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The performance of the optimized three-section squared-off cascade is compared with that of a match abundance ratio cascade (MARC) for the enrichment of 92 Mo and 100 Mo isotopes from their natural composition to 99.99%. Two codes, namely, 3SQC–PSO and MARC–PSO, are developed for optimizing 200 centrifuge cascades using the particle swarm optimization (PSO) algorithms. The objective function is to maximize the cascade capacity, recovery factor, and the D-function and to minimize the total interstage flow. A comparison of the results shows that a MARC is able to enrich 100 Mo with the highest recovery and production capacity. Due to the fact that more than one separation step is required for the separation of 92 Mo, a MARC is beyond the capability to separate it to 99.99%, but a squared-off cascade is capable of making this. Therefore, if the goal is the separation of all or some of isotopes of an element, the squared-off cascade is the preferred option for economical industrialization and reducing installation.

Consideration has been given to the distinctive features of multistep concentration of all the molybdenum isotopes in a cascade with a varying type of stages as far as the number of gas centrifuges is concerned. A computational experiment on separation of molybdenum hexafluoride was conducted. A procedure of calculation from the cuts of partial flows of the stages was used which takes account of the dependence of the separation factors of gas centrifuges on their feed flow and the flow-division coefficient. It has been shown that the high efficiency of separation processes is attained with a large number of stages and gas centrifuges and small feed flows of the cascade.

A method has been developed for simultaneous concentration of molybdenum isotopes with intermediate atomic mass in two additional products of a multi-flow cascade with a given number of centrifuges in stages. The method takes into account the dependence of the separation factors of the cascade stages on the feed flow of gas centrifuges and the flow division coefficient, which makes it possible to calculate the most efficient operating modes. On its basis, a computational experiment on the separation of molybdenum hexafluoride was carried out. The influence of factors related to the cascade feed flow and to the number of stages and gas centrifuges is investigated. It is shown that the feed flows and the separation factors of the stages of gas centrifuge cascades differ significantly from rectangular and rectangular-partitioned cascades.

The molybdenum (Mo) isotope system is pivotal in reconstructing marine redox changes throughout Earth’s history and has emerged as a promising tracer for igneous and metamorphic processes. Understanding its composition and variation across major geochemical reservoirs is essential for its application in investigating high-temperature processes. However, there is debate regarding the δ 98/95 Mo value of the Earth’s mantle, with estimates ranging from sub-chondritic to super-chondritic values. Recent analyses of global mid-ocean ridge basalt (MORB) glasses revealed significant δ 98/95 Mo variations attributed to mantle heterogeneity, proposing a two-component mixing model to explain the observed variation. Complementary studies confirmed the sub-chondritic δ 98/95 Mo of the depleted upper mantle, suggesting remixing of subduction-modified oceanic crust as a plausible mechanism. These findings underscore the role of Mo isotopes as effective tracers for understanding dynamic processes associated with mantle-crustal recycling.

Estimates of the volume of the earliest crust based on zircon ages and radiogenic isotopes remain equivocal. Stable isotope systems, such as molybdenum, have the potential to provide further constraints but remain underused due to the lack of complementarity between mantle and crustal reservoirs. Here we present molybdenum isotope data for Archaean komatiites and Phanerozoic komatiites and picrites and demonstrate that their mantle sources all possess subchondritic signatures complementary to the superchondritic continental crust. These results confirm that the present-day degree of mantle depletion was achieved by 3.5 billion years ago and that Earth has been in a steady state with respect to molybdenum recycling. Mass balance modelling shows that this early mantle depletion requires the extraction of a far greater volume of mafic-dominated protocrust than previously thought, more than twice the volume of the continental crust today, implying rapid crustal growth and destruction in the first billion years of Earth’s history.

How serpentinites in the forearc mantle and subducted lithosphere become involved in enriching the subarc mantle source of arc magmas is controversial. Here we report molybdenum isotopes for primitive submarine lavas and serpentinites from active volcanoes and serpentinite mud volcanoes in the Mariana arc. These data, in combination with radiogenic isotopes and elemental ratios, allow development of a model whereby shallow, partially serpentinized and subducted forearc mantle transfers fluid and melt from the subducted slab into the subarc mantle. These entrained forearc mantle fragments are further metasomatized by slab fluids/melts derived from the dehydration of serpentinites in the subducted lithospheric slab. Multistage breakdown of serpentinites in the subduction channel ultimately releases fluids/melts that trigger Mariana volcanic front volcanism. Serpentinites dragged down from the forearc mantle are likely exhausted at >200 km depth, after which slab-derived serpentinites are responsible for generating slab melts. How the subducted oceanic lithosphere provides fluids and melts to flux the subarc mantle source of arc magmas is controversial. Here the authors use Mo and other isotopes to show serpentinites formed in both the forearc mantle and the subducted lithosphere contribute to generating arc magmas.

Late Archaean sedimentary rocks contain compelling geochemical evidence for episodic accumulation of dissolved oxygen in the oceans along continental margins before the Great Oxidation Event. However, the extent of this oxygenation remains poorly constrained. Here we present thallium and molybdenum isotope compositions for anoxic organic-rich shales of the 2.5-billion-year-old Mount McRae Shale from Western Australia, which previously yielded geochemical evidence of a transient oxygenation event. During this event, we observe an anticorrelation between thallium and molybdenum isotope data, including two shifts to higher molybdenum and lower thallium isotope compositions. Our data indicate pronounced burial of manganese oxides in sediments elsewhere in the ocean at these times, which requires that the water columns above portions of the ocean floor were fully oxygenated—all the way from the air–sea interface to well below the sediment–water interface. Well-oxygenated continental shelves were probably the most important sites of manganese oxide burial and mass-balance modelling results suggest that fully oxygenated water columns were at least a regional-scale feature of early Earth’s oceans 2.5 billion years ago.Before the Great Oxidation Event there was regional-scale, full water-column oxygenation above the continental shelf, according to molybdenum and thallium isotope records that indicate massive manganese oxide burial.

The careful compilation and interpretation of molybdenum isotopes can track the expansion of sulfidic bottom waters. A synthesis and analysis of data from two Mesozoic ocean anoxic events and the Palaeocene-Eocene thermal maximum applies these techniques to constrain past ocean deoxygenation. The expansion and contraction of sulfidic depositional conditions in the oceans can be tracked with the isotopic composition of molybdenum in marine sediments. However, molybdenum-isotope data are often subject to multiple conflicting interpretations. Here I present a compilation of molybdenum-isotope data from three time intervals: the Toarcian Oceanic Anoxic Event about 183 million years ago, Oceanic Anoxic Event 2 about 94 million years ago, and two early Eocene hyperthermal events from 56 to 54 million years ago. A comparison of data from sites located in different hydrographic settings tightly constrains the molybdenum cycle for these intervals, allowing a direct comparison of the expanse of sulfidic conditions in each interval compared to today. Nonetheless, tracing rates of redox change over such rapid climatic events using molybdenum isotopes remains challenging. Future efforts to achieve this goal might be accomplished by analysing specific mineral phases, using complementary redox-sensitive geochemical techniques and by linking isotopic observations with Earth system modelling. Such improvements will make it possible to more fully assess the links between ocean deoxygenation, climatic and oceanographic changes, and biotic turnover.

During the early Cenozoic greenhouse period, counterintuitive contractions in tropical Pacific oxygen‐deficient zones have been linked to enhanced deep‐ocean ventilation, yet direct geological evidence remains limited. Here we present molybdenum (Mo) isotopic records from International Ocean Discovery Program Site U1509. Raman spectroscopy shows that Mn and Fe occur mainly as MnO2 and Fe–Mn oxides. The δ98/95Mo values show a sustained negative shift from ∼1‰ to −2‰ between ∼59.5 and 50.5 Ma, and this trend is best explained by strengthened Mo adsorption onto Mn and Fe bearing oxides at the sediment–water interface. This mechanism provides a direct basis for interpreting the Mo isotope depletion, indicating prolonged bottom‐water oxygenation within early Cenozoic greenhouse conditions. At ∼50.5 Ma, a sharp decline in silicate εNd values and coeval rises in Ti, Zr, and Sc enrichment factors indicate intensified continental weathering that supplied isotopically light Mo. These results provide new constraints on early Cenozoic redox evolution.

Although carbonates are the primary form of carbon subducted into the mantle, their fate during recycling is debated. Here we report the first coupled high-precision Zn and Mo isotope data for Cenozoic intraplate basalts from western China. The exceptionally high δ66Zn values (+0.39 to +0.50‰) of these lavas require involvement of recycled carbonates in the mantle source. Variable δ98Mo compositions (−0.39 to +0.27‰) are positively correlated with Mo/Ce, best interpreted as mixing between isotopically light Mo from dehydrated oceanic crust and heavy Mo from recycled carbonates, which is also supported by positive coupling between δ66Zn and δ98Mo. Modeling reveals that involvement of ≤5% carbonate-bearing oceanic crust fully resolves the observed δ66Zn–δ98Mo mantle heterogeneity probed by intracontinental basalts. Our study demonstrates that combined δ66Zn–δ98Mo data sets for mantle-derived magmas can track recycled surficial carbonates in Earth's interior, providing a powerful geochemical tool for deep carbon science.