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At least 163 records · Page 9

Post-transition state dynamics and product energy partitioning following thermal excitation of the F∙∙∙HCH 2 CN transition state: Disagreement with experiment

Born-Oppenheimer direct dynamics simulations were performed to study atomistic details of the F + CH 3 CN → HF + CH 2 CN H-atom abstraction reaction. The simulation trajectories were calculated with a combined M06-2X/MP2 algorithm utilizing the 6-311++G** basis set. In accord with experiment and assuming the accuracy of transition state theory (TST), the trajectories were initiated at the F-HCH 2 CN abstraction TS with a 300 K Boltzmann distribution of energy and directed towards products. Recrossing of the TS was negligible, confirming the accuracy of TST for the simulation. HF formation was rapid, occurring within 0.014 ps of the trajectory initiation. The intrinsic reaction coordinate (IRC) for reaction involves rotation of HF about CH 2 CN and then trapping in the CH 2 CN-HF post-reaction potential energy well of ~10 kcal/mol with respect to the HF + CH 2 CN products. In contrast to this IRC, five different trajectory types were observed, with the majority involving direct dissociation and only 11% approximately following the IRC. The HF vibrational and rotational quantum numbers, n and J, were calculated when HF was initially formed and they increase as potential energy is released in forming the HF + CH 2 CN products. The population of the HF product vibrational states is only in qualitative agreement with experiment, with the simulations showing depressed and enhanced populations of the n = 1 and 2 states as compared to experiment. From the simulations and with an anharmonic zero-point energy constraint, the percentage partitioning of the product energy to relative translation, HF rotation, HF vibration, CH 2 CN rotation and CH 2 CN vibration is 5, 11, 60, 7, and 16%, respectively. In contrast the experimental energy partitioning percentages to HF rotation and vibration are 6 and 41%. Comparisons are made between the current simulation and those for other F + H-atom abstraction reactions. The simulation product energy partitioning and HF vibrational population for F + CH 3 CN → HF + CH 2 CN are similar to those for these other reactions. Finally, a detailed discussion is given of possible origins of the difference between the simulation and experimental energy partitioning dynamics for the F + CH 3 CN → HF + CH 2 CN reaction. The F + CH 3 CN reaction also forms the CH 3 C(F)N intermediate, in which the F-atom adds to the C≡N bond. However, this intermediate and the F---CH 3 CN and CH 3 CN-F van der Waals complexes are not expected to affect the F + CH 3 CN → HF + CH 2 CN product energy partitioning.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Genetic characterization of a Sorghum bicolor multiparent mapping population emphasizing carbon-partitioning dynamics

Sorghum bicolor, a photosynthetically efficient C4 grass, represents an important source of grain, forage, fermentable sugars, and cellulosic fibers that can be utilized in myriad applications ranging from bioenergy to bioindustrial feedstocks. Sorghum’s efficient fixation of carbon per unit time per unit area per unit input has led to its classification as a preferred biomass crop highlighted by its designation as an advanced biofuel by the U.S. Department of Energy. Due to its extensive genetic diversity and worldwide colonization, sorghum has considerable diversity for a range of phenotypes influencing productivity, composition, and sink/source dynamics. To dissect the genetic basis of these key traits, we present a sorghum carbon-partitioning nested association mapping (NAM) population generated by crossing 11 diverse founder lines with Grassl as the single recurrent female. By exploiting existing variation among cellulosic, forage, sweet, and grain sorghum carbon partitioning regimes, the sorghum carbon-partitioning NAM population will allow the identification of important biomass-associated traits, elucidate the genetic architecture underlying carbon partitioning and improve our understanding of the genetic determinants affecting unique phenotypes within Poaceae. We contrast this NAM population with an existing grain population generated using Tx430 as the recurrent female. Genotypic data are assessed for quality by examining variant density, nucleotide diversity, linkage decay, and are validated using pericarp and testa phenotypes to map known genes affecting these phenotypes. We release the 11-family NAM population along with corresponding genomic data for use in genetic, genomic, and agronomic studies with a focus on carbon-partitioning regimes.

multiparental populations↗

Order conditions for nonlinearly partitioned Runge-Kutta methods

Recently, a new class of nonlinearly partitioned Runge–Kutta (NPRK) methods was proposed for nonlinearly partitioned systems of autonomous ordinary differential equations y' = F(y, y). The target class of problems are those in which different scales, stiffnesses, or physics are coupled in a nonlinear way, wherein the desired partition cannot be written in a classical additive or component-wise fashion. Here we use a rooted-tree analysis to derive full-order conditions for NPRKM methods, where M denotes the number of nonlinear partitions. Due to the nonlinear coupling and thereby the mixed product differentials, it turns out that the standard node-colored rooted tree analysis used in analyzing ODE integrators does not naturally apply. Instead we develop a new edge-colored rooted-tree framework to address the nonlinear coupling. The resulting order conditions are enumerated, are provided directly for up to fourth order with M = 2 and third order with M = 3, and are related to existing order conditions of additive and partitioned RK methods. We conclude with an example that shows how the nonlinear order conditions can be used to obtain an embedded estimate of the state-dependent nonlinear coupling strength in a dynamical system.

97 MATHEMATICS AND COMPUTING↗

Silicon Partitioning Between Iron-Rich Metal and Silicate Melt: New Constraints From Aerodynamic Laser Levitation Furnace Experiments

The partitioning of light elements (e.g., Si, C, H, etc.) between silicate melts and iron metal alloys as a function of pressure and temperature is a critical constraint in defining the compositional evolution of planetary interiors. While there are a significant number of experimental studies in the literature that examine the various influences of oxygen fugacity, temperature, pressure, and composition on the metal-melt partitioning of silicon, it is difficult to disentangle the effects of each variable due to the nominally independent parameters (e.g., pressure, temperature, composition) being collinear. To better test for the independent effects of pressure, temperature, and melt composition on the partitioning of silicon between iron alloy and silicate melt, new high temperature (1800°–2500°C), rapid quench (~700°C/s) aerodynamic levitation laser-heating experiments in the Fe-Si-Mg-O (En65-Fa5-Si3-Fe27) system were conducted. This high temperature, low pressure method is ideal for these experiments because it eliminates the metal container as a sink for elements of interest to partition into, and it has a rapid quench rate that minimizes potential exsolution of silicon from the metal phase during quench cooling. Given the short run times of the levitation experiments (30–60 seconds), a time series at a lower temperature (1700°C) in a vertical gas-mixing muffle tube furnace was also conducted to assess equilibrium times of the bulk composition. All successful runs were imaged using back-scatter electron imaging and analyzed for phase composition using a JEOL 8530F field emission microprobe. These new data were added to a comprehensive and internally consistent data set created from published experiments, and subsequently modeled using parameters designed to minimize collinearity (e.g., optical basicity is used as a proxy for melt composition). High collinearity is found in the data set however between temperature and oxygen fugacity, precluding any model that contains both as nominally independent variables. The resulting model demonstrates a statistically significant effect of pressure, temperature, and melt composition on the partitioning of silicon in Fe-rich metal, which has implications for the formation of planetary cores in rocky planets and provides important constraints on potential bulk core compositions.

Metal↗

Partition Thickness Considerations for Additively Manufactured Acoustic Liners

Three types of uniform-depth liners are evaluated to explore the effects of partition thickness on the surface impedance achieved with additively manufactured liners. A transmission line code is used to predict the effects of sound transmission through empty chambers and wire mesh facesheets, and is combined with the Motsinger and Kraft model to account for sound transmission through perforated facesheets. The inclusion of partitions causes a blockage effect, i.e., a portion of the surface is ‘blocked’ (nonactive surface). For liners with no facesheet, these blockage effects are incorporated simply by accounting for the change in cross sectional area between the individual chamber and the unit cell that includes half of a partition thickness around the perimeter of this chamber. Comparison of impedances predicted in this manner with data acquired in the NASA Langley Normal Incidence Tube (NIT) confirms the efficacy of this modeling approach. Two approaches are considered to account for the inclusion of a wiremesh or perforated plate facesheet on these same cores. The first accounts for the effects of partition thickness before including the transfer impedance across the facesheet, while the second reverses these steps. A comparison of data acquired in the NASA NIT with modeled impedances suggests the first approach is best when the facesheet is a wire mesh, but the second approach is preferred when a perforated plate facesheet is used. It is hypothesized that this is due to the fact that a lumped element model is used to compute the transfer impedance across a wire mesh, while the corresponding transfer impedance across a perforated sheet explicitly incorporates the efffects of the liner core. However, comparisons of data acquired in the NASA Langley Grazing Flow Impedance Tube with modeled impedances seem slightly better when the first approach is employed with a perforated plate facesheet. Thus, the effects of partition thickness on liners with perforated sheets subjected to grazing incidence sound require further review

acoustic↗

Graph Partitioning and Sparse Matrix Ordering using Reinforcement Learning and Graph Neural Networks

We present a novel method for graph partitioning, based on reinforcement learning and graph convolutional neural networks. Our approach is to recursively partition coarser representations of a given graph. The neural network is implemented using SAGE graph convolution layers, and trained using an advantage actor critic (A2C) agent. We present two variants, one for finding an edge separator that minimizes the normalized cut or quotient cut, and one that finds a small vertex separator. The vertex separators are then used to construct a nested dissection ordering to permute a sparse matrix so that its triangular factorization will incur less fill-in. The partitioning quality is compared with partitions obtained using METIS and SCOTCH, and the nested dissection ordering is evaluated in the sparse solver SuperLU. Our results show that the proposed method achieves similar partitioning quality as METIS and SCOTCH. Furthermore, the method generalizes across different classes of graphs, and works well on a variety of graphs from the SuiteSparse sparse matrix collection.

97 MATHEMATICS AND COMPUTING↗

Registration of the sorghum carbon–partitioning nested association mapping (CP–NAM) population

The sorghum [ Sorghum bicolor (L.) Moench] carbon-partitioning nested association mapping (CP_NAM) (Reg. no. MP-4, NSL 542189 MAP) population was developed at Clemson University, SC, using 11 diverse, male founder accessions, each crossed with a recurrent female parent ‘Grassl’. The male parents represent all five major botanical races and the four major agronomic types: cellulosic (5), sweet (3), grain (2) and forage (1). A set of 11 recombinant inbred line (RIL) families CP_NAM01 to CP_NAM011 were maintained, which consisted of 2,484 (F 6 ) individuals. Each RIL family contained a minimum of 193 individuals (CP_NAM01) and a maximum of 287 individuals (CP_NAM06). For the development of this population, the founder lines were judiciously selected from the sorghum Bioenergy Association Panel based on carbon-partitioning phenotypes that make this population an ideal genetic resource for dissecting a wide range of agronomic and compositional traits for basic and applied research. The founder accessions of the CP_NAM were phenotypically characterized for various traits, including agronomic, biomass and related components, and additional compositional components. Each of the 11 F 6 RIL families of the CP_NAM were genotyped using genotyping-by-sequencing analysis, and 144,087 single nucleotide polymorphisms were generated for each individual. Genotypic information along with phenotypic data were used for the characterization of this population and to explore the range of phenotypes that permits the understanding of carbon-partitioning dynamics. This population is a unique resource for researchers to study a wide range of contrasting carbon-partitioning characteristics in sorghum to understand the genetic architecture underlying whole-plant carbon partitioning and allocation.

59 BASIC BIOLOGICAL SCIENCES↗

On N = 1 partition functions without R-symmetry

Here, we examine the dependence of four-dimensional Euclidean N = 1 partition functions on coupling constants. In particular, we focus on backgrounds without R-symmetry, which arise in the rigid limit of old minimal supergravity. Backgrounds preserving a single supercharge may be classified as having either trivial or SU(2) structure, with the former including S 4 . We show that, in the absence of additional symmetries, the partition function depends non-trivially on all couplings in the trivial structure case, and (anti)-holomorphically on couplings in the SU(2) structure case. In both cases, this allows for ambiguities in the form of finite counterterms, which in principle render the partition function unphysical. However, we argue that on dimensional grounds, ambiguities are restricted to finite powers in relevant couplings, and can therefore be kept under control. On the other hand, for backgrounds preserving supercharges of opposite chiralities, the partition function is completely independent of all couplings. In this case, the background admits an R-symmetry, and the partition function is physical, in agreement with the results obtained in the rigid limit of new minimal supergravity. Based on a systematic analysis of supersymmetric invariants, we also demonstrate that N = 1 localization is not possible for backgrounds without R-symmetry.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Energetics of native defects, solute partitioning, and interfacial energy of Q precipitate in Al-Cu-Mg-Si alloys

The compound Al 3 Cu 2 Mg 9 Si 7 , is known as the Q-phase and forms as a thermodynamically stable precipitate during aging in the quaternary Al-Cu-Mg-Si system. We perform atomic-scale density functional theory (DFT) calculations of defect properties, solute partitioning, and interfacial stability of the Al 3 Cu 2 Mg 9 Si 7 (Q) precipitate. We find: (i) simple native point defect (i.e., vacancies and anti-sites) thermodynamics can partially explain the experimentally observed off-stoichiometry, such as the observed variation of compositions, Al 3+δ Cu 2 Mg 9-δ Si 7 (Mg-deficient and Al-rich) in experiment. (ii) Calculated solute-partitioning energies of common solutes allow us to define general rules for site-preference in the Q-phase in terms of electronic structure and atomic radius. To validate our DFT predictions, we perform atom-probe tomography (APT) experiments for six-different elements (Zn, Ni, Mn, Ti, V, and Zr). The results show that the partitioning behavior of solutes Ni, Zn, and Mn are consistent with DFT predictions, but the transition elements (Ti, V, and Zr), which are anomalously slow diffusers in Al, partition to the Q-phase in constrast to DFT partitioning energies. (iii) For the low energy interface ($11\bar{2}$) Q //(510) Al observed in needle shaped Q-precipitate, we survey various terminations and orientations and derive a low-energy interfacial structure. Here we find this low-energy interfacial model has Cu atoms nearest to the interface, which is in agreement with previous literature on Cu interfacial segregation at the Q'//α-Al interface. The computed interfacial energy (0.52 J/m 2 ) and the corresponding structure will be useful input to future multi-scale modeling of microstructural evolution.

36 MATERIALS SCIENCE↗

Development of a new generation of quench and partitioning steels: Influence of processing parameters on texture, nanoindentation, and mechanical properties

A novel quenching and partitioning process (Q&P) including the hot stamping (HS) process was studied, using two stamping temperatures (750 °C and 800 °C) and two quenching temperatures (318 °C and 328 °C). This combination is here called Hot Stamping and Quenching and Partitioning process (HSQ&P). The partitioning step was performed at 400 °C for 100 s in all cycles. Microstructural features were comprehensively studied using electron backscattered diffraction and nanoindentation techniques. HSQ&P samples showed a good combination of ductility and high-strength due to the presence of: retained austenite, inter-critical ferrite with low stored internal strain energy, grain refinement via DIFT-effect (deformation induced ferrite transformation), martensite, and bainite. Significant internal stress relief was caused by carbon partitioning, which was induced by the DIFT-effect and the partitioning stage. This also led to a considerable stored energy, which was characterized by the Kernel average dislocation and geometrically necessary dislocation analysis. In addition, predominant {110}//strain direction crystallographic texture was identified, which promotes slip deformation and enhances the mechanical properties. Moreover, remarkable amounts of fine film-like retained austenite oriented along compact crystallographic directions (i.e., $\langle$111$\rangle$ and $\langle$112$\rangle$) were observed. Finally, subsize tensile test verified the optimum mechanical behavior of HSQ&P specimens.

36 MATERIALS SCIENCE↗

A Semi‐Mechanistic Model for Partitioning Evapotranspiration Reveals Transpiration Dominates the Water Flux in Drylands

Abstract Popular evapotranspiration (ET) partitioning methods make assumptions that might not be well‐suited to dryland ecosystems, such as high sensitivity of plant water‐use efficiency (WUE) to vapor pressure deficit (VPD). Our objectives were to (a) create an ET partitioning model that can produce fine‐scale estimates of transpiration (T) in drylands, and (b) use this approach to evaluate how climate controls T and WUE across ecosystem types and timescales along a dryland aridity gradient. We developed a novel, semi‐mechanistic ET partitioning method using a Bayesian approach that constrains abiotic evaporation using process‐based models, and loosely constrains time‐varying WUE within an autoregressive framework. We used this method to estimate daily T and weekly WUE across seven dryland ecosystem types and found that T dominates ET across the aridity gradient. Then, we applied cross‐wavelet coherence analysis to evaluate the temporal coherence between focal response variables (WUE and T/ET) and environmental variables. At yearly scales, we found that WUE at less arid, higher elevation sites was primarily limited by atmospheric moisture demand, and WUE at more arid, lower elevation sites was primarily limited by moisture supply. At sub‐yearly timescales, WUE and VPD were sporadically correlated. Hence, ecosystem‐scale dryland WUE is not always sensitive to changes in VPD at short timescales, despite this being a common assumption in many ET partitioning models. This new ET partitioning method can be used in dryland ecosystems to better understand how climate influences physically and biologically driven water fluxes.

Environmental Sciences & Ecology↗

Size-dependent forced PEG partitioning into channels: VDAC, OmpC, and α-hemolysin

Significance With consequences for the selective partitioning of large molecules in cells, polymer partitioning into nanopores is instructive for single-molecule sensing as well as for polymer-assisted transport and packaging. Here we detect and analyze not only passive but also forced size-dependent partitioning of binary mixtures of differently sized PEGs. We probe three structurally different channels exhibiting forced partitioning that can be understood conceptually as well as quantitatively within a “polymers-pushing-polymers” model, allowing good estimates for the size-dependent pore penetration energy differences. Beyond proof of concept, forced partitioning in cells can now be recognized and used as a new tool for molecule-selective transport and active osmotically regulated packaging.

36 MATERIALS SCIENCE↗

Entanglement spectrum of a random partition: Connection with the localization transition

We study the entanglement spectrum of a translationally invariant lattice system under a random partition, implemented by choosing each site to be in one subsystem with probability p ϵ[0,1]. We apply this random partitioning to a translationally invariant (i.e., clean) topological state, and argue on general grounds that the corresponding entanglement spectrum captures the universal behavior about its disorder-driven transition to a trivial localized phase. Specifically, as a function of the partitioning probability p , the entanglement Hamiltonian H A must go through a topological phase transition driven by the percolation of a random network of edge states. For example, we analytically derive the entanglement Hamiltonian for a one-dimensional topological superconductor under a random partition, and demonstrate that its phase diagram includes transitions between Griffiths phases. We discuss potential advantages of studying disorder-driven topological phase transitions via the entanglement spectra of random partitions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Spectral-partitioned Kohn-Sham density functional theory

Here we introduce a general, variational scheme for systematic approximation of a given Kohn-Sham free-energy functional by partitioning the density matrix into distinct spectral domains, each of which may be spanned by an independent diagonal representation without requirement of mutual orthogonality. It is shown that by generalizing the entropic contribution to the free energy to allow for independent representations in each spectral domain, the free energy becomes an upper bound to the exact (unpartitioned) Kohn-Sham free energy, attaining this limit as the representations approach Kohn-Sham eigenfunctions. A numerical procedure is devised for calculation of the generalized entropy associated with spectral partitioning of the density matrix. The result is a powerful framework for Kohn-Sham calculations of systems whose occupied subspaces span multiple energy regimes. As a case in point, we apply the proposed framework to warm- and hot-dense matter described by finite-temperature density functional theory, where at high energies the density matrix is represented by that of the free-electron gas, while at low energies it is variationally optimized. We derive expressions for the spectral-partitioned Kohn-Sham Hamiltonian, atomic forces, and macroscopic stresses within the projector-augmented wave (PAW) and the norm-conserving pseudopotential methods. It is demonstrated that at high temperatures, spectral partitioning facilitates accurate calculations at dramatically reduced computational cost. Moreover, as temperature is increased, fewer exact Kohn-Sham states are required for a given accuracy, leading to further reductions in computational cost. Finally, it is shown that standard multiprojector expansions of electronic orbitals within atomic spheres in the PAW method lack sufficient completeness at high temperatures. Spectral partitioning provides a systematic solution for this fundamental problem.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Efficient Hierarchical State Vector Simulation of Quantum Circuits via Acyclic Graph Partitioning

Early but promising results in quantum computing have been enabled by the concurrent development of quantum algorithms, devices, and materials. Classical simulation of quantum programs has enabled the design and analysis of algorithms and implementation strategies targeting current and anticipated quantum device architectures. In this paper, we present a graph-based approach to achieve efficient quantum circuit simulation. Our approach involves partitioning the graph representation of a given quantum circuit into sub-graphs/circuits that exhibit better data locality. Simulation of each sub-circuit is organized hierarchically, with the iterative construction and simulation of smaller state vectors, improving overall performance. Also, this partitioning reduces the number of passes through data, improving the total computation time. We present three partitioning strategies and observe that acyclic graph partitioning typically results in the best time-to-solution. In contrast, other strategies reduce the partitioning time at the expense of potentially increased simulation times. Experimental evaluation demonstrates the effectiveness of our approach.

Fang, Bo↗

Partitioning Models for Scaling Parallel Sparse Matrix-Matrix Multiplication

We investigate outer-product--parallel, inner-product--parallel, and row-by-row-product--parallel formulations of sparse matrix-matrix multiplication (SpGEMM) on distributed memory architectures. For each of these three formulations, we propose a hypergraph model and a bipartite graph model for distributing SpGEMM computations based on one-dimensional (1D) partitioning of input matrices. Here, we also propose a communication hypergraph model for each formulation for distributing communication operations. The computational graph and hypergraph models adopted in the first phase aim at minimizing the total message volume and balancing the computational loads of processors, whereas the communication hypergraph models adopted in the second phase aim at minimizing the total message count and balancing the message volume loads of processors. That is, the computational partitioning models reduce the bandwidth cost and the communication hypergraph models reduce the latency cost. Our extensive parallel experiments on up to 2048 processors for a wide range of realistic SpGEMM instances show that although the outer-product--parallel formulation scales better, the row-by-row-product--parallel formulation is more viable due to its significantly lower partitioning overhead and competitive scalability. For computational partitioning models, our experimental findings indicate that the proposed bipartite graph models are attractive alternatives to their hypergraph counterparts because of their lower partitioning overhead. Finally, we show that by reducing the latency cost besides the bandwidth cost through using the communication hypergraph models, the parallel SpGEMM time can be further improved up to 32%.

97 MATHEMATICS AND COMPUTING↗

TDAG: Tree-based Directed Acyclic Graph Partitioning for Quantum Circuits

We propose the Tree-based Directed Acyclic Graph (TDAG) partitioning for quantum circuits, a novel quantum circuit partitioning method which partitions circuits by viewing them as a series of binary trees and selecting the tree containing the most gates. TDAG produces results of comparable quality (number of partitions) to an existing method called ScanPartitioner (an exhaustive search algorithm) with an 95% average reduction in execution time. Furthermore, TDAG improves compared to a faster partitioning method called QuickPartitioner by 38% in terms of quality of the results with minimal overhead in execution time.

Clark, Joseph↗

Eu speciation in apatite at 1 bar: An experimental study of valence-state partitioning by XANES, lattice strain, and Eu/Eu* in basaltic systems

Abstract Partition coefficients for rare earth elements (REEs) between apatite and basaltic melt were determined as a function of oxygen fugacity (fO2; iron-wüstite to hematite-magnetite buffers) at 1 bar and between 1110 and 1175 °C. Apatite-melt partitioning data for REE3+ (La, Sm, Gd, Lu) show near constant values at all experimental conditions, while bulk Eu becomes more incompatible (with an increasing negative anomaly) with decreasing fO2. Experiments define three apatite calibrations that can theoretically be used as redox sensors. The first, a XANES calibration that directly measures Eu valence in apatite, requires saturation at similar temperature-composition conditions to experiments and is defined by: ( E u 3 + ∑ E u ) Apatite = 1 1 + 10 - 0.10 ± 0.01 × l o g ⁡ ( f o 2 ) - 1.63 ± 0.16 . The second technique involves analysis of Sm, Eu, and Gd in both apatite and coexisting basaltic melt (glass), and is defined by: ( Eu E u * ) D Sm × Gd = 1 1 + 10 - 0.15 ± 0.03 × l o g ⁡ ( f o 2 ) - 2.46 ± 0.41 . The third technique is based on the lattice strain model and also requires analysis of REE in both apatite and basalt. This calibration is defined by ( Eu E u * ) D lattice strain = 1 1 + 10 - 0.20 ± 0.03 × l o g ⁡ ( f o 2 ) - 3.03 ± 0.42 . The Eu valence-state partitioning techniques based on (Sm×Gd) and lattice strain are virtually indistinguishable, such that either methodology is valid. Application of any of these calibrations is best carried out in systems where both apatite and coexisting glass are present and in direct contact with one another. In holocrystalline rocks, whole rock analyses can be used as a guide to melt composition, but considerations and corrections must be made to either the lattice strain or Sm×Gd techniques to ensure that the effect of plagioclase crystallization either prior to or during apatite growth can be removed. Similarly, if the melt source has an inherited either a positive or negative Eu anomaly, appropriate corrections must also be made to lattice strain or Sm×Gd techniques that are based on whole rock analyses. This being the case, if apatite is primary and saturates from the parent melt early during the crystallization sequence, these corrections may be minimal. The partition coefficients for the REE between apatite and melt range from a maximum DEu3+ = 1.67 ± 0.25 (as determined by lattice strain) to DLu3+ = 0.69 ± 0.10. The REE partition coefficient pattern, as observed in the Onuma diagram, is in a fortuitous situation where the most compatible REE (Eu3+) is also the polyvalent element used to monitor fO2. These experiments provide a quantitative means of assessing Eu anomalies in apatite and how they be used to constrain the oxygen fugacity of silicate melts.

Geochemistry & Geophysics↗