radial distribution function
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2021 ◽  
Vol 8 ◽  
Author(s):  
Alexander D. Greenhalgh ◽  
Liurukara D. Sanjeewa ◽  
Piotr Luszczek ◽  
Vasileios Maroulas ◽  
Orlando Rios ◽  
...  

As a powerful analytical technique, atom probe tomography (APT) has the capacity to acquire the spatial distribution of millions of atoms from a complex sample. However, extracting information at the Ångstrom-scale on atomic ordering remains a challenge due to the limits of the APT experiment and data analysis algorithms. The development of new computational tools enable visualization of the data and aid understanding of the physical phenomena such as disorder of complex crystalline structures. Here, we report progress towards this goal using two steps. We describe a computational approach to evaluate atomic ordering in the crystal structure by generating radial distribution functions (RDF). Atomic ordering is rendered as the Fractional Cumulative Radial Distribution Function (FCRDF) which allows for greater visibility of local compositions at short range in the structure. Further, we accommodate in the analysis additional parameters such as uncertainty in the atomic coordinates and the atomic abundance to ascertain short-range ordering in APT data sets. We applied the FCRDF analysis to synthetic and experimental APT data sets for Ni3Al. The ability to observe a signal of atomic ordering consistent with the known L12 crystal structure is heavily dependent on spatial uncertainty, irrespective of abundance. Detection of atomic ordering is subject to an upper limit of spatial uncertainty of atoms described with Gaussian distributions with a standard deviation of 1.3 Å. The FCRDF analysis was also applied to the APT data set for a six-component alloy, Al1.3CoCrCuFeNi. In this case, we are currently able to visualize elemental segregation at the nanoscale, though unambiguous identification of atomic ordering at the Ångstrom (nearest-neighbor) scale remains a goal.


2021 ◽  
Vol 933 ◽  
Author(s):  
Andrew D. Bragg ◽  
Adam L. Hammond ◽  
Rohit Dhariwal ◽  
Hui Meng

Expanding recent observations by Hammond & Meng (J. Fluid Mech., vol. 921, 2021, A16), we present a range of detailed experimental data of the radial distribution function (r.d.f.) of inertial particles in isotropic turbulence for different Stokes number, $St$ , showing that the r.d.f. grows explosively with decreasing separation r, exhibiting $r^{-6}$ scaling as the collision radius is approached, regardless of $St$ or particle radius $a$ . To understand such explosive clustering, we correct a number of errors in the theory by Yavuz et al. (Phys. Rev. Lett., vol. 120, 2018, 244504) based on hydrodynamic interactions between pairs of small, weakly inertial particles. A comparison between the corrected theory and the experiment shows that the theory by Yavuz et al. underpredicts the r.d.f. by orders of magnitude. To explain this discrepancy, we explore several alternative mechanisms for this discrepancy that were not included in the theory and show that none of them are likely the explanation. This suggests new, yet-to-be-identified physical mechanisms are at play, requiring further investigation and new theories.


2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Dongling Yu ◽  
Huiling Zhang ◽  
Jiaqi Yi ◽  
Yongzhen Fang ◽  
Nanxing Wu

To explore the deformation law of nanoindentation dislocations of different crystal plane groups of 3C-SiC by cube indenter. The molecular dynamics simulation method is used to construct the different crystal plane family models of 3C-SiC, select the ensemble, set the potential function, optimize the crystal structure, and relax the indentation process. The radial distribution function, shear strain, and dislocation deformation of nanoindentation on (001), (110), and (111) planes were analyzed, respectively. In the radial distribution function, the change in g r in the (110) crystal plane is the most obvious. Shear strain and dislocation occur easily at the boundary of square indentation defects. During the indentation process, the shear strain is enhanced along the atomic bond arrangement structure, (001) crystal plane shear strain is mainly concentrated around and below the indentation defects and produce a large number of cross dislocations, (110) the crystal plane shear strain is mainly concentrated in the shear strain chain extending around and below the indentation defect, which mainly produces horizontal dislocations, and (111) the crystal plane shear strain is mainly concentrated in four weeks extending on the left and right sides in the direction below the indentation defect and produces horizontal and vertical dislocations. The direction of shear stress release is related to the crystal structure. The crystal structure affects the direction of atomic slip, resulting in the results of sliding in different directions. The final dislocation rings are different, resulting in different indentation results.


Minerals ◽  
2021 ◽  
Vol 11 (10) ◽  
pp. 1080
Author(s):  
Jinxia Zhang ◽  
Chao Yang ◽  
Fusheng Niu ◽  
Shuling Gao ◽  
Jiajing Dong

Molecular dynamics of the interaction between four metal oxides (ZnO, Fe2O3, Al2O3, and CaO) present in zinc-bearing dust sludge and choline chloride (ChCl)-malonic acid (MA)(1:2) was studied in this work using Materials Studio software. The interaction mechanism was revealed by analyzing the interaction energy and radial distribution function from the perspective of quantum mechanics, and the simulation results were verified by single factor leaching experiments. The calculation results show that the complete cleavage surface of the four metal oxides is the (001) surface, and ChCl-2MA forms a stable structure with multiple intermolecular hydrogen bonds centered on the chlorine atom. The dynamic simulation of the interaction model shows that strength of interaction between ChCl-2MA and the four metal oxides follows the order: ZnO > Fe2O3 > Al2O3 > CaO. ChCl-2MA mainly interacts with ZnO by chemical adsorption, while ChCl-2MA mainly interacts with Fe2O3, Al2O3, and CaO by physical adsorption. The radial distribution function shows that Cl in ChCl-2MA and C=O in MA form chemical bonds with Zn in ZnO, and the choline cation (Ch+) forms C-H···O with ZnO. Among these bonds, the Cl-Zn bond energy is stronger. During the interaction between ChCl-2MA and Fe2O3 and Al2O3, O-H···O and C-H···O are formed and interact with CaO by van der Waals force. Single factor leaching experiments show that, under the same leaching conditions, the leaching rate of ZnO by ChCl-2MA is greater than 90%, while the leaching rate of Fe2O3, Al2O3, and CaO is about 10%. These results indicate good selectivity of ChCl-2MA for ZnO in the zinc-bearing dust sludge. The above conclusions have important theoretical significance and provide an in-depth understanding of the leaching mechanisms of zinc-bearing dust sludge in deep eutectic solvents.


2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Daping Zhou ◽  
Haijun Wei ◽  
Shuye Xue ◽  
Ye Qiu ◽  
Shen Wu ◽  
...  

Asphaltene aggregation and precipitation are one of the major issues for marine low-sulfur fuel oil used on board. Many research studies have been carried out to investigate the aggregation behavior of asphaltene under different conditions, but the mechanism of asphaltene aggregation in low-sulfur fuel oil at the molecular level is still unclear. In this work, molecular dynamics (MD) simulations were performed to calculate the solubility parameters, intermolecular interaction energies, and radial distribution function (RDF) curves of each component in marine low-sulfur fuel oil to examine their mutual compatibility. Simulation results indicate that the solubility parameter of resin gains the highest value and it is close to asphaltene. The solubility parameters of aromatic, hexadecane, and saturate decrease successively. The interaction energy between resin and asphaltene molecules is higher than that between the same kind of molecules, which means that resin can inhibit the aggregation of asphaltene molecules. Typically, a light distillate component (hexadecane) is added to heavy fuel oil to yield low-sulfur oil, and our calculations reveal that this has a negative effect on asphaltene aggregation. Specifically, asphaltene is more likely to self-aggregate, as shown by the increase in peak height in the radial distribution function of the asphaltene-asphaltene pair. The findings of this study will provide theoretical support for the production of marine low-sulfur fuel.


2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Dung Nguyen Trong ◽  
Van Cao Long

This study aims to study the effect of several structural factors, such as number of atoms (N), shell thickness (d), and temperature (T), on the structure of amorphous iron nanoparticle (amorphous nano-Fe) by using the molecular dynamics (MD) method with Sutton–Chen (SC) dip interaction and free boundary conditions. The structural parameters of amorphous nano-Fe include their size (D), energy (E), radial distribution function (RDF), coordination number (CN), and coordination number density (CNd). The results show that the glass temperature ( T g ) and the first peak position (r) of radial distribution function (RDF) have the values of T g  = 900 K and r = 2.55 Å, respectively. Furthermore, the values of parameters D and E are always proportional to N−1/3 and N−1, respectively. Regarding the effect of number of atoms, shell thickness, and the temperature on the structure of amorphous nano-Fe, we found that the increase in atoms number leads to decrease in the RDF height and increase in the coordination number (CN). However, increasing temperature leads to decreasing the shell thickness of amorphous nano-Fe.


2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Tuan Tran Quoc ◽  
Dung Nguyen Trong ◽  
Ştefan Ţălu

The influence of the number of atoms, N = 3000, 5000, 7000, and 9000 atoms, at temperature T = 300 K and temperatures T = 300, 500, 700, 900, 1100, 1300, and 1500 K at N = 9000 atoms, on microscopic structure, phase transition temperature, and mechanical property of bulk aluminium in an amorphous state is studied by the molecular dynamics method with the Sutton–Chen embedded interaction potential and the periodic boundary condition. Structural results are analyzed through the radial distribution function, the total energy of the system, the size, and the common neighbor analysis. The phase transition temperature is determined by the relationship between the total energy of the system and temperature. The mechanical property is derived from the deformation along the Z-axis. It can be noted that when the number of atoms increases, the first peak’s position for radial distribution function changes, the first peak’s height decreases, the number of FCC and HCP structural units decreases, the number of Amor structural units increases, and the total energy of system increases. It can be seen that when temperature increases, the first peak’s position changes, the first peak’s height decreases, the number of FCC and HCP structural units decreases, the number of Amor structural units increases, and the total energy of the system decreases. The obtained results are very useful for experimental studies in the future.


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