow you to control the technological processes of obtaining nanomaterials from any materials with
desired properties.
Keywords. Surface tension, surface layer thickness, size effect, melting point, nanostructure.


Introduction. Atomically smooth surfaces of
solids, especially semiconductors, are urgently needed
to study the fundamental nature of surface phenomena
[1-4]. They are also needed in the manufacture of
modern semiconductor devices [5]. It is believed tha t
only on atomically smooth surfaces can nanostr uctures
be created that undergo crystal self -organization during
crystal growth [6, 7]. The atomic -smooth surfaces of
solids began to be studied recently because of the rapid
growth of nanotechnology (see, fo r example, [8 –10]).
In this post, we consider at omically smooth
nanostructures based on our works [11, 12], paying
attention to Patents.
Description of the model. In [11], the proposed
model of the surface layer of atomically smooth metals
is generalized. The surface layer of an atomically
smooth metal consists of two layers - d(I) and d(II). A
layer with h = d is called layer (I), and a layer at h≈10d
is called layer (II) of an atomically smooth crystal. At
h≈10d, the size dependence of the physical proper ties
of the material begins to appear. To determ ine the
thickness of the surface layer, we used the size
dependence of the physical property A(r) [11]:
()= 0⋅(1−d/r ),>> d, ()= 0⋅(1−d/d +),≤ d. (1)

The parameter d is related to the su rface tension σ
by the formula:
�= 2σ�/RT . (2)
Here σ is the surface tension of a massive sample;
υ is the volume of one mole; R is the gas constant; T is
the temperature. It was shown in [11] that, to within
3%,:
= 0,7 ⋅10−3⋅�, (3)
where T m is the melting point of a solid (K). The
ratio holds for all metals and for crystalline compounds.
At T = T m, we obtain:
�()= 0,17 ⋅10−3�. (4)
Equation (4) shows that the thickness of the
surface layer d (I) is determined by one fundamental
parameter - the molar (atomic) volume of the element
(υ = M/ ρ, M is the molar mass (g/mol), ρ is the density
(g/cm 3).
For a number of metals, the value of d(I) is
presented in table. 1.
The thickness of the surface layer d(I) of pure
metals at a temperature close to the melting temperature
ranges from 0.8 nm (Be) to 12.1 (Cs) nm, i.e. refers to
the nanostructure. This layer thickness can be
experimentally determined by the method of sliding
scattering of x -rays in internal ref lection. For gold, this
layer thickness i s 1.2 nm at room temperature [13],
which coincides with thermal expansion with its value
from the table. 1 - d(I) = 1.7 nm.
Table 1
The thickness of the surface layer d(I) of some pure metals (Me)
Me d(I), nm Me d(I),
nm Me d(I), nm Me d(I),
nm Me d(I), nm Me d(I), nm
Li 2,2 Sr 5,9 Sn 2,8 Cd 3,4 Fe 1,2 Gd 3,4
Na 4,5 Ba 6,6 Pb 3,1 Hg 1,8 Co 1,1 Tb 3,3
K 7,7 Al 1,6 Se 2,8 Cr 1,2 Ni 1,1 Dy 3,3
Rb 10 ,0 Ga 2,0 Te 3,5 Mo 1,8 Ce 3,6 Ho 3,2
Cs 12,1 In 2,7 Cu 1,2 W 1,6 Pr 3,5 Er 3,2
Be 0,8 Tl 2,4 Ag 1,7 Mn 1,1 Nd 3,4 Tm 3,1
Mg 2,4 Si 2,1 Au 1,7 Tc 1,4 Sm 3,4 Yb 4,2
Ca 4,4 Ge 2,4 Zn 1,6 Re 1,5 Eu 5,0 Lu 3,0
In the d(I) layer with pure metal atoms,
reconstruction and relaxation associated with surface
rearrangement occur [13]. For gold, the lattice constant
is a = 0.41 nm and the surface is rearranged at a distance
of three atomic monolayers.
Determination of the thickness of the surface
layer, surface tension, and the melting temperature
of dielectric nanostructures [14 –16].
The method was used to determine the surface
tension of dielectric KCl crystals. The X -ray
luminescence intensity was determined by the standard
photoelectric method. The dielectric grain size was
determined using a MIM -8 type metal lographic
microscope. The results are shown in Figure 1.
In the coordinates A(r) = I ~ 1/r, the experimental
curve is straightened in accordance with (1), giving a
value of d = 6.4 nm. For KCl, υ = 37.63 cm3 / mol and
from (2) for surface tension it was o btained: σ = 0.734
J/m 2. A value of d = 6.4 nm gives us a thickness of d(I).
Substituting the parameter d into formula (1) and taking
the value of T0 from the reference book, we determine
the melting temperature of KCl nanoparticles. The
results for KCl na noparticles of various radii are given
in table. 1. Parti cles r = 1 nm of potassium chloride are
unstable at room temperature (300 K). Using the
claimed method will allow to control the technological
processes of obtaining dielectric materials of micro -
and nanoelectronics with desired properties and
products f rom them.

34 American Scientific Journal № ( 39 ) / 2020
Figure 1 - Dependence of the intensity of X -ray luminescence KCl on the grain size of the phosphor
Table 1 - Melting point of KCl nanoparticles

dielectric Т0, К d, nm Т(r) , К
r = 1 nm Т(r) , К
r = 1 0 nm
Т(r) , К
r = 5 0 nm
KCl 1043 6,4 208,6 745,0 965,7

Determination of the thickness of the surface
layer and the surface tension of magnetic
nanostructures [17, 18]. In this case, the measured
surface tangent of the magnetic susceptibility of the
magnetic material versus the inverse radius of i ts
par ticles calculates its surface tension. The dependence
of the magnetic susceptibility of the magnetic material
on the particle size is also described by formulas (1) and
(2). The constructed dependence in the coordinates
A(r)=æ (is the inverse radius of par ticles, magnetic
material), we obtain a straight line, the tangent of the
angle of inclination, which determines d, and the
surface tension of the magnetic material ( σ) is
calculated by formula (2). The method was used to
determine the surface tensio n of m agnetites of the
Sokolovsky deposits. Specific magnetization was
measured using a vibrating magnetometer. The grain
size of magnetite was determined using a
metallographic microscope. The results are shown in
fig. 2. In coordinates æ, the experimenta l curv e is
straightened in accordance with formula (1), giving a
value of d=0.36 μm. For magnetite υ=44.5 cm 3/mol,
and from relation (2) for surface tension it was
obtained: σ=10.1 10 3 erg/cm.

Figure 2 Relative magnetic permeability versus radius (a) and inv erse radius (b) of magnetite particles

American Scientific Journal № ( 39 ) / 2020 35

Calculations using the formulas of the theory of
magnetism using experimental values of saturation
magnetization yielded a value of σ = 10.1 10 3 erg/cm,
which practically coincides with the above. The
formu las of the theory of magnetism, however, are
applicable for a limited number of materials, while the
proposed method allows one to determine σ
experimentally for any magnetic minerals.
Determination of the thickness of the surface
layer and the melting tem perature o f
nanostructures of metals and alloys [19 -21].
The dependence of the electrical conductivity σ
and the dielectric constant ε of the material on the film
thickness h is also described by a formula of the type
(1) (Figure 3). The constructed depend ence in th e
coordinates A(r) = σ ~ 1/h(1/h is the inverse thickness
of the metal or alloy film) is a straight line, the slope
that determines d - the thickness of the surface layer of
the metal or alloy. The proposed method has no
analogues and allows you to determi ne the most
important characteristic of metals and alloys - the
thickness of the surface layer, which determines the
operational properties of metals and alloys and
products from them, allows you to purposefully create
new structural materials.

Figure 3 - Generalized dependence of electrical conductivity on the size of a small particle

The method was used to determine the thickness
of the surface layer of metals: copper, zinc, aluminum,
tin, lead, gold, silver and alloys: 10% copper -90% tin.
20% zinc -80% aluminum, 15% tin - 85% lead.
A metal or alloy film was deposited thermally in
vacuum on a VUP -5 vacuum unit on a quartz one. Film
thickness was determined using a JEOL JSM -5910
microscope. The electrical conductivity of the met al
film was deter mined using a standard three -electrode
circuit, or by the method of [22]. The results of
determining the thickness of the surface layer are given
in table. 2.
The melting point of a nanoparticle of radius R is
determined by the formula:
()= 0⋅(1− �
�+), (5)
where T 0 is the melting temperature of a massive
sample of a metal or alloy, which is experimentally
determined for all pure metals and for most alloys and
is presented in numerous reference books. The method
was used to dete rmine the melting temperature of metal
nanoparticles: zinc, aluminum, tin, lead, copper, gold,
silver. Substituting the parameter d from Table 2 into
formula (5) and taking the value of T 0 from the
directory, we determine the melting point of the metal
nan oparticle s. The results for nanoparticles of various
radii are given in table. 3.
Table 2
The thickness of the surface layer of metals and alloys
Metal or alloy d, nm Metal or alloy d, nm
Cu 1,2 Au 1,7
Zn 1,6 Ag 1,7
Al 1,6 10 % Cu -90% Sn 2,03
Sn 2,8 20% Zn -80% Al 2,06
Pb 3.1 15% Sn - 85% Pb 2,51
Table 3
The melting point of pure metal nanoparticles
Metal Т0, К d, nm Т(R) , К
R = 1 nm Т(R) , К
R = 1 0 nm
Т(R) , К
R = 5 0 nm
Zn 693 1,6 277 ,2 602,6 672,8
Al 933 1,6 291 ,6 764,8 933,0
Sn 505 2,8 168,3 420,8 485, 6
Pb 600 3,1 166,7 600,0 600,0
Cu 1356 1,2 411 ,0 1102,4 1296,4
Ag 1234 1,7 301,0 942,0 1162,0
Au 1336 1,7 310,7 1004,5 1253,3

36 American Scientific Journal № ( 39 ) / 2020
In the widely known and often cited paper [23], an
experimental value of the melting temperature of 305 –
310 K was obtained f or gold nanoparticles 1 nm in size,
which practically coincides with our value. This is in
favor of the proposed method for determining the
melting temperature of nanoparticles.
Using the claimed method will allow to control the
tec hnological processes of obtaining nanomaterials
from metals and alloys with desired properties.
Conclusion
The use of Patents and the utility model
descriptions for a patent [14 -21] provides simple
formulas for calculating or experimentally determining
the thickness of the surfac e layer, surface tension and
the melting temperature of nanostructures of
dielectri cs, magnetic materials, metals and alloys. The
experimental determination of these values will allow
you to control the technological processes of obtaining
nanomaterials from any materials with desired
properties. Further research prospects relate to th e
study of physical and chemical processes in
nanostructures of various compositions.
The work was carried out under the program
of the Ministry of Education and Science of the
Republic of Kazakhstan. Grants No. 0118РК000063
and No. Ф.0781.

References
1. Li J., Schneider W. -D., Berndt R., Crampin S..
Electron confinement to nanoscale Ag islands on
Ag(111): a quantitative study. // Phys. Rev. Lett. –
1998, V. 80. - P. 3332 -3335.
2. Stipe B.C., Rezaei M.A., Ho W.. Inducing and
viewing the rotational motion of a si ngle molecule. //
Sci. Rep., 1998, V. 279. - P. 1907 -1909.
3. Kalff F.E., Rebergen M.P., Fahrenfort E.,
Girovsky J., Toskovic R., Lado J.L., Fernandez -Rossier
J., Otte A.F. A k ilobyte rewritable atomic memory. //
Nat. Nanotechnol. Lett., 2016, V. 11. - P. 926 -930.
4. Drost R., Ojanen T., Harju A., Liljeroth P.
Topological states in engineered atomic lattices. // Nat.
Phys. Lett., 2017, V. 13. - P. 668 -672.
5. Karkare S., Bazarov I.. E ffects of surface
nonuniformities on the mean transverse energy from
photocathodes. // Phys. Rev. Appl., 2015, V. 4. - P.
024015.
6. Teichert C. Self -organization of
nanostructures in semiconductor heteroepitaxy. // Phys.
Rep., 2002, V. 365. - P. 335 -432.
7. Xu F., Huang P.W., Huang J.H., Lee W.N.,
Chin T.S., Ku H.C., Du Y.W.. Self-assembly and
magnetic properties of MnAs nanowires on GaAs(001)
substrate. // J. Appl. Phys., 2010 , V. 107. - P. 063909.
8. Odinokova E.V., Panfilov Yu.V., Yurchenko
P.I. Prospects for ob taining nanometer surface
roughness by the ion beam method. // Engine ering
Journal: Science and Innovation, 2013, no. 6. URL:
http://engjournal.ru/catalog/nano/hidden/801.html.
9. Zakharov P.V., Korznikova E.A., Dmitriev
S.V. Discrete breathers near the surfa ce of the Pt 3Al
intermetallic alloy // Materials Physics and Mechanics,
2017, V. 33. - P. 69 -79.
10. Kazantsev D.M. Modeling of processes of
thermal smoothing and disordering of the surface of
semiconductors. - Diss. Candidate Phys. -Math.
Sciences, Novosibirsk , 2018 . -- 112 p.
11. Yurov V.M. The thickness of the surface lay er
of atomically smooth crystals // Physicochemical
aspects of the study of clusters, nanostructures and
nanomaterials, 2019, Vol. 11. - P. 389 -397 .
12. Yurov V.M. The inverse Hall -Petch effect in
atomically smooth metals // LXVI International
Scientific Readi ngs (in memory of L.D. Landau): a
collection of articles at the International Scientific and
Practical Conference (Moscow, 02.22.2020). -
Moscow: EFIR, 2020. - P. 17 -22.
13. Oura K., Lifshits V.G., S aranin A.A.,
Zotov A.V., Katayama M. .. Introduction to surfa ce
physics. M .: Nauka, 2006. - 490 p.
14. Yurov V.M., Portnov V.S., Puzeeva M.P. A
method of measuring surface tension and density of
surface states of dielectrics. Pat. 58155, Republic of
Kazakhsta n, publ. 12/15/2008, Bull. Number 12.
15. Yurov V.M., Guchenko S. A., Laurinas V.Ch.,
Zavatskaya O.N. Method for measuring the thickness
of the surface layer of dielectrics // Description of the
utility model for the patent, No. 3748, Publ.
03/07/2019, bull. No . 10.
16. Yurov V.M., Guchenko S.A., Laurinas V.Ch.,
Zavatskaya O .N. A method for determining the melting
temperature of dielectric nanoparticles // Description of
the utility model for the patent, No. 3749, Publ.
03/07/2019, bull. Number 10 .
17. Yurov V.M., Portn ov V.S., Puzeeva M.P. A
method of measuring the surface tensi on of magnetic
materials. Pat. 58158 Republic of Kazakhstan. Publ.
12/15/2008, Bull. Number 12.
18. Yurov V.M., Guchenko S.A., Laurinas V.Ch.
A method of measuring the thickness of the surface
layer of magnetic materials // Description of the utility
model for the patent, No. 3747, Publ. 03/07/2019, bull.
No. 10.
19. Yurov V.M., Guchenko S.A., Ibraev N.Kh. A
method of measuring the surface tension of deposited
coatings. Pat. 66095 Republic of Kazakhstan, publ.
11/15/2010, Bull. Number 11.
20. Yurov V.M., Guchenko S.A., Laurinas V.Ch.
The method of measuring the thickness of the surface
layer of metals and alloys // Description of the utility
model for the patent, No. 3751, Publ. 03/07/2019, bull.
No. 10.
21. Yurov V.M., Guchenko S.A., Laurinas V.Ch.,
Zavatskaya O.N. A metho d for determining the melting
temperature of nanoparticles of metals and alloys //
Description of the utility model for the patent, No.
3750, Publ. 03/07/2019, bull. Number 10 .
22. Surin Yu.V., Shimk o V.N., Matveev V.V.
Non -contact method for measuring the res istivity of
wafers of semiconductors and epitaxial layers //
Zavodskaya Lab, 1966, v.32, No. 9. - P.1086 -1088.
23. Buffat Ph., Borel J. -P. Size effect on the
melting temperature of gold particles // Phys. Rev . A,
1976, V.13, №6. – P. 2287 -2298.