Natalie P Holmes
email: natalie.holmes@sydney.edu.au

Sylvain Chambon
email: chambon@iis.u-tokyo.ac.jp

Alexandre Holmes

Xiaoxue Xu

Kazuhiko Hirakawa

Elise Deniau

Christine Lartigau-Dagron

Antoine Bousquet
email: antoine.bousquet@univ-pau.fr

Organic Semiconductor Colloids: From the Knowledge Acquired in Photovoltaics to the Generation of Solar Hydrogen Fuel

Keywords: nanoparticle, solar fuel, photocatalysis, hydrogen evolution, morphology, semiconductor, conjugated polymer

The recent interest in the application of organic semiconductor colloids to photocatalytic hydrogen evolution has sparked the need for an assessment of the current state of this research field. Here we showcase how the lessons learnt from organic photovoltaics (OPV) research can be applied to new applications in the generation of solar fuels, such as in photocatalytic hydrogen evolution. Photovoltaics generated from organic semiconductor nanoparticles started out with a power conversion efficiency (PCE) at less than 0.01% in 2003, since then the technology witnessed a steady climb to 7.5% reported in 2018. A large fraction of this technology improvement can be attributed to morphology improvement of the organic semiconductor colloids, improvements which can now be transferred to benefit the field of photocatalytic hydrogen evolution. We begin with an introduction to conjugated materials, then move to a thorough description of nanoparticle dispersion processes, comprising the miniemulsion and the nanoprecipitation methods, before moving to a summary of the different morphologies encountered in organic nanoparticles, their impact on OPV performance and how this parameter is of crucial importance for photocatalytic hydrogen generation. Indeed, organic semiconductor colloids conveniently provide the field of photocatalytic hydrogen generation with a nanoengineering toolkit upon which to customize morphologies in order to increase photocatalytic activity and enhance hydrogen evolution rates (HER).

Introduction

As a vast source of energy, the sun's photons are one of the best candidates to solve the energy and environmental crisis the world is facing. The main drawback of photovoltaics is that the electricity produced should be consumed instantaneously otherwise it is lost. Batteries and solar fuels, which transform solar irradiation into chemical bonds have been developed as energy storage systems. Batteries are challenged by the frequent use of lithium and most of the fuels are producing CO2 as a side product, which obviously will not answer the global warming problem. However, hydrogen (H2) is a clean fuel because it only produces electricity and H2O.

Nowadays, the vast majority (>95%) of global hydrogen is produced from fossil steam methane reforming, a process emitting CO2. Recently, H2 production via photocatalytic water splitting has emerged as a fantastic solution to store solar energy in a dispensable fuel that does not produce CO2, neither at the fabrication nor consumption stages. In this context, Pinaud et al.

have modeled and calculated by life cycle analysis that a colloidal system, in which the photocatalysts are in the form of nanoparticles dispersed in water, would be the cheapest way to produce H2, mainly because of increased interface area compared to a film but also due to lower initial capital cost. [START_REF] Pinaud | Technical and Economic Feasibility of Centralized Facilities for Solar Hydrogen Production via Photocatalysis and Photoelectrochemistry[END_REF] In 1985, Yanagida et al. paved the way for the use of organic semiconductors to perform photocatalytic hydrogen evolution, by demonstrating the performance of conjugated poly(p-phenylene) as a photocatalyst. [START_REF] Yanagida | Poly(p-Phenylene)-Catalysed Photoreduction of Water[END_REF] In this review we will demonstrate how the more recent knowledge acquired from the field of organic photovoltaics, in particular in organic semiconductor nanoparticle synthesis, has advanced the development of efficient systems to produce H2.

The development of organic nanoparticles as preparations of colloidal inks has received significant consideration for various applications in the past three decades. Recently, nanoparticles were developed from semiconducting conjugated polymers for the photovoltaics application, opening the field of environmentally-friendly processes as alternatives to classical options which are typically in toxic organic solvents. Although this field is very young, many lessons and insights were extracted from the global research effort. Recently, Holmes et al. published a review on this specific subject, and we invite the reader to access this article for a deeper understanding of the impact of nanoparticle synthesis on organic photovoltaic device performance. [START_REF] Holmes | Review of Waterborne Organic Semiconductor Colloids for Photovoltaics[END_REF] Nanoparticles of organic semiconductors are produced via a self-assembly process, rather than a growth process (polymerization), hence we begin this review by briefly comparing the two main routes of nanoparticle preparation to provide context for a broader audience in the colloid science space. Functional nanoparticles are synthesized via two main routes, growth or selfassembly, the choice of route being dependent on the nature of the starting materials and the final application of the nanomaterials.

Growth: The formation process of nanoparticles (either inorganic or organic) from a solution of ions (for inorganic nanoparticles) or small molecules (for organic nanoparticles) is predominantly via nucleation and growth. [START_REF] Wu | Nucleation and Growth in Solution Synthesis of Nanostructures -From Fundamentals to Advanced Applications[END_REF][START_REF] Rymaruk | RAFT Dispersion Polymerization of Benzyl Methacrylate in Silicone Oil Using a Silicone-Based Methacrylic Stabilizer Provides Convenient Access to Spheres, Worms, and Vesicles[END_REF] Nucleation is the process whereby droplets/nuclei (seeds) act as templates for polymerization (for organic nanoparticles) or crystal growth (for inorganic nanoparticles). Homogeneous nucleation, a typical classical nucleation process, occurs when nuclei form uniformly throughout the parent (or continuous) phase. [START_REF] Sugimoto | Monodispersed Particles[END_REF] Self-Assembly: By comparison, the formation of nanoparticles via self-assembly of macromolecules is a post-polymerization route for forming organic nanoparticles. The driving force for the self-assembly formation is usually a surface energy minimization process, where each material type moves to its final location in order for the system to reach equilibrium. For example, the self-assembly of nanoparticles from diblock copolymers, where block A is insoluble (or hydrophobic in a hydrophilic parent phase) compared to block B and hence selfassembly into a core-shell structure with a block A core and block B shell occurs. [START_REF] Howe | Functionalization-Induced Self-Assembly of Block Copolymers for Nanoparticle Synthesis[END_REF] When beginning instead with two immiscible liquid phases and employing a surfactant, a nanoparticle dispersion can be generated first by forming a liquid-liquid colloidal dispersion (an emulsion), and then a solid-liquid colloidal dispersion by removing the solvent of the dispersed phase droplets via evaporation, hence converting the polymer material originally dissolved in that phase to solid nanospheres.

The development of organic semiconductor nanoparticles was mainly motivated by the search for avenues to reduce the environmental impact of OPV technology and the replacement of halogeno-aromatic solvents. As a consequence, developing water or alcohol based colloidal inks would afford environmentally-friendly processability of photovoltaic modules. The nanoscale morphology of the organic active layer is of utmost importance in the OPV field. Indeed, in order to reach optimum photovoltaic performance, a large part of the research in the OPV field is dedicated to optimization of the bulk heterojunction (BHJ) morphology to reach, on the one hand, nanoscale domain size that more closely matches exciton diffusion length (approx. 10 nm) and, on the other hand, conduction pathways for both charges. Due to this specific target for domain size, much research effort has been invested into producing organic semiconductor nanoparticles with controlled morphologies and sizes, including core-shell, molecularly intermixed, distributed nano-domains and biphasic/Janus. This detailed morphology investigation and optimization can now benefit the field of photocatalytic hydrogen evolution in which a strong drawback of organic materials is the loss of excitons before reaching the interface with water, the solvent of the H + reagent. This is only one example of the formidable lessons extracted from photovoltaics and others will be reported herein.

The plan of this review is to start with (macro)molecules, the building blocks, move to nanoparticle synthesis, and end with hydrogen photocatalysis applications. We describe the basics of conjugated materials which constitute the organic semiconductors used as building blocks for the organic nanoparticles. Then we detail the organic nanoparticle preparation via colloidal dispersion processes, both the miniemulsion and the nanoprecipitation methods being covered, and the key parameters controlling the morphology and how it has impacted OPV performance. Finally, we detail the new application area of photocatalytic hydrogen evolution and showcase how the knowledge of nanoparticle material development for photovoltaics can be applied to this alternate field.

Conjugated Materials

The unexpected observation of a conducting polyacetylene thin film, thanks to the undeliberate addition of a catalyst amount 1000 times higher than the traditional amount by a student of Hideki Shirakawa, ushered in the use of conjugated polymers in electronics. [START_REF] Ito | Simultaneous Polymerization and Formation of Polyacetylene Film on the Surface of Concentrated Soluble Ziegler-Type Catalyst Solution[END_REF] This discovery was awarded to him and his collaborators Alan Heeger and Alan MacDiarmid with the Nobel Prize in chemistry in 2000. From this starting point in the field of synthetic metals, several discoveries of conjugated polymers in the early 1990s, such as the electroluminescence of poly(p-phenylene vinylene) (PPV) or the ultra-fast charge transfer from PPV to fullerene, took place.

The semiconducting behavior in organic materials originates from the alternation of single () and double () carbon bonds, termed -conjugation. Each sp 2 carbon presents three sp 2 hybridized orbitals providing covalent -bonds with neighboring carbons, plus the remaining unhybridized 2pz orbital. Therefore, the overlap of these pz orbitals forms a delocalized out-ofplane -electron cloud along the conjugated backbone (Figure 2a). This leads to the electron motion owing to the optoelectronic and charge transport properties in these materials.

In comparison with inorganic semiconductors, the valence band corresponds to the highest occupied molecular orbital (HOMO), and the conduction band to the lowest unoccupied molecular orbital (LUMO). The HOMO-LUMO energy difference is called the energy band gap. As shown in Figure 2b, this difference decreases as the number of conjugated bonds in the backbone increases. The energy corresponding to the first optical transition explains the bathochromic absorption. In an infinite chain, the molecular orbitals are so close to each other that they become indiscernible and constitute the valence and conduction bands. In the band model, the electronic structure affords the electrical properties of the material, among metals, semiconductors and insulators. Semiconductors are characterized by an energy band gap below 3 eV. Semiconducting conjugated polymers (donor) are good candidates to be used in an active layer, mixed with an electron acceptor material, either fullerene, small molecule or polymer in organic photovoltaic devices. The photoconversion then consists of photon absorption by either the donor or the acceptor material, generating a highly bound electron-hole pair (exciton) that can only be separated by an internal field created by proximity of the donor and acceptor materials (Figure 2c). Nevertheless, the properties of organic semiconductor materials make them suitable for different types of electronic devices: organic light-emitting diodes, organic thin film transistors, sensors or even for hydrogen production, which is the scope of this review.

Dispersion Processes

Nanoparticles (NPs) of conjugated materials are prepared mainly by post-polymerization techniques such as miniemulsion and nanoprecipitation. In the miniemulsion process, organic semiconductor nanoparticles are formed from an emulsified droplet solution, and usually require a water-immiscible solvent. By contrast, in nanoprecipitation the semiconductors are precipitated by rapidly mixing the material solution with the anti-solvent, and require two miscible solvents. In both cases, the organic solvent is finally removed under high temperature.

Interestingly, experimental parameters used in the preparation show a significant influence on the size of nanoparticles. In the following section we describe both techniques by emphasizing their advantages and limitations in the dispersion of conjugated polymer nanoparticles.

Miniemulsion is the most common method used for the preparation of conjugated nanoparticles. The conjugated material is first dissolved in a good solvent (most of the time chloroform), and an aqueous phase containing surfactant molecules is then added to the organic solution. Nanodroplets of organic phase are produced by applying high shear using ultrasonic waves or high-speed homogenization. Evaporation of the organic solvent from the dispersed phase leads to the formation of solid nanoparticles dispersed in water. An additional step aiming to remove the excess of free-surfactant and also to reduce the volume of the aqueous phase, in order to concentrate the dispersion, is often required (Figure 3).

The first report of the preparation of nanoparticles of organic semiconductors via a miniemulsion process was in 2002 by Landfester et al. [START_REF] Landfester | Semiconducting Polymer Nanospheres in Aqueous Dispersion Prepared by a Miniemulsion Process[END_REF] The authors prepared nanoparticles of three different conjugated polymers (methyl substituted ladder-type poly(p-phenylene) (Me-LPPP), polyfluorene (PF) and polycyclopenta-dithiophene. They used sodium dodecyl sulfate (SDS) as surfactant to stabilize the droplets from collision and aggregation and the polymer solution was sufficiently hydrophobic to prevent Ostwald ripening. Stable dispersions were obtained with nanoparticle sizes ranging from 75 to 250 nm, by varying the amount of SDS, yielding a solids content of 2.2 to 9.3 wt% after evaporation of the organic solvent (chloroform in this case).

Varying the experimental parameters of the miniemulsion preparation can easily control the nanoparticle size. Indeed, the size of the nanoparticles is strongly influenced by the initial concentration of the conjugated polymer in the organic phase: the higher the concentration, the larger the diameter. For example, Xie et al. reported the increase of the active material (poly(diketopyrrolopyrrole-quinquethiophene)) low band gap alternating copolymer (PDPP5T) and phenyl-C71-butyric acid methyl ester (PC71BM) concentration from 15 to 40 mg.mL -1 leading to an increase in the nanoparticle size from 5 to 107 nm. [START_REF] Xie | Overcoming Microstructural Limitations in Water Processed Organic Solar Cells by Engineering Customized Nanoparticulate Inks[END_REF] The trend can be explained by the presence of more active material in the polymer solution droplets during the miniemulsion generation, resulting in an increase in the nanoparticle size after organic solvent evaporation. Depending on the semiconductor used, it is however important to adjust the organic phase concentration as a function of its solubility in the primary organic solvent, in order to avoid aggregation.

The shear force applied during the miniemulsion process, by using sonifiers or high-pressure homogenizers, is also a highly important parameter. Increasing the sonication power and/or the sonication time enables the formation of smaller nanoparticles.

The presence of surfactant enhances the colloidal stability of the dispersion but can also affect the particle size. Increasing the amount of surfactant leads to smaller and more numerous nanodroplets leading to smaller nanoparticles. For certain applications in organic electronics, the presence of surfactant is a limitation due to its insulating character. However, thanks to the presence of these molecules, the miniemulsion method enables the preparation of highly stable dispersions exhibiting high solids content.

Nanoprecipitation is an alternative to the miniemulsion technique, enabling the generation of surfactant-free nanoparticle dispersions. It requires the selection of a solvent and a non-solvent of the conjugated materials that are fully miscible. The process is simple: the semiconductor is first dissolved in an organic solvent and then mixed into a large volume of anti-solvent under stirring. In general, the solvent/anti-solvent couple is THF/water however chloroform/alcohol systems have also been reported. The solution becomes an anti-solvent for the conjugated material and leads to its precipitation into small particles in a continuous phase of both solvent and anti-solvent (Figure 3). The addition rate is quite important in order to obtain stable dispersions exhibiting narrow size distributions. Although the literature mostly reports a slow addition of the organic phase into the anti-solvent under stirring, it has been shown that a quick addition of a large volume of anti-solvent into the organic phase leads to more homogeneous dispersion with a narrow size distribution of nanoparticles (Ouzo effect). [START_REF] Valera | Elaboration of PCBM Coated P3HT Nanoparticles: Understanding the Shell Formation[END_REF] In addition, the use of suitable mixing techniques, which increases the homogenization rate (high-shear and ultra-sonification process), leads to smaller nanoparticles and narrow size distributions.

The main advantage of using nanoprecipitation is that the preparation does not involve the use of surfactants. Moreover, using this method, it is also possible to tune the size of nanoparticles by adjusting the polymer concentration. The final size reached by the nanoparticles varies as a power law of the polymer concentration in the solvent. Additionally, the polymer molar mass influences the nanoparticle size, with larger nanoparticles obtained for higher polymer molar mass.

The main drawback of the nanoprecipitation process is the low colloidal stability for high solids content, limiting the final dispersion to low solids content. The addition of a surfactant in the nanoprecipitation process is a way to enhance the stability of the dispersion, and produce more concentrated dispersions. Xie et al. reached a final nanoparticle concentration of 2.5 mg.mL -1 prior to concentration, using Pluronic F127, a poloxamer and non-ionic surfactant. This surfactant has the advantage of possessing a temperature-sensitive critical micelle concentration (TS-CMC) enabling the removal of the surfactant excess by centrifugal dialysis at low temperature. [START_REF] Xie | Overcoming Efficiency and Stability Limits in Water-Processing Nanoparticular Organic Photovoltaics by Minimizing Microstructure Defects[END_REF] The authors showed that efficient and environmentally-friendly solar cells could be processed by using an aqueous dispersion, holding the current record in PCE for OPV devices made from nanoparticles at 7.5% for the PBQ-QF:ITIC system. This value directly compared to a PCE of 4.4% when using SDS as surfactant and the miniemulsion technique.

Amphiphilic copolymers can also be used as surfactant. Several studies reported the use of a polystyrene-comb-poly(ethylene oxide) copolymer as surfactant and showed that stabilizing the conjugated NPs with this surfactant greatly improved the photocatalytic performance of hydrogen evolution compared to the pristine nanoparticles. [START_REF] Pati | An Experimental and Theoretical Study of an Efficient Polymer Nano-Photocatalyst for Hydrogen Evolution[END_REF][START_REF] Tseng | Design and Synthesis of Cycloplatinated Polymer Dots as Photocatalysts for Visible-Light-Driven Hydrogen Evolution[END_REF][START_REF] Kosco | Residual Pd Enables Photocatalytic H2 Evolution from Conjugated Polymers[END_REF] Figure 3. Preparation of conjugated polymer nanoparticles by miniemulsion or nanoprecipitation technique.

From Photovoltaics Knowledge…

Organic semiconductor nanoparticles were first used in the field of organic photovoltaics with the work of Landfester et al. in 2002. [START_REF] Landfester | Semiconducting Polymer Nanospheres in Aqueous Dispersion Prepared by a Miniemulsion Process[END_REF] In their first article utilizing organic semiconductor nanoparticles to fabricate OPV devices, they selected two conjugated polymers, PFB (poly(9,9dioctylfluorene-co-N,N-bis(4-butylphenyl)-N,N-diphenyl-1,4-phenylenediamine) as electron donor material and F8BT (poly(9,9-dioctylfluorene-co-benzothiadiazole) as electron acceptor material and prepared composite nanoparticles using the miniemulsion technique. Although device efficiency was very low (1.7% maximum external quantum efficiency), a photovoltaic effect had been achieved as a proof of concept for the use of organic nanoparticles in electronic devices. [START_REF] Kietzke | Novel Approaches to Polymer Blends Based on Polymer Nanoparticles[END_REF] For the entire journey in the development of organic electronic devices based on colloidal dispersions, probing the precise nanostructure of the colloidal nanoparticles of donor and acceptor materials has been of great interest to researchers due to the substantial influence nanostructure has on device performance. While the available morphology categories of nanoparticles range from phase-separated core-shell, biphasic and eccentric to molecularly intermixed, for two component systems, the most reported morphology type for donor-acceptor nanoparticles has been limited to two categories: core-shell and molecularly intermixed. A core-shell morphology (Figure 4a,b) is most commonly reported when the miniemulsion method is applied to nanoparticle preparation. Here the donor and acceptor materials selfarrange in the miniemulsion droplets to minimize surface energy while the oil-phase solvent (e.g. chloroform or o-xylene [START_REF] Pan | Environmentally Friendly Preparation of Nanoparticles for Organic Photovoltaics[END_REF] ) is being removed via thermal evaporation. When a polymer donor is combined with a fullerene acceptor, the fullerene acceptor invariably has a higher surface energy, 38.2 mJ m -2 for PC61BM and 39 mJ m -2 for PC71BM, and moves to the core of the nanoparticle, while the polymer moves to occupy the shell (Figure 4a). Hence a donor-rich shell and acceptor-rich core is formed, which was reported for TQ1:PC71BM [START_REF] Holmes | Nano-Pathways: Bridging the Divide Between Water-Processable Nanoparticulate and Bulk Heterojunction Organic Photovoltaics[END_REF] and P3HT:PC61BM [START_REF] Holmes | Probing the Origin of Photocurrent in Nanoparticulate Organic Photovoltaics[END_REF] nanoparticles. In the OPV field, fullerene derivatives (PC61BM, PC71BM, ICBA) have been for a long time the standard organic semiconductor used as acceptor material.

However, with nanoparticles being the new building blocks of the active layer, the core-shell morphology achieved with these high surface energy materials is detrimental for OPV performance since after exciton dissociation, electrons can be trapped in the core. As a consequence, power conversion efficiencies of such devices were lower than that achieved with active layers deposited from organic solvents: 2.5% and 2.15 for P3HT:ICBA NPs 21 and P3HT:PC61BM [START_REF] Gehan | Multiscale Active Layer Morphologies for Organic Photovoltaics through Self-Assembly of Nanospheres[END_REF] respectively. Kosco et al. also reported an acceptor-rich core / donor-rich shell for nanoparticles synthesized by miniemulsion (surfactant: SDS) and using PTB7-Th as donor and a non-fullerene acceptor eh-IDTBR. [START_REF] Kosco | Enhanced Photocatalytic Hydrogen Evolution from Organic Semiconductor Heterojunction Nanoparticles[END_REF] They attributed this morphology to the chloroform/(SDS)water interfacial tension being higher for chloroform solution with eh-IDTBR compared to chloroform solution with PTB7-Th. With a solar hydrogen fuel setup, this type of morphology led to a low H2 production, as electrons trapped in the core could not reach the nanoparticle surface.

If we transition completely from fullerene to non-fullerene acceptor materials, the synthetic versatility of this new suite of materials opens up the possibility of a larger range in surface energies for the acceptor, hence in some cases promoting the formation of a donor-rich core / acceptor-rich shell nanoparticle morphology (inverted core-shell) (Figure 4b). For example, when non-fullerene acceptor eh-IDTBR, with a surface energy of 18.3 mJ m -2 , is combined with P3HT, with a surface energy of 26.9 mJ m -2 , eh-IDTBR-rich shell / P3HT-rich core nanoparticles are formed. 24 Similarly, when the non-fullerene acceptor N2200 (surface energy = 23.7 mJ m -2 ) is combined with TQ1 (surface energy = 29 mJ m -2 ), N2200-rich shell / TQ1rich core nanoparticles are formed. Chambon et al. 25 demonstrated that a donor-rich core / acceptor-rich shell morphology (inverted core-shell) is also achievable using the nanoprecipitation method if strategic successive solvent displacement is applied. Here P3HTrich core / PC61BM-rich shell nanoparticles were formed by first precipitating P3HT via the addition of DMSO to THF, and then precipitating PC61BM on the surface of the P3HT nanoparticles by the addition of water to DMSO. Such type of core-shell structure might also be detrimental for OPV and solar hydrogen fuel production setups, as in this case the holes would be trapped in the core. However, the study of Barr et al. highlighted that choosing donoracceptor material combinations with matched surface energies could be an efficient strategy to target molecularly intermixed nanostructures using the miniemulsion process. This morphology has proven to improve the performance of both OPV devices and nanoparticlebased H2 production setups (vide infra).

Molecularly intermixed (Figure 4c) is another frequently reported internal morphology type for organic semiconductor nanoparticles, and it is mostly reported when the nanoprecipitation method is applied. During the nanoparticle formation, the quenching action of the non-solvent leaves little time for the donor and acceptor material to self-arrange according to their differing surface energies, hence forming a molecularly intermixed nanoparticle internal structure. In the case of P3HT:PC61BM nanoparticles, utilizing chloroform as solvent and ethanol as nonsolvent in the nanoprecipitation process led to intermixed nanoparticles and unresolvable subdomains in scanning transmission X-ray microscopy (STXM). [START_REF] Darwis | Surfactant-Free Nanoparticulate Organic Photovoltaics[END_REF] This type of morphology of organic semiconductor nanoparticles appeared to be more suitable for OPV. Indeed, Gartner et al. [START_REF] Gärtner | Eco-Friendly Fabrication of 4% Efficient Organic Solar Cells from Surfactant-Free P3HT:ICBA Nanoparticle Dispersions[END_REF] in 2014 and Saxena et al. [START_REF] Saxena | Pyridine End-Capped Polymer to Stabilize Organic Nanoparticle Dispersions for Solar Cell Fabrication through Reversible Pyridinium Salt Formation[END_REF] in 2021 prepared P3HT:ICBA composite nanoparticles by nanoprecipitation using chloroform/alcohol (ethanol or methanol) as solvent/anti-solvent systems and used them in OPV devices. The champion cells gave PCEs of 4.1% and 3.5% for chloroform/methanol and chloroform/ethanol, respectively. [START_REF] Gärtner | Eco-Friendly Fabrication of 4% Efficient Organic Solar Cells from Surfactant-Free P3HT:ICBA Nanoparticle Dispersions[END_REF] Interestingly, Saxena et al.

showed that P3HT:ICBA devices prepared from colloidal dispersions gave similar performance to those prepared from halogeno-aromatic solvents, 3.5% and 3.6% respectively. [START_REF] Saxena | Pyridine End-Capped Polymer to Stabilize Organic Nanoparticle Dispersions for Solar Cell Fabrication through Reversible Pyridinium Salt Formation[END_REF] But more importantly, the performance was improved compared to devices with the same donor:acceptor combination but prepared from the miniemulsion technique (2.5%), [START_REF] Ulum | The Role of Miscibility in Polymer:Fullerene Nanoparticulate Organic Photovoltaic Devices[END_REF] highlighting the beneficial effect of a molecularly intermixed morphology. In 2018, Xie et al.

reported a thorough study of P3HT:ICBA nanoparticles formed by nanoprecipitation using chloroform/alcohol as the solvent/anti-solvent system and a robot-based high-throughput method [START_REF] Xie | Robot-Based High-Throughput Engineering of Alcoholic Polymer: Fullerene Nanoparticle Inks for an Eco-Friendly Processing of Organic Solar Cells[END_REF] and managed to improve the performance of these types of devices up to 4.52%. The morphology of active layers prepared from the colloidal dispersions was studied by STXM and revealed a finer phase-separation, finer than that obtained with miniemulsion. The morphology was finer than what is resolvable with STXM, a technique with a resolution limit of 30 nm, hence the domain size was <30 nm. This intermixed morphology improves exciton dissociation and charge transport which is likely to explain the better performance in OPV.

Nanoparticles with non-fullerene acceptors have also been prepared by nanoprecipitation. Xie et al. compared the performance of OPV devices fabricated with four different kinds of donor:acceptor nanoparticles prepared either by miniemulsion (using SDS as surfactant, SDS-NP) or by surfactant assisted nanoprecipitation (using F127 surfactant, cs-NP). [START_REF] Xie | Overcoming Efficiency and Stability Limits in Water-Processing Nanoparticular Organic Photovoltaics by Minimizing Microstructure Defects[END_REF] In all four cases, the devices fabricated with nanoparticles synthesized by nanoprecipitation (cs-NP) outperformed those fabricated with nanoparticles synthesized by miniemulsion (SDS-NP). We can highlight that, with PBQ-QF:ITIC as donor:acceptor combination, the authors achieved 6.97% average PCE with cs-NP and only 3.98% average PCE for SDS-NP. [START_REF] Xie | Overcoming Efficiency and Stability Limits in Water-Processing Nanoparticular Organic Photovoltaics by Minimizing Microstructure Defects[END_REF] The authors attributed the improved performance to efficient removal of the surfactant and higher crystallinity of the materials. Even though the morphology of cs-NP has not been deeply studied, it is likely to be molecularly intermixed since the morphology is generally quenched during the nanoprecipitation process and it may play a role in the performance enhancement compared to SDS-NP. The analysis of the impact of molecularly intermixed nanoparticle morphology on OPV devices shows that it improves the device efficiency by allowing both high exciton dissociation rate and conduction pathways for charge extraction. Therefore, it is likely that this type of molecular arrangement in the nanoparticle is also more suitable for nanoparticle-based hydrogen solar fuel production setups, as electrons and holes will have pathways to reach the surface of the nanoparticle.

A similar morphology category, described as distributed nano-domains (Figure 4d), was reported by Subianto et al. [START_REF] Subianto | Sulfonated Thiophene Derivative Stabilized Aqueous Poly(3-Hexylthiophene):Phenyl-C61-Butyric Acid Methyl Ester Nanoparticle Dispersion for Organic Solar Cell Applications[END_REF] and Kosco et al. [START_REF] Kosco | Enhanced Photocatalytic Hydrogen Evolution from Organic Semiconductor Heterojunction Nanoparticles[END_REF] This morphology was achieved by using a surfactant which has a functional group with greater affinity for the donor material and a second functional group with greater affinity for the acceptor material. reported PTB7-Th:eh-IDTBR nanoparticles exhibiting a morphology comprised of distributed nano-domains, when using TEBS as surfactant. They suggested that such morphology was obtained due to similar chloroform/water interfacial tensions whether PTB7-Th or eh-IDTBR is dissolved in the oil phase, which is not the case when SDS is used. In hydrogen solar fuel production setups, the distributed nanodomain morphology improved the H2 evolution rate from 3,044 ± 332 µmol h -1 g -1 to 28,133 ± 3,067 µmol h -1 g -1 , compared to the core-shell morphology. [START_REF] Kosco | Enhanced Photocatalytic Hydrogen Evolution from Organic Semiconductor Heterojunction Nanoparticles[END_REF] This improvement was attributed to the available conduction pathways for electrons to reach the nanoparticle surface (See "… To Solar Hydrogen Fuel Production" section for details).

A fifth morphology category, biphasic/Janus (Figure 4e), while familiar to the field of nanoparticles in general, is less common to organic semiconductor nanoparticles and has only been theorized by Landfester et al. [START_REF] Kietzke | Phase Separation of Binary Blends in Polymer Nanoparticles[END_REF] using a model system of polystyrene:poly(propylene carbonate) (PS:PCC). The authors showed that biphasic nanoparticles were formed from these two immiscible polymers by the miniemulsion process. They theorized that biphasic nanoparticles could also be formed of immiscible combinations of donor and acceptor semiconductor polymers, such as PFB:F8BT. This morphology has not been tested in devices, neither OPV nor hydrogen solar fuel production setups. However, it is expected to be the ideal morphology since Janus nanoparticle of small diameters (< 40 nm) could combine high exciton dissociation rate and perfect conduction pathways for both charges. 4. Nanoparticle morphology categories reported in the literature. With (a) core-shell, (b) inverted core-shell, (c) molecularly intermixed, (d) distributed nano-domains and (e) biphasic/Janus morphologies. Chemical structures of organic semiconductors (and polymers) described can be found in panel (f). Scale bars are 600 nm (Holmes et al. [START_REF] Holmes | Nano-Pathways: Bridging the Divide Between Water-Processable Nanoparticulate and Bulk Heterojunction Organic Photovoltaics[END_REF][START_REF] Holmes | Probing the Origin of Photocurrent in Nanoparticulate Organic Photovoltaics[END_REF] ), 1 µm (Barr et al. 24 ) and 500 nm (Darwis et al. [START_REF] Darwis | Surfactant-Free Nanoparticulate Organic Photovoltaics[END_REF] ).

…To Solar Hydrogen Fuel Production

The many lessons taken from research in organic photovoltaics allowed the recent use of conjugated polymers as photocatalysts for hydrogen evolution to be rapidly efficient. Let us present the basics of this technology. Solar energy can be stored in the form of the chemical bond of a fuel and later be supplied on H2 is the cleanest solar fuel since it only releases water as a product and electricity. H2 is produced from photocatalytic water splitting through the reaction 𝐻 2 𝑂 → 𝐻 2 + 1 2 𝑂 2 with an energy barrier of 1.23 eV. This barrier can be overcome by the energy brought by the photons, absorbed by the semiconductors. The absorption generates the exciton from which electron (e -) and hole (h + ) take part in reduction and oxidation processes respectively (Figure 5). Therefore, the basic conditions for the use of semiconductors as light harvesting materials for hydrogen evolution are: i) a band-gap allowing the absorption of the solar irradiation (mainly from 1 to 3 eV vs vacuum), ii) a LUMO presenting a potential lower than the one used to reduce H + (2𝐻 + + 2𝑒 -→ 𝐻 2 , at pH = 0, E = 0 V vs NHE or 4.44 eV vs vacuum) and iii) a HOMO energy set at a higher potential than the one needed to oxidize water (2 ℎ + + 2𝐻 2 𝑂 → 4𝐻 + + 1 2 𝑂 2 , at pH = 0, E = 1.23 V vs NHE or 5.67 eV vs vacuum).

For H2 evolution especially, this last point can be overcome with the use of a sacrificial organic electron donor (for example trimethylamine or ascorbic acid) to fill the semiconductor HOMO and regenerate the material. In this case, an acidic medium is required to provide enough protons. We chose here to present the recent studies that are elegant strategies to understand the overall mechanism and improve the efficiency of the hydrogen photocatalysis by organic nanoparticles.

In 2016, Tian and co-workers were the first to use nanoparticles made of poly[(9,9'dioctylfluorenyl-2,7-diyl)-co-(1,4-benzo-{2,1',3} thiadiazole)] (PFBT in Figure 5) for H2 evolution. The particles (30 to 50 nm diameter) were prepared by nanoprecipitation, stabilized with an amphiphilic comb copolymer polystyrene-comb-poly(ethylene oxide) classically used for photovoltaics. The particles were then dispersed in water at pH 4, with ascorbic acid as a sacrificial electron donor and the reactor was irradiated with an LED lamp ( > 420 nm). An initial rate constant for hydrogen generation of 8 mmolh -1 g -1 was measured. They demonstrated that stabilizing the nanoparticles using this surfactant greatly improved the catalytic activity, by creating small nanoparticles. However, after 1 hour exposure, particle aggregation led to a loss of activity. [START_REF] Wang | Organic Polymer Dots as Photocatalysts for Visible Light-Driven Hydrogen Generation[END_REF] Years later, in 2021, the same group increased the stability of the catalytic activity by anchoring the PFBT dots at the surface of commercially available cross-linked dextran beads. [START_REF] Liu | In Situ Preparation and Immobilization of Semiconducting Polymer Dots on Microbeads for Efficient and Stable Photocatalytic Hydrogen Evolution[END_REF] By precipitating the mixture of the conjugated polymer and the microbeads from THF to water, they created raspberry-like microparticles in which polymer dots and their clusters were formed upon the microbead substrates. With the of this template, the immobilized PFBT increased the hydrogen evolution as compared to the unsupported polymer dots. The stability of the catalytic activity was elongated from several hours to more than 80 h.

In 2017, Pati et al. improved the efficiency of the H2 evolution rates (HER) to 50 mmolh -1 g -1 by reducing the polymer bandgap, a well-known strategy to harvest more photons from the sunlight, introducing thiophene spacers between the donor and acceptor units (PFODTBT in Figure 5). Most importantly, they proved, by density functional theory calculation, that the nitrogen atoms are the catalytic binding sites with protons. [START_REF] Pati | An Experimental and Theoretical Study of an Efficient Polymer Nano-Photocatalyst for Hydrogen Evolution[END_REF] A co-catalyst, such as platinum (Pt), can also be used to increase the rate of the hydrogen production by providing active reaction sites and suppressing the charge recombination and reverse reactions. [START_REF] Yang | Roles of Cocatalysts in Photocatalysis and Photoelectrocatalysis[END_REF] With the aim to bind the co-catalyst, Chou and co-workers synthesized a conjugated cycloplatinated polymer, in which the platinum complex unit is linked to the conjugated backbone (PFTFQ-PtPy in Figure 5). The authors used the same preparation process as Tian and co-workers and measured a HER of 12 mmolh -1 g -1 that was lower than previously reported, but the stability was increased to 10 hours. [START_REF] Tseng | Design and Synthesis of Cycloplatinated Polymer Dots as Photocatalysts for Visible-Light-Driven Hydrogen Evolution[END_REF] Alike platinum, palladium (Pd 0 ) is known as a highly active HER electrocatalyst. Yet, many conjugated polymers (including the one mentioned in Tian and Chou's papers) [START_REF] Pati | An Experimental and Theoretical Study of an Efficient Polymer Nano-Photocatalyst for Hydrogen Evolution[END_REF][START_REF] Tseng | Design and Synthesis of Cycloplatinated Polymer Dots as Photocatalysts for Visible-Light-Driven Hydrogen Evolution[END_REF][START_REF] Wang | Organic Polymer Dots as Photocatalysts for Visible Light-Driven Hydrogen Generation[END_REF] are synthesized by cross-coupling reaction catalyzed by Pd, which is difficult to completely eliminate at the purification stage. Thus, Kosco et al. investigated the HER of particles made of the same polymer poly(9,9-dioctyl fluorene-alt-benzothiadiazole) containing different amounts of residual Pd, from 1 to 1000 ppm. [START_REF] Kosco | Residual Pd Enables Photocatalytic H2 Evolution from Conjugated Polymers[END_REF] When all Pd was removed (1 ppm), no H2 evolution was observed. Then the HER increased with Pd content until it reached a plateau up to 160 µmolh -1 g -1 at around 200 ppm. It is thus important to always measure the residual catalyst content in these types of studies.

Chemistry will certainly be an efficient tool to improve the performance of organic nanoparticles. Hu et al. synthesized three polymers based on the same conjugated backbone but bearing different side chains, one alkyl hydrophobic and two hydrophilic oligo(ethylene oxide) (EO) presenting 4 and 7 units (see Figure 5, PBDTBT-7EO). [START_REF] Hu | Conjugated Polymers with Oligoethylene Glycol Side Chains for Improved Photocatalytic Hydrogen Evolution[END_REF] The PBDTBT-7EO could improve the HER by a factor of 90 over that of alkyl-functionalized conjugated polymers. This was attributed to the positive effects of OE; (i) the creation of smaller particles (around 6 nm) which increased the interfacial area of NPs/water, (ii) the creation of interactions between EO side chains and both Pt co-catalyst and protons, which improved charge transfer.

Extensively demonstrated through the photovoltaic field, organic semiconductors suffer from their high exciton binding energies, which lead to short exciton diffusion lengths. Therefore, most of the excitons generated by light absorption recombine before reaching the nanoparticle interface with water. Kosco et al. then had the idea to introduce in the particles a bulk heterojunction of two materials, the PTB7-Th polymer donor and the non-fullerene acceptor eh-IDTBR (Figure 5), to increase exciton dissociation. [START_REF] Kosco | Enhanced Photocatalytic Hydrogen Evolution from Organic Semiconductor Heterojunction Nanoparticles[END_REF] The authors prepared nanoparticles by miniemulsion using two different surfactants, SDS and sodium 2-(3thienyl)ethyloxybutylsulfonate (TEBS), which lead to different morphologies, core-shell and bulk heterojunction (distributed nano-domains), respectively. The first conclusion is that the HER of the blends were higher than the single-component nanoparticles, by at least a factor of 30 (Pt is used as a co-catalyst). The second point is that the core-shell morphology, in which the core is formed by the acceptor, is 9 times less efficient (the electrons are trapped in the core) in catalyzing the H2 evolution than the bulk heterojunction (distributed nano-domains) morphology. Finally, by optimizing the Pt loading, the authors reached a HER record of 64 mmolh -1 g -1 . At the same time of Kosco's report, Cooper's group published a large library of 237 binary and ternary donor/acceptor nanoparticles made by nanoprecipitation without the use of a surfactant. 36 They used five different polymer electron donors and four small molecule electron acceptors, either fullerene or non-fullerene. They found that binary or ternary blends greatly outperform the pure constituent donor or acceptor particles in terms of H2 production. The blends made from the non-fullerene acceptor ITIC-2F gave highest initial photocatalytic performance, which again relates to recent progress in OPV, but experienced a very low stability due to rapid aggregation. The PCDTBT/PC61BM blend was eventually the champion, with a high hydrogen evolution rate of 105.2 mmol h -1 g -1 ( = 420 nm, platinum, ascorbic acid) and a stability of around one day. Interestingly, in some cases, the ternary blends outperformed the parent's binary blends. Although the authors could not investigate this point, it opens the door for potential future optimization. Indeed, in 2021, Liu et al. 37 reported the use of panchromatic ternary polymer dots consisting of two organic conjugated polymers (PFBT and PFODTBT) as energy and electron donors and a small molecule (ITIC) as energy and electron acceptor to complementarily harvest the photons from 350 to 750 nm. They produced particles of 90 nm by nanoprecipitation with a polystyrene-poly(ethylene glycol) copolymer used as surfactant. They measured a maximum photocatalytic hydrogen evolution of 60.8 ± 6.7 mmolh -1 g -1 with the assistance of a Pt cocatalyst and ascorbic acid as sacrificial electron donor. Interestingly, this highest efficiency was achieved when the ITIC content was 55% of the blend corresponding to the ratio when the highest ITIC fluorescence quenching yield was observed by steady-state fluorescence measurement. The stability of the hydrogen generation was held at 50% of the initial performance after 120 h. Given the complex nature of the system, three components, the charge and energy transfer pathways were investigated in detail by transient absorption spectroscopy measurements. They discovered that excitation energy transfer from excited PFBT to PFODTBT and ITIC within 600 fs occurred, and charge transfer between PFODTBT and ITIC happened within 200 fs.

Conclusion and Perspectives

The development of organic semiconductor colloidal dispersions has shown significant progress in the past decade for applications in both photovoltaics and photocatalytic hydrogen evolution. The key benefit of nanoparticles for photocatalytic hydrogen evolution over thin films being the increased interface area for the reaction to take place. In addition, the benefits of organic semiconductors over existing photocatalysts, such as inorganic semiconductors, include a broader absorbance, higher quantum efficiency and lower toxicity.

The extensive research on the organic photovoltaic side led to the development of different methods to overcome the issues limiting the efficiency of the devices, and in particular on the control over nanoparticle morphology. The morphology of the nanoparticle has shown to be tunable either by i) matching surface energies of the donor and acceptor materials and/or ii) playing with the interfacial energy via the use of alternative surfactants. From the experience developed in the OPV field, it appears that the molecularly intermixed morphology is more suitable for OPV devices since it can both enable high exciton dissociation rate and conduction pathways for charge extraction. Such characteristics are also likely to be a requirement for solar fuel production and the first reports showed that an intermixed morphology outperforms a coreshell morphology.

Although the field of organic semiconductor nanoparticles for solar fuel production is very young, interesting findings were achieved thanks to the knowledge gained from photovoltaics research, such as the promising use of a bulk heterojunction to increase exciton dissociation efficiency and thus HER. These ideas might also be applicable to carbon dioxide reduction to produce other solar fuels like ethanol. Wang et al. have fabricated a biohybrid material made of chloroplast and conjugated polymer nanoparticles to improve photosynthesis. 38 The nanoparticles were added to increase the absorption of the chloroplast in the UV region.

Improving photocatalytic activity will require an interdisciplinary field of action to better understand and improve the charge transfer from light absorber to co-catalyst and protons. The development of nanoparticles bearing covalently attached catalytic sites (to prevent from catalyst delamination), the use of earth-abundant elements (instead of rare-metal platinum), or the synthesis of porous or proton permeable particles, are strategies that need to be pursued in the future. Of course, the main issue towards the viability of this technology lies in the stability of the conjugated materials in the condition of potential and pH in a water and oxygen medium, even more if the oxidation of water is involved to cover the all-water splitting. This point will need to be extensively studied by applying standardized methodologies that are applicable in the different laboratories involved in the field.

Conflicts of Interest

There are no conflicts of interest to declare.

A large library of 237 binary and ternary blends of organic semiconductors were screened for photocatalytic H2 activity, in nanoparticulate form utilizing nanoprecipitation synthesis. PCDTBT/PC61BM nanoparticles showed the highest H2 evolution rate of 105.2 mmol h -1 g -1 .

(

Figure 1 .

 1 Figure 1. Graphical overview of the focus of this review. Applying organic semiconductor colloids in photocatalytic hydrogen generation using the knowledge acquired from photovoltaics research.

Figure 2 .

 2 Figure 2. (a) Illustration of sp 2 hybridization along a π-conjugated polymer chain; (b) calculated band structure of polythiophene (adapted from Salzner et al. 9 ); (c) processes occurring during photoconversion in an organic solar cell, in particular the ultra-fast charge transfer.

Figure 4

 4 Figure 4 presents a library of organic semiconductor nanoparticle morphology types and examples of such morphologies being reported in the literature, in order to provide a comprehensive overview of categorization of morphologies. The internal morphology of organic semiconductor nanoparticles forms via self-assembly, particularly in the case of miniemulsion-prepared nanoparticles of donor and acceptor.

  Subianto et al. utilized the thiophene-based surfactant 2-(3-thienyl)ethyloxybutylsulfonate sodium salt (TEBS) to produce nanoparticles of P3HT:PC61BM via the miniemulsion process, reporting a morphology type of distributed nano-domains from small angle neutron scattering (SANS) data. Kosco et al.

Figure

  Figure 4. Nanoparticle morphology categories reported in the literature. With (a) core-shell, (b) inverted core-shell, (c) molecularly intermixed, (d) distributed nano-domains and (e) biphasic/Janus morphologies. Chemical structures of organic semiconductors (and polymers) described can be found in panel (f). Scale bars are 600 nm (Holmes et al.[START_REF] Holmes | Nano-Pathways: Bridging the Divide Between Water-Processable Nanoparticulate and Bulk Heterojunction Organic Photovoltaics[END_REF][START_REF] Holmes | Probing the Origin of Photocurrent in Nanoparticulate Organic Photovoltaics[END_REF] ), 1 µm (Barr et al.24 ) and 500 nm (Darwis et al.[START_REF] Darwis | Surfactant-Free Nanoparticulate Organic Photovoltaics[END_REF] ).

Figure 5 .

 5 Figure 5. a) H2 photocatalysis mechanism. b) Organic semiconductors used in the selected studies.

  37) **Liu, A.; Gedda, L.; Axelsson, M.; Pavliuk, M.; Edwards, K.; Hammarström, L.; Tian, H. Panchromatic Ternary Polymer Dots Involving Sub-Picosecond Energy and Charge Transfer for Efficient and Stable Photocatalytic Hydrogen Evolution. J. Am. Chem. Soc. 2021, 143 (7), 2875-2885.Reports the use of panchromatic ternary nanoparticles consisting of two polymers, PFBT and PFODTBT, as energy and electron donors, and one small molecule, ITIC, as energy and electron acceptor, effectively harvesting photons from 350 to 750 nm. A maximum photocatalytic hydrogen evolution of 60.8 ± 6.7 mmol h -1 g -1 was achieved. (38) Wang, Y.; Li, S.; Liu, L.; Lv, F.; Wang, S. Conjugated Polymer Nanoparticles to Augment Photosynthesis of Chloroplasts. Angew. Chemie 2017, 129 (19), 5392-5395.

Acknowledgements N.P.H. acknowledges the equipment and expertise provided by the Sydney Node of Microscopy Australia, located at the University of Sydney. This work was made possible thanks to the financial support of E2S (Energy and Environment Solutions) of the Université de Pau et Pays de l'Adour. S.C. acknowledges the support provided by the ANR through the WATER-PV project N°ANR-20-CE05-0002-01 and IRP NextPV-II, through CNRS (INC and INSIS) and RCAST/University of Tokyo. The work at LIMMS/CNRS and IIS, University of Tokyo has been partly supported by KAKENHI from JSPS (20H05660).


Matthew C Brennan
email: mcbrennan@g.harvard.edu

Rebecca A Fischer

Samantha Couper

Lowell Miyagi

Daniele Antonangeli

Guillaume Morard

High-Pressure Deformation of Iron-Nickel-Silicon Alloys and Implications for Earth's Inner Core

The inner core's seismic anisotropy can be explained by crystallographic alignment of a hexagonal close-packed iron-rich alloy.

• Sample textures suggest that silicon-bearing alloy deformation may be dominated by pyramidal and basal slip at low and high T, respectively.

• Silicon-bearing alloys are stronger (harder to deform) at inner core conditions than pure iron and iron-nickel alloys.

Introduction

Since the discovery of the inner core [START_REF] Lehmann | P[END_REF] and its identification as a solid iron alloy [START_REF] Birch | Elasticity and Constitution of the Earth's Interior[END_REF], seismic studies have revealed it to be complexly structured and seismically anisotropic. On average, seismic waves move through the inner core several percent faster on paths parallel to Earth's axis of rotation compared to perpendicular paths (e.g., [START_REF] Deuss | Heterogeneity and Anisotropy of Earth's Inner Core[END_REF]. This anisotropy is well documented by travel time (e.g., [START_REF] Creager | Anisotropy of the inner core from differential travel times of the phases PKP and PKIKP[END_REF] and normal mode (e.g., [START_REF] Durek | Inner core anisotropy inferred by direct inversion of normal mode spectra[END_REF] observations, and deviations from this large-scale anisotropy have been used to suggest other inner core structural features (e.g., [START_REF] Irving | Hemispherical structure in inner core velocity anisotropy[END_REF][START_REF] Ishii | The innermost inner core of the earth: Evidence for a change in anisotropic behavior at the radius of about 300 km[END_REF][START_REF] Ouzounis | Isotropy overlying anisotropy at the top of the inner core[END_REF]Su & Dziewoński, 1995). These secondary structures are frequently invoked as evidence for various proposed mechanisms of the primary anisotropy's development.

As with many instances of seismic anisotropy, the Earth's inner core structure likely arises from preferred orientation of crystallites (i.e., texture). Solid Fe-rich alloys (including those in the Fe-Ni-Si system) are expected to exist in the hexagonal close-packed (hcp) crystal structure (ε-Fe) at inner core pressures (P) and temperatures (T) (e.g., [START_REF] Sakai | Stability field of the hcp-structure for Fe, Fe-Ni, and Fe-Ni-Si alloys up to 3 Mbar[END_REF][START_REF] Tateno | The structure of iron in earth's inner core[END_REF][START_REF] Tateno | The structure of Fe-Ni alloy in Earth's inner core[END_REF][START_REF] Tateno | The structure of Fe-Si alloy in Earth's inner core[END_REF]. Since hcp crystals are seismically fast parallel to their c-axes [START_REF] Bergman | Elastic and attenuation anisotropy in directionally solidified (hcp) zinc, and the seismic anisotropy in the Earth's inner core[END_REF], a preferential alignment of the inner core's crystals with Earth's axis of rotation is widely accepted as responsible for the inner core anisotropy (e.g., [START_REF] Antonangeli | Elastic anisotropy in hcp metals at high pressure and the sound wave anisotropy of the Earth's inner core[END_REF][START_REF] Sakai | Stability field of the hcp-structure for Fe, Fe-Ni, and Fe-Ni-Si alloys up to 3 Mbar[END_REF][START_REF] Sayers | Seismic anisotropy of the inner core[END_REF][START_REF] Stixrude | High-pressure elasticity of iron and anisotropy of earth's inner core[END_REF][START_REF] Vočadlo | Ab initio calculations of the elasticity of hcp-Fe as a function of temperature at inner-core pressure[END_REF]). This explanation is experimentally supported by observations of strong c-axis aligned deformation textures in hcp metals, including ε-Fe (e.g., [START_REF] Antonangeli | Elastic anisotropy in hcp metals at high pressure and the sound wave anisotropy of the Earth's inner core[END_REF][START_REF] Merkel | Texture and elastic strains in hcp-iron plastically deformed up to 17.5 GPa and 600 K: experiment and model[END_REF][START_REF] Merkel | In situ radial X-ray diffraction study of texture and stress during phase transformations in bcc-, fcc-and hcp-iron up to 36 GPa and 1000[END_REF][START_REF] Miyagi | In situ phase transformation and deformation of iron at high pressure and temperature[END_REF][START_REF] Wenk | The plastic deformation of iron at pressures of the Earth's inner core[END_REF]. It is worth noting that cubic Fe polymorphs cannot deform to produce a texture compatible with the observed anisotropy [START_REF] Lincot | Multiscale model of global inner-core anisotropy induced by hcp alloy plasticity[END_REF].

There is considerable diversity amongst the mechanisms proposed to create this texture. One class of models relies on preferred orientation developing during crystallization (e.g., [START_REF] Karato | Inner core anisotropy due to the magnetic field-induced preferred orientation of iron[END_REF][START_REF] Bergman | Measurements of electric anisotropy due to solidification texturing and the implications for the Earth's inner core[END_REF]. However, if crystals instead solidify in random orientations, texture must develop by plastic flow in the solid aggregate. This can result from solid-state convection (e.g., [START_REF] Buffett | Onset and orientation of convection in the inner core[END_REF][START_REF] Deguen | Thermal convection in Earth's inner core with phase change at its boundary[END_REF][START_REF] Jeanloz | Convection and anisotropy of the inner core[END_REF] or from west-to-east translation due to preferential solidification in one hemisphere (e.g., Alboussiere et al., 2010;[START_REF] Bergman | Grain growth and loss of texture during annealing of alloys, and the translation of Earth's inner core[END_REF][START_REF] Monnereau | Lopsided growth of Earth's inner core[END_REF]. Flow may also be driven by forces external to the inner core, such as electromagnetism (e.g., Buffet & Wenk, 2001;[START_REF] Takehiro | Fluid motions induced by horizontally heterogeneous Joule heating in the Earth's inner core[END_REF] or outer core convection (e.g., [START_REF] Aubert | Thermochemical flows couple the Earth's inner core growth to mantle heterogeneity[END_REF][START_REF] Yoshida | Growth model of the inner core coupled with the outer core dynamics and the resulting elastic anisotropy[END_REF]. Experimentally, [START_REF] Gleason | Strength of iron at core pressures and evidence for a weak Earth's inner core[END_REF] found that Fe is very weak at ultra-high pressures. If this holds true for the inner core, post-solidification texturing could be driven by almost any source of differential stress, making it difficult to discriminate between various models.

An important caveat of previous studies is that they have investigated pure ε-Fe, but the core is known to also contain other elements. Ni is expected to be present at approximately 5 weight percent (wt%) (e.g., [START_REF] Mcdonough | The composition of the Earth[END_REF], but Fe-Ni is too dense and seismically fast to account for core properties, so a much lighter element must also be present [START_REF] Birch | Density and composition of mantle and core[END_REF]. The identity of the light element(s) is one of the most controversial problems in deep Earth geophysics, but Si is a leading contender based on its ability to partition into the metallic phase during core formation (e.g., Fischer et al., 2015;[START_REF] Siebert | Terrestrial accretion under oxidizing conditions[END_REF] and the isotopic [START_REF] Georg | Silicon in the Earth's core[END_REF] and major-element [START_REF] Ringwood | Silicon in the metal phase of enstatite chondrites and some geochemical implications[END_REF] ratios of terrestrial rocks. Estimates of inner core Si based on density range as high as 7 wt% [START_REF] Fischer | Equations of state in the Fe-FeSi system at high pressures and temperatures[END_REF][START_REF] Tateno | The structure of Fe-Si alloy in Earth's inner core[END_REF], but this should be considered an upper bound since Si is unlikely to be the sole alloying light element (e.g., [START_REF] Edmund | Velocity-Density Systematics of Fe-5wt%Si: Constraints on Si Content in the Earth's Inner Core[END_REF][START_REF] Ozawa | High-pressure melting experiments on Fe-Si alloys and implications for silicon as a light element in the core[END_REF].

The presence of alloying elements may alter the deformation mechanisms and resultant texture of the inner core. Metallurgical studies have demonstrated that Ni (e.g., [START_REF] Ledbetter | Elastic Properties of Metals and Alloys, I. Iron, Nickel, and Iron-Nickel Alloys[END_REF] and Si (e.g., [START_REF] Ruiz | Study of deformation and aging behaviour of iron-silicon alloys[END_REF] can significantly alter the mechanical properties of Fe. A previous experimental study [START_REF] Reagan | The effect of nickel on the strength of iron nickel alloys: Implications for the Earth's inner core[END_REF] on Fe-Ni alloys at high pressure did not characterize textures but found that addition of 5.5 wt% Ni could increase the strength (defined as the shear stress needed to induce plastic deformation) of Fe by 25% at inner core conditions. This increase alone is unlikely to change the dominant mechanism of inner core texturing, but a light element, possibly combined with strain hardening [START_REF] Bergman | Deformation of directionally solidified alloys: Evidence for microstructural hardening of Earth's inner core[END_REF], could further strengthen the alloy. Geodynamical models have difficulty reproducing seismic observations by imposing plausible flows on ε-Fe (Lasbleis & Deguen, 2015;[START_REF] Lincot | Seismic response and anisotropy of a model hcp iron inner core[END_REF], but this issue may disappear if alloy deformation textures are distinct from those of pure Fe. In this study, we measure both the strength and texture of deformed Fe-Ni-Si alloys to determine whether an alloying light element significantly changes the mode of plastic deformation or the interpreted strength of the inner core.

Methods

We investigated the properties of five Fe-Ni-Si alloys: Fe-9wt% Si (hereafter Fe-9Si) was a powder (Goodfellow FE166014); Fe-6Ni-8Si was synthesized in a piston-cylinder press at Harvard University (composition checked by energy dispersive spectroscopy); and Fe-5Si, Fe-5Ni-5Si, and Fe-5Ni-10Si were synthesized as foils by ultra-rapid quenching at the Institut de Chimie et des Matériaux de Paris-Est (details in [START_REF] Morard | Melting of Fe-Ni-Si and Fe-Ni-S alloys at megabar pressures: implications for the coremantle boundary temperature[END_REF]. Non-foil samples were loaded as powders and foil samples were laser-drilled into cylindrical slugs. All samples filled the sample chambers, which were 50 μm diameter cylindrical holes drilled into amorphous boron gaskets contained in Kapton supporting rings. This configuration allows X-rays to pass radially through the gasket and sample [START_REF] Merkel | X-ray transparent gasket for diamond anvil cell high pressure experiments[END_REF]. A Pt flake was loaded along with each sample as a pressure standard [START_REF] Fei | Toward an internally consistent pressure scale[END_REF]. Samples were compressed between diamonds with 200 μm diameter culets in panoramic piston-cylinder type diamond anvil cells to initial pressures of 2-3 GPa. Additional compression was accomplished by an inflating gas membrane once the cell was on the beamline. We repeated the Fe-5Si experiment with double-sided laser heating during compression. For that experiment, gaskets were laser drilled from cubic boron nitride, and MgO flakes were used as thermal insulators and pressure standards [START_REF] Speziale | Quasi-hydrostatic compression of magnesium oxide to 52 GPa: Implications for the pressure-volumetemperature equation of state[END_REF].

Experiments were conducted at Advanced Light Source beamline 12.2.2 (λ = 0.4613 or 0.4592 Å) with the diamond anvil cell mounted with its compression axis orthogonal to the Xray beam [START_REF] Kunz | A beamline for high-pressure studies at the Advanced Light Source with a superconducting bending magnet as the source[END_REF]. The detector was a mar345 positioned 385 or 386 mm from the sample, and the calibrant was CeO2 at ambient conditions. For each pressure step, a diffraction pattern was collected with a 120 second exposure. We used the program Dioptas [START_REF] Prescher | DIOPTAS: A program for reduction of twodimensional X-ray diffraction data and data exploration[END_REF] for live pattern integration, which allowed us to monitor phase changes and sample pressure during the experiment. Diffraction patterns were collected as the samples were compressed gradually to 50-60 GPa, near the maximum stability of the boron gaskets [START_REF] Merkel | X-ray transparent gasket for diamond anvil cell high pressure experiments[END_REF]. Membrane pressure was then released over several hours while simultaneously collecting decompression patterns. Diffraction data were analyzed via Rietveld refinement [START_REF] Mccusker | Rietveld refinement guidelines[END_REF] in the crystallographic software package MAUD [START_REF] Lutterotti | MAUD (material analysis using diffraction): a user friendly Java program for Rietveld texture analysis and more[END_REF]. We analyzed several diffraction patterns for each experiment, including at least one pattern in the body-centered cubic (bcc) and the bcc-hcp transition regions, and at least four in the hcp region. Patterns were chosen based on their diffraction intensity, possession of sufficient Pt diffraction to refine an accurate pressure, and equally spaced coverage of the experiment's pressure range. These patterns were refined over a 2θ range of 11.5-25°and refined unit cell dimensions and elastic strains were compiled for the hcp phase of each sample (Supporting Information Table S1). Textures were calculated using the Extended Williams-Imhof-Matthies-Vinel (E-WIMV) model [START_REF] Chateigner | Quantitative texture analysis and combined analysis[END_REF] with fiber symmetry imposed about the axis of compression. Orientation density functions were refined at a resolution of 15°, exported to BEARTEX [START_REF] Wenk | BEARTEX: A Windows-based program system for quantitative texture analysis[END_REF], and smoothed with a 10° Gaussian filter prior to plotting as inverse pole figures (Section 3). The pressures of phase transitions in 300 K samples may not necessarily be the same as at equilibrium due to sluggish kinetics, starting material effects, and non-hydrostaticity, but the measured texture and strength of the phases present are still accurate.

Deformation Textures

As in pure Fe, our alloy samples transformed from the bcc (or bcc-like: [START_REF] Fischer | Phase relations in the Fe-FeSi system at high pressures and temperatures[END_REF] structure to the hcp structure upon compression. The deformation textures of our roomtemperature experiments are shown in Figure 1. The bcc textures are near-identical to those of pure Fe (e.g., [START_REF] Merkel | Deformation of polycrystalline iron up to 30GPa and 1000K[END_REF][START_REF] Miyagi | In situ phase transformation and deformation of iron at high pressure and temperature[END_REF], varying only in the strength of the 100 maximum. The similarity across compositions suggests that sufficient plastic flow occurred prior to the bcc-hcp transition to homogenize the textures (except for possibly in Fe-9Si, which may have led to its distinctive hcp texture). Once the transition to hcp is complete, the alloy textures show two distinct maxima: one near 112 � 0 and one near 0001. The non-foil samples (Fe-9Si and Fe-6Ni-8Si) are distinguished by the absence of the latter maximum; these were mechanically strong (Section 4) but weakly textured, perhaps indicating that plastic flow was impeded in these experiments. The non-foil textures are likely the result of compressive {21 � 1 � 2}〈21 � 1 � 3〉 twinning. This deformation mechanism is known to occur at large strains and low temperatures in ε-Fe [START_REF] Kanitpanyacharoen | Significance of mechanical twinning in hexagonal metals at high pressure[END_REF][START_REF] Merkel | Deformation of polycrystalline iron up to 30GPa and 1000K[END_REF], so its presence at 300 K in our strongest alloys is reasonable. The foil experiments were more strongly textured (showing strong maxima at 112 � 0 and 0001), so they may be better representatives of texture development by dislocations (the type of deformation texturing proposed to occur in the inner core, see Section 4.4). Polycrystal plasticity simulations of hcp metals (e.g., [START_REF] Chapuis | Simulations of texture evolution for HCP metals: Influence of the main slip systems[END_REF][START_REF] Kanitpanyacharoen | Significance of mechanical twinning in hexagonal metals at high pressure[END_REF][START_REF] Miyagi | In situ phase transformation and deformation of iron at high pressure and temperature[END_REF][START_REF] Wenk | The plastic deformation of iron at pressures of the Earth's inner core[END_REF] have shown that basal (0001)〈21 � 1 � 0〉 slip produces the 0001 maximum, while pyramidal {21 � 1 � 2}〈21 � 1 � 3〉 slip produces the 112 � 0 maximum. A large pyramidal contribution can result in a ~30° shift in the 0001 maximum [START_REF] Miyagi | In situ phase transformation and deformation of iron at high pressure and temperature[END_REF][START_REF] Merkel | In situ radial X-ray diffraction study of texture and stress during phase transformations in bcc-, fcc-and hcp-iron up to 36 GPa and 1000[END_REF], as is seen in the Fe-5Ni-10Si textures. Together, these foil textures show evidence of significant pyramidal slip. Since basal slip is typically observed to dominate ε-Fe deformation at 300 K (e.g., [START_REF] Nishihara | Deformation-induced crystallographic-preferred orientation of hcp-iron: An experimental study using a deformation-DIA apparatus[END_REF] we surmise that addition of Si increases the activity of pyramidal slip. Prismatic {101 � 0}〈1 � 21 � 0〉 slip is also likely to be active without producing a distinct textural signature [START_REF] Merkel | Deformation of polycrystalline iron up to 30GPa and 1000K[END_REF].

Figure 1.

Inverse pole figures (IPFs) showing alloy deformation textures at room temperature. The bcc textures were collected before the appearance of hcp, "transition" textures were collected in the bcc-hcp coexistence region, "compression" textures were collected during compression near peak sample pressure (in the hcp-only regime), and "decompression" textures were collected after the sample had relaxed by 5-10 GPa. Textural differences appear upon transformation to hcp and become more pronounced upon compression. Sample textures remained consistent upon decompression, in contrast to [START_REF] Miyagi | In situ phase transformation and deformation of iron at high pressure and temperature[END_REF]. Asterisks indicate non-foil starting materials (Section 2). All IPFs are plotted on the same intensity scale, quantified as multiples of randomly distributed crystallographic orientations (mrd). Typical pressure uncertainties are ~5%.

Laser-heated deformation textures of a different Fe-5Si experiment are shown in Figure 2. Compared to the 300 K data, the high-temperature textures show a basal slip maximum focused in the 0001 direction and much stronger in intensity than the pyramidal maximum at 112 � 0. Consistent with the phase relations reported by [START_REF] Komabayashi | Phase transition boundary between fcc and hcp structures in Fe-Si alloy and its implications for terrestrial planetary cores[END_REF], a few facecentered cubic (fcc) grains (< 2 volume % from the Rietveld refinement) crystalized above 1400 K (Supporting Information Figure S3), but they are likely too scarce to have influenced the texture; [START_REF] Miyagi | In situ phase transformation and deformation of iron at high pressure and temperature[END_REF] did not observe hcp textural changes even at higher fcc abundances. Focused 0001 textures previously observed in pure Fe have been attributed to basal slip [START_REF] Nishihara | Deformation-induced crystallographic-preferred orientation of hcp-iron: An experimental study using a deformation-DIA apparatus[END_REF][START_REF] Wenk | The plastic deformation of iron at pressures of the Earth's inner core[END_REF] and tensile twinning [START_REF] Merkel | Texture and elastic strains in hcp-iron plastically deformed up to 17.5 GPa and 600 K: experiment and model[END_REF]. Since heating disrupts twinning mechanisms, and there is no textural evidence for strong pyramidal slip (unlike at 300 K), it seems that deformation at high temperatures favors basal slip. This effect was previously suggested for ε-Fe by [START_REF] Steinle-Neumann | Elasticity of iron at the temperature of the Earth's inner core[END_REF] and could be associated with the high temperature breakdown of 〈𝑐𝑐 + 𝑎𝑎〉 deformation mechanisms observed in other hcp metals [START_REF] Fan | Temperature effects on the mobility of pyramidal <c + a> dislocations in magnesium[END_REF][START_REF] Poirier | TEM study of an analogue of the Earth's inner core ε-Fe[END_REF].

Figure 2.

IPFs of the hcp phase from diffraction images taken in the laser-heated Fe-5Si experiment. The 300 K pole figure was collected at 24 GPa (prior to any laser heating), and the others were taken consecutively during a cycle of simultaneous heating and compression at 43-46 GPa. The basal slip maximum at high temperatures is stronger and more focused on 0001 compared to 300 K textures, while a weaker local maximum appears to persist at 112 � 0, suggesting continued pyramidal slip activity. This texture persisted upon temperature quenching. Geometries and intensity scales are the same as in Figure 1. Typical temperature uncertainties are ~10%.

The relative dominance of basal and pyramidal slip systems may be significant to our understanding of the inner core. As mentioned above, most studies predict basal slip to dominate ε-Fe deformation at deep-Earth conditions since this mechanism produces strong 0001 textures analogous to the observed polar anisotropy (e.g., [START_REF] Wenk | The plastic deformation of iron at pressures of the Earth's inner core[END_REF]. We see this same texture in our heated experiment, so we cannot rule out this interpretation. However, some studies (e.g., [START_REF] Lincot | Multiscale model of global inner-core anisotropy induced by hcp alloy plasticity[END_REF][START_REF] Steinle-Neumann | Elasticity of iron at the temperature of the Earth's inner core[END_REF] have suggested that pyramidal slip may be required to match seismic observations. In that case, our finding of significant pyramidal activity in Si-bearing alloys may help explain the discrepancy between the observed and expected modes of plastic deformation. Of course, it is also possible that the inner core texture is a solidification product and was not created by plastic deformation at all (Section 4.4).

Alloy Strength

Our experiments allow us to measure elastic stress in the sample and quantify its dependence on pressure and temperature. Calculating mechanical strength also requires knowledge of the alloys' shear moduli, the values of which were taken from previous studies. We extrapolate these parameters to inner core conditions to compare the mechanical strength implied by our Si-bearing experiments to previously-published estimates for Fe and Fe-Ni.

Strength calculations

The yield strength of a material is defined by the boundary between stresses low enough to be supported elastically and stresses high enough to induce plastic deformation (i.e., flow). In our experiments, the elastic stress resolved on a specific diffraction peak is determined by the dimensionless parameter 𝑄𝑄(ℎ 𝑘𝑘 𝑙𝑙), where h, k, and l are the Miller indices of the peak. This parameter is related to deviatoric (i.e., differential) stress by:

𝑄𝑄(ℎ 𝑘𝑘 𝑙𝑙) = 𝑡𝑡 3 � α 2𝐺𝐺 𝑅𝑅 (ℎ 𝑘𝑘 𝑙𝑙) + (1 -α) 2𝐺𝐺 𝑉𝑉 � (1)
where 𝐺𝐺 𝑉𝑉 is the Voight approximation shear modulus, 𝐺𝐺 𝑅𝑅 (ℎ 𝑘𝑘 𝑙𝑙) is the Reuss approximation shear modulus of the peak [START_REF] Anderson | Determination and Some Uses of Isotropic Elastic Constants of Polycrystalline Aggregates Using Single-Crystal Data[END_REF], α is a weighting factor, and 𝑡𝑡 is the deviatoric stress:

𝑡𝑡 = σ 1 -σ 3
(2) where σ 1 and σ 3 are the maximum and minimum stress components, respectively [START_REF] Singh | Analysis of lattice strains measured under nonhydrostatic pressure[END_REF]. Calculating 𝐺𝐺 𝑅𝑅 (ℎ 𝑘𝑘 𝑙𝑙) requires single-crystal compliance moduli (𝑆𝑆 𝑖𝑖𝑖𝑖 ) for the sample material under conditions of hydrostatic pressure. Since these are seldom available, it is common to assume 𝐺𝐺 𝑅𝑅 (ℎ 𝑘𝑘 𝑙𝑙) = 𝐺𝐺 𝑉𝑉 = 𝐺𝐺, where G is the aggregate shear modulus, a measurable quantity. These assumptions reduce Equation 1 to: 𝑡𝑡 = 6𝐺𝐺〈𝑄𝑄(ℎ 𝑘𝑘 𝑙𝑙)〉

(3) where 〈𝑄𝑄(ℎ 𝑘𝑘 𝑙𝑙)〉 (hereafter Q) is an average across all observed peaks in a diffraction pattern. If the sample's yield strength has been exceeded and it is plastically flowing, elastic deformation cannot accommodate any more strain, the peaks are expressing their maximum possible Q, and 𝑡𝑡 is equal to the material's yield strength [START_REF] Hemley | X-ray imaging of stress and strain of diamond, iron, and tungsten at megabar pressures[END_REF]. Determining alloy strengths at conditions relevant to the inner core requires extrapolating both G and Q to high pressures (>330 GPa) and temperatures (>3000 K).

Extrapolation of Q

The pressure dependence of Q in our experiments is shown in Figure 3. Each experiment shows a positive linear relationship between P and Q, with four of the five experiments having similar slopes and Fe-5Ni-5Si exhibiting a shallower pressure dependence. There are no apparent experimental reasons for this deviation; Fe-5Ni-5Si is intermediate among the sample compositions, did not have large uncertainties in Q, had the same dimensions as the other samples, and the other two foil experiments did not exhibit shallow slopes. Extrapolating each trend to inner core pressures (Figure 3 inset) results in indistinguishable values for each experiment except Fe-5Ni-5Si. Since there does not appear to be a compositional trend in Q values, and we cannot rule out the shallower 𝜕𝜕𝑄𝑄 𝜕𝜕𝜕𝜕 � , the following analysis will present results using both a fit to all the experimental alloys ( 𝜕𝜕𝑄𝑄 𝜕𝜕𝜕𝜕 � = (1.1 ± 0.1) × 10 -4 GPa -1 ) and a fit to only Fe-5Ni-5Si ( 𝜕𝜕𝑄𝑄 𝜕𝜕𝜕𝜕 � = (4.4 ± 0.9) × 10 -5 GPa -1 ). Both fits are steeper than literature values for Si-free alloys. For example, the highest value found by Regan et al. ( 2018) was 𝜕𝜕𝑄𝑄 𝜕𝜕𝜕𝜕 � ≈ 3 × 10 -5 GPa -1 for Fe-20Ni.

Figure 3.

Pressure evolution of 〈𝑄𝑄(ℎ 𝑘𝑘 𝑙𝑙)〉 for the hcp phase of each composition at 300 K. Relative strengths between the alloys do not appear to show significant compositional dependence, even within the three experiments (Fe-5Si, Fe-5Ni-5Si, Fe-5Ni-10Si) synthesized as foils. All these data were collected on compression. Fits to 𝜕𝜕𝑄𝑄 𝜕𝜕𝜕𝜕 � for each composition (not shown) and to all data (solid line; dashed lines are 95% confidence intervals) were calculated by orthogonal distance regression considering the error bars of each point. Inset: These fits (and 95% confidence intervals) extrapolated to 329 GPa, the inner core boundary pressure. At this pressure, Fe-5Ni-5Si is noticeably weaker than the other alloys.

Our laser-heated Fe-5Si experiment allows us to estimate the effect of temperature on Q. As expected, high temperatures enhance plastic deformation, reducing the elastically-supported strain and resulting in Q reduction at a rate of 𝜕𝜕𝑄𝑄 𝜕𝜕𝜕𝜕 � = (-1.60 ± 0.36) × 10 -6 K -1 (Supporting Information Figure S1). There are significant experimental limitations to this technique; the minimum power threshold for laser emission prevents measurements at intermediate temperatures, and laser heating generates large temperature gradients in the sample. However, [START_REF] Merkel | In situ radial X-ray diffraction study of texture and stress during phase transformations in bcc-, fcc-and hcp-iron up to 36 GPa and 1000[END_REF] constrained the temperature effect on pure Fe by compiling data from several resistively-heated diamond anvil cell and multi-anvil experiments, and their reported alloy strengths imply 𝜕𝜕𝑄𝑄 𝜕𝜕𝜕𝜕 � consistent with our value for reasonable (i.e., H. [START_REF] Mao | Erratum: Elasticity and rheology of iron above 220 GPa and the nature of the Earth's inner core[END_REF] values of G (Equation 3). Previous studies that extrapolated experimental values to inner core conditions [START_REF] Gleason | Strength of iron at core pressures and evidence for a weak Earth's inner core[END_REF]Regan et al., 2018) assumed 𝜕𝜕𝑄𝑄 𝜕𝜕𝜕𝜕 � = 0 K -1 , meaning their calculated inner core strengths were upper bounds. In the following analysis, we recalculate their results using our estimated 𝜕𝜕𝑄𝑄 𝜕𝜕𝜕𝜕 � value.

Extrapolation of G

In addition to Q, it is necessary to extrapolate shear modulus G to core-relevant conditions (Equation 3). Although [START_REF] Dubrovinsky | Aggregate shear moduli of iron up to 90 GPa and 1100 K[END_REF] describes a technique to determine G values by Rietveld refinement, this requires high-quality and quasi-hydrostatic diffraction, restrictions incompatible with radial geometry experiments. Relatively few studies report shear modulus values, but from the relationships

𝑉𝑉 𝑆𝑆 = � 𝐺𝐺 ρ (4) 𝑉𝑉 𝑃𝑃 = � 𝐾𝐾+ 4 3 𝐺𝐺 ρ (5)
(where VS is shear velocity, VP is compressional velocity, ρ is density, and K is bulk modulus), G can be extracted from simultaneous density and velocity measurements. Figure 4 shows G versus P for available experimental data from the literature on Si-bearing hcp alloys. There is a clear difference between experimental techniques, with nuclear-resonant inelastic X-ray scattering (NRIXS) studies finding systematically lower G values than inelastic X-ray scattering (IXS) or acoustic methods. We will use NRIXS values for the following calculations since experimental uncertainties are sufficient to make extrapolated results of the techniques overlap at inner core conditions (Figure 4 inset). Note that while a linear G versus P relationship is experimentally supported at least to 220 GPa (H. [START_REF] Mao | Erratum: Elasticity and rheology of iron above 220 GPa and the nature of the Earth's inner core[END_REF], a sublinear relationship could potentially reduce the shear modulus at inner core conditions.

Following the method of previous high-pressure strength studies [START_REF] Gleason | Strength of iron at core pressures and evidence for a weak Earth's inner core[END_REF][START_REF] Reagan | The effect of nickel on the strength of iron nickel alloys: Implications for the Earth's inner core[END_REF], we extrapolated G using the formalism of Steinburg et al. (1980):

𝐺𝐺(𝜕𝜕, 𝜕𝜕) = 𝐺𝐺 0 + 𝜕𝜕𝐺𝐺 𝜕𝜕𝑃𝑃 𝑃𝑃 � ρ ρ 0 � � 1 3 � + 𝜕𝜕𝐺𝐺 𝜕𝜕𝜕𝜕 (𝜕𝜕 -300) (6)
where subscript 0 indicates ambient conditions (T = 300 K, P = 1 bar) and ρ is molar density.

Values of 𝐺𝐺 0 and 𝜕𝜕𝐺𝐺 𝜕𝜕𝜕𝜕 � are taken from the NRIXS fit in Figure 4, ρ 0 is from equation of state literature (Fe-5Si from [START_REF] Edmund | Velocity-Density Systematics of Fe-5wt%Si: Constraints on Si Content in the Earth's Inner Core[END_REF]Fe-5Ni-5Si from Edmund et al., 2020; other alloys calculated from these and the pure Fe values of [START_REF] Dewaele | Quasihydrostatic equation of state of Iron above 2 Mbar[END_REF], ρ is the PREM inner core density, and G(P,T) is calculated from ρ and the PREM inner core shear velocity [START_REF] Dziewonski | Preliminary Reference Earth Model[END_REF]. Selecting locations in the inner core, namely the inner core boundary (ICB) and inner core center (ICC), allows 𝜕𝜕𝐺𝐺 𝜕𝜕𝜕𝜕 � to be solved at the corresponding pressure and temperature conditions. This calculation implicitly assumes that the inner core has the same composition as the material used to derive the other parameters, which is most reasonable for compositions with Ni and Si. The calculation is also subject to the large (but difficult to quantify) uncertainty on the temperature of the inner core (e.g., [START_REF] Karato | Deformation of Earth Materials -An Introduction to the Rheology of Solid Earth[END_REF]. Considering this, we elected to use the same inner core temperatures as [START_REF] Gleason | Strength of iron at core pressures and evidence for a weak Earth's inner core[END_REF] and [START_REF] Reagan | The effect of nickel on the strength of iron nickel alloys: Implications for the Earth's inner core[END_REF] (5500 K at the ICB, 6200 K at the ICC) to ensure that our results are directly comparable to their Si-free results; the differences between studies are not dependent on the specific pressure and temperature conditions. Calculated 𝜕𝜕𝐺𝐺 𝜕𝜕𝜕𝜕 � values vary little between compositions; average values are -0.050 ± 0.008 GPa K -1 at the ICB and -0.043 ± 0.006 GPa K -1 at the ICC. These values are smaller than the corresponding values of Fe-12Ni [START_REF] Reagan | The effect of nickel on the strength of iron nickel alloys: Implications for the Earth's inner core[END_REF] and Fe [START_REF] Gleason | Strength of iron at core pressures and evidence for a weak Earth's inner core[END_REF]) by a factor of 1.25 and a factor of 2 respectively because of our smaller 𝜕𝜕𝐺𝐺 𝜕𝜕𝜕𝜕 � term.

Figure 4.

Published experimental values of the shear moduli of hcp alloys in the Fe-Si and Fe-Ni-Si systems at 300 K, either explicitly reported or implied (Equations 4 and 5). The pink line is a fit to data collected by IXS and picosecond acoustic techniques (triangles and squares, respectively), excluding [START_REF] Sakairi | Sound velocity measurements of hcp Fe-Si alloy at high pressure and high temperature by inelastic X-ray scattering[END_REF]. The blue line is a fit to NRIXS data (circles) and is corrected for 57 Fe enrichment. For context, a fit to experimental measurements of pure hcp-Fe would plot about halfway between these lines (e.g., H. [START_REF] Mao | Erratum: Elasticity and rheology of iron above 220 GPa and the nature of the Earth's inner core[END_REF]. Both fits (solid lines) are calculated irrespective of composition by orthogonal distance regression and are shown with 95% confidence intervals (dashed lines). Inset: These fits (and confidence intervals) extrapolated to 329 GPa. At this pressure, the techniques are indistinguishable within error.

Predicted inner core strength

Calculated alloy strength as a function of temperature is shown in Figure 5. [START_REF] Merkel | In situ radial X-ray diffraction study of texture and stress during phase transformations in bcc-, fcc-and hcp-iron up to 36 GPa and 1000[END_REF] calculated trends directly as a function of t (rather than treating G and Q individually) based on several data spanning different studies and techniques. Extrapolating, their results imply stronger Fe than [START_REF] Gleason | Strength of iron at core pressures and evidence for a weak Earth's inner core[END_REF] but still consistently weaker than our Si-bearing values. Even the Fe-5Ni-5Si experiment (with shallower 𝜕𝜕𝑄𝑄 𝜕𝜕𝜕𝜕 � ) is stronger than all Si-free compositions. If solid state deformation occurs in the inner core, this enhanced strength may influence our interpretation of whether deformation is dominated by the flow of atoms towards concentrations of vacancy defects (diffusion creep) or the movement of lattice dislocations (power-law creep). [START_REF] Van Orman | On the viscosity and creep mechanism of Earth's inner core[END_REF] suggested the additional possibility of dislocation flow via "Harper-Dorn creep", but this mechanism is controversial (e.g., [START_REF] Kassner | Fundamentals of creep in metals and alloys[END_REF]. Adjudicating between mechanisms is important because diffusion creep typically does not produce lattice-preferred orientation and thus would not generate anisotropy. Therefore, if the inner core is in a diffusion-dominated regime, this would tend to support anisotropy developing during crystallization rather than afterwards. [START_REF] Gleason | Strength of iron at core pressures and evidence for a weak Earth's inner core[END_REF] concluded that their pure Fe data were consistent with dislocation-dominated (power-law) creep since mechanical weakness enhances dislocation mobility, allowing geophysically-plausible stresses to produce the required strain rates. Figure 6 (panels a and b) compares their results to those of [START_REF] Reagan | The effect of nickel on the strength of iron nickel alloys: Implications for the Earth's inner core[END_REF] and this study. For a given differential stress, dislocation velocities and strain rates are about one order of magnitude reduced for Si-bearing alloys compared to pure Fe. An approximately equal depression is obtained (for both velocity and strain rate) by moving from the ICB to the ICC for a given alloy. Figure 6c shows a calculation of the boundary between diffusion-and dislocation-dominated regimes based on the parametrization of [START_REF] Reaman | Predictive mechanism for anisotropy development in the Earth's inner core[END_REF], which depends on 𝐺𝐺(𝜕𝜕, 𝜕𝜕) and ρ, but not explicitly on t. Here, the depressed G values of Si-bearing alloys slightly enlarge the dislocation-dominated field. It is important to note that our knowledge of inner core properties is incomplete. Estimates of the inner core stress field (τ) span at least five orders of magnitude (Buffet & Wenk, 2001;[START_REF] Koot | Viscosity of the Earth's inner core: Constraints from nutation observations[END_REF][START_REF] Yoshida | Growth model of the inner core coupled with the outer core dynamics and the resulting elastic anisotropy[END_REF]. Likewise, estimates of the inner core's grain size vary widely, with constraints from earlier studies (e.g., [START_REF] Bergman | Estimates of the Earth's inner core grain size[END_REF] permitting crystallites as small as several centimeters while more recent studies (e.g., [START_REF] Yamazaki | Grain growth of ε-iron: Implications to grain size and its evolution in the Earth's inner core[END_REF] prefer much larger grain sizes. These uncertainties make it impossible to say definitively which field the inner core falls in. Additionally, inner core viscosity, itself a poorly constrained parameter, determines the relationship between applied stress and strain rate. [START_REF] Gleason | Strength of iron at core pressures and evidence for a weak Earth's inner core[END_REF] suggested a viscosity range of 10 15 -10 19 Pa s assuming a pure Fe inner core and simple isotropic shear; our "all alloys" fit would be one order of magnitude more viscous under the same conditions. 2018) assume that study's experimentally-determined strength ratio between Fe-5.5Ni and Fe-20Ni is constant with pressure and temperature. At inner core conditions, Si-bearing alloys are significantly stronger than alloys without light elements. The magnitude of this effect is reduced for the Fe-5Ni-5Si fit due to its smaller 𝜕𝜕𝑄𝑄 𝜕𝜕𝜕𝜕 � .

The enhanced strength of Si-bearing Fe alloys is well known in the bcc regime (e.g., [START_REF] Ruiz | Study of deformation and aging behaviour of iron-silicon alloys[END_REF] and attributed to the impedance of lattice dislocations by the presence of solute atoms [START_REF] Labusch | A Statistical Theory of Solid Solution Hardening[END_REF]. This "solid-solution hardening" effect is enhanced for alloying elements with atomic radii dissimilar to the solvent, hence Fe-Ni alloys (where solute and solvent have nearly identical radii) shows little or no strengthening (e.g., [START_REF] Kotan | An in situ experimental study of grain growth in a nanocrystalline Fe91Ni8Zr1 alloy[END_REF]. Solid solution hardening is known to occur in other hcp metals (e.g., [START_REF] Toda-Caraballo | Modelling solid solution hardening in high entropy alloys[END_REF] and reduced dislocation mobility may influence hcp deformation mechanisms (e.g., [START_REF] Yoo | Nonbasal deformation modes of HCP metals and alloys: Role of dislocation source and mobility[END_REF], so both the strengths and textures of inner core alloys may be functions of their solutes' atomic radii. Dislocation velocity (a), strain rate (b), and critical grain size (c) as functions of differential stress τ. Equations and constants used are from [START_REF] Gleason | Strength of iron at core pressures and evidence for a weak Earth's inner core[END_REF] and [START_REF] Reaman | Predictive mechanism for anisotropy development in the Earth's inner core[END_REF] and are listed in the Supporting Information. For clarity, only the "all alloys" ICB line is plotted in (c); the other ICB lines would be similarly offset from their corresponding ICC lines. The shaded "thermal gradients" [START_REF] Jeanloz | Convection and anisotropy of the inner core[END_REF] and "Joule heating" [START_REF] Takehiro | Fluid motions induced by horizontally heterogeneous Joule heating in the Earth's inner core[END_REF] regions are representative examples of proposed inner core stress ranges (see main text).

Conclusions

We investigated hcp Fe-Ni-Si alloy deformation textures and strengths with highpressure radial X-ray diffraction experiments. These alloys plastically deform by the same principal mechanisms documented in other hcp metals, though possibly with greater pyramidal slip activity compared to pure ε-Fe at 300 K. Upon laser heating, we observed a change in the distribution of crystallographic preferred orientations which may suggest that basal slip is preferred at high temperatures. Experimental Fe-Ni-Si compositions are strong compared to previous Fe and Fe-Ni data and show significantly larger 𝜕𝜕𝑄𝑄 𝜕𝜕𝜕𝜕 � values. Extrapolating to inner core conditions, Si-bearing alloys may be up to an order of magnitude stronger than pure Fe. This would reduce the mobility of anisotropy-favoring lattice dislocations by an equal factor. A mechanically strong inner core generally favors deformation by non-texturing diffusion creep and thus anisotropy as a crystallization (rather than a post-solidification) phenomenon. However, the large uncertainties on experimental and observational inner core parameters make it premature to conclude whether the strengthening effect of Si is significant in this regard.

Figure 5 .

 5 Figure 5.

  Figure 6.

Acknowledgments

We thank Timothy Cavanaugh for performing the alloy EDS measurements, Martin Kunz and Andrew Doran for their assistance on beamline 12.2.2, Feng Lin for his experimental assistance, two anonymous reviewers for their valuable comments, and the editor for handling this manuscript. This work was funded in part by a National Science Foundation Graduate Research Fellowship awarded to M.C.B. (DGE1745303) and by a Henry Luce Foundation award to R.A.F. L.M. acknowledges support from the National Science Foundation through EAR-1654687. This work has been partially supported by the US Department of Energy National Nuclear Security Administration through the Capital-DOE Alliance Center which provided financial support for S.C. (DE-NA0003858). D.A. has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (grant agreement No. 724690). The Advanced Light Source is a Department of Energy Office of Science User Facility (contract no. DE-AC02-05CH11231). Beamline 12.2.2. is funded in part by the Consortium for Materials Properties Research in Earth Sciences (COMPRES) under NSF Cooperative Agreement EAR 10-43050. Part of this work was performed at the Harvard University Center for Nanoscale Systems, a member of the National Nanotechnology Coordinated Infrastructure Network, which is supported by the National Science Foundation (award no. 1541959). Supporting Information for this study, including values used to generate Figures 3-6, is available at https://doi.org/10.7910/DVN/QFE7CW.