Disordered enthalpy–entropy descriptor for high-entropy ceramics discovery

The need for improved functionalities in extreme environments is fuelling interest in high-entropy ceramics1–3. Except for the computational discovery of high-entropy carbides, performed with the entropy-forming-ability descriptor4, most innovation has been slowly driven by experimental means1–3. Hence, advancement in the field needs more theoretical contributions. Here we introduce disordered enthalpy–entropy descriptor (DEED), a descriptor that captures the balance between entropy gains and enthalpy costs, allowing the correct classification of functional synthesizability of multicomponent ceramics, regardless of chemistry and structure. To make our calculations possible, we have developed a convolutional algorithm that drastically reduces computational resources. Moreover, DEED guides the experimental discovery of new single-phase high-entropy carbonitrides and borides. This work, integrated into the AFLOW computational ecosystem, provides an array of potential new candidates, ripe for experimental discoveries.

Regarding the borides, there is a description of sintering that results in the microstructures shown in Figure 3.Both carbonitrides and borides were sintered using similar techniques (i.e., spark plasma sintering), but in different equipment.An HP5--7010G system was used for the borides and an FCT system was used for the carbonitrides.Why change equipment?Would this have an effect on oxide impurities considering changes in vacuum in the two systems used?And again, does this have an effect on the phase stability in the materials?Also, in some cases, extra carbon was added to reduce oxides.Does this then have an effect on the phase stability?Can this be correlated to the computational work in some way?
If better controlled specimens can be prepared (without oxide contamination), this manuscript would be outstanding.At the moment, however, there is a lack of rigor in the experiments, variability is not clear from sample to sample (for example, did the authors prepare more than just one sample of each composition?), and there seems to be changes in methodologies for sintering that are not fully justified.

Referee #2 (Remarks to the Author):
In this manuscript, the authors present a disordered enthalpy-entropy descriptor, called DEED, that provides a classification of the so-called "synthesizability" of multicomponent ceramics.They show the application of DEED to high-entropy carbides, carbonitrides and borides based on the published experimental data together with several new compounds synthesized by the authors.The results, as summarized in Table 1, show improved classification compared to other descriptors such as valence electron concentration (VEC) and entropy-forming-ability (EFA).
Overall, the descriptor DEED serves to provide a classification of multicomponent ceramics only in terms of the formation of single vs. multi-phases.It has a limited value and lacks a general applicability for guiding the development of new multicomponent ceramics.Hence, the work lacks general relevance and potential impact to warrant its publication in Nature.
A serious issue of the work is that the candidate materials considered are limited to the stoichiometric compounds consisting of early transition metal elements with a priori knowledge of a specific lattice structure.It is not clear if the DEED can be used to address some of the more basic questions on the synthesis of multicomponent ceramics, such as whether a crystalline or an amorphous structure will form; what type of crystal structure(s) will form for single or multi-phase systems; what is the applicability of DEED for non-stoichiometric ceramics.
Anther serious issue is that the term of "synthesizability" is used vaguely throughout the manuscript.The calculated DEED value is not directly connected to any experimentally measurable material property.For the ceramic systems studied in the manuscript, the threshold value of DEED for classification is dependent on each specific set of constituent elements chosen, and likely dependent sensitively on (stoichiometric/non-stoichiometric) composition and crystal structure, etc.It is not clear how the threshold value is determined and what is the amount of experimental input is needed.Moreover, as the authors state, "synthesizability depends on the experimental process".Considering all of those limitations, the descriptor of DEED does not have a general and strong value for guiding the synthesis of multicomponent ceramics.
I regret to summarize that I feel this work does not represent a clear and significant advancement for the development of multicomponent ceramics.It shows one improved descriptor for classification of formation of single vs. multi-phases within a limited range of material design space.The work does not represent a strong breakthrough which should be the main criterion for a journal as Nature.

[Text and figure redacted]
The article has been modified as follow (changes are highlighted in blue): Page 5in the "DEED for carbides" section The addition of even more carbon and increasing its chemical potential (with extra pressure, for example) can also be described by DEED.It requires the recalculation of the enthalpy-stability landscape, the fonnation enthalpies distances of the POCC-tiles, and the statistical momenta as function of the reference carbon chemical potential.It can then be a priori predicted if the carbide synthesizability is preserved or if other phases, with smaller metal solubility, are promoted.

Reviewer Reports on the First Revision:
Referees' comments: Referee #1 (Remarks to the Author): In response to my original review, the authors have provided complete and highly suitable responses to my original concerns.Congratulations to the authors on their excellent work.--Olivia A. Graeve Referee #2 (Remarks to the Author): I have carefully reviewed both the revised manuscript and the authors' response to the previous review comments.I find that the main criticisms from my initial review still apply.While the authors present lengthy arguments, they have not effectively addressed the fundamental weaknesses in their work.Therefore, I regret to conclude that this paper does not represent a clear and significant advancement for the development of high-entropy ceramics.It introduces an improved descriptor, but it falls short of meeting the criteria for publication in a journal like Nature, which typically seeks groundbreaking contributions.
As I emphasized in my previous review, the authors framed their work around the abstract and loosely defined concept of "synthesizability".In the revised manuscript, they acknowledge that "The lack of consensus about "synthesizability" in literature does not translate into an operative procedure for the synthesis…".To address this issue, they revise "synthesizability" to "functional synthesizability", which they use to convey that "synthesizability is a functional of both the material and the synthesis conditions"."Functional" is a mathematical term, and its exact definition varies depending on the subfield.According to Wikipedia, a functional often refers to the mapping of a function to the value of the function at a point.The newly introduced concept of "functional synthesizability" may potentially confuse most readers even more than the vague one of "synthesizability" did.Clearly, the authors' difficulty in defining "synthesizability" demonstrates a fundamental weakness in their work.Furthermore, the authors add an assertion that "functional synthesizability is intrinsically connected to a given manufacturing process", i.e., hot-pressed sintering for transition-metal disordered ceramics in this work.However, they later state that "different processes, structures, and chemistries can be captured by the DEED framework".To validate the broad applicability of the DEED framework, it should be demonstrated for various processing routes and compared with hot-pressed sintering processes.I will not further iterate other concerns I raised in my previous review.
To summarize, the DEED descriptor appears to provide improved classification of early transition metal element ceramics, primarily in terms of single versus multi-phase formation.Its utility is limited, and it lacks the generality needed to guide the development of new high-entropy ceramics.Consequently, the work does not have sufficient general relevance and potential impact to warrant publication in Nature.

Q2.2. As I emphasized in my previous review, the authors framed their work around the abstract
and loosely defined concept of "synthesizability".In the revised manuscript, they acknowledge that "The lack of consensus about "synthesizability" in literature does not translate into an operative procedure for the synthesis…".To address this issue, they revise "synthesizability" to "functional synthesizability", which they use to convey that "synthesizability is a functional of both the material and the synthesis conditions"."Functional" is a mathematical term, and its exact definition varies depending on the subfield.According to Wikipedia, a functional often refers to the mapping of a function to the value of the function at a point.The newly introduced concept of "functional synthesizability" may potentially confuse most readers even more than the vague one of "synthesizability" did.Clearly, the authors' difficulty in defining "synthesizability" demonstrates a fundamental weakness in their work.A2.2.We respectfully disagree.In our previous detailed report, we provided evidence to address all of the referee's concerns.Still, to avoid any potential confusion, we revised the paragraph discussing "functional synthesizability" (first page second column, blue text is the modified part).

It now reads:
Defining functional synthesizability.Synthesizability depends on both the material and the synthesis conditions, and the user needs to explore the appropriate path across these two degrees of freedom.The conundrum lies in the observer's reference.Usually, the priority is put on "synthesizability as an intrinsic material property" with synthesis conditions to be determined later; i.e., from the materials' point of view.Unfortunately, this approach, along with the lack of consensus about "synthesizability" [28-35], does not translate into Author Rebuttals to First Revision: an operative procedure for the synthesis, critical for autonomous materials discovery [36].Instead, to maximize the outcome, we focus on the complementary direction, or the process' point of view; i.e., starting from a chosen process, we build a descriptor to establish which materials are synthesizable with it.We define this as "functional synthesizability", to specify that it is intrinsically a function of the chosen manufacturing process.In the present casetransition-metals disordered ceramicsthe process is hotpressed sintering with all its various implementations [2], and the classes of materials are high-entropy carbides, carbonitrides and borides.
We have also added a line in the "conclusion".It now reads: We have introduced DEED, a descriptor that captures the balance between entropy gains and enthalpy costs upon the formation of homogeneous solid-solutions.We have also introduced the concept of functional synthesizability associated to the process' point of view.Our experimental results, combined with published data, con-firm DEED as a reliable tool enabling computational discovery of novel high-entropy ceramics…….
For our definition of "functional synthesizability", we dismiss Wikipedia for its lack of scientific authority.Q2.3.Furthermore, the authors add an assertion that "functional synthesizability is intrinsically connected to a given manufacturing process", i.e., hot-pressed sintering for transition-metal disordered ceramics in this work.However, they later state that "different processes, structures, and chemistries can be captured by the DEED framework".To validate the broad applicability of the DEED framework, it should be demonstrated for various processing routes and compared with hot-pressed sintering processes.I will not further iterate other concerns I raised in my previous review.

A2.3.
We respectfully disagree since do not find any contradictions between the two assertions.In addition, regarding experiments, Referee 1, a world expert in synthesis of ceramics, has commended the authors for their "excellent" work, stating that all of her concerns have been satisfactorily answered.We did not address any Referee 2's experimental concerns because there were none in the previous review.
Q2.4.To summarize, the DEED descriptor appears to provide improved classification of early transition metal element ceramics, primarily in terms of single versus multi-phase formation.Its utility is limited, and it lacks the generality needed to guide the development of new high-entropy ceramics.Consequently, the work does not have sufficient general relevance and potential impact to warrant publication in Nature.A2.4.We thank the Referee for the time invested in evaluating the manuscript.We respectfully disagree with the final opinion.