Relative of lime and mint

As a detective solving the mystery of this crossword clue, my first thought was to focus on the words ‘lime and ‘mint’. These two words are commonly associated with colors; lime green and mint green. As such, I considered gems that have green hues such as emeralds or peridots. However, the clue explicitly stated a ‘relative’ of lime and mint. It was then that I remembered that jade, often associated with China and the Orient, is a gem that also comes in green shades. Furthermore, jade’s green is a distinct shade that resembles lime and mint. Therefore, all signs pointed to the answer being jade. With this in mind, I confidently filled out the crossword, feeling proud of the deduction that led me to the answer.