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The elastic constants of the B1 structure NaCl under pressure are obtained by using the ab initio plane-wave pseudopotential density functional theory method. The obtained zero pressure lattice constant and elastic constants are in good agreement with the available experimental data. It is found that the elastic constants C-11 and C-12 and the bulk modulus B increase monotonically with pressure P, however C-44 increases monotonically when P <= 28 GPa and decreases when P > 28 GPA. Moreover, we discuss the B1-B2 structure phase transition of NaCl and obtain the transition pressure of 28.3 GPa.

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