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of >35% silica, the system behaves as a simple eutectic, producing first melts with an invariant composition of 46% silica. Melts possess this composition until either quartz (for systems 35–46% silica component) or enstatite (for systems >46% silica component) is completely melted. Subsequent melting of the remaining mineral causes the liquid to change composition up the liquidus. These behaviors once again demonstrate the ways in which melt compositions depend both on the percentage of partial melting and on the composition of the original rock. For compositions of <35% silica, melting involves peritectic reactions. In these systems, whenever the system reaches the peritectic, some or all of the enstatite remaining in the solid fraction melts to produce both forsterite and melt at the peritectic (35% silica component). This behavior is essentially the reverse of what happens when systems cool through the peritectic, and melt plus olivine yields enstatite. Such behavior, in which the melting of one crystalline material produces both a new crystalline material and a melt of different composition, is called incongruent melting. It also illustrates how silica oversaturated melts might be obtained from the partial melting of silica undersaturated, forsterite‐rich rocks such as ultramafic peridotites in the mantle.

3.3 ISOTOPES

      This section provides a brief introduction to the uses of some radioactive isotopes and stable isotopes important in the understanding of Earth materials and processes. Isotope studies provide powerful insights concerning the age, behavior and history of Earth materials. In geology, a thorough understanding of both stable and radioactive isotopes is essential for determining the ages and origin of minerals and rocks. Isotope ratios, determined by mass spectroscopy, are also instrumental in understanding a variety of other phenomena discussed in this book, including the determination of:

      1 Source rocks from which magmas are derived.

      2 Origin of water on Earth's surface.

      3 Timing of mountain building events involving igneous intrusions and metamorphism.

      4 Timing of unroofing of such rocks and the dispersal of their erosional products by sedimentary agents.

      5 Source rocks for petroleum and natural gas.

      6 Changes in ocean water temperatures, biological productivity and circulation.

      7 History of ice age glacial expansions and contractions.

      8 Climate change.

      3.3.1 Stable isotopes

      Stable isotopes contain nuclei that do not tend to change spontaneously. Instead, their nuclear configurations (number of protons and neutrons) remain constant over time. Many elements occur in the form of multiple stable isotopes with different atomic mass numbers. In many cases, these isotopes, because of their different mass, exhibit subtly different behaviors in Earth environments. These differences in behavior are recorded as differences in the ratios between isotopes that can be used to infer the conditions under which the isotopes were selectively incorporated into Earth materials. We will use oxygen and carbon isotopes to illustrate the uses of stable isotope ratios to increase our understanding of Earth materials and processes. Other stable isotopes that are commonly utilized in such studies include those of sulfur, nitrogen, and helium (Chapter 13, Box 13.2).

       Oxygen isotopes

      Three isotopes of oxygen occur in Earth materials (Chapter 2): oxygen‐18 (¹⁸O), oxygen‐17 (¹⁷O), and oxygen‐16 (¹⁶O). Each oxygen isotope contains eight protons in its nucleus; the remaining mass results from the number of neutrons (10, 9, or 8 respectively) in the nucleus.¹⁶O constitutes >99.7% of the oxygen on Earth,¹⁸O constitutes ~0.2%, and¹⁷O is relatively rare. The ratio¹⁸O/¹⁶O is widely used to infer important information concerning Earth history.

During evaporation, water with lighter¹⁶O is preferentially evaporated relative to water with heavier¹⁸O. During the evaporation of ocean water, water vapor in the atmosphere is enriched in¹⁶O relative to¹⁸O (lower¹⁸O/¹⁶O) while the remaining ocean water is preferentially enriched in¹⁸O relative to¹⁶O (higher¹⁸O/¹⁶O). Initially (Epstein and Mayeda 1953), these ratios were related to temperature because evaporation rates are proportional to temperature. It was proposed that higher¹⁸O/¹⁶O ratios in ocean water record higher temperatures, which cause increased evaporation and preferential removal of lighter¹⁶O. It was quickly understood that organisms using oxygen to make calcium carbonate (CaCO₃) shells could preserve this information as carbonate sediments accumulated on the sea floor over time. Such sediments would have the potential to record changes in water temperature over time; especially when the changes are large and the signal is clear (see Box 3.1).

However, it was soon realized that small, short‐term temperature signals could be largely obliterated by a second set of processes. These involve changes in global ice volumes associated with the expansion and contraction of continental glaciers, e.g., during ice ages. Glaciers expand when more snow accumulates each year than is ablated (Chapter 12). This produces a net growth in glacial ice volume. Because atmospheric water vapor largely originates by evaporation, the snow (eventually converted to ice) is enriched in¹⁶O and has a low¹⁸O/¹⁶O ratio. As glaciers expand, they store huge volumes of water with low¹⁸O/¹⁶O ratios, causing the¹⁸O/¹⁶O ratio in ocean water to progressively increase. As a result, periods of maximum glacial ice volume correlate with global periods of maximum¹⁸O/¹⁶O in marine sediments. Prior to the use of oxygen isotopes, the record of Pleistocene glaciation was known largely from glacial till deposits on the continent, and only four periods of major Pleistocene glacial expansion had been established. Subsequently, the use of oxygen isotope records from marine sediments and ice (H₂O) cores in Greenland and Antarctica has established a detailed record that involves dozens of glacial ice volume expansions and contractions during the Pliocene and Pleistocene.

      ¹⁸O/¹⁶O ratios are generally expressed with respect to a standard in terms of δ¹⁸O. One standard is the¹⁸O/¹⁶O ratio in a belemnite from the Cretaceous Pee Dee Formation of South Carolina, called PDB. δ¹⁸O is usually expressed in parts per thousand (mils) and calculated from:

Box 3.1 The Paleocene–Eocene thermal maximum

      In the mid‐nineteenth century, scientists recognized a rapid change in mammalian fossils that occurred early in the Tertiary era. The earliest Tertiary epoch, named the Paleocene (early life), was dominated by archaic groups of mammals that had mostly been present during the preceding Mesozoic Era. The succeeding period, marked by the emergence and rapid radiation of modern mammalian groups, was called the Eocene (dawn of life). The age of the Paleocene–Eocene boundary is currently judged to be 55.8 Ma. Later workers noted that the boundary between the two epochs was also marked by the widespread extinction of major marine groups, most prominently deep‐sea benthic foraminifera (Pinkster 2002; Ivany et al. 2018). The cause of these sudden biotic changes initially remained unknown. Oxygen and carbon isotope studies have given us some answers.

      Kennett and Stott (1991) reported a rapid rise in δ¹⁸O at the end of the Paleocene, which they interpreted as resulting from a rapid rise in temperature, since they believed that no prominent ice sheets existed at this time. Subsequent work (e.g., Zachos et al. 1993; Rohl et al. 2000; Gehler et al. 2016; Ivany et.al. 2018) has confirmed that temperatures rose ~6–8 °C at high latitudes and ~3–5 °C at low latitudes over a time interval not longer than 10 000

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