Earth factories: Creation of the elements from nuclear transmutation in Earth’s lower mantle

Stellar nucleosynthesis is a widely acknowledged theory for the formation of all elements in our universe; traditionally, we say that the highest mass stars transmuted lighter elements into heavier elements lighter than iron. Here, we propose that the formation of 25 elements with smaller atomic numbers than iron resulted from an endothermic nuclear transformation of two nuclei confined in the natural compound lattice core of the Earth’s lower mantle at high temperatures and pressures. This process is accompanied by the generation of neutrinos and is influenced by excited electrons generated by stick-sliding during supercontinent evolution, mantle convection triggered by major asteroid collisions, and nuclear fusion in the Earth’s core. Therefore, our study suggests that the Earth itself has been able to create lighter elements by nuclear transmutation. © 2021 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0061584


I. INTRODUCTION
The Big Bang theory 1 proposes that hydrogen, helium, and trace amounts of lithium were the only elements in existence when the universe first formed. In other words, Big Bang nucleosynthesis produced elements no heavier than lithium. Hotter and heavier stars then transmuted lighter elements (i.e., the first elements) into heavier elements (i.e., the secondary elements, some of which were generated by the CNO cycle 2 ) up to and including iron through exothermic stellar nucleosynthesis in their cores. Because the fusion of iron nuclei does not create energy, high mass star cores must collapse, resulting in supernovae. When supernovae explode, many neutrons passing through the outer regions of the stars collide with the atoms of elements lighter than iron (number 26 in the periodic table), resulting in elements heavier than iron via neutron incorporation. 3 This theory is the basis of convention for the formation of all elements in our universe. Regarding Earth formation, it is generally believed that the terrestrial planets have formed by accretion of solid materials that condensed from the solar nebula ∼4.56 × 10 9 years ago. 4 As a result, whole-Earth geochemical models, which are primarily based on cosmochemical abundances, provide specific limits on the possible chemical composition of the Earth's deep interior. 5 In disagreement with this theory, Fukuhara proposed a model for the formation of nitrogen, oxygen, and water using circumstantial evidence based on the history of the Earth's atmosphere. This hypothesis suggests that heavier elements result from an endothermic nuclear transformation of carbon and oxygen nuclei confined in the aragonite CaCO 3 lattice of the Earth's mantle or crust, which is enhanced by the attraction caused by high temperatures ≥2510 K and pressures ≥58 GPa in the Earth's interior, 6 2 12 C + 2 16 O + 4e * + 4ve → 2 14 N 2 ↑ + 16 O 2 ↑ + 1 H 2 16 O↑ + 2n − 10.58 MeV. (1) The above-described reaction is favored by the physical catalysis exerted by excited electrons (e * ) that were generated through stick-sliding during the evolution of supercontinents and mantle conversion triggered by collisions of major asteroids and antielectron neutrinos ve coming from the universe, especially from the young sun from the Archean era to the present time, 7 or by the radioactive decay of elements such as U and Th and nuclear fusion in the Earth's core that is described later. Equation (1) denotes the endothermic formation of N, O, and water. In contrast to the origin of nitrogen in the Earth, Grewal, Dasgupta, and Marty 8 inferred that original nitrogen in the Earth is derived from a mixture of both inner and outer solar system materials because the 15 N/ 14 N ratio in the Earth falls between those of the inner and outer solar system. However, their paper cannot explain the reason why a rapid formation of 14 N would have continued for 1.3 × 10 9 years from 2.5 to 3.8 × 10 9 years ago in the Archean era. 9 Furthermore, Fukuhara 10,11 postulated a model for the origin of thermal energy within the Earth's interior, which is devoid of harmful radioactive waste, in which the generated heat is attributed to the three-body nuclear fusion of the deuteron (D) confined within hexagonal FeDx core-center crystals, The above reaction demonstrates the exothermic formation of the lightest elements H and He. When juxtaposing the conditions for electron degeneracy pressure and temperature for the cores of Jupiter, Saturn, and Earth with those of WISE 1828+2650, 12 the coldest brown dwarf, deuteron nuclear fusion was found to be possible in the cores of Earth, Jupiter, and Saturn, as well as in WISE 1828+2650. 13 Thus, there is a possibility that Eqs. (1) and (2) show the creation of elements in the Earth's lower mantle or crust and inner core, respectively. Inductively, we considered the possibility of element production from lighter to heavier elements in minerals of the Earth's interior at high pressure and temperature in terms of endothermic nuclear transformable reactions. However, to the best of our knowledge, theories of element creation have not been previously developed in the context of an "Earth factory" as described herein.

II. METHODS
The crystal structures of mineral compounds were drawn by using ATOMS 6.4 (atoms and polyhedra) and Corel-DRAW2020 (auxiliary lines and symbols), with the structural data obtained from single-crystal x-ray diffraction measurements 14 for the γ-orthopyroxene (Mg 0.44 Fe 0.56 ) SiO 3 mineral, ab initio calculations 15 for Cmcm-MgAl 2 O 4 , and our ab initio calculations (VASP 5.3) for the high-pressured kyanite (Al 2 SiO5) III phase.
To calculate the smallest endothermic formation energies, an algorithm was written to iterate through reactant elements and calculate the final values, after which filtering was conducted based on the element type and the final values were obtained. The program provided a total of ∼150 000 equations, which could then be filtered in a spreadsheet format.

A. Comparison of element concentrations of Earth, Mercury, Venus, and Mars
We compare element concentrations of terrestrial planets, namely, Mercury, Venus, Earth, and Mars, which are formed by similar materials. Figure 1(a) shows the variation in the composition of Mercury, 16 Venus, 16 Earth, 16 and Mars 17 for elements with atomic numbers up to 40. The concentrations of Venus, Earth, and Mars elements are roughly similar, unlike Mercury, which is lighter (1/18 of Earth's mass) and hotter (∼700 K). 16 The concentrations increase to Si and then decrease with the increasing atomic number, regardless of the planet type. Figure 1(b) presents the weight differences of Venus and Mars compared with Earth for elements with atomic numbers from 6 (C) to 26 (Fe), excluding Ne and Ar. The elemental weight differences of Venus and Mars were calculated from their mass ratios relative to that of Earth. The positive values in Fig. 2(b) represent an absolute increase in these elements in Venus and Mars compared with Earth, and negative values indicate a higher ratio on Earth compared to Venus and Mars. The positive values for C and N and the negative values for Cr and Mn in Venus could be derived from the suppression effect, as its atmospheric pressure is ∼98-fold  higher than that on Earth, 18 and the high vaporization effect of chromium and manganese, 19 respectively. Consequently, C, N, P, S, Cr, Mn, and Fe may have been produced in the Earth's interior after the formation of the terrestrial planets ∼4.56 × 10 9 years 4 ago. Even if one considers the collision of asteroids over the past 2.5 × 10 9 years, 20 the sum of all asteroid masses could not exceed over 10 16 kg.
On the other hand, recent research has reported that large amounts of terrestrial N 2 , 21,22 noble gases, 22 and O 2 23 have been transported to the Moon via solar wind. This suggests that the atmospheric mass is continuously dispersed into space, and thus, our atmosphere could not keep the pressure needed to support life on Earth without a continuous resupply of these gasses from Earths' interior.

B. Formation of lighter elements in Earth's inside
In Sec. III A, to support the formation of elements in the Earth's internal structure, weight differences of lighter elements of Earth were compared with those of Venus and Mars. Despite the likelihood of the proposed phenomena, it is not possible to secure positive evidence by comparing these data alone.
According to the theory of the fundamental process, 26 hadronic interaction conserves isospin before and after the endothermic reaction of nuclei. Given that Eqs. (6)-(45) are non-equilibrium (irreversible) equations, they do not obey the rules of parity and momentum balance. In the irreversible endothermic reaction proposed by Glansdorff and Prigogine, 27 remarkable enhancement of formation energy is expected based on the thermal factor of exp (−ΔG/kT), where ΔG is the change in Gibbs energy for the whole system. The formation energies with the first and second lowest values are shown in Fig. 2, as functions of atomic number (a) and Clarke index (b), which is the relative abundance of a chemical element in the Earth's crust (i.e., ∼1 km below the surface). The lowest energies are below −100 keV, except for Mn. This is especially true for Eqs. (7), (10), (12)-(17), (19), and (20), where Be, N, F, Ne, Na, K, Mg, Al, Si, S, Ti, Ca, and V appear to be formed by endothermic energies below 50 keV. These endothermal energies are approximately close to the acceleration of the d + d reactions in metal lithium acoustic cavitation with deuteron bombardment up to 70 keV. 28 If a three-body reaction occurs in place of the above-described two-body reactions, all formation energies in Eqs. (6)-(45) could decrease further. 7 On the other hand, there is no dependence ARTICLE scitation.org/journal/adv between the Clarke number and energy. The Clarke number does not provide the abundance ratio for the entire mass of Earth. Thus, there is a possibility for element creation in the Earth's interior, provided that suitable temperatures and pressures are applied to natural minerals with reactant elements in natural compounds (minerals) of the Earth's interior. Given that the reactions for Eqs. (6)-(45) are necessary conditions for the nuclear transmutation of lighter elements in Earth's interior, we must investigate sufficient conditions for elements up to iron using minerals at high temperature and pressure. We then considered the potential for nuclear transmutation of natural minerals containing Mg with Fe, Al with Mg, and Al with Si as examples.

C. Transmutation reaction from Mg and Fe
To investigate the endothermic nuclear reaction of 32 11 S and 48 22 3 14 in its high-pressure form at a temperature exceeding 800 K and pressure above 11.6-21.1 GPa (depending on the ferrosilite content), as a reactant mineral. Figure 3 illustrates the configuration of the Mg-Fe bond on the (400) plane in the γ-orthopyroxene (Mg 0.44 , Fe 0.56 ) SiO 3 structure of the high-pressure phase. When γ-orthopyroxene is compressed at a high pressure of 32 GPa, the shortest Mg-Fe distance (d 1 ) on the (400) plane can be calculated as 0.272 nm. The shrinkage ratio η 1 is 0.9096 (= 0.272/0.299). However, the distance d 1 exceeded the distance required for a dynamic nuclear reaction (∼0.094 nm 32 ). Therefore, we must consider the pressure, temperature, and physical catalysis effects accelerating the confinement of magnesium and iron nuclei in the γ-orthopyroxene lattice.

D. Confinement due to high pressure
The outer shell electrons of Mg and Fe atoms in the γorthopyroxene (Mg, Fe) SiO 3 lattices behave as free electrons, 33 and the resulting screening effect provides relief from the repulsive Coulomb force between Mg and Fe nuclei. The Mg-Fe distance (d 1 ) of γ-orthopyroxene at 130.3 GPa and 3221 K corresponding 2600 km below the Earth's surface (Sec. 1 in the supplementary material) can be estimated as 0.1905 nm (see Sec. 2 in the supplementary material). The shrinkage ratio η 1 is 0.6370 (= 0.1905/0.299). However, this distance is still considerable compared to the distance required for a dynamic nuclear reaction.

E. Confinement due to high temperature
Next, we considered the effect of temperature on the reaction rate k. The rate can be expressed using the Arrhenius equation as follows: 34 where f S , f Ti , f Mg , and f Fe are the partition functions of 24 12 Mg, 56 26 Fe, 32 11 S, and 48 22 Ti, respectively, and k B and R and E are the Boltzmann and gas constants and the activation energy of the reaction, respectively. Because f S ≒ f Ti ≒ f Mg ≒ f Fe , we can express the ratio of the rates at temperatures T 0 and T 1 as follows: If T 0 = 300 K and T 1 = 3221 K, we obtain According to the first principle of the symmetry of force, which is associated with a binding energy, the following potential form expresses the repulsive interaction between atoms: 35

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where B is an empirical parameter. The interaction provides a shrinkage ratio η 2 of 0.8205. Considering the effect of temperature on the reaction rate, we obtained a decreased distance as follows: However, this radius is approximately double the critical distance (0.094 nm).

F. Effect of physical catalysis on the dynamic reactions between Mg and Fe
The introduction of neutral pions remarkably reduces the internuclear distance between Mg and Fe nuclei, enhancing the fusion rate, which is comparable to physical catalysis 36 (Sec. 5 in the supplementary material). Based on the result of symmetrical meson theory of nuclear force 37 and the tendency of energy to clump bosons together, the interaction energy of two nucleons at separation r can be expressed as follows: where A is a coupling constant. Because the addition of two neutral pions increases the attraction force by a factor of 14 when there is a 14-fold increase in the interaction force, we obtain a shrinkage ratio η 3 of 0.5170. The shortest Mg-Fe distance d 3 is calculated using the following formula: This value would promote a nuclear reaction between Mg and Fe nuclei. Thus, γ-orthopyroxene is a candidate material for nuclear transmutation in the lower mantle.

G. Transmutation reaction involving Al and Mg
Next, we selected MgAl 2 O 4 , the main constituent of the mantle, for the endothermic nuclear reaction of 23 11 Na and 28 14 Si in natural compounds, as described by Eq. (33). Compounds such as MgAl 2 O 4 and Mg 2 SiO 4 (olivine) in the mantle are major drivers of plate tectonics and largely determine the physical properties of Earth-type planets. 38 MgAl 2 O 4 is known to transform from a calcium ferrite (CaFe 2 O 4 , CF)-typed structure to a calcium titanate (CaTi 2 O 4 , CT)typed structure at a pressure of ∼40 GPa. 39 An ab initio linear combination of atomic orbitals (LCAO) calculation by Catti 15 demonstrated that the calcium titanate structure is more stable compared to the calcium ferrite structure at pressures greater than ∼39 to 57 GPa. 40 Thus, we considered nuclear transmutation between Al and Mg nuclei in CT-type MgAl 2 O 4 . Figure 4 presents the structure of Cmcm-MgAl 2 O 4 under a high pressure of 60 GPa using data obtained from the LCAO calculation. 39 Given that the shortest Mg-Al distance (d 1 ), 0.335 nm, on the (200) plane obtained from Fig. 4 exceeds the distance (∼0.094 nm 32 ) required for a dynamic nuclear reaction, we then accounted for pressure, temperature, and physical catalysis effects accelerating the confinement of magnesium and aluminum nuclei in the Cmcm-MgAl 2 O 4 lattice. Using shrinkage ratios η 1 (0.7654), η 2 (0.8203), and η 3 (0.5170) for pressure, temperature, and physical catalysis effects, respectively, and provided that Cmcm-MgAl 2 O 4 exists at 3221 K and 117 GPa corresponding to a depth of 2600 km in the lower mantle region, we obtained the Mg-Al distance d 3 as follows (Sec. 3 in the supplementary material): This value would lead to a nuclear reaction between Mg and Al nuclei. The reactant product 28 14 Si may then be transferred as a constituent element of olivine Mg 2 SiO 4 .

H. Transmutation reaction involving Al and Si
We then selected a stable aluminosilicate mineral Al 2 SiO5 with a smaller lattice constant at high pressure and high temperature, anticipating the formation of 16 8 O and 39 19 K by endothermic nuclear transmutation between Al and Si in natural compounds, as described in Eq. (30). Al 2 SiO5 is a representative aluminosilicate compound originating from the mantle, which crystallizes near the Earth's surface. It also crystallizes into the three polymorphs, andalusite, sillimanite, and kyanite, 40 common minerals in metamorphic rocks and important indicators of the pressure and temperature required to form these minerals. 41 Thus, we choose kyanite (Al 2 SiO5) III, 40 which exists at a high-pressure form at temperatures exceeding 2300 K and pressures above 14 GPa, as a reactant mineral. Figure 5 illustrates the configuration of the Al-Si-Al chain on the (503) plane in the monoclinic Al 2 SiO5 structure of the highpressure phase kyanite III. When kyanite is compressed at a high pressure of 23 GPa, 42 which corresponds to the pressure conditions of the lower-upper mantle boundary, the shortest Al-Si distance (d 1 ) on the (503) plane can be calculated as 0.2767 nm. However, d 1 exceeds the distance (∼0.094 nm 32 ) required for a dynamic nuclear reaction. Therefore, we must consider the pressure, temperature, and physical catalysis effects accelerating the confinement of Al and Si nuclei in the kyanite III lattice. Using the shrinkage ratios η 1 (0.7339), η 2 (0.8203), and η 3 (0.5170) for pressure, temperature, and physical catalysis effects, respectively, and provided that the kyanite III phase exists at 3221 K and 117 GPa, corresponding to a depth of 2600 km in the lower mantle region, we obtained the Mg-Al distance This value would favor a nuclear reaction between Al and Si nuclei. Kyanite III is a candidate material available for nuclear transmutation in the lower mantle. Andalusite, sillimanite, and kyanite indeed contain some amounts of potassium, which may be indirect evidence for the formation of 39 19 K. Thus, the formation of lighter elements 32 11 S and 48 22 Ti, 16 8 O and 39 19 K, and 23 11 Na and 28 14 Si from natural minerals, such as γorthopyroxene (Mg, Fe) SiO 3 , Cmcm MgAl 2 O 4 , and kyanite III (Al 2 SiO5), respectively, provides a suitable basis for the interpretation of endothermal nuclear reactions. These generated elements immediately react with high-pressure mineral phases of iron magnesium silicates (Mg, Fe) SiO 3 and magnesiowüstites (a combination of magnesium oxide MgO and wüstite FeO), thus forming mixed oxides.
Additionally, we could not select natural compounds containing elements other than Mg, Fe, Al, and Si nor could we identify crystal data relating to pressures over 50 GPa for other minor compound minerals.

I. Geological conditions for the generation of lighter elements
Finally, we considered the geological conditions for the generation of lighter elements. Although the lower mantle could already be present before the formation of the first bona fide continent three billion years ago, 20 the generation of large amounts of lighter elements appears to be linked to plate tectonics. The tectonic recycling of ancient materials consisting of granitic magmas has not occurred prior to three billion years ago. 43 The mantle convection governing plate tectonics and volcanic activity would have occurred after the nucleation of the liquid core. The nucleation period is thought to have occurred either 3.4-3.45 × 10 9 years ago according to geodynamic measurements 44

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Based on the above-described results, the existence of a lower mantle at high temperatures over 3321 K and pressures over 117.3 GPa at a depth of 2600 km could have played a crucial role in the generation of lighter elements. However, the lowest 200 km of the mantle (D ′′ ; i.e., a region bordering on the coremantle boundary 46 ) is the most chemically heterogeneous active region of the Earth's interior. 47 In contrast, a suitable region for the generation of lighter elements is likely restricted to locations with a uniform composition and structure up to 2600 km in depth. 48 The highly active tectonic plate movement coupled with the convection currents of the Earth's mantle (asthenosphere) favors the reactions that mediate the formation of lighter elements. The lithosphere subduction caused by plate tectonics would deliver high quantities of fresh (Mg, Fe) SiO 3 perovskites, MgAl 2 O 4 , and aluminosilicate Al 2 SiO5 minerals to the lower mantle, which serve as raw materials for the production of lighter elements. Figure 6 illustrates the process of lighter element formation and discharge by convection currents of the asthenosphere. However, the mantle undergoes slow plastic deformation due to convection speeds of only a few centimeters per year. 47 Consequently, the upward movement of the resulting compounds occurs over the course of tens to hundreds of millions of years.
As shown in Fig. S5 (supplementary material), asteroid collision events strongly affect the generation of lighter elements 41 due to their important role in continental growth, the intrusion of granitic magmas, and shifting of the mantle's convection patterns. 49,50 Studies have reported the occurrence of strong local seismic anisotropy just above the outer core, suggesting the possibility of fluid-dynamical instabilities due to heat from the core trigger plumes of hot rock "jetting" upward toward the surface after tens of millions of years. 51 Nitrogen and helium gases are discharged by volcanic and hydrothermal activities into the atmosphere and are released from the Earth's atmosphere into outer space.
Regarding the physical catalysis attraction mechanism responsible for accelerating the confinement of two nuclei in the natural compound lattices, excited electrons and neutrinos are thought to have been generated by stick sliding 52,53 during supercontinent evolution, 54 shifting of the mantle's convection pattern triggered by major asteroid collisions, 51 and nuclear fusion in the Earth's core. 10 The pressure ionization generated under pressures greater than 100 GPa near the Earth's inner core produces excited electrons. 55,56 Neutrinos are known to be generated by the sun 57 or in the flares of t-Tauri stars 58 in the Archean era. Neutrinos are also produced in the Earth's mantle by nuclear fusion in its core 10,11 or the radioactive decay of elements. Therefore, we propose that there is a very real possibility that nuclear transformation coupled with physical catalysis may have occurred in the Earth's lower mantle. We place our hopes on a future demonstration for the formation of these elements under high temperature and pressure conditions.
The mechanisms proposed in this study were likely influenced by excited electrons generated by stick sliding during the evolution of supercontinents, mantle convection triggered by major asteroid collisions, and nuclear fusion in the Earth's core. The formation of elements heavier than iron will be described in a future paper.

IV. CONCLUSIONS
Our study proposes a potential model for the creation of light element nuclei up to 56 26 Fe with an atomic number of 26 in Earth's interior. The proposed process would result from the endothermal nuclear transmutation of the constituent elements of natural mineral compounds confined by high temperatures and pressures in the lower mantle due to mantle convection dynamics driven by plate tectonics. This study will have a great impact on the geophysical field and as a result will indicate the possible research directions for the potential for the creation of the elements required in future space development.

SUPPLEMENTARY MATERIAL
See the supplementary material for the depth dependence of pressure and temperature in Earth's inside, estimation of the atomic distance between Mg and Fe elements in the γ-orthopyroxene (Mg 0.44 , Fe 0.56 ) SiO 3 structure at 2650 km below the Earth surface, estimation of the atomic distance between Mg and Al in Cmcm-MgAl 2 O 4 at 2600 km below the Earth surface, estimation of the atomic distance between Al and Si in kyanite III Al 2 SiO5 at 2600 km below the Earth surface, degenerate electrons and pion condensates in the lower mantle region, and asteroid collision-induced atmospheric evolution.