Atomic structure and energy of {001}<110> edge dislocations

in AgCl and NaCl: A first principles study

Masaya Ukita1, Kazuaki Toyoura 1, Atsutomo Nakamura1, and Katsuyuki Matsunaga1,2

1 Department of Materials Science and Engineering, Nagoya University, Nagoya 464-8603, Japan 2 Nanostructures Research Laboratory, Japan Fine Ceramics Center, Nagoya 456-8587, Japan

AgCl and NaCl have the same rock-salt crystal structure, but they exhibit

different mechanical properties at low temperatures. In NaCl, only the primary slip

system of {110}<110> is activated, whereas multiple slip systems on the {001}, {011}

and {111} planes are activated in AgCl [1]. Therefore, AgCl is more ductile than NaCl.

Such a difference cannot be explained from a simple ionic picture of interatomic bonding,

and thus should be closely related to the atomic structures at the dislocation cores. In this

study, atomic structures of dislocation cores in both crystals were investigated in a first-

principles manner. Especially, self-energies of edge dislocations for the slip system of

{001}<110> in the two crystals were evaluated, and were compared with those from an

isotropic elastic theory.

All the calculations were performed on the basis of the projector augmented

wave (PAW) method in the framework of the density functional theory (DFT) as

implemented in the VASP code [2]. The generalized gradient approximation (GGA) was

selected for the exchange correlation potential [3]. As an initial structure, a pair of edge

dislocations with opposite signs of the Burgers vectors was introduced to the triclinic

supercell for DFT calculations. Structure optimizations was performed until residual

forces on atoms were less than 0.01 eV/Ǻ. The distance between adjacent dislocations

was taken about 3.4 nm in the supercells. In this case, a self-energy ( ) of a single

dislocation per angstrom is given by

, (1)

where is a total energy of the optimized supercell, and is a total

energy of the perfect crystal.

The obtained was compared with that from an isotropic elasticity theory

( ). An value can be expressed as

, (2)

where is the Poisson’s ratio, is the shear modulus, is the length of Burgers vector,

is the radius of elastic strain field and is the radius of dislocation core, respectively

[4]. It should be noted here that the lattice parameters are 5.60 Å for AgCl and 5.64 Å for

NaCl and thus the absolute values of the Burgers vectors only differs 0.7 % between the

two crystals. For the and , reported values in previous experiments were used (

= 0.40, = 0.25, = 6.21 GPa and = 12.61 GPa) [5, 6]. The value of

𝑅 was considered as a half of the distances between dislocations. In order to include the

core energy in Eq. (2), is usually selected. In the case of , the

and were evaluated to be 0.23 and 0.38 eV/Å, respectively.

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Figure 1 shows the optimized structures of the {001}<110> edge dislocation in

AgCl and NaCl. The strain becomes smaller with increasing the distance from the center

of dislocations in both structures. Regarding the atomic configurations at the dislocation

core, it was found that larger atomic relaxation is present in the case of AgCl. The

calculated was 0.21 eV/Å for AgCl and 0.48 eV/Å for NaCl. These self-energies

from first principles roughly agreed with those from the elastic theory ( ). The lower

value for AgCl than that for NaCl may indicate that dislocations due to the {001}<110>

system in AgCl can be more easily activated, as compared to those in NaCl, namely more

ductility of AgCl.

Acknowledgment

This study was supported by a Grant-in-Aid for Scientific Research on Innovative Areas

"Nano Informatics" (grant numbers 25106002) from Japan Society for the Promotion of

Science (JSPS). A part of this study was supported by JSPS KAKENHI Grant Numbers

20419675 and 15K14122.

References

[1] F. Vavra et al., Czech. J. Phyz. B 22 (1972)138.

[2] G. Kresse et al., Phys. Rev. B 54 (1996) 11169.

[3] J.P. Perdew et al., M. Phys. Rev. Lett. 77 (1996) 3865.

[4] J.P. Hirth et al., Theory of dislocations. 2nd ed., New York: Wiley (1982).

[5] L.S. Combes et al., J. Opt. Soc. Am. 41 (1951) 215.

[6] W. C. Hughes et al., Phys. Rev. B 53 (1996) 5174.

Fig. 1. Atomic configurations of the {001}<110> edge dislocation in (a) NaCl and (b)

AgCl.

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AMTC Letters　Vol. 5 (2016) ©2016 Japan Fine Ceramics Center