High magnesium mobility in ternary spinel chalcogenides

Magnesium batteries appear a viable alternative to overcome the safety and energy density limitations faced by current lithium-ion technology. The development of a competitive magnesium battery is plagued by the existing notion of poor magnesium mobility in solids. Here we demonstrate by using ab initio calculations, nuclear magnetic resonance, and impedance spectroscopy measurements that substantial magnesium ion mobility can indeed be achieved in close-packed frameworks (~ 0.01–0.1 mS cm–1 at 298 K), specifically in the magnesium scandium selenide spinel. Our theoretical predictions also indicate that high magnesium ion mobility is possible in other chalcogenide spinels, opening the door for the realization of other magnesium solid ionic conductors and the eventual development of an all-solid-state magnesium battery.

however the applied methods are not scientifically of high level. In the later part, the authors have correctly p edicted that pure DFT approaches fail to reproduce the band gaps of Mg chalcogenides, rather they have utilized the HSE06 approach for this purpose. The study should be uniform: HSE06 approach should be used for all the parts of study from the very beginning. Based on the available literature data on ion diffusion in solids, it is known that pure DFT approaches underestimate the experimental (microscopic diffusion) activation barriers whereas the HF/DFT hybrid approaches give close agreement to the experimental values. Therefore, 'very close agreement' of the DFT activation barriers with the experimental values will create huge doubt in the readers' minds. The authors should have also investigated the frequency calculations to verify the saddle points and minima. 3. In the structural characterization (S2), the authors have predicted enthalpy of formation at 0K, it is rather useless. They should have done high temp Freq based calculations to draw the conclusion at high temp or at least at room temperature. By this way, the conclusions could be different. 4. In the SLR investigation, it is shown that the magnetism plays a key role, as can be seen that the diamagnetic MgSc2Se4 has fast ionic conductivity. There is no theoretical investigation of magnetism of the considered materials. 5. The considered models for the theoretical investigation are not 'ideal ones'. The authors have models the balance of excess electrons by a uniform background charge. Rather the electrons should be treated with open shell spin polarized methods and of course, the magnetism for all the cases should be checked by energy/enthalpy calculations. 6. The size of the supercell is not clear. In experiment, the vacancy concentration is very low. In order to model this, they should have used a very large supercell.
In general the quality of this paper is too poor. I recommend an immediate rejection of this paper. No further review required. Thank you for sending us the referee comments on our manuscript. We are grateful to all the referees for bringing up important points that can improve the overall quality and readability of this novel and original work. Based on the suggestions of the reviewers, changes have been introduced to further strengthen our manuscript. Please find below a detailed response to all the comments and suggestions raised by the reviewers. In general, we appreciate the very positive comments of both reviewers 1 and 2. Many of the comments and criticisms reviewer 3 brings up relate to well established methods and procedures in the field of computational materials science, and energy storage in particular. Hence, we argue that reviewer 3 is not qualified, and shows remarkable bias against the work, as evidenced by the language used. We hope that the revised manuscript will convince the referee(s) and the editor of the timely importance of this work for the development of materials with high Mg mobility, resulting in a swift publication.

Reviewer 1:
This paper reports the discovery of a novel Mg-ion solid conductor with exceptionally high Mg diffusivity at room temperature. This is a very important finding in Mg battery research. The paper is very nicely written and combines computational, solid-state NMR, and impedance measurement/modeling to address a challenge that has previously been considered impossible in the materials science community. It is a transformative contribution to the rapidly evolving field.
We appreciate Reviewer 1, who identifies the importance of this work-"the discovery of a novel Mg-ion solid conductor with exceptionally high Mg diffusivity at room temperature." Before it can be published, the authors must address the following questions/comments. Fig. S20  The revised manuscript (see the Introduction section) includes a sentence and the citation suggested by the reviewer, explaining that ion diffusion can be enhanced by expanding the interlayer distance in layered materials. We are grateful that Reviewer 2 recognizes that we have found a fast Mg conductor. The original manuscript summarizes the 3 main criteria followed to short-list the Mg conductors studied in this paper, which are: i) find materials where Mg resides in its less preferred anion coordination environment (i.e. coordination of 4), ii) find materials with large volume per anion (typically introduced by anions with large ionic radii, e.g. S, Se and Te), and iii) find materials without redox-active metals. The revised Supplementary Information

It is well-known that the GGA underestimates the barriers compared with the experimental results. As mentioned by the authors their DFT results agree remarkable well with the experiments. Does the diffusion barrier affect the functional used?
To answer the referee's comment, we compare in Table 1 the experimental and the GGA computed activation energies (E a ) and ionic conductivities (s) for Li and Na diffusion in several solid electrolytes. Table 1 clearly shows that the agreement between theory and experiment is not fortuitous, suggesting that GGA activation energies are indeed reliable. Note that all the systems listed in Table 1 consist of closed-shell metals or semi-metals, such as Ge, Sn, La, etc.  Figure 1 shows a correlation plot of experimental vs. PBE-GGA computed activation energies, demonstrating further that the level of approximation adopted for our calculations captures the appropriate physics of ion diffusion in these solid electrolytes.

Reviewer 3:
The paper entitled "High Mg 2+  We regret that reviewer 3 sees no positive value at all in our work, and thinks of the applied methods as "too poor". We believe that the reviewer is erroneous on this matter.
1. The authors mentioned the topic as "High Mg 2+ Cation Mobility in Solids", however the most part of the study contains results on MgSc 2 Se 4 . It seems that they want to "Make a mountain out of a molehill".
Contrary to the referee comment, the manuscript computationally covers multiple spinel chemistries, i.e. AX 2 Z 4 structures (with A = Mg or Zn, X= Sc, Y and In, and Z = S, Se and Te). To assess Mg mobility experimentally in this class of materials, we focused on MgSc 2 Se 4 and MgY 2 Se 4 , due to the low Mg migration barriers calculated theoretically (~360 meV). While the manuscript covers in detail the experimental on MgSc 2 Se 4 as one example of this class of materials, the manuscript and the supporting information also extensively documents our attempts at synthesizing a phase-pure MgY 2 Se 4 , which seems to have been overlooked by the referee! The experimental data clearly supports the computational predictions and confirms that high Mg 2+ mobility is possible. We do not believe that this making a "mountain out of a molehill" We strongly disagree with these reviewer's statements, all of which are unsupported by even a single reference. There are several flaws in his/her arguments, and we would argue that these arguments are "too poor" to constitute a knowledgeable and unbiased review. a) In contrast to the referee's views, the main conclusion of this paper is not solely based on activation barriers from theoretical predictions. Indeed, we have employed sophisticated variable temperature 25 Mg NMR and impedance spectroscopy measurements to verify our theoretical calculations of high Mg 2+ mobility in MgSc 2 Se 4 . The referee must also note that the objective of this paper is not to improve existing theoretical methods and/or experimental techniques, but the discovery, for the first time, of high divalent cation mobility in close-packed solids. Hence the comment of the referee, "the applied methods are not scientifically of high level" is unfair and unwarranted, particularly in light of the supportive comments by reviewers 1 and 2. The theoretical methods used in the paper are very commonly used to investigate the phase stability and mobility in ionic conductors. b) The argument of reviewer 3, "it is known that pure DFT approaches underestimate the activation barriers" is not correct. In Figure 1 and Table 1, we have demonstrated that GGA-based activation barriers can reliably predict activation barriers in several Li-and Na-solid electrolytes, all of which consist of closed-shell metals, in our response to point 3 of reviewer 2's comments. There is no basis to assume that hybrid functionals would do better in reproducing barriers.

The main conclusion is based on the theoretical investigations of activation energy calculated by DFT
c) The reviewer suggestion that HSE should be used for the complete study is wrong. Each functional has its own issue, which is why we use different functionals to obtain different properties. It is part of the skill in doing computational materials science to understand the benefits and limitations of each approach in addressing various scientific questions. Hence, until there is a perfect functional, the reviewer's suggestion that a study must be performed uniformly with a single functional is poor advice, and has no grounds in any facts.

In the structural characterization (S2), the authors have predicted enthalpy of formation at 0K, it is rather useless. They should have done high temp Freq based calculations to draw the conclusion at high temp or at least at room temperature. By this way, the conclusions could be different.
The approach of calculating 0K enthalpies to get a sense of phase stability is ubiquitous in first principles materials science, to the point where there are multiple hundreds of papers that use the approach, and some representative publications are listed at the end of this letter. 1-16 So it is definitely not "rather useless" as the reviewer states. In addition, experimental facts in this class of materials support our approach, given that the MgSc 2 Se 4 spinel considered in our manuscript has been previously synthesized for superconductor applications, indicating that their formation is favorable thus supporting our DFT findings.

In the SLR investigation, it is shown that the magnetism plays a key role, as can be seen that the diamagnetic MgSc 2 Se 4 has fast ionic conductivity. There is no theoretical investigation of magnetism of the considered materials.
Since the metals of all the compounds considered (In, Sc, and Y) exhibit closed-shell electronic configurations (d 0 for Sc/Y and d 10 for In), magnetism is not a concern for evaluating Mg mobility in these compunds. Indeed, no 25 Mg-NMR resonances were found within a +/-20000 ppm range while scanning MgSc 2 Se 4 samples, indicating the absence of any paramagnetic Mg environment. In addition, the signal found at 53.3 ppm was not found to shift significantly with temperature, ruling out paramagnetic effects due to the well-known temperature dependence of Fermi-contact shifts or signatures of a Korringa relationship typically found in metals. These experimental findings suggest that the theoretical ivestigation of magnetism is clearly out of the scope of this work.

The considered models for the theoretical investigation are not 'ideal ones'. The authors have models the balance of excess electrons by a uniform background charge. Rather the electrons should be treated with open shell spin polarized methods and of course, the magnetism for all the cases should be checked by energy/enthalpy calculations.
The reviewer seems to grasp at straws here in a his/ her rather unprofessional attempt to discredit our work. Magnetism is not all relevant here as all ions are closed shell ions. We have addressed the issue of using uniform background charges in question No. 2 of referee 2. The background correction has been routinely used for more than 20 years in theoretical studies assessing the formation of point defects in solids and well documented in reviews such as, e. the charge density of a charge-compensated Li 2 S cell and a chemically doped cell (with Mg 2+ ) do not vary significantly. Thus, modeling Mg migration in the spinels considered in this work, with a compensating background charge, should lead to an accurate evaluation of the migration barriers. If the reviewer has issues with these well-established method, as he/she seems to have with many other well established methods, I suggest that he/she writes a paper documenting his/her gripes with these methods so that the objections, if they exist at all, can enter the arena of scientific discussion, rather than anonymous review reports.
6. The size of the supercell is not clear. In experiment, the vacancy concentration is very low. In order to model this, they should have used a very large supercell.
The method section of the updated manuscript explicitly mentions that we utilized a 2x2x2 supercell of the primitive spinel structure, which corresponds to a cell with composition Mg 16

Gerbrand Ceder Chancellor's Professor of Materials Science and Engineering
I think that this work should be published in a more specific journal. I did not see any obvious improvement made by the authors. While they cited many previous results, they did not report the corresponding results to clarify the worries including Referee 3's.
Reviewer #4 (Remarks to the Author): The manuscript provides interesting theoretical and experimental results. The major concerns of the initial reviewers have been adequately addressed in the revision. After addressing the minor comments below, publication in Nature Communications is recommended.
A more specific title is recommended for this article, which recognizes the focus of the article of spinel structures with AX2Z4 chemistries, such as: "High Mg2+ Cation Mobility in Solids: An investigation of spinel structures with AX2Z4 chemistries".
Based on the discussion in the text and SI, details for construction of the impedance cell are important. Therefore Ta/MgSc2Se4/Ta cell for impedance measurement should be described in more detail, including the thickness of the MgSc2Se4 pellet, and the Ta coating/foil used for the measurement, and the method of cell assembly.
This review article describing Mg-ion transport and electrochemistry in cathode materials should be added to the introduction section: -Coordination Chemistry Reviews, 2015, 287, 15-27.
Mg-ion electrochemistry of other spinel structure materials should be cited and discussed in the manuscript, in particular: -MgMn2O4: Chem. Commun., 2017,53, 3665-3668 Reviewer #5 (Remarks to the Author): This is a most interesting paper. It reports a joint computational/experimental study of Mg2+ migration in solids. This is a key problem in the current field of solid state ionics where there is a strong incentive to develop solid electrolytes based on Mg mobility. As the authors argue, a major problem is the generally low mobility of Mg2+ in solids. In this paper, by combining qualitative design considerations together with DFT calculations supported by experiment, the authors demonstrate that high Mg2+ mobility can be achieved in a new class of solids.
I have some reservations about the use of GGA-DFT in modelling activated processes in solids, but I note that the work does achieve good agreement between calculations and experiment.
Overall, I consider this to be novel work of high calibre and of general interest which I can recommend for publication in Nature Communications Thank you for sending us the referee comments on our manuscript. We are grateful to all the referees for bringing up important points that can improve the overall quality and readability of this novel and original work. Based on the suggestions of the reviewers, changes have been introduced to further strengthen our manuscript. Please find below a detailed response to all the comments and suggestions raised by the reviewers. In general, we appreciate the constructive comments of both reviewers 4 and 5. We hope that the revised manuscript will convince the referee(s) and the editor of the timely importance of this work for the development of materials with high Mg mobility, resulting in a swift publication.
We have adjusted the layout of the manuscript and the supplementary information to comply with the standards of Nature

Communications.
We would like Nature Communications to include the reviewer reports in the Supporting Information.

Reviewer #4
The manuscript provides interesting theoretical and experimental results. The major concerns of the initial reviewers have been adequately addressed in the revision. After addressing the minor comments below, publication in Nature Communications is recommended.
A more specific title is recommended for this article, which recognizes the focus of the article of spinel structures with AX2Z4 chemistries, such as: " High Mg2+ Cation Mobility in Solids: An investigation of spinel structures with AX2Z4 chemistries".
According to the referee's suggestion and the guidelines provided by Nature Communication we have modified the orignal title as: "High Magnesium Mobility in Solids: an Investigation of Ternary Spinel Chalcogenides" Based on the discussion in the text and SI, details for construction of the impedance cell are important. Therefore Ta/MgSc2Se4/Ta cell for impedance measurement should be described in more detail, including the thickness of the MgSc2Se4 pellet, and the Ta coating/foil used for the measurement, and the method of cell assembly.
The revised manuscript now includes a detailed procedure (as below) describing the construction of the Swagelok cell used for the impedance measurements, as well as the thickness information for both electrolyte pellets and the Ta foils that were used as blocking electrodes.
"The resulting pellet, typically with the thickness of 0.5 ─ 1.0 mm, was assembled into a spring-loaded Swagelok cell, using stainless steel rods as current collectors covered with tantalum foils (~0.05 mm thick) (Sigma Aldrich, ≥99.9%). The preparation of the sample and the Swagelok cell was entirely completed in an Argon glove box." I have some reservations about the use of GGA-DFT in modelling activated processes in solids, but I note that the work does achieve good agreement between calculations and experiment.
Overall, I consider this to be novel work of high calibre and of general interest which I can recommend for publication in Nature Communications.
We are thankful for the referee comment.

Reviewer #2
I think that this work should be published in a more specific journal. I did not see any obvious improvement made by the authors. While they cited many previous results, they did not report the corresponding results to clarify the worries including Referee 3's.
We have no further comments on this statement. We have cited existing literature when appropriate to argue the validity of various approaches, rather than re-validate every method in this paper. This is standard in scientific work.

Gerbrand Ceder
Chancellor's Professor of Materials Science and Engineering