An emerald - Rather the garnet, which when cut with a convex face is termed the carbuncle.

A sapphire - Not the stone now called the sapphire; the lapis-lazuli is most probably meant.

A diamond - There is no trace of evidence that the ancients ever acquired the skill to engrave on the diamond, or even that they were acquainted with the stone. The "diamond" here may possibly be some variety of chalcedony, or (perhaps) rock crystal.

Exodus 28:18 Parallel Commentaries

Joshua and the Angel
The steady advancement made by the builders of the temple greatly discomfited and alarmed the hosts of evil. Satan determined to put forth still further effort to weaken and discourage God's people by holding before them their imperfections of character. If those who had long suffered because of transgression could again be induced to disregard God's commandments, they would be brought once more under the bondage of sin. Because Israel had been chosen to preserve the knowledge of God in the earth, …
Ellen Gould White—The Story of Prophets and Kings