Abstract

Using first-principles calculations within hybrid functional, chromium defects in α-Al<inf>2</inf>O<inf>3</inf> are investigated, which are believed to be the cause of red color in ruby. It is found that the chromium substitution for aluminum (Cr<inf>Al</inf>) defect has low formation energy under both Al- and O-rich growth conditions, whereas the formation energy of the Cr substitution for O (Cr<inf>O</inf>) defect is much higher, except under p-type and Al-rich growth conditions. In addition, Cr interstitial (Cr<inf>i</inf>) also has low formation energy under p-type and Al-rich conditions, and its formation energy is somewhat lower than that of Cr<inf>O</inf>. However, natural sapphire is an insulator indicating that the Fermi-level position should be around the midgap. This confirms that Cr is likely to substitute for Al atom. By exploring the optical properties of the Cr<inf>Al</inf> defect to identify the origin of red color in ruby, the absorption energies associated with the transition of (Formula presented.) to (Formula presented.) and (Formula presented.) to (Formula presented.) are 2.12 and 2.73 eV, respectively. The former and latter can be assigned to the observed U and Y bands, respectively, which are believed to be the origin of red color in ruby. Further, it is suggested that the emission lines R, R', and B are associated with other defects or other mechanisms.