CC BY
17
UDC 538.911
DOI: 10.20310/1810-0198-2016-21-3-845-849
STRUCTURAL TRANSFORMATIONS IN Pt NANOWIRES UNDER UNIAXIAL TENSILE STRAIN IN DIRECTION <001> AT LOW TEMPERATURE
© M.M. Aish12), M.D. Starostenkov2)
1) Physics Department, Faculty of Science, Menoufia University, Menoufia, Egypt, e-mail: [email protected] 2) I.I. Polzunov Altai State Technical University, Barnaul, Russian Federation, e-mail: [email protected]
In the paper feature of atomic transformation was considered of Pt nanowires during dynamic deformation. The transformation of atomic planes displacements and defects forming during tension has been studied. The investigation was revealed three main deformation processes, Quasi-elastic deformation, slipping and alloy fracture. Every stage is characterized by behavior of stored energy curve and some types of defects appearance. Vacancies, Frenkel pairs and interstitial atoms were found during first stage. Atomic displacement, dislocation, antiphase boundary and grain boundary forming were occurred during second stage. During third stage twin's creation from grain boundaries has occurred. Key words: Pt nanowires; dynamic deformation; slip; fracture; tension; Vacancies and Frenkel pairs.
Platinum nanowires and its alloys are used in instrumentation, electronics, electrical and jewelry. Platinum is indispensable for modern electrical, automation, remote control, radio, and precise instrument because of stability of electric, thermoelectric and its mechanical properties. The scientific literature has paid much attention to the study of nanomaterials. Nowadays, there is a large variety of the unique properties of nano-objects which can be used in the design and development of new materials. Nano-wires and nanotubes are determined in the groups of nano-structures and nanomaterials. Nanowires based on ordered alloys and intermetallic compounds are an interesting group of nanomaterials for their research. Major studies of metallic nanowires are devoted to the study of the influence of the configuration and structure of nanowires on the physical and mechanical properties. There are a number of publications on the mechanical properties of Ni nanowires in literature [1-5; 10-11].
MATHEMATICAL AND COMPUTER SIMULATION MODEL
Molecular Dynamics (MD) simulations have been carried out on pure Platinum with face-centered cubic (FCC) lattice upon application of uniaxial tension at nanolevel. The experiment was made on the calculated block of crystal simulating three-dimensional Pt nanowires. To calculate the dynamics of the atomic structure, the method of molecular dynamics using Morse pair potentials was used [6]:
q>0v) = Dße^ (ße^ - 2).
(1)
Where D - energy parameter corresponding to the depth of the potential hole; a - the parameter determining the stiffness of the interatomic bonds; P = ear°; r0 - some average equilibrium distance in the focal areas where the interac-
tion between atoms takes place. The interaction between atoms is taken into account up to the first three coordination spheres. The duration of one iteration was equal to 10-14 s-1 at the calculation by the molecular dynamics method.
The use of Morse potential justifies well at the research of the majority of defects formed during structure-energetically transformations in the deformation process.
The potential energy of a system of N atoms is represented as:
, N N
E=1 Z (|r-rvI).
i=1,i* j j=1
Where rt - radius vectors of f'h atom.
The potential is determined, the atomic force F is given as the derivative of the potential energy, namely
F =
dqKL (r) dr
Mathematical model of the molecular dynamics method [2] describes a system of ordinary differential equations of motion of Newton. The equation of motion in the classical form is represented by:
du, rr dr .
-— = F -— = u,1 = 1,2,
dt 1 dt 1
, N.
Where mi and vt - mass and velocity of f' atom - time.
To solve the system of ordinary differential equations by numerical Euler method with half-step. Temperature of the atoms in a perfect crystal, calculated using the formula:
T -
2k
3 Nkb 3 Nkb
Y.fmtvf.
Where kb, Boltzmann constant and K, is the total Kinetic energy.
A computer experiment is performed at a temperature corresponding to 10, 200 and 300 K, at any stage of deformation involving the possibility of chilling calculation unit for detailed analysis of the structural changes occurring in it.
There are many researches of the behavior of the defects of various types using the given potential as for two-dimensional models, so for three-dimensional models [79]. The Morse potential is widely applied at the research of such defects as grain boundaries and anti-phase boundaries which are of great importance for deformation processes of intermetallic compounds and ordered alloys [1-5].
A three-dimensional Pt nanowire with rectangular cross-section is simulated as in fig. 1. The size of the calculated block of the nanowire made from 6912 atoms that corresponded to the packing from 24 atoms along the side in the basis (9.281 nm) and 24 atoms in its height (4.64 nm) to 27678 atoms that corresponded to the packing from 24 atoms along the side in the basis (9.281 nm) and 96 atoms in its height (18.56 nm). Free boundary conditions were applied to the calculated block of the crystal in directions <010> and <001> and rigid boundary conditions in direction <100>.
The total sample consists of two parts. One part is designed as the active zone in which atoms move according to the inter-atomic potential; the other part is the boundary zone where positions of atoms are given by prescribed boundary conditions. The periodic boundary condition is applied in the length direction, i.e., the Z axis. The surfaces in the X and Y directions are free (fig. 1). The existence of those free surfaces will result in relaxation motion of the atoms near the surfaces, which then minimizes the total energy of the system.
In each simulation the temperature is kept constant by the direct velocity scaling method [1]. After full relaxation, extension strain loading is applied by uniformly scaling the Z coordinates. The atoms at each end are constrained, and can only displace in the Z direction during each loading step. The stepwise tensile strain is 0.02. It is relaxed for some time in each step. Both the strain step and relaxation time determine the strain rate. The tension/relaxation step is repeated until the model fails.
At any stage of deformation, the possibility of further cooling of the calculated block to 0 K by energy dissipation outside its limits was assumed to make the detailed analysis of structural transformations taken place in it.
In the experiment process, the reserved energy per a separate atom was calculated at each stage of deformation in the dependence on time. The visualization of the three-dimensional atomic calculated block of crystal with possibility of turn and allocation of the atomic planes in the given directions has been made to observe the evolution of defect structure at the atomic level.
RESULTS AND DISCUSSIONS
Structural-energetic changes taking place of the ordered alloy of Pt nanowires with Fcc crystal lattice under the influence of uniaxial tension deformation in the directions <001> and <100> were studied by the method of molecular dynamics. in this part we will discuss a series of experiments for the deformation of 24x24x48 (atomic layer) of Pt nanowire at 300 K in detail and compare with
another series of experiments for different size and orientation of Pt nanowires at different temperature.
Having studied the graphs behavior "stored energy -time of deformation" (fig. 2). In the graphs, four main stages of structure-energetic transformations: quasi-elastic deformation, plastic deformation, flow (necking) and destruction can be distinguished.
The initial stage - quasi-elastic deformation, when small displacements of atoms take place and the defects are not observed. In the given section of the graph, the stored energy according to a parabolic law. The first stage comes to the end at the point of energy bifurcation.
Consecutive splitting of the family of atomic planes in {100} into monatomic ones, was observed at the first stage due to the differences in the distances between the atomic layers in the directions <100> and <010>. It led to considerable (in comparison with orientation of the axis of deformation direction <001> (fig. 3 and 4)) elongation of alloy stage without manifestation of the signs of plastic deformation at the first step.
The described splitting of the planes family in {001} into monatomic planes takes place in the central part of the alloy more intensively. At the end of the first stage of splitting, the deformation of planes family in {001} was observed near rigid captures that led to the formation of the crack on the boundary of the section between absolutely rigid captures and the calculated block of the alloy. The significant atomic displacements were determined near the captures at the end of the first deformation stage. The tension
Fig. 1. Geometry of nanowire subjected to uniaxial tension under constant strain rate
Fig. 2. The change of the stored energy of 24x24x48 Pt nanowire during the deformation in the direction <100> at 300 K
Fig. 3. End of the first stage of 24x24x48 Pt nanowire, at 25 ps in the direction <001> at 300 K, Estored = 0.105 eV / atom
Fig. 4. Disturbance of the structure in the plane (110), for fig. 3
Fig. 5. Atomic configuration of the second stage of 24x24x48 Pt nanowire, the formation of a domain in the central portion at 45ps deformation in the direction <001>
at captures reached 21 GPa. The boundaries of the substructure units contained twins (fig. 5), the atoms at the boundaries of the block had hcp topology nearest neighbors (see fig. 6). Stage of plastic deformation changes from 45 to 350 Ps. The energy change in a horizontal increases from 0.024 to = 0.1130 eV/atom for <100>.
At the end of the plastic deformation shows the place of formation of a "neck" (fig. 7). Structural and energy conversion were observed only in the neck area. In the third stage (early break) restructuring is primarily near the "neck" (fig. 8), which is reflected in the change of the schedule stored energy (fig. 2) at the site. The energy change in a horizontal increases from 0.1130 to = 0.1170 eV/atom for <100>.
In the fourth stage (fracture) the nanowire split into two parts and stored energy decrease (fig. 9), which is reflected in the change of the schedule stored energy (fig. 2) at the site. The energy change in a horizontal decreases from
0.1170 to 0.1159 eV/atom for <100>. After the division of the nanowire split into two groups of atoms relative to each other, there is only the vibration of the atoms with rate corresponding to a given temperature and single atomic transitions. In the fracture stage clearly twins and grain boundaries found (fig. 9 and 10), which began to form in the second stage of deformation.
The intensity of energy and deformation time for all stages depends on experiment temperature. With the growth of temperature, duration of quasi-elastic deformation decreases, and duration of plastic deformation and a flow stages increases. It is shown that anisotropy of structure- energetic changes taking place in alloys depends on orientation of the alloy. In particular, the development of plastic deformation stages in the direction <001> occurs the formation of anti-phase boundaries and C-domains.
Fig. 6. Atoms with hcp topology nearest neighbors for fig. 5
Fig. 7. Atomic configuration of the end second stage of 24x24x48 Pt nanowire, at 350ps deformation in the direction <001>
Fig. 8. Atomic configuration of end flow deformation of 24x24x48 Pt nanowire, the formation of a domain in the central portion at 468ps deformation in the direction <001>
Fig. 9. Atomic configuration of fracture of 24x24x48 Pt nanowire, at 520 ps deformation in the direction <001>
wm » »—
Fig. 10. Disturbance of the structure in the plane (101), for fig. 9
CONCLUSION
The process of formation of defects in the dynamic deformation of Fcc metallic Pt nanowires at low temperature deformation at all three stages was studied. Structural differences between the structural and energy transformations were as follows:
As a result of studies of structural and energy transformations during tensile deformation of Pt nanowires at low temperature, identified four stages of structural and energy transformations: the quasi-elastic, plastic, flow and fracture.
1. The first stage of structural and energy transformations in the deformation process ends with formation sliding on the substructure of Pt nanowires. At the first stage of deformation, we can see rotation the central portion of nanwire and C-domain formation in the second stage of deformation.
2. It was found that the features of structural and energy transformations for cubic symmetry of nanowires in the second stage of deformation affects the orientation of the axis of tension. The first step is the formation of vacancies,
Frenkel pairs and interstitials. In the second stage occur collective atomic bias, the formation of dislocations and grain boundaries
3. The neck area occur in the third stage of structural and energy transformations. Stored strain energy in that period varies only slightly. In the third step, formation of grain boundaries and twins.
4. The nature of the destruction of blocks corresponds to brittle fracture at low temperatures. After fracture of nanowire for all size, found planar defects such as twins and packing defects.
5. The influence of temperature on the mechanisms of deformation and fracture was investigated. The change of the part of atoms with an ideal short order in the process of deformation was considered. Experiments have shown that when the temperature decreases the elastic region deformation, the plastic deformation increases, and in the neck area intensively developing a process disorder. Experiment with the crystal unit completely disordered showed that the first stage of deformation is narrowed, and the second stage increases.
REFERENCES
1. Aish M.M., Moneeb T.M. Shatnawi, Starostenkov M.D. Characterization of strain-induced structural transformations in CdSe nanowires using molecular dynamics simulation. Materials Physics and Mechanics, 2015, vol. 24, no. 4, pp. 403-409.
2. Aish M.M., Starostenkov M.D. Modeling and simulation of Ni nano-film using morse pair potential. Materials Physics and Mechanics, 2015, no. 24, pp 139-144.
3. Starostenkov M.D., Aish M.M. Molecular dynamic study for ultrathin Nickel nanowires at the same temperature. Materials Physics and Mechanics, 2014, vol. 21, no. 1, pp. 1-7.
4. Starostenkov M.D., Aish M.M. Effect of length and cross-sectional area on Ni3Fe alloy plasticity. Advanced Materials Research, 2014, vol. 1013, pp. 242-248.
5. Aish M.M., Starostenkov M.D. Effect of volume on the mechanical properties of nickel nanowire. Materials Physics and Mechanics, 2013, vol. 18, no. 1, pp. 53-62.
6. Yang X., Liu L., Zhai P., Zhang Q. Computational Materials Science, 2009, no. 44, p. 1390.
7. Colin de Verdiere M., Skordos A.A., Walton A.C. Michael May, Influence of loading rate on the delaminating response of unstuffed and tufted carbon epoxy non-crimp fabric composites. Mode II, Engineering Fracture Mechanics, 2012, vol. 96, pp. 1-10.
8. Nielsena K.L., Niordsona C.F., Hutchinson J.W. Strain gradient effects on steady state crack growth in rate-sensitive materials. Engineering Fracture Mechanics, 2012, vol. 96, pp. 61-71.
9. Xin Wang. Two-parameter characterization of elastic-plastic crack front fields: Surface cracked plates under uniaxial and biaxial bending. Engineering Fracture Mechanics, 2012, vol. 96, pp. 122-146.
10. Aish M.M., Starostenkov M.D. International Journal of Theoretical and Applied Physics (IJTAP), 2014, vol. 4, no. 1, pp. 79-84.
11. Starostenkov M.D., Aish M.M. Feature deformation and breaking of Ni nanowire. Letters on Materials, 2014, vol. 4, no. 2, pp. 89-92.
Received 10 April 2016
2016. Т. 21, вып. 3. Физика
УДК 538.911
DOI: 10.20310/1810-0198-2016-21-3-845-849
СТРУКТУРНЫЕ ПРЕВРАЩЕНИЯ ДЛЯ Pt НАНОПРОВОДОВ ПРИ ОДНООСНОМ РАСТЯЖЕНИИ В НАПРАВЛЕНИИ <001> ПРИ НИЗКИХ ТЕМПЕРАТУРАХ
© М.М. Айш12), М.Д. Старостенков2)
11 Минофийский университет, г. Минофия, Египет, e-mail: [email protected] 2) Алтайский государственный технический университет, г. Барнаул, Российская Федерация,
e-mail: [email protected]
В статье рассмотрены атомные превращения, которые наблюдаются в платиновых нанопроводах во время динамической деформации. Изучено превращение атомных плоскостей смещения и дефекты, образующиеся во время растяжения. В ходе исследований было выявлено три основных деформационных этапа: квазиупругой деформации, скольжения и разрушения сплава. Каждый этап характеризуется энергетической кривой и появлением некоторых видов дефектов. Вакансии, пары Френкеля и междоузельные атомы были обнаружены в ходе первого этапа. Атомные смещения, дислокации, антифазные границы и границы зерен образуются во время второго этапа. На третьем этапе наблюдается двойникование от границы зерна.
Ключевые слова: К нанопровода, динамическая деформация, скольжения, разрушение, растяжение, вакансии и пары Френкеля.
СПИСОК ЛИТЕРАТУРЫ
1. Aish M.M., Moneeb T.M. Shatnawi, Starostenkov M.D. Characterization of strain-induced structural transformations in CdSe nanowires using molecular dynamics simulation // Materials Physics and Mechanics. 2015. V. 24. № 4. P. 403-409.
2. Aish M.M., Starostenkov M.D. Modeling and simulation of Ni nanofilm using morse pair potential // Materials Physics and Mechanics. 2015. № 24. P. 139144.
3. StarostenkovM.D., Aish M.M. Molecular dynamic study for ultrathin Nickel nanowires at the same temperature // Materials Physics and Mechanics. 2014. V. 21. № 1. P. 1-7.
4. Starostenkov M.D., Aish M.M. Effect of length and cross-sectional area on Ni3Fe alloy plasticity // Advanced Materials Research. 2014. V. 1013. P. 242248.
5. Aish M.M., Starostenkov M.D. Effect of volume on the mechanical properties of nickel nanowire // Materials Physics and Mechanics. 2013. V. 18. № 1. P. 53-62.
6. YangX., Liu L., Zhai P., Zhang Q. // Computational Materials Science. 2009. № 44. P. 1390.
7. Colin de VerdiereM., Skordos A.A., Walton A.C. Michael May, Influence of loading rate on the delaminating response of unstuffed and tufted carbon epoxy non-crimp fabric composites // Mode II, Engineering Fracture Mechanics. 2012. V. 96. P. 1-10.
8. Nielsena K.L., Niordsona C.F., Hutchinson J.W. Strain gradient effects on steady state crack growth in rate-sensitive materials // Engineering Fracture Mechanics. 2012. V. 96. P. 61-71.
9. Xin Wang. Two-parameter characterization of elastic-plastic crack front fields: Surface cracked plates under uniaxial and biaxial bending // Engineering Fracture Mechanics. 2012. V. 96. P. 122-146.
10. Aish M.M., Starostenkov M.D. // International Journal of Theoretical and Applied Physics (IJTAP). 2014. V. 4. № 1. P. 79-84.
11. StarostenkovM.D., Aish M.M. Feature deformation and breaking of Ni nanowire // Letters on Materials. 2014. V. 4. № 2. P. 89-92.
Поступила в редакцию 10 апреля 2016 г.
Айш М/эхаммед Махмуд, Менофийский университет, г. Менофия, Египет, доктор физико-математических наук, Факультет наук, кафедра физики, e-mail: [email protected]
Aish Mohammed Mahmoud, Menoufia University, Menoufia, Egypt, PhD, Faculty of Science, Physics Department, e-mail: [email protected]
Старостенков Михаил Дмитриевич, Алтайский государственный технический университет им. И.И. Ползунова, г. Барнаул, Российская Федерация, доктор физико-математических наук, профессор, зав. кафедрой общей физики, e-mail: [email protected]
Starostenkov Mikhail Dmitrievich, Altai State Technical University named after I.I. Polzunov, Barnaul, Russian Federation, Doctor of Рhysics and Mathematics, Professor, Head of General Physics Department, e-mail: [email protected]
