Final answer:
The main variables used to value gem beryl, particularly emeralds, are related to impurities of chromium ions (Cr³⁺) in the crystal structure, which give emeralds their green color and determine their quality and value.
Step-by-step explanation:
The valuation of gem beryl, notably emerald, is influenced by several key variables. When evaluating emerald, which is a green variety of beryl, the presence of chromium ions (Cr³⁺) is a significant factor. In a pure beryl crystal, which has the chemical formula Be₃Al₂Si₆O₁₈, the replacement of just 1% of the Al³⁺ ions with Cr³⁺ ions results in the characteristic green color of emeralds. The colors of both emerald and ruby, which have a similar cause due to the Cr³⁺ impurities, are attributed to these impurities occupying octahedral sites within the metal oxide lattice structure. Thus, the concentration and distribution of chromium impurities are critical in determining the color and quality of the gem, and consequently its value.