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THE THICKNESS OF THE SURFACE LAYER OF DIAMONDS
YUROV VICTOR MIKHAILOVICH
Candidate of phys.-math. sciences, associate professor, Vostok LLP, Karaganda, Kazakhstan
ZHANGOZIN KANAT NAKOSHEVICH
Candidate of phys.-math. sciences, associate professor, Vostok LLP, Ust-Kamenogorsk,
Kazakhstan
GONCHARENKO VLADIMIR IVANOVICH
Doctor of technical sciences, professor, Moscow Aviation Institute, Moscow, Russia
OLESHKO VLADIMIR STANISLAVOVICH
Candidate of technical sciences, associate professor, Moscow Aviation Institute, Moscow, Russia
Abstract: a model of a surface layer of diamond is proposed, which occurs due to the reconstruction of its surface. The surface layer of diamond consists of two parts - R(I) and R(II). At the same time, R(II) ~ 9R(I), and R(I) depends on the molar mass and density of the diamond. The total thickness of the surface layer of diamond H(hki) is from 3 nm for the plane (100) to 7 nm for the plane (111) and is a nanostructure in which dimensional effects of the collective type occur. Between the surface layer and the rest of the crystal there are large internal stresses, leading to diamond-graphite hybrids with sp3x-hybridization. The surface energy of the H(hkl) layer is three times less than that of the rest of the volume, the strength of the surface layer is three times less than that of the rest of the volume. This effect is used by jewelers, I polish diamond diamonds. The fact that in the surface layer of the diamond is located graphite follows from the fact that it is a "cost" to turn the diamond into graphite when it is heated to temperatures of2000-3000 °C without oxygen access.
Key words: diamond, graphite, surface layer, nanostructure, surface.
Introduction
There are two approaches to today: Gibbs approach [1], in which the surface layer is conditionally considered as a geometric surface that does not have thickness; The approach of Van-Der Vaals, Guuggenheim, Rusanov, in which the surface layer is considered as a layer of final thickness [2]. According to modern representations [3], a super thin film (surface layer), which is in an equilibrium state with a crystalline base (substrate), the properties and structure of which are different from volumetric properties, is understood as a superficial phase. However, the question of the theoretical "thickness" of this surface layer for various substances until 2018 remained open. Only after our works [4, 5] became clear how theoretically could it determine the thickness of the surface layer, which plays a large role in nanotechnology [6].
In the work [4, 5], for the first thickness of the R(I) of the surface layer, we received:
R(I) = 0,17-10-9-a-u (m) . (1)
Schematically this model is presented in Fig. 1a [7]. Equation (1) shows that R(I) is determined by one parameter - a molar (atomic) volume of the element (u = M/p, M - molar mass (kg/mol), p - density (kg/m3), a =1 mol/m2, in order to preserve the size of the values), which periodically changes in line with the table D.I. Mendeleev (Fig. 1b) [7].
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\»rfm* Imrr Kilfh
~ ~ f w -Ч» -w «<4, <v Л/ /v 'и 'J "^j- Л» Л/ ^ -V Л/ «V <v л< -v -v -v л/ <v JV ^V JV JV JV ЛУ ^ JV ~ ~ ~ ~ ~ ~ ~ '^Sr- • i V /V iV v Л/ л. w V Л. у Лг *V -y A. Inanition later
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а)
b)
Figure 1. Schematic image of the surface layer (a), periodic change in the atomic volume of elements (b) [7].
[8] shows that with an accuracy of 3% performed:
y = 7,016-10-4 • Tm [J/m2], (2)
where y is surface energy (J/m2), Tm is the melting temperature of the solid body (K).
For accounting for anisotropy, ratios were used [9]:
Fd3m, Z = 8, 1100 = R(I)/2, 1110 = R(I)/V2, 1m = 2R(I)/V3 (3)
In this article, we determine the thickness of the surface layer of a typical diamond and how this characteristic is associated with their fundamental properties.
Model, results and their discussion
The properties of diamond and literature on it are given in the works [10-12]. Modern ideas about the genesis of diamonds were set out in the work [13]. Carbon atoms in diamond have an ultraresistant connection, which determines the already known properties of the diamond: abnormal hardness; resistance to an aggressive chemical environment (alkalis and acid); fragility. The paradox of the diamond is that, on the one hand, this is the most durable mineral on the planet. But on the other, it is very fragile and it is easy to damage it with a strong blow. The structure of the diamond consists completely of carbon (Fig. 2a) and belongs to the symmetry of Fd3m. The lattice parameter a = 0.35667 nm, melting temperature (today) Tm = 4300 K, density p = 3.52 (g/cm3), molar mass M = 12.01 (g/mol) [10]. The work [14] depicts all the known forms of the existence of free carbon in the form of a circuit-triangle (Fig. 2b), in the vertices of which there are chemical compounds, which are characterized by one type of hybridization of carbon atom (sp, sp2 or sp3). The phase diagram of the carbon of bandits is shown in Fig. 2c [15].
а)
b)
c)
Figure 2. Elementary diamond cell (a); a schematic image of allotropie modifications of carbon (b) [14]; The phase diagram of carbon bands (c) [15].
Using the formula (1), we calculate the parameters of the diamond.
Table 1. Diamond structure parameters
Diamond (hkl) Structure R(I), nm R(II), nm Y, [16] mJ/m2 Tm, К (2)
С 100 Fd3m 0,29 (1) 2,61 (7) 9100 13000
110 0,41(1) 3,69 (7) 6274 8963
111 0,68 (1) 6,12 (7) 5270 7529
In brackets, the number of monolayers in the layers R(I) and R(II) is given, where n = rhkl/ahkl (a - constant crystal lattices). The surface energy of у was calculated in the work of Harkins [16], published back in 1942, theoretically on the basis of the thermodynamics of Gibbs. Assuming the energy of the C-C communication in a diamond equal to 90 kcal/mol, and the energy of the diamond coghesia is equal to doubled surface energy, it received the value of yhkl, shown in the table. 1.
The results of the experimental measurement of the surface energy of the diamond by the Griffith method were carried out in 2017 in [17] along the plane (111) and gave the following result - Y(111) = (4999 ± 355) mJ/m2, which is not very different from Harkins. In the last column table. 1 shows Tm, calculated according to the formula (2). These values are 2-3 times different from the current values of Tm = 4300 K. The empirical formula (2) was determined based on data from 54 elements from the D.I. Mendeleev.
Such a discrepancy in the melting temperature of the diamond is due to the fact that it is problematic to measure Tm diamond to date. In the air, the diamond burns at a temperature of 8501000 °C, and when heated to temperatures about 1800-2000 °C without air access, the diamond passes into graphite. From Fig. 2C it follows that the diamond is a phase of high pressure and its Tm below 5000 K. Most experiments on quasistatic ("slow") heating show melting temperatures close to 4000 K, while submicrosecond heating gives temperatures above 6500 K [17].
From the table. 1 It follows that the number of carbon monofrys in the layer R (I) diamond is equal to one, like graphene. The total thickness of the surface layer H = R(I) + R(II) is equal to: H«i00» = 2.9 nm; Н«ш» = 4.1 nm; Н«ш» = 6.8 nm. The work [18] shows that with the size of the surface layer of less than 6-8 layers of the energy of quantum states, it changes in a stepped way.
Moreover, each step includes appropriate quantum states. This means that the surface layer H(hkl) is a nanostructure where the dimensional effects of the collective type occur [19].
Many authors [10] believe that the physical characteristics of the surface layer should not differ from the characteristics of the volumetric part of the crystal. However, most authors and we also believe that the characteristics of the surface layer have obvious distinctive features from the properties of the volume. These features are clearly detected by photoluminescence and are not due to the origin of the diamond (Fig. 3) [20].
Figure 3. Photoluminescence of various samples of diamond [20].
From Fig. 3 shows that the surface layer of diamond differs sharply in properties from the rest of the crystal. In this layer, which is in contact with the external environment or vacuum, large internal stresses occur, which lead to a large number of defects and nanotreshchins [21]. There it was also obtained that the surface energy of the layer N is three times less than that of the rest of the volume, the strength of the surface layer is three times less than that of the rest of the volume: W = Y S (s is the area of diamond). This effect is used by jewelers, I polish diamonds to diamonds - Fig. 4.
1
a) b)
Figure 4. The diamond plate «111»: Ra = 0.12 nm, Rq = 0.15 nm (a); Ra = 0.27 nm, Rq = 0.34
nm, Ry = 3.09 nm (b) [22].
As indicated above, the surface layer of diamond Цш) is a nanostructure, the first review of which was made in 2003 [23] and the last review in 2022 [24, 25]. The internal stresses in the H(hki) layer occur due to the reconstruction of the surface of the diamond due to the difference between the properties of surface atoms from atoms in the volume of the crystal (Fig. 5). Reconstruction has two types: conservative and unconditional. An example of the first is the mating of superficial atoms with the formation of dimers, and the second is the formation of a new phase with a different
type of symmetry of a crystal lattice in the upper surface layer of the new phase than in volume.
oo oo oo o o o o o o o o o o o o o o o o o o
reconstruction
Figure 5. Reconstruction of the surface of the crystal.
In the work [26], we showed that to divide the layer H(hkl) from the rest of the crystal, we need to spend energy called the energy of adhesion:
Wa — Yi + У2 - Yi2 ~ Yi +У2 — 1-3Y2,
(4)
where 71, 72 and 712 is the surface energy of the layer H(hkl), volume and interface border, respectively; 712 = 0, due to the phase transition II of the kind, and yi = 0.3 72.
The internal stresses O(hkl) between the phases 71 and 72 are calculated by the formula [27]:
• Ä/H
(hkl) ^ a (hkl) J
where E is the Yung module (for the natural diamond E = 825 GPA).
The elastic parameters of the surface layer of diamond are shown in table. 2.
(5)
Table 2. Properties of the surface layer of diamond
Diamond (hkl) H(hki), nm Wa, J/m2 G(hki), GPa
С 100 2,9 11,83 58
110 4,1 8,16 41
111 6,8 6,85 29
From the table 2 it follows that the high internal stresses О(Ш) lead to the formation in the underly layer of the new phase with a different type of symmetry of the crystal lattice than in volume. This is also indicated by Fig. 3, where the luminescence of the surface layer differs sharply from the luminescence of the volume. Since the structure of the diamond (with the exception of impurity defects) is only a carbon atom, it is it that is able to create a new phase-diamond-graphite hybrids with sp3-x-hybridization [28]. Grates of graphite and diamond can be considered as carbon atoms built from hexagonal rings, flat in both types of graphite, but folded in the form of a boat for hexagonal diamond and a S-shaped form or a stool for cubic diamond [28]. The fact that in the surface layer of the diamond is the graphite follows from the fact that it is a "cost" to turn the diamond into graphite when it is heated to temperatures of 2000-3000 °C without oxygen access [10].
In [29], the process of graphitization is divided into four stages:
1. The formation of the graphicized layer on the surface of the diamond during heat treatment at a temperature above 900 °С due to interaction with oxygen molecules.
2. The formation of grades of graphite in the size of 5-10 nm on the surface of the diamond.
3. Migration of grades of graphite on the surface of the diamond and the formation of a nest with increased density of aggregated nuclei in size of 10-100 nm.
4. The development of graphitization from aggregated embryos along the rhomboid planes {211}; Formation of figures of graphitization. The graphite figure {0001} has the same superficial density as the rhomboid plane {211}; This contributes to the formation of graphite {0001} along the rhomboid plane {211}.
In our case, the surface layer of diamond is diamond-graphite hybrids with sp3-x hybridization
and their size for atomically smooth diamond ranges from 3 to 7 nm. At the same time, it is not taken into account that in the surface layer of diamond there is a change in the density of the diamond material due to an increase in ground and impurity defects. There are ten varieties of diamonds in nature [30], each of which has its own surface layer. GOSTs for polished and industrial diamonds are given separately [31, 32].
Conclusion
All information about the behavior of a diamond in the external environment and under various influences on the diamond (grinding, polishing, laser ablation, etc.) occurs through its surface and surface layer. Knowledge of the structure and properties of the surface layer is necessary for such a field as the physics of nanodiamonds, where surface properties play a decisive role. The model we presented for the surface layer of diamond can serve as a basis for studying the properties of nanodiamonds.
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