2.15 Compositional Model for the Earth’s Core W. F. McDonough University of Maryland, College Park, USA 2.15.1 INTRODUCTION 547 2.15.2 FIRST-ORDER GEOPHYSICS 548 2.15.3 CONSTRAINING THE COMPOSITION OF THE EARTH’S CORE 550 2.15.3.1 Observations from Meteorites and Cosmochemistry 551 2.15.3.2 Classification of the Elements 552 2.15.3.3 Compositional Model of the Primitive Mantle and the Bulk Earth 553 2.15.4 A COMPOSITIONAL MODEL FOR THE CORE 554 2.15.4.1 Major and Minor Elements 555 2.15.4.2 The Light Element in the Core 556 2.15.4.3 Trace Elements in the Core 558 2.15.5 RADIOACTIVE ELEMENTS IN THE CORE 561 2.15.6 TIMING OF CORE FORMATION 562 2.15.7 NATURE OF CORE FORMATION 563 2.15.8 THE INNER CORE, ITS CRYSTALLIZATION, AND CORE–MANTLE EXCHANGE 564 2.15.9 SUMMARY 565 ACKNOWLEDGMENTS 566 REFERENCES 566 2.15.1 INTRODUCTION the top of the inner core is even less securely known (,3,500–4,500 8C).) The pressure The remote setting of the Earth’s core tests range throughout the core (i.e., 136 GPa to our ability to assess its physical and chemical .360 GPa) makes recreating environmental characteristics. Extending out to half an Earth conditions in most experimental labs imposs- radii, the metallic core constitutes a sixth of the ible, excepting a few diamond anvil facilities or planet’s volume and a third of its mass (see those with high-powered, shock-melting guns Table 1 for physical properties of the Earth’s (see Chapter 2.14). Thus, our understanding of core). The boundary between the silicate mantle the core is based on very few pieces of direct and the core (CMB) is remarkable in that it is a evidence and many fragments of indirect zone of greatest contrast in Earth properties. observations. Direct evidence comes from The density increase across this boundary seismology, geodesy, geo- and paleomagnetism, represents a greater contrast than across the and, relatively recently isotope geochemistry crust-ocean surface. The Earth’s gravitational (see Section 2.15.6). Indirect evidence comes acceleration reaches a maximum (10.7 m s22)at from geochemistry, cosmochemistry, and the CMB and this boundary is also the site of meteoritics; further constraints on the core the greatest temperature gradient in the Earth. system are gained from studies in experimental (The temperature at the base of the mantle petrology, mineral physics, ab initio calcu- (,2,900 8C) is not well established, and that at lations, and evaluations of the Earth’s energy 547 548 Compositional Model for the Earth’s Core Table 1 Physical properties of the Earth’s core. Units Refs. Mass Earth 5.9736E þ 24 kg 1 Inner core 9.675E þ 22 kg 1 Outer core 1.835E þ 24 kg 1 Core 1.932E þ 24 kg 1 Mantle 4.043E þ 24 kg 1 Inner core to core (%) 5.0% Core to Earth (%) 32.3% Depth Core–mantle boundary 3,483 ^ 5km2 Inner–outer core boundary 1,220 ^ 10 km 2 Mean radius of the Earth 6,371.01 ^ 0.02 km 1 Volume relative to planet Inner core 7.606E þ 09 (0.7%) km3 Inner core relative to the bulk core 4.3% Outer core 1.694E þ 11 (15.6%) km3 Bulk core 1.770E þ 11 (16.3%) km3 Silicate earth 9.138E þ 11 (84%) km3 Earth 1.083E þ 12 km3 Moment of inertia constants Earth mean moment of inertia (I) 0.3299765 Ma2 1 2 Earth mean moment of inertia (I) 0.3307144 MR0 1 2 2 Mantle: Im/Ma 0.29215 Ma 1 2 2 Fluid core: If/Ma 0.03757 Ma 1 2 2 Inner core: Iic/Ma 2.35E24 Ma 1 2 2 Core: Ifþic/Mfþicaf 0.392 Ma 1 1—Yoder (1995),2—Masters and Shearer (1995). M is the Earth’s mass, a is the Earth’s equatorial radius, R0 is the radius for an oblate spheroidal Earth, Im is the moment of inertia for the 2 mantle, If is the moment of inertia for the outer (fluid) core, Iic is the moment of inertia for the inner core, and Ifþic/Mfþicaf is the mean moment of inertia for the core. Figure 1 The relative relationship between disciplines involved in research on the Earth’s core and the nature of data and information that come from these various investigations. Studies listed in the upper row yield direct evidence on properties of the core. Those in the middle row yield indirect evidence on the composition of the Earth’s core, whereas findings from disciplines listed on the bottom row provide descriptions of the state conditions for the core and its formation. budget (e.g., geodynamo calculations, core 2.15.2 FIRST-ORDER GEOPHYSICS crystallization, heat flow across the core–mantle boundary). Figure 1 provides a synopsis of The Earth’s three-layer structure (the core, research on the Earth’s core, and the relative the silicate shell (mantle and crust), and the relationship between disciplines. Feedback loops atmosphere–hydrosphere system) is the product between all of these disciplines refine other’s of planetary differentiation and is identified as the understanding of the Earth’s core. most significant geological process to have First-order Geophysics 549 occurred since the formation of the Earth. Each lines of evidence. Wiechert was a very interesting layer is distinctive in its chemical composition, scientist; he invented a seismograph that saw the nature of its phase (i.e., solid, liquid, and gas), widespread use in the early twentieth century, was and physical properties. Evidence for the exist- one of the founders of the Institute of Geophysics ence and nature of the Earth’s core comes from at Go¨ttingen, and was the PhD supervisor of Beno laboratory studies coupled with studies that Gutenberg. The discoverer of the Earth’s core is directly measure physical properties of the Earth’s considered to be Richard Dixon Oldham, a British interior including its magnetic field, seismological seismologist, who first distinguished P (compres- profile, and orbital behavior, with the latter provid- sional) and S (shear) waves following his studies ing a coefficient of the moment of inertia and a of the Assam earthquake of 1897. In 1906 Oldham model for the density distribution in the Earth. observed that P waves arrived later than expected There is a long history of knowing indirectly or at the surface antipodes of epicenters and directly of the existence of Earth’s core. Our recognized this as evidence for a dense and earliest thoughts about the core, albeit indirect and layered interior. Oldham placed the depth to the unwittingly, may have its roots in our under- core–mantle boundary at 3,900 km. Later, standing of the Earth’s magnetic field. The Gutenberg (1914) established the core–mantle magnetic compass and its antecedents appear to boundary at 2,900 km depth (cf. the modern be ,2,000 yr old. F. Gies and J. Gies (1994) report estimate of 2,891 ^ 5 km depth; Masters and that Chinese scholars make reference to a south- Shearer, 1995) and suggested that the core was at pointing spoon, and claim its invention to ca. AD 83 least partly liquid (Gutenberg, 1914). Sub- (Han dynasty). A more familiar form of the sequently, Jeffreys (1926) established that the magnetic compass was known by the twelfth outer core is liquid, and Lehmann (1936) identi- century in Europe. With the discovery of iron fied the existence of a solid inner core using meteorites followed by the suggestion that these seismographic records of large earthquakes, extraterrestrial specimens came from the interior of which was later confirmed by Anderson et al. fragmented planets in the late-nineteenth century (1971) and Dziewonski and Gilbert (1972) using came the earliest models for planetary interiors. Earth’s free-oscillation frequencies. Finally, Thus, the stage was set for developing Earth Washington (1925) and contemporaries reported models with a magnetic and metallic core. Later that an iron core would have a significant nickel development of geophysical tools for peering into content, based on analogies with iron meteorites the deep Earth showed that with increasing depth and the cosmochemical abundances of these the proportion of metal to rock increases with a elements. significant central region envisaged to be wholly The seismological profile of the Earth’s core made up of iron. (Figure 2) combined with the first-order A wonderful discussion of the history of the relationship between density and seismic wave 0:5 discovery of the Earth’s core is given in the Brush speed velocity (i.e., Vp ¼ððK þ 4=3mÞ=rÞ ; Vs ¼ 0:5 2 (1980) paper. The concept of a core perhaps ðm=rÞ ; dr=dr ¼ 2GMrrðrÞ=r F (the latter being begins with understanding the Earth’s magnetic the Adams–Williamson equation), where Vp is field. Measurements of the Earth’s magnetic field have been made since the early 1500s. By 1600 the English physician and physicist, William Gilbert, studied extensively the properties of magnets and found that their magnetic field could be removed by heating; he concluded that the Earth behaved as a large bar-magnet. In 1832, Johann Carl Friedrich Gauss, together with Wilhelm Weber, began a series of studies on the nature of Earth’s magnetism, resulting in the 1839 publication of Allgemeine Theorie des Erdmagne- tismus (General Theory of the Earth’s Magnet- ism), demonstrating that the Earth’s magnetic field was internally generated. With the nineteenth-century development of the seismograph, studies of the Earth’s interior and core accelerated rapidly.