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I’ll be the first to admit: my coursework during my undergraduate and graduate years has been focused on physics, astrophysics, and planetary astronomy.  I probably couldn’t tell a peridotite from most other mafic rocks unless really pressed (no pun intended), and I certainly don’t have much of an intuition for isotope geochemistry.  This field requires an entirely new alphabet and vocabulary; an appreciation for isotope fractionation lines; and most importantly, an understanding of what that difference in the millions’ place of a decimal means for the evolution of Earth’s mantle.

One way isotope geochemists measure differences between two similar values, say a sample and an established standard, is by taking the ratio of these two values, then subtracting one, since the ratio of these values is usually very close to unity.  Some isotope ratios differ by one part in 1,000, so for those, we use delta notation.  Oxygen isotopes, for example, are measured compared to the stable 16 and 18 isotopes:

$$\delta^{18}O = \left[ \frac{\left ( \frac{^{18}O}{^{16}O} \right )_{sample}}{\left ( \frac{^{18}O}{^{16}O} \right )_{standard} }- 1 \right ] \times 1,000$$

δ¹⁸O values can be used to measure changes in sea level and climate in ice cores, and are calculated compared to a standard for water with a specific set of isotopes.  At present, a δ¹⁸O of ~0 corresponds to that of equatorial ocean waters on Earth.  This notation has been used since at least the 1950’s, so if you see delta notation in the literature, it should refer to parts in 1,000.

When Günter Lugmair started investigating concentrations of neodymium in Apollo and meteorite samples, most of the interesting variation was less than one part in 1,000, so he started to use epsilon notation to represent parts in 10,000:

$$\epsilon^{143}Nd = \left[ \frac{\left ( \frac{^{143}Nd}{^{144}Nd} \right )_{sample}}{\left ( \frac{^{143}Nd}{^{144}Nd} \right )_{standard} }- 1 \right ] \times 10,000$$

Note that, unlike delta notation, for epsilon the lighter isotope is on top in the ratios.

When Richard Carlson started with osmium isotope analysis, he continued this trend and coined “gamma” as measuring parts in 100:

$$\gamma^{187}Os =  \left[ \frac{\left ( \frac{^{187}Os}{^{188}Os} \right )_{sample}}{\left ( \frac{^{187}Os}{^{188}Os} \right )_{standard} }- 1 \right ] \times 100$$

Though there is not yet a consistent unit for parts per million, some have started using μ:

$$\mu^{142}Nd = \left[ \frac{\left ( \frac{^{142}Nd}{^{144}Nd} \right )_{sample}}{\left ( \frac{^{142}Nd}{^{144}Nd} \right )_{standard} }- 1 \right ] \times 1,000,000$$

For ε¹⁴³Nd and μ¹⁴²Nd, it’s important to be consistent with what you’re using as the standard in these calculations, as most use a terrestrial standard such as La Jolla, making ε¹⁴³Nd or μ¹⁴²Nd equal to 0. However, if you’re using a chondrite standard, your values would change. There’s enough variation in ¹⁴²Nd in chondrites that sticking with a terrestrial standard is the most safe at the moment.