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    • From our calculations by Eq eV Difference

    2018-11-05

    From our calculations by Eq. (3)= 2.12eV. Difference between this value and other DFT calculations [52] is less than 1%. Using Eq. (4) we found that the formation of complex H–V reduces the vacancy formation buy CM-272 by 0.26eV. It is considerably higher than the average kinetic energy of atoms ∼3/2kBT = 0.039eV at 300K. The binding energies calculated by Eq. (5) for the titanium lattice are presented in Table 5. We can conclude from Table 5 that the maximum number of hydrogen atoms that can be trapped by a monovacancy in HCP titanium lattice is four. Earlier DFT calculations [51] have shown that a monovacancy in HCP titanium lattice can contain up to three these atoms. The difference between our calculations and those of Ref. [51] is explained by the simplified relaxation of initial atomic configurations of complexes used in Ref. [51] that led to a configuration in the local energy minimum. Using molecular-dynamics modeling before relaxation at 0K we obtained more energetically favorable atomic configurations with number of hydrogen atoms more than three. Trapping of hydrogen atoms by vacancies can lead to reduction of the vacancy formation energy and consequently to an increase in the vacancy concentration by several orders of magnitude as was found by Fukai in the nickel lattice for the first time [2].
    Conclusions Using density functional theory calculations, we investigated the interactions of the impurity atoms of hydrogen, carbon, nitrogen and oxygen with monovacancies in the HCP titanium and FCC aluminum lattices. The results of this work can be summarized as follows:
    Introduction Electron spectroscopy and mass spectrometry currently are by far the main tools for analyzing substances and materials. They are of great importance not only in fundamental research, but also in industry and applied science where they have extensive uses. Regardless of the type of study and object examined, it is a flux of charged particles that is subjected to analysis. For effective performance the analyzed beams should be formed according to the geometry and configuration of energy and mass analyzers [1–3]. Additionally, since it is the charged particles that carry all the information about the studied object, losses of electrons or ions should be minimized at all stages prior to their analysis, which poses the problem of creating a corpuscular-optical matching element, capable of providing the maximal yield of charged particles in the vicinity of the source and transmitting them to the analyzer input with minimal losses. This task is partially solved by using electrostatic and magnetic lens [4], but this approach involves constructing a rectilinear path, which in turn increases the overall size of the system. Using mirrors or various deflecting systems is not entirely satisfactory, since it is not always possible to provide the desired particle flux configuration. This study demonstrates an approach to synthesizing devices that serve as both turning units and lenses focusing and transporting beams. Successful search for such systems has been carried out based on the scientific ideology of inverse dynamics problems, with the analytical theory for this ideology developed by professor Golikov (St. Petersburg Polytechnic University). This ideology has found its practical implementation in the design of devices with record-breaking performance and unique features [5].
    Problem statement In its most general form, the problem is formulated as the need to deliver the beam of analyzed particles from point A to point B. Additional requirements may also be imposed on organizing the particle packet in the analyzer input, for example, a packet with a fixed angular spread.
    Conformal transformation of coordinates The scientific ideology of the concept of conformal coordinate transformation in the Hamilton–Jacobi equation and its application to the synthesis of electrostatic fields combining perfect focusing in the plane of symmetry and energy dispersive properties have been described in Ref. [6]. Golikov was the first to propose this conversion algorithm for potential structures and to later put into practice the synthesis of corpuscular-optical systems [5]. Let us establish the main points of this method and provide the necessary commentary to the terms and equations used.