What is Equilibrium isotope effect, fractionation factor, δ value?

The equilibrium isotope effect of a reaction is the ratio $K_{\mathrm{light}}/K_{\mathrm{heavy}}$ of its equilibrium constants with the light and the heavy isotope. The fractionation factor between two phases or compounds A and B is $\alpha_{\mathrm{A/B}} = R_{\mathrm A}/R_{\mathrm B}$, where $R$ is the ratio of the heavy to the light isotope (for example $\ce{^{18}O}/\ce{^{16}O}$). The $\delta$ value of a sample is $\delta = (R_{\mathrm{sample}}/R_{\mathrm{standard}} - 1) \times 1000$, in per mil (‰).