Article

# Computational investigation of chalcogenide spinel conductors for all-solid-state Mg batteries

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## Abstract

Seven MgLn 2 X 4 (Ln = lanthanoid, X = S, Se) spinels are calculated with density functional theory to have low barriers for Mg migration (< 380 meV) and are stable or...

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... 25,28 Furthermore, it has been shown that for chalcogenide spinels containing lanthanoids the Mg mobility increases with the size of the lanthanoids. 29 Note that spinel structures including transition metal ions such as Ti, Mn, Fe and Co exhibit magnetic properties due to the unfilled 3d shell. The 3d electrons in the spinel compounds cause significant distortions of the crystal lattice, namely trigonal distortion. ...
... It is interesting to note that an analogous trend has been found in a recent computational study of Mg migration in lanthanoid chalcogenide spinels. 29 In these systems, apparently the height of the Mg migration barriers increases with higher f -state occupancy. ...
... In order to understand this trend, one should first note that according to Eq. 4 both distances d(cn 4 ) and d(cn 6 ) become larger with increasing u in the parameter range that is considered here. However, for purely ionic interactions between non-polarizable spherically symmetric ions, the competition in the energetic stability between two different structures does not depend on the absolute distances, only on the ratio of distances, 29,54,55 as reflected in the simple estimate Eq. 7. Consequently, these results can only be explained assuming that the interaction is not purely ionic and that it falls off stronger than 1/d with distance d. ...
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In the area of sustainable energy storage, batteries based on multivalent ions such as magnesium have been attracting considerable attention due to their potential for high energy densities. Furthermore, they are typically also more abundant than, e.g., lithium. However, as a challenge their low ion mobility in electrode materials remains. This study addresses the ionic conductivity of magnesium in spinel host materials based on periodic density functional theory calculations in order to identify the critical parameters which determine the mobility and insertion of ions. We will in particular highlight the critical role that trigonal distortions of the spinel structure play for the ion mobility. In detail, we will show that it is the competition between coordination and bond length that governs the Mg site preference in ternary spinel compounds upon trigonal distortions which can only be understood by also taking covalent interactions into account. Based on our theoretical study, we rationalize the impact of the metal distribution in the host material and the ion concentration on the diffusion process. Furthermore, cathode-related challenges for practical devices will be addressed. Our findings shed light on the fundamentional mechanisms underlying ionic conductivity in solid hosts and thus may contribute to improve ion transport in battery electrodes.
... Reversible intercalation of magnesium ions into oxide spinels could be verified (Kim et al., 2015;Yin et al., 2017) and several spinel phases were identified as suitable cathode materials Bayliss et al., 2019). Interestingly, the ion conductivity of spinel materials can be further increased by moving towards sulfide (Emly and Van der Ven, 2015;Liu et al., 2016;Sun et al., 2016;Kulish et al., 2017) and selenide based (Canepa et al., 2017a;Wang et al., 2019;Koettgen et al., 2020) spinels. The volume per anion increases in the order of O 2− < S 2− < Se 2− and is connected to a rising polarizability, which is beneficial for the cation mobility (Canepa et al., 2017a). ...
... As already stated, the size of the charge carrier ions can be quantified by their ionic radii (Koettgen et al., 2020). However, these ionic radii are obtained by employing a set of assumptions, including independence of the structure type. ...
Article
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Periodic density functional theory calculations have been performed to study the migration of various charge carriers in spinel‐type MgSc2Se4. This compound exhibits low barriers for Mg ion diffusion, making it a potential candidate for solid electrolytes in Mg-ion batteries. In order to elucidate the decisive factors for the ion mobility in spinel-type phases, the diffusion barriers of other mono- and multivalent ions (Li⁺, Na⁺, K⁺, Cs⁺, Zn²⁺, Ca²⁺, and Al³⁺) in the MgSc2Se4 framework have been determined as well. This allows for disentangling structural and chemical factors, showing that the ion mobility is not solely governed by size and charge of the diffusing ions. Finally, our results suggest that charge redistribution and rehybridization caused by the migration of the multivalent ions increase the resulting migration barriers.
... For example, Canepa et al. (46), using DFT-NEB (and supplemented by AIMD) calculations, calculated E m for Mg in a large set of spinel materials, as shown in Figure 9. Selected migration barriers in Figure 9 were also corroborated by SS-NMR and AC-IS measurements (123). Recently Koettgen et al. (124) have extended the results presented in Figure 9 to rare-earth-containing Mg spinels. Assuming the absence of spinel inversion (38), the E m values shown in Figure 9 are associated with the typical migration mechanism of tetrahedral → octahedral → tetrahedral (tet-oct-tet) (22,28,31,32,38,46,116,124), and several design rules can be extracted: ...
... Recently Koettgen et al. (124) have extended the results presented in Figure 9 to rare-earth-containing Mg spinels. Assuming the absence of spinel inversion (38), the E m values shown in Figure 9 are associated with the typical migration mechanism of tetrahedral → octahedral → tetrahedral (tet-oct-tet) (22,28,31,32,38,46,116,124), and several design rules can be extracted: ...
Article
The development of inexpensive batteries based on magnesium (Mg) chemistry will contribute remarkably toward developing high-energy-density storage systems that can be used worldwide. Significant challenges remain in developing practical Mg batteries, the chief of which is designing materials that can provide facile transport of Mg. In this review, we cover the experimental and theoretical methods that can be used to quantify Mg mobility in a variety of host frameworks, the specific transport quantities that each technique is designed to measure or calculate, and some practical examples of their applications. We then list the unique challenges faced by different experimental and computational techniques in probing Mg ion transport in materials. This review concludes with an outlook on the directions that the scientific community could soon pursue as we strive to construct a pragmatic Mg battery. Expected final online publication date for the Annual Review of Materials Research, Volume 52 is July 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.
... The ionic conductivity of these spinels is also significantly higher (almost 0.04%) than that of the other ionic conductors (as the lithium and sodium have 10 -4 % and 10 -6 % ionic conductivity) [19]. Very recently seven new MgLn 2 X 4 (Ln = lanthanide and X = S, Se) ternary spinels have been reported which are predicted at the level of GGA and Meta GGA approaches [20]. In this study, Koettgen et al. showed that these spinels were mostly stable and offered a low-level barrier to magnesium ion conductivity i.e. less than 380 meV in comparison to other competitive structures and compositions. ...
... In this study, Koettgen et al. showed that these spinels were mostly stable and offered a low-level barrier to magnesium ion conductivity i.e. less than 380 meV in comparison to other competitive structures and compositions. Moreover, it was also demonstrated, as the size of the lanthanide increases, the stability of the magnesium spinels decreases but magnesium mobility increases [20]. Furthermore, in another DFT study on MgIn 2 X 4 (X = S, Se), Mahmood et al. reported optoelectronic and thermoelectric properties [21] of the MgIn 2 X 4 and they observed the modification in their bandgap energy in the UV-Vis range when sulphur is replaced with selenium. ...
Article
Computational investigations, concerning structural, elastic, electronic, optical, and thermometric properties of the MgLu2X4 (X = S, Se) spinel compounds are performed. The calculations are carried out by employing the first-principles L(APW + lo) method designed within density functional theory (DFT). Our ground-state calculations are found to be consistent with experimental data wherever available. Similarly, calculations of the elastic constants demonstrate that both MgLu2S4 and MgLu2Se4 are brittle and anisotropic in nature. The dominant bonding between the atoms is found covalent and strongly favouring their mechanical stability. From the calculations of electronic band structure, both compounds are found direct bandgap semiconductors at Γ- Γ with bandgap energy of 3.119 eV for MgLu2S4 and 2.480 eV for MgLu2Se4. Our analysis of electronic and optical parameters suggest them suitable candidates for optoelectronic devices particularly from visible to extreme violet region applications whereas the calculated results of thermoelectric properties highlight their remarkable thermoelectric response for a workable range of temperature.
... 25,28 Furthermore, it has been shown that for chalcogenide spinels containing lanthanoids the Mg mobility increases with the size of the lanthanoids. 29 Note that spinel structures including transition metal ions such as Ti, Mn, Fe and Co exhibit magnetic properties due to the filling of the 3d shell which cause significant distortions of the crystal lattice, namely trigonal distortion, as we will show below. Such trigonal distortions have hardly been considered in determining the transport properties of sulfide and selenide spinels yet. ...
... It is interesting to note that an analogous trend has been found in a recent computational study of Mg migration in lanthanoid chalcogenide spinels. 29 In these systems, apparently the height of the Mg migration barriers increases with higher f -state occupancy. ...
Preprint
Full-text available
In the area of sustainable energy storage, batteries based on multivalent ions such as magnesium have been attracting considerable attention due to their potential for high energy densities. Furthermore, they are typically also more abundant than, e.g., lithium. However, as a challenge their low ion mobility in electrode materials remains. This study addresses the ionic conductivity in spinel host materials which represent a promising class of cathode and solid-electrolyte materials in Mg-ion batteries. Based on periodic density functional theory calculations, we identify the critical parameters which determine the mobility and insertion of ions. We will in particular highlight the critical role that trigonal distortions of the spinel structure play for the ion mobility. In detail, we will show that it is the competition between coordination and bond length that governs the Mg site preference in ternary spinel compounds upon trigonal distortions. This can only be understood by also taking covalent interactions into account. Furthermore, our calculations suggest that anionic redox plays a much more important role in sulfide and selenide spinels than in oxide spinels. Based on our theoretical study, we rationalize the impact of the metal distribution in the host material and the ion concentration on the diffusion process. Furthermore, cathode-related challenges for practical devices will be addressed. Our findings shed light on the fundamentional mechanisms underlying ionic conductivity in solid hosts and thus may contribute to improve ion transport in battery electrodes.
... A popular choice of XC functional (for DFT-NEB and AIMD) is the Perdew-Burke-Ernzerhof 20 (PBE) generalized gradient approximation (GGA), due to its reasonable trade-off between computational cost and accuracy [21][22][23][24] . However, PBE suffers from several shortcomings, such as self-interaction errors (SIE) in transition-metal (TM) systems 25,26 , overbinding of the oxygen gas molecule [27][28][29] , and the inability to account for van der Waals interactions associated with layered frameworks [30][31][32] . ...
Article
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Facile ionic mobility within host frameworks is crucial to the design of high-energy-density batteries with high-power-densities, where the migration barrier (Em) is the governing factor. Here, we assess the accuracy and computational performance of generalized gradient approximation (GGA), the strongly constrained and appropriately normed (SCAN), and their Hubbard U corrections, GGA+U and SCAN+U, within the density functional theory-nudged elastic band framework, in the prediction of Em as benchmarked against experimental data. Importantly, we observe SCAN to be more accurate than other frameworks, on average, albeit with higher computational costs and convergence difficulties, while GGA is a feasible choice for “quick” and “qualitative” Em predictions. Further, we quantify the sensitivity of Em with adding uniform background charge and/or the climbing image approximation in solid electrolytes, and the Hubbard U correction in electrodes. Our findings will improve the quality of Em predictions which will enable identifying better materials for energy storage applications.
... The tantalizing possibility of literally thousands of undiscovered solids having these structure types has been predicted by high-throughput computational studies. [9][10][11] One main reason that cation-exchange routes have remained predominantly unrealized is that these structure types appear, by most sensible arguments, to unfortunately restrict the possibility of any significant ion interdiffusion at low temperatures. Only recently has this notion been proven demonstrably false by the budding renaissance of research into cation exchange within solids having three-dimensional close-packed structures. ...
Article
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Recently, many new, complex, functional oxides have been discovered with the surprising use of topotactic ion‐exchange reactions on close‐packed structures, such as found for wurtzite, rutile, perovskite, and other structure types. Despite a lack of apparent cation‐diffusion pathways in these structure types, synthetic low‐temperature transformations are possible with the interdiffusion and exchange of functional cations possessing n s 2 stereoactive lone pairs (e.g., Sn(II)) or unpaired n d x electrons (e.g., Co(II)), targeting new and favorable modulations of their electronic, magnetic, or catalytic properties. This enables a synergistic blending of new functionality to an underlying three‐dimensional connectivity, i.e., [‐M‐O‐M‐O‐] n , that is maintained during the transformation. In many cases, this tactic represents the only known pathway to prepare thermodynamically unstable solids that otherwise would commonly decompose by phase segregation, such as recently been applied to the discovery of many new small bandgap semiconductors.
... Spinel-type chalcogenides are potential materials to provide both types of carriers and increase electrical conductivity reasonably [5]. The general formula of spinel chalcogenides is AB 2 X 4 , where A is tetrahedral and B is octahedral sites in the crystal structure, and X is the chalcogen atoms forming tetrahedron and octahedron around these metal cations [6,7]. The characteristics of these materials depend upon the cationic distribution and the nature of chalcogen atoms. ...
Article
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Magnesium containing chalcogenides received considerable attention for solar cells. Herein, using modified Backe and Johnson potential the electronic, characteristics of MgLa2(S/Se)4 are computed, and band gaps of 2.4 and 2.1 eV were found for MgLa2S4 and MgLa2Se4, respectively. The absorption in visible increases their significance for optoelectronic applications. The optical characteristics were determined by dielectric constant and refractive index and as absorption coefficient. Moreover, the thermoelectric characteristics, including thermal and electrical conductivities, Seebeck coefficient, power factor, and figure of merit, were analyzed by BoltzTraP code. The calculated Pugh (> 1.75) and Poisson (> 0.26) values revealed their ductile behavior. MgLa2S4 showed a high value of melting and Debye temperature as compared to MgLa2Se4. Finally, partial covalent bonding was found by electron density plots.
... These visual assessments of the pristine and the charged particles are further confirmed by the depth profile of Mn's K-edge energy shown in Fig. 2h. While the relative homogeneity of the Mn valence state distribution in the pristine particle is anticipated 43 , the observed depth-dependent Mn valence in the charged LirNMC particle is somewhat a surprise, specifically because of its non-monotonicity. This observation motivates a more systematic study of all the transition metal cations (Mn, Co, and Ni) in the LirNMC particle in a correlative manner. ...
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Lithium-rich nickel-manganese-cobalt (LirNMC) layered material is a promising cathode for lithium-ion batteries thanks to its large energy density enabled by coexisting cation and anion redox activities. It however suffers from a voltage decay upon cycling, urging for an in-depth understanding of the particle-level structure and chemical complexity. In this work, we investigate the Li1.2Ni0.13Mn0.54Co0.13O2 particles morphologically, compositionally, and chemically in three-dimensions. While the composition is generally uniform throughout the particle, the charging induces a strong depth dependency in transition metal valence. Such a valence stratification phenomenon is attributed to the nature of oxygen redox which is very likely mostly associated with Mn. The depth-dependent chemistry could be modulated by the particles’ core-multi-shell morphology, suggesting a structural-chemical interplay. These findings highlight the possibility of introducing a chemical gradient to address the oxygen-loss-induced voltage fade in LirNMC layered materials.
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We have investigated Mg intercalation into orthorhombic V$_2$O$_5$, one of only three cathodes known to reversibly intercalate Mg ions. By calculating the ground state Mg$_x$V$_2$O$_5$ configurations and by developing a cluster expansion for the configurational disorder in $\delta$-V$_2$O$_5$, a full temperature-composition phase diagram is derived. Our calculations indicate an equilibrium phase separating behavior between fully demagnesiated $\alpha$-V$_2$O$_5$ and fully magnesiated $\delta$-V$_2$O$_5$, but also motivate the existence of potentially metastable solid solution transformation paths in both phases. We find significantly better mobility for Mg in the $\delta$ polymorph suggesting that better performance can be achieved by cycling Mg in the $\delta$ phase.
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Some 50 ternary sulfides were explored by the authors which included many of the ternary sulfides involving Ca and Mg, in addition to all of those involving Zn and Cd, with Sc and Y and all but two rare-earth elements (Eu and Pm). The results show that many of these ternary sulfides have bandgaps in the visible region (e. g. , 2. 1 and 2. 3 eV, respectively, for ZnSc//2S//4 and CdSc//2S//4), and that electrically conducting specimens could be obtained by doping with suitable impurities.
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Over 14 000 coordination environments of 100 different cations retrieved from the Inorganic Crystal Structure Database have been analyzed. For comparison predicted coordination numbers (PCN's) have been calculated using ionic radius ratios. The observed coordination numbers are generally smaller than or equal to the PCN's and their range, for most cations, can be predicted from a knowledge of the Lewis-base strengths of available anions and the requirement that these strengths be close to the Lewis-acid strength of the cation. The occurrence of smaller coordination numbers is associated with strongly directed bonds (electronic effects) and is found for main-group elements in low oxidation states and for closed-d-shell cations of Groups 11, 12 and 13. An analysis of the results shows that to use ionic radii to predict both coordination numbers and interatomic distances it is necessary to use cation and anion radii that both vary in the same way with the cation coordination number (N). The value found for the oxygen radius is 1.12 + 0.23In(N-2)/~. The average observed coordination number is used to calculate cation Lewis-acid strengths which are shown to correlate with electronegativity.
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The Tao-Perdew-Staroverov-Scuseria (TPSS) meta-generalized-gradient-approximation (MGGA) and its revised version, the revTPSS, are implemented self-consistently within the framework of the projector-augmented-wave (PAW) method, using a plane wave basis set. Both TPSS and revTPSS yield accurate atomization energies for the molecules in the AE6 set, better than those of the standard Perdew-Burke-Ernzerhof (PBE) generalized-gradient-approximation. For lattice constants and bulk moduli of 20 diverse solids, revTPSS performs much better than PBE, and on average as well as PBEsol and Armiento-Mattsson (AM05), GGAs designed for solids. The latter two overestimate the atomization energies for molecules to an unacceptable degree. However, the revTPSS presents only a slight improvement over PBEsol for the prediction of cohesive energies for solids, and some deterioration with respect to PBE. We also study the magnetic properties of Fe, for which both TPSS and revTPSS predict the right ground-state solid phase, the ferromagnetic body-centered-cubic (bcc) structure, with an accurate magnetic moment.
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From a theory of Hohenberg and Kohn, approximation methods for treating an inhomogeneous system of interacting electrons are developed. These methods are exact for systems of slowly varying or high density. For the ground state, they lead to self-consistent equations analogous to the Hartree and Hartree-Fock equations, respectively. In these equations the exchange and correlation portions of the chemical potential of a uniform electron gas appear as additional effective potentials. (The exchange portion of our effective potential differs from that due to Slater by a factor of 23.) Electronic systems at finite temperatures and in magnetic fields are also treated by similar methods. An appendix deals with a further correction for systems with short-wavelength density oscillations.
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Generalized gradient approximations (GGA{close_quote}s) for the exchange-correlation energy improve upon the local spin density (LSD) description of atoms, molecules, and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental constants. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential. {copyright} {ital 1996 The American Physical Society.}
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A comparison of chain-of-states based methods for finding minimum energy pathways (MEPs) is presented. In each method, a set of images along an initial pathway between two local minima is relaxed to find a MEP. We compare the nudged elastic band (NEB), doubly nudged elastic band, string, and simplified string methods, each with a set of commonly used optimizers. Our results show that the NEB and string methods are essentially equivalent and the most efficient methods for finding MEPs when coupled with a suitable optimizer. The most efficient optimizer was found to be a form of the limited-memory Broyden-Fletcher-Goldfarb-Shanno method in which the approximate inverse Hessian is constructed globally for all images along the path. The use of a climbing-image allows for finding the saddle point while representing the MEP with as few images as possible. If a highly accurate MEP is desired, it is found to be more efficient to descend from the saddle to the minima than to use a chain-of-states method with many images. Our results are based on a pairwise Morse potential to model rearrangements of a heptamer island on Pt(111), and plane-wave based density functional theory to model a rollover diffusion mechanism of a Pd tetramer on MgO(100) and dissociative adsorption and diffusion of oxygen on Au(111).
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