The fraction of binary stars (fb) is one of most valuable tool to probe the star formation and evolution of multiple systems in the Galaxy. We focus on the relationship between fb and stellar metallicity ([Fe/H]) by employing the differential radial velocity (DRV) method and the large sample observed by the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST). Main-sequence stars from A- to K-types in the third data release (DR3) of LAMOST are selected to estimate fb. Contributions to a profile of DRV from radial velocity (RV) error of single stars (sigma) and orbital motion of binary stars are evaluated from the profile of DRV. Finally, we employ 365,911 stars with randomly repeating spectral observations to present a detailed analysis of fb and sigma in the two-dimensional (2D) space of Teff and [Fe/H]. The A-type stars are more likely to be companions in binary star systems than other stars. Furthermore, the reverse correlation between fb and [Fe/H] can be shown statistically, which suggests that fb is a joint function of Teff and [Fe/H]. At the same time, sigma of the sample for different Teff and [Fe/H] are fitted. Metal-rich cold stars in our sample have the best RV measurement.
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