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Acta Metall Sin  2020, Vol. 56 Issue (1): 112-118    DOI: 10.11900/0412.1961.2019.00257
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Relationships Between Elastic Constants and EAM/FS Potential Functions for Cubic Crystals
DUAN Lingjie,LIU Yongchang()
State Key Lab of Hydraulic Engineering Simulation and Safety, School of Materials Science and Engineering, Tianjin University, Tianjin 300354, China
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Abstract  

Potential functions are extensively applied in molecular dynamics (MD) simulation of metals. Selection of them is a very important step in MD simulations due to its effects of the precision and reliability of the simulations. They are one of the most important reference data during the process of calculation. In order to cover the shortage of pairwise potentials for modelling transition metals, EAM/FS many-body potentials have been introduced since 80's of last century. For the sake of determining parameters in the EAM/FS potential functions of bcc and fcc crystals through macro mechanical properties, relations between the EAM/FS potential functions and elastic constants were investigated in this work. Expressions of the pressure (P) and the bulk modulus (B), elastic constant (C44) and shear elastic modulus (Cp=(C11-C12)/2) in terms of the embedding function, pair potential function and the electron density distribution function were deduced for bcc and fcc structures, respectively. It was found that the magnitude of the C44 and Cp depends on the distances between the considered atom and surrounding atoms, but also the configuration of surrounding atoms. Finally, by converting five fitting equations about the cohesive energy (utot) and P, B, C44, Cp into an optimization model of finding minimum value, the values of the six undetermined parameters in the cohesive energy were given for five typical bcc crystals (V, Mo, Nb, Ta and W) and three typical fcc crystals (Cu, γ-Fe, Ni), respectively. For each crystal, calculation errors show accuracy of parameter values. The obtained calculation results, for the minimum cohesive energy and the corresponding atomic distance, fit well with the reported experimental data, by adopting the above values of the parameters, which indicates the effectiveness for our method.

Key words:  cubic crystal      elastic constant      EAM potential      FS potential     
Received:  01 August 2019     
ZTFLH:  TG111.3  
  TG113.2  
  O733  
Fund: National Natural Science Foundation of China(U1660201);National Magnetic Confinement Fusion Energy Research Project(2015GB119001)
Corresponding Authors:  Yongchang LIU     E-mail:  ycliu@tju.edu.cn

Cite this article: 

DUAN Lingjie,LIU Yongchang. Relationships Between Elastic Constants and EAM/FS Potential Functions for Cubic Crystals. Acta Metall Sin, 2020, 56(1): 112-118.

URL: 

https://www.ams.org.cn/EN/10.11900/0412.1961.2019.00257     OR     https://www.ams.org.cn/EN/Y2020/V56/I1/112

Crystala / nmutot / eVBC44Cp
V0.30399-5.311.5510.4260.546
Mo0.31472-6.822.6261.0891.516
Nb0.33008-7.571.7100.2810.567
Ta0.33058-8.101.9610.8240.524
W0.31652-8.903.1041.6061.590
Table 1  Experimental data for the five typical bcc structure crystals (elastic constants with dimension 1011 Pa)[8]
CrystalcdAc0c1c2ER
V3.16283.87991.711018.83-16.253.9725.125×10-11
Mo3.23174.36251.3678262.85-200.7038.8809.408×10-10
Nb3.39274.09492.590926.30-22.685.4051.103×10-10
Ta3.48634.29682.049825.13-17.983.5849.312×10-12
W3.26014.47631.5395275.77-207.6739.6552.896×10-3
Table 2  Fitted values of potential parameters for the five typical bcc structure crystals
Crystala / nmutot / eVBC44Cp
Cu0.3615-3.541.4200.8180.257
γ-Fe0.3591-4.291.6701.1700.475
Ni0.3518-4.451.8761.3170.552
Table 3  Experimental data for the three typical fcc structure crystals (elastic constants with dimension 1011 Pa)[17,31]
CrystalcdAc0c1c2ER
Cu4.02054.01860.753712.1130-1.44710.251400.001806
γ-Fe3.99213.99720.717783.1839-2.30860.415890.002837
Ni3.91073.91660.764073.6419-2.70790.500410.013935
Table 4  Fitted values of potential parameters for the three typical fcc structure crystals
Fig.1  utot-R curves for five typical bcc structure crystals (R—measurement of atomic spacing)
Fig.2  utot-R curves for three typical fcc structure crystals
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