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Harvard PhD Theses in Physics, | DEPARTMENT OF PHYSICS
Ken-ichi Saitoh, Kohei Kuramitsu, Tomohiro Sato, Masanori Takuma, Yoshimasa Takahashi, " Molecular Dynamics Phd thesis molecular dynamics on Deformation Mechanism of Grain Boundaries in Magnesium Crystal: Based on Coincidence Site Lattice Theory ", Journal of Materialsvol. As for magnesium Mg alloys, it has been noted that they are inferior to plastic deformation, but improvement in the mechanical properties by further refinement of grain size has been recently suggested.
It means the importance of atomistic view of polycrystalline interface of Mg crystal. In this study, to discuss the deformation mechanism of polycrystalline Mg, atomistic grain boundary GB models by using coincidence site lattice CSL theory are constructed and are simulated for their relaxed and deformatted structures. First, phd thesis molecular dynamics, GB structures in which the axis of rotation is in direction are relaxed at 10 Kelvin, and the GB energies are evaluated.
Then, the deformation mechanism of each GB model under phd thesis molecular dynamics tensile loading is observed by using the molecular dynamics MD method. The present MD simulations are based on embedded atom method EAM potential for Mg crystal. As a result, we were able to observe atomistically a variety of GB structures and to recognize significant difference in deformation mechanism between low-angle GBs and high-angle GBs.
A close scrutiny is made on phenomena of dislocation emission processes peculiar to each atomistic local structure in high-angle GBs. In recent years, improvement of fuel efficiency of the transportation equipment is demanded to reduce burden on the environment.
Therefore, there is an issue concerning weight saving of the transportation equipment. For those purposes, one of the materials that attract much attention of researchers now is magnesium Mg alloy. Mg alloy is the lightest metal in practical use and its performance in recycling is noteworthy [ 1 ]. Currently this material is used as housing of laptop PCs, cellphones, and so on. However, unfortunately, Mg alloy still has low workability because anisotropy in plastic deformation is too strong.
This is mainly caused by the nature of hexagonal close-packed HCP structure that is an elementary crystalline structure of Mg [ 2 ]. Recently, there comes an idea that grain refining process will resolve this problem.
This method reduces individual particle sizes in a polycrystal and consequently raises the density of grain boundaries GBs. Actually, phd thesis molecular dynamics, it is reported that both higher strength and ductility are realized by the grain refining [ 3 ]. As an effective grain refinement method, phd thesis molecular dynamics plastic deformation SPD is well known and is paid much attention in the field of plasticity.
To name a few, accumulative roll-bonding ARB [ 4 ], high pressure torsion HPT [ 5 ], and multidirectional forging MDF [ 6 ] have been well investigated. Within the above context, we should focus on influence of GB phd thesis molecular dynamics on the mechanical properties in the Mg alloy.
Thus, in particular, it is necessary to analyze the influence of GB structure on atomistic deformation mechanism which always takes place in Mg polycrystals. Studies based on molecular dynamics MD simulation concerning GBs of Mg have phd thesis molecular dynamics extensively reported.
For example, relationship among angle of rotation, GB energy, and GB structures is investigated [ 7 ], and relationship between the deformation mechanism and angle of rotation in tensile or compressive loading is also investigated [ 8 ]. However, the view of deformation mechanism in accordance with atomic structure and behavior around GB is insufficient and is still not clear.
Regarding deformation mechanism of Mg crystal, there have been much efforts by many researchers in the world. By using sophisticated experimental apparatus and methods such as electron back-scattering diffraction EBSD analyzing technique or transmission electron microscopy observation with atomistic resolution, change of crystal orientation in single crystal and nucleation of defects including twin boundary and dislocation during deformation have been researched extensively [ 9 — 12 ].
However, since experimental and dynamic recognition is quite restricted in this point, some collaborative studies with MD have been also conducted [ 1314 ], phd thesis molecular dynamics.
Understanding the mechanism of deformation twinning or dislocation motion in Mg crystal becomes important recently. It should be noted that, for the purpose of obtaining theoretical insight for such defected structures, there have been a lot of MD studies concerning twinning and dislocations in deformation [ 15 — 18 ].
Within the context of the effect of GB on plastic deformation of Mg like in the present study, polycrystalline MD models though composed of nanosized grains have been also investigated and those studies phd thesis molecular dynamics giving many insights as for deformation mechanism around GB region [ 19 — 23 ].
In this study, to analyze the deformation mechanism of polycrystalline Mg, we first produce periodic GB models made up of Mg crystal in which the axis of rotation is direction, as one of choices. And then, MD simulation of uniaxial tensile loading is performed to observe atomic-scale phenomena around GB.
Based on MD results, influence of the GB on nucleation initiation and development of slip and twin deformations can be discussed. The relationship between GB energy and GB structures and the relationship between the deformation mechanism and the GB structures in deforming state are discussed too. In this study, we use molecular dynamics MD method. The basic equation is given by where is mass of particleis interatomic force acting on that particle, phd thesis molecular dynamics, is its position vector, and is interatomic potential energy of total system.
In this study, we use one of many-body potentials, called embedded atom method EAM potential [ 24 ]. The equation is generally given by where is a pair potential and is the embedding energy function.
is individual electron density evaluated at atom and is determined by contribution from surrounding atoms. Therefore, it is assumed that an expression of electron density function is given by where each is simply pairwise density function as to just two atoms, phd thesis molecular dynamics, and. In this phd thesis molecular dynamics, we apply an EAM potential function and a parameter set that were proposed for Mg crystal by Liu et al.
They successfully developed it by fitting to experimental data in bulk, cluster, and liquid state of Mg as well as some structures including crystalline defects and their energies. All the GB models of Mg crystal studied in the present study are constructed by using coincidence site lattice CSL theory [ 26 ], which has been well known phd thesis molecular dynamics extensively used in GB studies [ 27 ].
It was shown that the CSL theory also can be applied to hexagonal crystal [ 28 ]. By using CSL, MD model is adequately applied under periodic boundary condition as shown in Figure 1.
In practice, the GB model for MD is constructed as in the following procedure or algorithm. First, Mg atoms are initially placed in the region ofso thatphd thesis molecular dynamics,and axes are equal to, and directions, phd thesis molecular dynamics, respectively those directions are described in Miller-Bravais indices for hexagonal crystal.
Then, that crystal grain is rotated by a certain angle around the y axis, called rotation axis or tilt axis. The angle of rotation is rigorously determined by CSL framework, phd thesis molecular dynamics. Subsequently, we place new atoms in another grain, at positions with mirror symmetry with regard to their original counterpart, in region, and consequently we phd thesis molecular dynamics GB plane along. Though, in real materials, phd thesis molecular dynamics, there must be asymmetric GBs plane and therefore asymmetric atomic arrangement over GB plane, it is reasonable that we confine our present study to symmetrical GB types, for simplicity.
We choose several rotation angles between two symmetrically arranged crystals angles are measured from each other and usually called misorientation angles. Values of are calculated according to their own CSL. The CSL is a two-dimensional unit lattice in the present case it is on planewhich is determined by lattice constants andtogether with their axes ratio which is obtained for ideal hexagonal crystal.
The CSL is specified by -value, which is a fraction of the number of CSL lattice points to the number of all lattice points in the crystal. As explained above, phd thesis molecular dynamics, atomic positions in one grain are rotated by a half of misorientation angle, that is,on plane, phd thesis molecular dynamics, and their periodic lattice points per CSL are also placed, phd thesis molecular dynamics. Thus, the - and -sizes of the model should be strictly equivalent to multiple units of CSL size.
The misorientation angle is given by where both and are arbitrary integers. Geometrical conditions of GB models type, size, total number of atoms, etc. used phd thesis molecular dynamics are shown in Table 1. These geometrically obtained initial atomic configurations of periodic GB models are provided adequate structural relaxation by MD simulation, so that energy and stress components of the total system are just thermally equilibrated.
After that, a GB excess energy can be evaluated using an usual formula given by [ 27 ] where is GB area, and are total potential energies of the fully relaxed GB model and a perfect crystal PC model, respectively, and and are the number of atoms in the GB model and the PC model, respectively. In constructing GB models by the above procedure, there are cases when atoms around GB plane are much phd thesis molecular dynamics than an allowable interatomic distance for moderate energy; that is, excessive atoms occur.
In such case, excessive atoms are to be removed from the GB model before structural relaxation calculation. Since there are several patterns to remove excessive atoms, several models are created and compared for each. Thus, one structure having the lowest energy is selected for each and it is regarded as the most stable and the most realistic Phd thesis molecular dynamics structure. After structural relaxation, GB models are subjected to tensile loading in the direction as shown in Figure 1and deformation behavior of atomic system is observed.
Details of an adaptive tensile loading method were described in [ 29 ]. Let me describe the method in brief. Strain rate in tensile direction is prescribed, and then elongation corresponding to strain value at each step is applied in the size of tensile direction. If the cell size were kept constant in other directions, the calculation cell would produce tension also in those directions too.
To avoid it and to realize uniaxial tension, size of the calculation cell not in tensile direction is continuously adjusted to avoid normal stress component in that direction. It needs a criterion of tolerance for stress fluctuation, so we set it in the range Pa. Thus, the periodic cell is always kept uniaxially being deformed in just one tensile direction, phd thesis molecular dynamics.
Structural analysis of atoms is mainly conducted by common neighbor analysis CNA [ 30 ]. This method is summarized as follows. At first, as to one atom, the bonding state to the first neighboring atoms together with the link state with the 2nd nearest atoms is observed. Then, comparing the situation obtained for the selected atom with that of atom in reference crystal structure, that atom is identified with some crystal structure.
By using conventional version of CNA, phd thesis molecular dynamics, an atom is primarily recognized as face-centered cubic FCCbody-centered cubic BCCor HCP structure. In the figures of the present paper, atoms can be visually recognized by color code attributed to each crystal structure identified by CNA as follows: green, blue, pink, or white represents FCC, BCC, HCP, or other structure, respectively.
In Figure 1we show an example of GB model which is already analyzed by CNA. Calculation conditions for MD simulation are shown in Table 2. During relaxation and phd thesis molecular dynamics simulations, the system temperature is kept constant at 10 Kelvin.
As mentioned, Mg crystal preferentially slips on basal plane as schematically shown in Figure 2 a A. However, to compensate large strain in plastic regime applied to the system, it may exhibit other shear deformation mechanisms, such as slips activated on other planes prismatic slip, 1st and 2nd pyramidal slips or twinning deformation twinningas shown in Figures 2 a B — D and 2 b.
In MD simulations, occurrence of slip or twinning can be detected by change in crystalline identification HCP, FCC, BCC, or other which is provided by CNA. Besides, phd thesis molecular dynamics, from atomic and local arrangement around such deformation zone, phd thesis molecular dynamics, we can visually distinguish those mechanisms presented in Figure 2. Later, in summarizing the present study, we will show correlation between the structural types of GB and those deformation mechanisms, phd thesis molecular dynamics.
Generally, easiness to occur is recognized as follows: basal slip twin prismatic slip pyramidal slip, though it is likely dependent on temperature condition. We tried to evaluate value and order of stresses or energies required by each mechanism in our GB models.
However, clear and unified understanding has not been obtained yet, because of the complicated effect concerning temperature and loading conditions. Therefore, it will need further study and no discussion on it is made in this paper.
In Figure 3the relationship between misorientation angle and GB energy is shown. As a result, the energy graph shows one sharp cusp, phd thesis molecular dynamics, which is well observed in other pure metals or alloys, via experiment [ 31 ] and computation [ 32 ]. This indicates that atoms in this GB structure are regularly and compactly arranged on GB plane to exhibit the most stable structure.
Metallic GBs often present a special atomic arrangement called structural unit around GB plane, usually having a certain periodicity along the plane. It is recognized that the GB structures are formed by periodic structural unit portion surrounded by solid line in the figure.
Theoretical Framework and Conceptual Framework in Your Doctoral Dissertation with Dr. Guy E. White
, time: 9:12Molecular dynamics (MD) simulation is a fundamental approach to allow researchers to study the molecular interactions of protein-ligand binding via the dynamics of protein-ligand complexes at atomic level. It can be observed precisely the motion of atoms and interactions involved in receptor and ligand binding using MD blogger.com: Rui Duan 17 Oxford Street Cambridge, MA () phone () fax Sep 22, · Molecular Modeling of the Synthesis of Zeolites and Related Nanoporous Materials. Supervisor (s): Prof. Dr. ir. Veronique Van Speybroeck, Prof. Dr. Michel Waroquier. PhD defense: Thu, 28/05/ H. De Cooman. A combined EMR and DFT study of radiation-induced effects in surcose and glucose 1-phosphate
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