A Recipe for a Great Meal: A Benchtop Route from Elemental Se to Superior Thermoelectric ß-Ag2Se.

The low-temperature modification of ß-Ag2Se has proven to be useful as a near-room-temperature thermoelectric material. Over the past years, research has been devoted to interstitial, vacancy, and substitutional doping into the parent ß-Ag2Se structure, aiming at tuning the material's charge and heat transport properties to enhance thermoelectric performance. The transformation of ß-Ag2Se into α-Ag2Se at ∼134 °C and the low solubility of dopants are the main obstacles for the doping approach. Herein, we report a facile, safe, scalable, and cost-effective benchtop approach to successfully produce metal-doped ß-Ag2Se. The doped materials display a remarkable enhancement of thermoelectric performance with a record-high peak zT of 1.30 at 120 °C and an average zT of ∼1.15 in the 25-120 °C range for 0.2 at. % Zn-doped Ag2Se. The enhancement in zT is attributed to point defects created by Zn doping into Ag vacancies/interstitials, which enhances the scattering of phonons and tunes the charge carrier properties, leading to the significant suppression of thermal conductivity. The simplicity of the synthetic method developed herein and the high performance of the final products provide an avenue to produce high-quality Ag2Se-based thermoelectric materials.

Metal Substitutions (M = Al, Ga, In; Sn, Ge; and Mn, Fe, Co) in ZnS: Sphalerite versus Wurtzite Formation.

A series of Zn1-xMxS polycrystalline samples were synthesized via a solid-state reaction in closed vessels to examine the solubility of foreign M cations within the wurtzite ZnS structure, employing quenching or slow cooling processes to favor specific polymorphs. X-ray diffraction (XRD) and transmission electron microscopy (TEM) analyses revealed diverse structural behaviors across different cations. Group 13 elements (Al and Ga) formed solid solutions with a wurtzite structure, while In showed complex layer stacking defects. For 3d magnetic cations (Mn, Fe, and Co), a broad solubility range in the hexagonal structure was noted for Mn, whereas Fe and Co more readily formed cubic structures, with solubilities similar to Mn in the sphalerite form. Despite structural differences, magnetic susceptibilities and spin freezing temperatures for Fe and Co were comparable. Group 14 elements showed varied behaviors: Sn was insoluble in ZnS, as attested by unchanged unit cell parameters and surface crystallite Sn, whereas Ge only formed in the cubic phase with a solubility limit of x ≈ 0.2. The study discusses these variations in solubility and structure in terms of oxidation states, ionic-covalent radius, and coordination preferences in sulfides.

Make Selenium Reactive Again: Activating Elemental Selenium for Synthesis of Metal Selenides Ranging from Nanocrystals to Large Single Crystals.

The inertness of elemental selenium is a significant obstacle in the synthesis of selenium-containing materials at low reaction temperatures. Over the years, several recipes have been developed to overcome this hurdle; however, most of the methods are associated with the use of highly toxic, expensive, and environmentally harmful reagents. As such, there is an increasing demand for the design of cheap, stable, and nontoxic reactive selenium precursors usable in the low-temperature synthesis of transition metal selenides with vast applications in nanotechnology, thermoelectrics, and superconductors. Herein, a novel synthetic route has been developed for activating elemental selenium by using a solvothermal approach. By comprehensive 77Se NMR, Raman, and infrared spectroscopies and gas chromatography-mass spectrometry, we show that the activated Se solution contained HSe-, [Se-Se]2-, and Se2- ions, as well as dialkyl selenide (R2Se) and dialkyl diselenide (R-Se-Se-R) species in dynamic equilibrium. This also corresponded to the first observation of naked Se22- in solution. The versatility of the developed Se precursor was demonstrated by the successful synthesis of (i) the polycrystalline room-temperature modification of the ß-Ag2Se thermoelectric material; (ii) large single crystals of superconducting ß-FeSe; (iii) CdSe nanocrystals with different particle sizes (3-10 nm); (iv) nanosheets of PtSe2; and (v) mono- and dibenzyl selenides and diselenides at room temperature. The simplicity and diversity of the developed Se activation method holds promise for applied and fundamental research.

Correction: 5D total scattering computed tomography reveals the full reaction mechanism of a bismuth vanadate lithium ion battery anode.

Correction for '5D total scattering computed tomography reveals the full reaction mechanism of a bismuth vanadate lithium ion battery anode' by Jonas Sottmann et al., Phys. Chem. Chem. Phys., 2022, 24, 27075-27085, https://doi.org/10.1039/D2CP03892G.

Fano-type Effect in Hydrogen-Terminated Pure Nanodiamond.

Two novel properties, unique for semiconductors, a negative electron affinity and a high p-type surface electrical conductivity, were discovered in diamond at the end of the last century. Both properties appear when the diamond surface is hydrogenated. A natural question arises: is the influence of the surface hydrogen on diamond limited only to the electrical properties? Here, for the first time to our knowledge, we observe a transparency peak at 1328 cm-1 in the infrared absorption of hydrogen-terminated pure (undoped) nanodiamonds. This new optical property is ascribed to Fano-type destructive interference between zone-center optical phonons and free carriers (holes) appearing in the near-surface layer of hydrogenated nanodiamond. This work opens the way to explore the physics of electron-phonon coupling in undoped semiconductors and promises the application of H-terminated nanodiamonds as a new optical material with induced transparency in the infrared optical range.

Selective Photocatalytic Dehydrogenation of Formic Acid by an In Situ-Restructured Copper-Postmetalated Metal-Organic Framework under Visible Light.

Formic acid is considered as one of the most promising liquid organic hydrogen carriers. Its catalytic dehydrogenation process generally suffers from low activity, low reaction selectivity, low stability of the catalysts, and/or the use of noble-metal-based catalysts. Herein we report a highly selective, efficient, and noble-metal-free photocatalyst for the dehydrogenation of formic acid. This catalyst, UiO-66(COOH)2-Cu, is built by postmetalation of a carboxylic-functionalized Zr-MOF with copper. The visible-light-driven photocatalytic dehydrogenation process through the release of hydrogen and carbon dioxide has been monitored in real-time via operando Fourier transform infrared spectroscopy, which revealed almost 100% selectivity with high stability (over 3 days) and a conversion yield exceeding 60% (around 5 mmol·gcat-1·h-1) under ambient conditions. These performance indicators make UiO-66(COOH)2-Cu among the top photocatalysts for formic acid dehydrogenation. Interestingly, the as-prepared UiO-66(COOH)2-Cu hetero-nanostructure was found to be moderately active under solar irradiation during an induction phase, whereupon it undergoes an in-situ restructuring process through intraframework cross-linking with the formation of the anhydride analogue structure UiO-66(COO)2-Cu and nanoclustering of highly active and stable copper sites, as evidenced by the operando studies coupled with steady-state isotopic transient kinetic experiments, transmission electron microscopy and X-ray photoelectron spectroscopy analyses, and Density Functional Theory calculations. Beyond revealing outstanding catalytic performance for UiO-66(COO)2-Cu, this work delivers an in-depth understanding of the photocatalytic reaction mechanism, which involves evolutive behavior of the postmetalated copper as well as the MOF framework over the reaction. These key findings pave the way toward the engineering of new and efficient catalysts for photocatalytic dehydrogenation of formic acid.

3D LiMn2 O4 Thin Film Deposited by ALD: A Road toward High-Capacity Electrode for 3D Li-Ion Microbatteries.

Miniaturized electronics suffer from a lack of energy autonomy. In that context, the fabrication of lithium-ion solid-state microbatteries with high performance is mandatory for powering the next generation of portable electronic devices. Here, the fabrication of a thin film positive electrode for 3D Li-ion microbatteries made by the atomic layer deposition (ALD) method and in situ lithiation step is demonstrated. The 3D electrodes based on spinel LiMn2 O4 films operate at high working potential (4.1 V vs Li/Li+ ) and are capable of delivering a remarkable surface capacity (≈180 µAh cm-2 ) at low C-rate while maintaining more than 40 µAh cm-2 at C/2 (time constant = 2 h). Both the thickness of the electrode material and the 3D gain of the template are carefully tuned to maximize the electrode performance. Advanced characterization techniques such as transmission electron and X-ray transmission microscopies are proposed as perfect tools to study the conformality of the deposited films and the interfaces between each layer: no interdiffusion or segregation are observed. This work represents a major issue towards the fabrication of 3D-lithiated electrode by ALD-without any prelithiation step by electrochemical technique-making it an attractive solution for the fabrication of 3D Li-ion solid-state microbatteries with semiconductor processing methods.

5D total scattering computed tomography reveals the full reaction mechanism of a bismuth vanadate lithium ion battery anode.

We have used operando 5D synchrotron total scattering computed tomography (TSCT) to understand the cycling and possible long term deactivation mechanisms of the lithium-ion battery anode bismuth vanadate. This anode material functions via a combined conversion/alloying mechanism in which nanocrystals of lithium-bismuth alloy are protected by an amorphous matrix of lithium vanadate. This composite is formed in situ during the first lithiation of the anode. The operando TSCT data were analyzed and mapped using both pair distribution function and Rietveld methods. We can follow the lithium-bismuth alloying reaction at all stages, gaining real structural insight including variations in nanoparticle sizes, lattice parameters and bond lengths, even when the material is completely amorphous. We also observe for the first time structural changes related to the cycling of lithium ions in the lithium vanadate matrix, which displays no interactions beyond the first shell of V-O bonds. The first 3D operando mapping of the distribution of different materials in an amorphous anode reveals a decline in coverage caused by either agglomeration or partial dissolution of the active material, hinting at the mechanism of long term deactivation. The observations from the operando experiment are backed up by post mortem transmission electron microscope (TEM) studies and theoretical calculations to provide a complete picture of an exceptionally complex cycling mechanism across a range of length scales.

Microwave-Assisted Solution Synthesis of Metastable Intergrowth of AgInS2 Polymorphs.

The intergrowth of stable and metastable AgInS2 polymorphs was synthesized using a microwave-assisted synthesis. The samples were synthesized in water and in a deep eutectic solvent (DES) consisting of choline chloride and thiourea. An increase in the metal precursor concentration improved the crystallinity of the synthesized samples and affected the particle size. AgInS2 cannot be synthesized from crystalline binary Ag2S or In2S3 via this route. The solution synthesis reported here results in the intergrowth of the thermodynamically stable polymorph (space group I4¯2d, chalcopyrite structure) and the high-temperature polymorph (space group Pna21, wurtzite-like structure) that is metastable at room temperature. A scanning transmission microscopy (STEM) study revealed the intergrowth of tetragonal and orthorhombic polymorphs in a single particle and unambiguously established that the long-thought hexagonal wurtzite polymorph has pseudo-hexagonal symmetry and is best described with the orthorhombic unit cell. The solution-synthesized AgInS2 polymorphs intergrowth has slightly lower bandgap values in the range of 1.73 eV-1.91 eV compared to the previously reported values for tetragonal I4¯2d (1.86 eV) and orthorhombic Pna21 (1.98 eV) polymorphs.

Impact of Solution Chemistry on Growth and Structural Features of Mo-Substituted Spinel Iron Oxides.

The effect of crystallizing solution chemistry on the chemistry of subsequently as-grown materials was investigated for Mo-substituted iron oxides prepared by thermally activated co-precipitation. In the presence of Mo ions, we find that varying the oxidation state of the iron precursor from Fe(II) to Fe(III) causes a progressive loss of atomic long-range order with the stabilization of 2-4 nm particles for the sample prepared with Fe(III). The oxidation state of the Fe precursor also affects the distribution of Fe and Mo cations within the spinel structure. Increasing the Fe precursor oxidation state gives decreased Fe-ion occupation and increased Mo-ion occupation of tetrahedral sites, as revealed by the extended X-ray absorption fine structure. The stabilization of Mo within tetrahedral sites appears to be unexpected, considering the octahedral preferred coordination number of Mo(VI). The analysis of the atomic structure of the sample prepared with Fe(III) indicates a local ordering of vacancies and that the occupation of tetrahedral sites by Mo induces a contraction of the interatomic distances within the polyhedra as compared to Fe atoms. Moreover, the occupancy of Mo into the thermodynamic site preference of a Mo dopant in Fe2O3 assessed by density functional theory calculations points to a stronger preference for Mo substitution at octahedral sites. Hence, we suggest that the synthetized compound is thermodynamically metastable, that is, kinetically trapped. Such a state is suggested to be a consequence of the tetrahedral site occupation by Mo ions. The population of these sites, known to be reactive sites enabling particle growth, is concomitant with the stabilization of very small particles. We confirmed our hypothesis by using a blank experiment without Mo ions, further supporting the impact of tetrahedral Mo ions on the growth of iron oxide nanoparticles. Our findings provide new insights into the relationships between the Fe-chemistry of the crystallizing solution and the structural features of the as-grown Mo-substituted Fe-oxide materials.

Local-Disorder-Induced Low Thermal Conductivity in Degenerate Semiconductor Cu22Sn10S32.

S-based semiconductors are attracting attention as environmentally friendly materials for energy-conversion applications because of their structural complexity and chemical flexibility. Here, we show that the delicate interplay between the chemical composition and cationic order/disorder allows one to stabilize a new sphalerite derivative phase of cubic symmetry in the Cu-Sn-S diagram: Cu22Sn10S32. Interestingly, its crystal structure is characterized by a semiordered cationic distribution, with the Cu-Sn disorder being localized on one crystallographic site in a long-range-ordered matrix. The origin of the partial disorder and its influence on the electronic and thermal transport properties are addressed in detail using a combination of synchrotron X-ray diffraction, Mössbauer spectroscopy, transmission electron microscopy, theoretical modeling, and transport property measurements. These measurements evidence that this compound behaves as a pseudogap, degenerate p-type material with very low lattice thermal conductivity (0.5 W m-1 K-1 at 700 K). We show that localized disorder is very effective in lowering κL without compromising the integrity of the conductive framework. Substituting pentavalent Sb for tetravalent Sn is exploited to lower the hole concentration and doubles the thermoelectric figure of merit ZT to 0.55 at 700 K with respect to the pristine compound. The discovery of this semiordered cubic sphalerite derivative Cu22Sn10S32 furthers the understanding of the structure-property relationships in the Cu-Sn-S system and more generally in ternary and quaternary Cu-based systems.

Clathrate XI K58 Zn122 Sb207 : A New Branch on the Clathrate Family Tree.

The compositional screening of K-Zn-Sb ternary system aided by machine learning, rapid exploratory synthesis using KH salt-like precursor and in situ powder X-ray diffraction yielded a novel clathrate type XI K58 Zn122 Sb207 . This clathrate consists of a 3D Zn-Sb framework hosting K+ ions inside polyhedral cages, some of which are reminiscent of known clathrate types while others are unique to this structure type. The complex non-centrosymmetric structure in the tetragonal space group I 4 ‾ 2 m was solved by means of single crystal X-ray diffraction as a 6-component twin due to pseudocubic symmetry and further confirmed by high-resolution synchrotron powder X-ray diffraction and state-of-the-art scanning transmission electron microscopy. The electron-precise composition of this clathrate yields narrow-gap p-type semiconductor with extraordinarily low thermal conductivity due to displacement or "rattling" of K cations inside oversized cages and as well as to twinning, stacking faults and antiphase boundary defects.

Thermodynamic Evidence of Proximity to a Kitaev Spin Liquid in Ag_{3}LiIr_{2}O_{6}.

Kitaev magnets are materials with bond-dependent Ising interactions between localized spins on a honeycomb lattice. Such interactions could lead to a quantum spin-liquid (QSL) ground state at zero temperature. Recent theoretical studies suggest two potential signatures of a QSL at finite temperatures, namely, a scaling behavior of thermodynamic quantities in the presence of quenched disorder, and a two-step release of the magnetic entropy. Here, we present both signatures in Ag_{3}LiIr_{2}O_{6} which is synthesized from α-Li_{2}IrO_{3} by replacing the interlayer Li atoms with Ag atoms. In addition, the dc susceptibility data confirm the absence of a long-range order, and the ac susceptibility data rule out a spin-glass transition. These observations suggest a closer proximity to the QSL in Ag_{3}LiIr_{2}O_{6} compared to its parent compound α-Li_{2}IrO_{3} that orders at 15 K. We discuss an enhanced spin-orbit coupling due to a mixing between silver d and oxygen p orbitals as a potential underlying mechanism.

High-Performance Thermoelectric Bulk Colusite by Process Controlled Structural Disordering.

High-performance thermoelectric bulk sulfide with the colusite structure is achieved by controlling the densification process and forming short-to-medium range structural defects. A simple and powerful way to adjust carrier concentration combined with enhanced phonon scattering through point defects and disordered regions is described. By combining experiments with band structure and phonons calculations, we elucidate, for the first time, the underlying mechanism at the origin of intrinsically low thermal conductivity in colusite samples as well as the effect of S vacancies and antisite defects on the carrier concentration. Our approach provides a controlled and scalable method to engineer high power factors and remarkable figures of merit near the unity in complex bulk sulfide such as Cu26V2Sn6S32 colusites.

Cubic Sodium Cobalt Metaphosphate [NaCo(PO3)3] as a Cathode Material for Sodium Ion Batteries.

Cubic-framework sodium cobalt-based metaphosphate NaCo(PO3)3 was recently demonstrated to be an attractive Na+ cationic conductor. It can be potentially used in the next-generation rechargeable Na ion batteries. The crystal structure and electrical conductivity were studied and found to have a three-dimensional framework with interconnecting tunnels for Na+ migration ( J. Solid State Electrochem. , 2016 , 20 , 1241 ). This inspired us to study the electrochemical (de)intercalation behavior of Na+ in the NaCo(PO3)3 assuming a cubic Pa3̅ framework. Herein, synergizing experimental and computational tools, we present the first report on the electrochemical activity and Na+ diffusion pathway analysis of cubic NaCo(PO3)3 prepared via conventional solid-state route. The electrochemical analyses reveal NaCo(PO3)3 to be an active sodium insertion material with well-defined reversible Co3+/Co2+ redox activity centered at 3.3 V (vs Na/Na+). Involving a solid-solution redox mechanism, close to 0.7 Na+ per formula unit can be reversibly extracted. This experimental finding is augmented with bond valence site energy (BVSE) modeling to clarify Na+ migration in cubic NaCo(PO3)3. BVSE analyses suggest feasible Na+ migration with moderate energy barrier of 0.68 eV. Cubic NaCo(PO3)3 forms a 3.3 V sodium insertion material.

Crystal Chemistry and Phonon Heat Capacity in Quaternary Honeycomb Delafossites: Cu[Li1/3Sn2/3]O2 and Cu[Na1/3Sn2/3]O2.

This work presents an integrated approach to study the crystal chemistry and phonon heat capacity of complex layered oxides. Two quaternary delafossites are synthesized from ternary parent compounds and copper monohalides via a topochemical exchange reaction that preserves the honeycomb ordering of the parent structures. For each compound, Rietveld refinement of the powder X-ray diffraction patterns is examined in both monoclinic C2/ c and rhombohedral R3̅ m space groups. Honeycomb ordering occurs only in the monoclinic space group. Bragg peaks associated with honeycomb ordering acquire an asymmetric broadening known as the Warren line shape that is commonly observed in layered structures with stacking disorder. Detailed TEM analysis confirms honeycomb ordering within each layer in both title compounds and establishes a twinning between the adjacent layers instead of the more conventional shifting or skipping stacking faults. The structural model is then used to calculate phonon dispersions and heat capacity from first principles. In both compounds, the calculated heat capacity accurately describes the experimental data. The integrated approach presented here offers a platform to carefully analyze the phonon heat capacity in complex oxides where the crystal structure can produce magnetic frustration. Isolating phonon contribution from total heat capacity is a necessary and challenging step toward a quantitative study of spin liquid materials with exotic magnetic excitations such as spinons and Majorana fermions. A quantitative understanding of phonon density of states based on crystal chemistry as presented here also paves the way toward higher efficiency thermoelectric materials.

Topochemical Approach for Transition-Metal Exchange Assisted by Copper Extrusion: from Cu2FeBO5 to Fe3BO5.

All fields of today's technology are concerned with multifunctional materials, the subject of constantly expanding research. Among them, metal transition oxides occupy a strategic place because of the properties directly correlated with metal valence linked with oxygen stoichiometry. To enhance or induce new properties, knowledge of the relationships between the structural and physical characteristics is of prime importance, but a design at low scale also appears to be a powerful tool to increase the chemical reactivity and stabilize new compounds. Herein, an unexpected reaction is reported that associates the exchange of copper and iron in a 3D ludwigite lattice with the huge release of oxygen (14% by weight) at moderate temperature (<450 °C). Annealing of Cu2FeBO5 in a reducing atmosphere leads to the extrusion of copper and the formation of Fe3BO5, the micro/nanostructural state of which facilitates the partial Cu2FeBO5 recovery associated with the capture of oxygen in oxidizing conditions.

Structure and Electronic Properties of the Quasi-One-Dimensional Ba2Co1-xZnxS3 Series.

This work focuses on the structure and physical properties of the solid solution Ba2Co1-xZnxS3 (0 ≤ x ≤ 1), a family of quasi-one-dimensional sulfides with end members Ba2CoS3 and Ba2ZnS3. The structure of selected compounds with increasing Zn2+ content has been analyzed using neutron diffraction, transmission electron microscopy, and extended X-ray absorption fine structure, and the physical properties have been analyzed via magnetic susceptibility and resistivity measurements. The progressive substitution of the nonmagnetic Zn2+ cation for Co2+ rapidly destroys the antiferromagnetic transition present at 46 K in the quasi-one-dimensional Ba2CoS3, leading to paramagnetic behavior down to the lowest investigated temperature (5 K) for compounds with x > 0.25. For compounds with x ≥ 0.4, a pure Curie-Weiss regime is recovered around 300 K, yielding effective moments consistent with the g factor of the tetrahedrally coordinated Co2+ previously determined for Ba2CoS3. The substitution of Zn2+ for Co2+ also removes the metallic-like behavior of Ba2CoS3, causing an increase in the value of the resistivity with all the Ba2Co1-xZnxS3 compounds showing semiconducting behavior. The negative magnetoresistance of Ba2CoS3 is improved by the substitution of Zn2+ for Co2+, with values of -6% for Ba2Co0.75Zn0.25S3, -9% for Ba2Co0.5Zn0.5S3, and -8% for Ba2Co0.25Zn0.75S3. However, there does not seem to be a correlation between the values of resistivity and magnetoresistance and the content of Zn2+, leading to the hypothesis that transport properties may be linked more closely to extrinsic properties.

Mn2TeO6: a Distorted Inverse Trirutile Structure.

Inverse trirutile Mn2TeO6 was investigated using in situ neutron and X-ray powder diffraction between 700 °C and room temperature. When the temperature was decreased, a structural phase transition was observed around 400 °C, from a tetragonal (P42/mnm) to a monoclinic phase (P21/c), involving a doubling of the cell parameter along b. This complex monoclinic structure has been solved by combining electron, neutron, and synchrotron powder diffraction techniques at room temperature. It can be described as a distorted superstructure of the inverse trirutile structure, in which compressed and elongated MnO6 octahedra alternate with more regular TeO6 octahedra, forming a herringbone-like pattern. Rietveld refinements, carried out with symmetry-adapted modes, show that the structural transition, arguably of Jahn-Teller origin, is driven by a single primary mode.

Inversion Boundaries and Phonon Scattering in Ga:ZnO Thermoelectric Compounds.

We investigated the high-temperature thermoelectric properties of Ga:ZnO bulk compounds, synthesized using a simple and scalable solid-state process. The effects of a low gallium content (x ≤ 0.04 in Zn1-xGaxO1+x/2) on the structural features and electrical/thermal properties are reviewed. Transmission electron microscopy analyses showed that 2D, nonperiodic defects had formed from a doping content as low as x = 0.01 Ga. The structural description of these nanoscale interfaces is, for the first time, carefully investigated in such low-Ga-content samples by HAADF-STEM analyses combined with structural modeling. It was found that the formation of head-to-head inversion twin (h-IT) boundaries and tail-to tail inversion boundaries (t-IB) in the bulk compounds is responsible for strong phonon scattering, while maintaining relatively good electrical conductivity and thereby enhancing the thermoelectric properties. The absolute value of the Seebeck coefficient decreases abruptly from 475 µV/K for x = 0 down to 60 µV/K for x = 0.005 at 350 K. At the same time, the electrical resistivity drops from 1 ohm cm for x = 0 to 1.7 × 10-3 ohm cm for x = 0.005. For higher Ga additions (x > 0.01), the increase in electrical resistivity is likely linked to the formation of interface defects at a larger extent in the wurtzite structure. The thermal conductivity also drops sharply with the increase in the Ga content from ∼33 W/m K for x = 0 to ∼8 for x = 0.04 at 350 K. This study is progress toward the synthesis of other thermoelectric materials where nanoscale interfaces in bulk compounds provide tremendous opportunities for further enhancing both the phonon scattering and the overall figure of merit.