Finnis-Sinclair Research Articles

Correlation between grain size and dynamic response of NiTi alloy during intense shock-induced multi-spallation

This work committed to performing non-equilibrium molecular dynamics simulations to explore the influence of grain size on multi-spall performance of nanocrystalline nickel-titanium (NiTi) alloy. By comparing the calculated Hugoniot relationship with present experimental results, the Finnis-Sinclair (FS) type potential used in this work was verified to be suited for reproducing the shock behavior of NiTi alloy at high strain rate. During shock wave evolution, a single plastic wave was clearly observed in the sample with grain size of 5 nm, while there was a more pronounced elastic-plastic double wave structure at larger grain size. According to the free surface velocity history, the predicted spall strength exhibited a decreasing tendency and subsequently increased when the grain size decreased from 50 to 5 nm, indicative of a critical grain size (10 nm). Correspondingly, there were multiple spall planes appearing in the sample, the grain size of which was not smaller than the critical one. Contrarily, a single spall plane was observed at 5 nm. By counting the void distribution statistic, we found that as the grain size increased, the void-nucleation behavior changed from the intergranular to intergranular/transgranular coexisting pattern. In consequence, more nucleation sites were provided to promote an increase in the number of voids. Interestingly, for intergranular, there were much more voids involved in spallation at smaller grain size, which was attributed to grain boundary effect. The results demonstrated that void evolutions rarely occurred at the grain boundaries parallel to the loading direction. Moreover, when the grain size was larger than 5 nm, the B19 phases were found to be produced around those potential void-nucleation sites. After void nucleation, these B19 phases decreased till disappearance, accompanied by the proliferation of a large number of [100] dislocations. Such dislocations accumulated in the region without voids could block the void growth in this region, which was expected to be the reason for the formation of multiple spall planes. On the contrary, the absence of dislocations at 5 nm was inclined to the fact that the space for dislocation emission and aggregation was preoccupied by nucleated voids.

Description of crystal defect properties in BCC Cr with extended Finnis–Sinclair potential

PurposeThe purpose of this study is to propose extended potentials and investigate the applicability of extended Finnis–Sinclair (FS) potential to Cr with the unit cell structure of body-centered cubic (BCC Cr).Design/methodology/approachThe parameters of each potential are determined by fitting the elastic constants, cohesive energy and mono-vacancy formation energy. Furthermore, the ability of the extended FS potential to describe the crystal defect properties is tested. Finally, the applicability of reproducing the thermal properties of Cr is discussed.FindingsThe internal relationship between physical properties and potential function is revealed. The mathematical relationship between physical properties and potential function is derived in detail. The extended FS potential performs well in reproducing physical properties of BCC Cr, such as elastic constants, cohesive energy, surface energy and the properties of vacancy et al. Moreover, good agreement is obtained with the experimental data for predicting the melting point, specific heat and coefficient of thermal expansion.Originality/valueIn this study, new extended potentials are proposed. The extended FS potential is able to reproduce the physical and thermal properties of BCC Cr. Therefore, the new extended potential can be used to describe the crystal defect properties of BCC Cr.

Modified extended Finnis Sinclair potential for cubic crystal metal

Unlike the modified embedded atom method (MEAM), which requires consideration of the bond angles, the embedded atom method (EAM) and Finnis Sinclair (FS) potential have achieved a wide range of applications in molecular dynamics simulations of amorphous alloys and disordered systems. In this paper, the potential functions of 10 cubic crystalline metals are reconstructed using the extended Finnis Sinclair (EFS) potential to improve the FS potential in terms of defects, surface energy and thermal properties. First of all, for the BCC crystal structure and FCC crystal structure, the fitted physical quantity expressions suitable for EAM potential and FS potential are deduced, including pressure, bulk modulus, shear elastic modulus elastic constant, vacancy formation energy and surface energy. Then, based on these physical quantities and the Rose equation of state, the least-squares method is used to fit the new potential parameters. Finally, using the current potential, the cohesive energy, elastic constants (C11, C12 and C44), vacancy formation energy, self-interstitial formation energy, surface energy, coefficient of thermal expansion, specific heat capacity and the melting point of 10 kinds of cubic crystals are calculated by molecular dynamics simulation. The reliability of the current potential is verified by comparing with other potential functions, experimental values and first-principles calculations. The results show that the current potential can well reproduce the characteristics of physical quantities such as lattice constant, cohesive energy and elastic constants (C11, C12 and C44). Compared with the previous EFS potential, the current potential is closer to the Rose equation of state. The calculated surface energy is more accurate, and the performance of defects and thermal properties shows the reliability of the current potential function, and these improvements are due to the improvement of the fitting method.

Shock-induced plasticity and phase transformation in single crystal magnesium: an interatomic potential and non-equilibrium molecular dynamics simulations

An effective and reliable Finnis–Sinclair (FS) type potential is developed for large-scale molecular dynamics (MD) simulations of plasticity and phase transition of magnesium (Mg) single crystals under high-pressure shock loading. The shock-wave profiles exhibit a split elastic–inelastic wave in the [0001]HCP shock orientation and a three-wave structure in the [10-10]HCP and [-12-10]HCP directions, namely, an elastic precursor, a followed plastic front, and a phase-transition front. The shock Hugoniot of the particle velocity (U p) vs the shock velocity (U s) of Mg single crystals in three shock directions under low shock strength reveals apparent anisotropy, which vanishes with increasing shock strength. For the [0001]HCP shock direction, the amorphization caused by strong atomic strain plays an important role in the phase transition and allows for the phase transition from an isotropic stressed state to the product phase. The reorientation in the shock directions [10-10]HCP and [-12-10]HCP, as the primary plasticity deformation, leads to the compressed hexagonal close-packed (HCP) phase and reduces the phase-transition threshold pressure. The phase-transition pathway in the shock direction [0001]HCP includes a preferential contraction strain along the [0001]HCP direction, a tension along [-12-10]HCP direction, an effective contraction and shear along the [10-10]HCP direction. For the [10-10]HCP and [-12-10]HCP shock directions, the phase-transition pathway consists of two steps: a reorientation and the subsequent transition from the reorientation hexagonal close-packed phase (RHCP) to the body-centered cubic (BCC). The orientation relationships between HCP and BCC are (0001)HCP ⟨-12-10⟩HCP // {110}BCC ⟨001⟩BCC. Due to different slipping directions during the phase transition, three variants of the product phase are observed in the shocked samples, accompanied by three kinds of typical coherent twin-grain boundaries between the variants. The results indicate that the highly concentrated shear stress leads to the crystal lattice instability in the elastic precursor, and the plasticity or the phase transition relaxed the shear stress.

Finnis–Sinclair-type potential for atomistic simulation of defects behaviour in V-Ti-Ta ternary system

• Interatomic potential for V-Ti-Ta ternary system based on F-S formalism has been developed. • The Ti potential well reproduce the point-defect properties of vacancy and self-interstitial atoms and the pressure-volume relation. • The typical defect energies of solute atoms Ti and Ta in the V matrix and Ti and V in the Ta matrix predicted by the present potential were in good agreement with DFT results. Vanadium (V)-based alloys are potential candidates for structural materials of fusion reactors because of their excellent properties; recently, the V–Ti–Ta alloy has received considerable attention. The irradiation-resistant performance is significant for the development and application of fusion reactor materials. In this study, combining with our previously developed potentials of V and Ta, we developed the V-Ti-Ta interatomic potential based on the Finnis–Sinclair (FS) formalism, which is an important step towards an atomic-scale investigation of V-based alloys. The potential parameters were determined by fitting to a large database of experimental data and density functional theory (DFT) calculations. The formation energies of vacancy and self-interstitial atoms, as well as the pressure-volume relation obtained from the present Ti potential, were well reproduced. The typical defect energies of solute atoms Ti and Ta in the V matrix and Ti and V in the Ta matrix, such as the formation energies of substitutional solute atoms, binding energies between solute atoms and point defects, agree well with DFT results. Thus, the developed potentials are expected to be suitable for atomistic simulations of point defects evolution in the V-Ti-Ta ternary system.

Development of Finnis-Sinclair potential of metal Nb and the influence of potential function form on the properties of material

<sec>Researchers’ work on computational materials is often hampered by the lack of suitable intera tomic potentials. In this paper, under the framework of Finnis-Sinclair (FS) potentials, the process of fitting, testing and correction of interatomic potential is given in detail by developing the FS potential for metal Nb. First, the relationship between the interatomic potential and the macroscopic properties of the material is established. Then, the Finnis-Sinclair potential of metal Nb is fitted by reproducing the experimental data, such as the cohesive energy, bulk modulus, surface energy, vacancy formation energy and equilibrium lattice constant, and the fitting mean square error is less than 10<sup>–7</sup>. In order to test the interatomic potential, the elastic constant, shear modulus and Cauchy pressure of metal Nb are calculated by the constructed interatomic potential. In addition, how the form of the interatomic potential function affects the interstitial performance is discussed, and the constructed interatomic potential is modified according to the results of density functional theory (DFT) of the interstitial formation energy. The treatment of cutoff distance is also discussed. In the paper, the results are as follows. 1) The original form of FS potential is not suitable for extending the atomic interaction to the third nearest neighbor. Through analysis and test, it is found that when the modified electron density function is in the form of the fourth power and the form of the pair potential function is in the form of the sixth power polynomial, the interatomic potential can better describe the interatomic interaction; 2) The result of interstitial formation energy is taken as the target value to modify the behavior of the pair potential function in the near distance, and the modified interatomic potential gives the interstitial formation energy close to the result of DFT. When the interstitial energy calculated by the interatomic potential is larger than the target value, the pair potential curve of near distance will be softened by the superposition of a polynomial term, otherwise, the pair potential curve will be stiffened; 3) When the physical quantity under equilibrium state is used as the fitting data, the fitted potential parameters and the elastic constant results will not be affected, while adjusting the curve form of the potential function, as long as none of the function value, the slope and the curvature of the function curve is changed at each neighbor position. The magnitude of interstitial energy will be affected by changing the shape of the curve that is less than the first neighbor range; 4) Under the cutoff strategy in this paper, changing the cutoff distance has almost no influence on the calculated results of potential parameters or crystal properties, but has a slight influence on the mean square error of the fitting results. </sec><sec>The results of this paper provide some information for the construction of interatomic potentials database, and lay a foundation for constructing the Nb-related interatomic potential of alloy. And it also provides a method and basis for developing and improving the quality of interatomic potential.</sec>

Empirical interatomic potential for Fe-C system using original Finnis-Sinclair potential function

The Finnis-Sinclair (FS) potential is one of the three-body potentials and the potential function is the simplest in them. We developed the FS potential for an Fe-C binary system without changing the original form of the function. The potential parameters for the Fe-C and C-C interactions were determined to fit the physical properties (structural parameters, bulk modulus and cohesive energy) of five iron carbides (γ′-Fe4C, θ-Fe3C, χ-Fe5C2ο-Fe7C3 and NaCl type-FeC). The developed potential reproduced fourteen iron carbides and migration energy barriers of interstitial carbon atoms in body-centered cubic (bcc) and face-centered cubic (fcc) irons. Moreover, the reproducibility of the phonon densities of states for the iron atoms of cementite (θ-Fe3C) and hexagonal-Fe7C3 (h-Fe7C3) was confirmed and the diffusion coefficient of carbon atoms in bcc iron was good agreement with the experimental value.

Empirical interatomic potential for Fe-N binary system based on Finnis–Sinclair potential

A new empirical potential for the Fe-N binary system based on the Finnis–Sinclair (FS) potential was developed in order to analyze the strengthening mechanism of N addition in ferritic and austenitic steels. The potential parameters for the Fe-N and N-N interactions were determined to reproduce the physical properties of the first principles calculation data of four iron nitrides (ZnS type-FeN, ε- Fe3N, γ′- Fe4N and α′′- Fe16N2) obtained in this study. Furthermore, we investigated the reproducibility of physical properties of the other nitrides (NaCl type-FeN, ε- Fe2N and ζ- Fe2N) and the N behavior in body-centered cubic (bcc) and face-centered cubic (fcc) iron. The results showed good agreement with reference data.

Thermophysical properties of undercooled liquid Ni-Zr alloys: Melting temperature, density, excess volume and thermal expansion

The thermophysical properties of undercooled liquid Ni-Zr binary alloys were investigated by molecular dynamics simulation combined with a Finnis-Sinclair (F-S) potential, including melting temperature, density, excess volume and thermal expansion. The melting temperatures were obtained by the evolution of crystal-liquid-crystal sandwich model, where there exist rather low differences of 4.14% for Ni77.8Zr22.2 alloy and 3.98% for Ni50Zr50 alloy when they were compared with the reported values. The calculated densities of liquid Ni-Zr alloys increase with the decrease of temperature, which agree well with the reported experimental values except for the Ni-rich composition alloys. Thus, the reported experimental density of liquid Ni77.8Zr22.2 alloy was employed to re-gauge the current F-S potential and the densities of the Ni-rich composition alloys were recalculated by the re-gauged potential. This binary liquid alloy system shows a negative excess volume, which could be attributed to the strong attractive interactions between Ni and Zr atoms. It is indicated that the Ni-Zr alloy system seriously deviates from the ideal solution, and the accuracy would be very low if the thermophysical properties are estimated by Neumann-Kopp rule. Meanwhile, the thermal expansion coefficients were also derived on the basis of the density data, which increase with the enhancement of temperature except for liquid Ni77.8Zr22.2 alloy.

Experimental and molecular dynamics simulation study of structure of liquid and amorphous Ni62Nb38 alloy.

The state-of-the-art experimental and atomistic simulation techniques were utilized to study the structure of the liquid and amorphous Ni62Nb38 alloy. First, the ab initio molecular dynamics (AIMD) simulation was performed at rather high temperature where the time limitations of the AIMD do not prevent to reach the equilibrium liquid structure. A semi-empirical potential of the Finnis-Sinclair (FS) type was developed to almost exactly reproduce the AIMD partial pair correlation functions (PPCFs) in a classical molecular dynamics simulation. This simulation also showed that the FS potential well reproduces the bond angle distributions. The FS potential was then employed to elongate the AIMD PPCFs and determine the total structure factor (TSF) which was found to be in excellent agreement with X-ray TSF obtained within the present study demonstrating the reliability of the AIMD for the simulation of the structure of the liquid Ni-Nb alloys as well as the reliability of the developed FS potential. The glass structure obtained with the developed potential was also found to be in excellent agreement with the X-ray data. The analysis of the structure revealed that a network of the icosahedra clusters centered on Ni atoms is forming during cooling the liquid alloy down to Tg and the Nb Z14, Z15, and Z16 clusters are attached to this network. This network is the main feature of the Ni62Nb38 alloy and further investigations of the properties of this alloy should be based on study of the behavior of this network.

Mechanical behavior of Cu—Zr bulk metallic glasses (BMGs): A molecular dynamics approach

In the present work, three-dimensional molecular dynamics simulation is carried out to elucidate the nanoindentation behaviors of CuZr Bulk metallic glasses (BMGs). The substrate indenter system is modeled using hybrid interatomic potentials including both many-body Finnis Sinclair (FS) and two-body Morse potentials. A spherical rigid indenter (diameter = 60 Å(1 Å = 10−10 m)) is employed to simulate the indentation process. Three samples of BMGs including Cu25Zr75, Cu50Zr50, and Cu75Zr25 are designed and the metallic glasses are formed by rapid cooling from the melt state at about 2000 K. The radial distribution functions are analyzed to reveal the dynamical evolution of the structure of the atoms with different compositions and different cooling rates. The mechanical behavior can be well understood in terms of load-depth curves and Hardness-depth curves during the nanoindentation process. Our results indicate a positive linear relationship between the hardness and the Cu concentration of the BMG sample. To reveal the importance of cooling rate provided during the processing of BMGs, we investigate the indentation behaviors of Cu50Zr50 at three different quenching rates. Nanoindentation results and radial distribution function (RDF) curves at room temperature indicate that a sample can be made harder and more stable by slowing down the quenching rate.

Melting curves and entropy of fusion of body-centered cubic tungsten under pressure

The melting curves and entropy of fusion of body-centered cubic (bcc) tungsten (W) under pressure are investigated via molecular dynamics (MD) simulations with extended Finnis-Sinclair (EFS) potential. The zero pressure melting point obtained is better than other theoretical results by MD simulations with the embedded-atom-method (EAM), Finnis-Sinclair (FS) and modified EAM potentials, and by ab initio MD simulations. Our radial distribution function and running coordination number analyses indicate that apart from the expected increase in disorder, the main change on going from solid to liquid is thus a slight decrease in coordination number. Our entropy of fusion of W during melting, ΔS, at zero pressure, 7.619 J/mol·K, is in good agreement with the experimental and other theoretical data. We found that, with the increasing pressure, the entropy of fusion ΔS decreases fast first and then oscillates with pressure; when the pressure is higher than 100 GPa, the entropy of fusion ΔS is about 6.575 ± 0.086 J/mol·K, which shows less pressure effect.

Improved Finnis–Sinclair potential for bcc vanadium solid

By introducing an exponential repulsion term to improve the repulsive interactions between the atoms, we refit the Finnis–Sinclair (FS) potential for bcc vanadium solid. The experimental cohesive energy, lattice constant and elastic constants of bcc vanadium solid are well reproduced. The agreement of calculated phonon dispersion and equation of state with experimental results further verify the good quality of our improved FS potential. The improved FS potential not only is able to give a better description of the fundamental properties of bcc vanadium solid, but also is suitable for simulation the structural damage due to neutron irritation in this material.

Energetics and diffusional properties of He in BCC Mo: An empirical potential for molecular dynamics simulations

This paper presents an interatomic potential for modeling He defects and bubbles in body-centered-cubic (BCC) Mo. We utilize three existing frameworks: the Finnis–Sinclair (FS) potential for Mo–Mo, the Effective-Medium-Theory (EMT) for He–Mo, and the Hartree–Fock-Dispersion (HFD) potential for He–He interactions. The energetics of He defects and the diffusivity of He interstitial given by this potential agree well with ab initio calculations and experimental measurements. Furthermore, in agreement with theoretical prediction, it is shown that the introduction of He gas suppresses the surface diffusivity of BCC Mo, which decays exponentially with increasing He pressure acting on the free surface. The decay constant, correlated with the characteristic interaction volume for He–Mo, is close to the atomic volume of BCC Mo. This suppression effect is important to understand the mobility of small He bubbles.

Long-range Finnis-Sinclair potential for Zn-Mg alloy

A set of optimal long-range Finnis-Sinclair (F-S) potential parameters of single Mg are achieved by fitting the lattice energy, lattice constants, and elastic constants to experimental results. With the same method, the set of the F-S potential parameters of single Zn are obtained through the introduction of modifying factor to the repulsive term. Finally, the lattice energy and lattice constants of Mg21 Zn25, MgZn2 and Mg2Zn11 alloys are further fitted to achieve the F-S potential parameters of Zn-Mg based on the previous F-S potential parameters of Mg-Mg and Zn-Zn. After that, a series of molecular dynamics simulations of single Mg, Zn, and Mg21 Zn25, MgZn2, Mg2Zn11 alloys is performed at 300 K with the achieved F-S potential parameters, thereby proving the F-S potential parameters to be appropriate for the description of Zn-Mg alloys. The long-range F-S potential parameters of Zn and Zn, Mg and Mg, Zn and Mg are obtained.

Model calculations of edge dislocation defects and vacancies in α-Iron lattice

Two models of defects in perfect α-iron lattice were discussed. In the perfect bcc iron lattice 42×42×42 ao (ao = 2,87 Å) an edge dislocation was created, moving the second half of the bulk on one ao distance. This action generates a little volume in the middle of the bulk witch increases of the positron lifetime (PLT) calculated using the superimposed-atom method of Puska and Nieminen [1]. The result of 118 ps PLT in simple edge dislocation's model is in a good concurrence with earlier publications and experimental data [2]. Through the dislocation line one, two and three vacancies were localized. These models give the results for PLT of 146, 157 and 167 ps respectively. The computer simulations were performed using Finnis–Sinclair (FS) N-body potential.

Long-range Finnis-Sinclair potential for molecular dynamics simulation of α-Al2O3

The molecular dynamics （MD） simulation of metal-metal oxide interface requires a uniform potential to simultaneously describe metal and metal oxide. Accordingly, we obtained a set of long-range Finnis-Sinclair （F-S） potential parameters of α-Al2O3. All of the parameters were fitted to the targets, i.e. the experimental lattice energy, lattice constants, and elastic constants of α-Al2O3. Meanwhile, we compared our results with those reported by EAM, Glue and modified Matsui （m-Matsui） potentials and found that our rcsults are equivalent or better. After that, MD simulation of α-Al2O3 at 300 K with our long-range F-S potential was performed and the pair correlation functions, coordination numbers were calculated. The good agreement between calculation results and experiments validated the feasibility of this set of F-S potential parameters to the description of α-Al2O3 system.

Effects of undersized Fe atoms on the stability of interstitials near a dislocation core in V studied by molecular dynamics simulation

It is well-known that the dislocation bias should be responsible for the large swelling. In V-Fe alloys, the extremely large swelling has been observed, which indicates that undersized Fe atoms must play a significant role for the modification of one-dimensional (1D) motion. In the present study, we performed molecular dynamics (MD) simulations with a newly constructed empirical potential based on the Finnis-Sinclair (FS) type embedded atom method (EAM) to investigate the effects of undersized Fe atoms on the static and dynamic properties of the interstitial migration under the strain field of several sizes of interstitial loops and an edge dislocation. The results show that the undersized Fe atoms tend to form a stable mixed-dumbbell configuration and the activation energy of migration towards a dislocation core is much lower than that of SIAs. Moreover, for V-Fe dumbbell the relative probability for intermediate configurations between 〈111〉-crowdion and 〈110〉-dumbbell below an edge dislocation core becomes significantly higher compared to that of V-V dumbbell. These results indicate that it is very likely that the continuous absorption of interstitial Fe atoms by a dislocation core would be possible and enhances the swelling in V-Fe alloys.

Molecular Dynamics Analysis on Crack Growth Behavior in Single and Nano-Crystalline Fe by the Use of FS-2NNMEAM Hybrid Potential

In recent years, nano-crystalline materials have attracted many researchers’ attention, but the fracture mechanism has not been fully clarified. In a molecular dynamics (MD) simulation, grain size and crystal orientation can be chosen, and their effects on the mechanical properties of nano-crystalline materials can be evaluated clearly. This research first compares the results of crack growth behavior in single crystalline Fe for three typical interatomic potentials (Embedded Atom Method (EAM), Finnis Sinclair (FS), and Second Nearest Neighbor Modified EAM (2NNMEAM) potentials) and a Hybrid potential method, which uses FS potential for bcc structure atoms and 2NNMEAM potential for non-bcc structure atoms. The 2NNMEAM potential is accurate, but the computation time is dozens of times that of FS potential, which is the simplest of the three interatomic potentials. Therefore, the 2NNMEAM potential requires too much calculation for the purpose of this research that analyzes the crack growth behavior in nano-crystalline metals. However, Hybrid potential is able to give results similar to those of the 2NNMEAM potential, and the calculation time is close to that of the FS potential. From these results, the crack extension behavior in relatively large nano-crystalline models is analyzed using the Hybrid potential, and we demonstrate the grain-size dependency of the fracture behavior.

Molecular Dynamics Analyses of Crack Growth Behaviors in Single Crystalline Fe by the Use of Hybrid Potential Method

In Molecular Dynamics (MD) simulations, interatomic potentials have significant effects on the results and calculation time, i.e. analysis sizes. In this paper, first, the crack growth behaviors in α-Fe calculated by three representative interatomic potentials, the Embedded Atom Method (EAM) potential fitted by Simonelli, G. et al., Finnis-Sinclair (FS) potential and Second Nearest-neighbor Modified EAM (MEAM) potential, are compared, and the reliability of the results obtained by the MEAM potential is confirmed based on the reproducibility of the important physical properties. Although the MEAM potential is reliable, we show that the computational time required by the MEAM potential is more than 50 times of the FS potential. Here, we propose “Hybrid Potential Method” which selectively uses different interatomic potentials according to the local atomic structure, and connects those potentials by the use of handshake method. We use FS potential, which is efficient in calculation, for bcc structure and the MEAM potential, which is accurate but time consuming, for non-bcc structures. The availability of the Hybrid Potential Method is demonstrated, and then the method is applied to crack growth simulations using large calculation models. We report the phase transformations and grain nucleation near the crack tip during crack growth.