On the Definition of Phase Diagram

Round 1

Reviewer 1 Report

 

This opinion paper by Kamil Dziubek discusses a variety of very interesting and challenging issues with the scientific communication of materials equations of state (EOS).  In particular, Dr. Dziubek addresses ambiguities concerning hysteresis, nonhydrostatic stress, and rate dependence inherent in reporting the pressure, temperature (P,T) EOS of stable, metastable, and transitional crystallographic phases.  The opinion is a well-thought out and illuminating review of difficulties associated with determining and communicating phase behavior.  As such, I believe it should be published, although I would like Dr. Dziubek to consider several modifications that would make this piece more useful to the community and easier to follow.

 

My primary criticism of the essay is that while excellent points are raised throughout the paper about the terminology and definition of what precisely is being communicated in a phase diagram, but there is no listing of these points in a concise way.  Dr. Dzuibek also suggests a variety of ways to clean up various ambiguities or misrepresentations found in the literature, but these suggestions are presented somewhat haphazardly throughout the essay.  I suggest that the issues and suggestions for improvements be assembled in the conclusion.  Dr. Dzuibek correctly suggests that a discussion of the issues identified should be held within the field and a clear statement of the problem and some preliminary suggestions in this paper would be a great start.

 

I raise several other issues that may help the readability of the essay:

 

1.     The paper would be improved if Dr. Dziubek defined several key terms used repeatedly in the paper, prior to the discussion beginning on line 60.  E.g. (based on my understanding of Dr. Dziubek’s position):

a.     An ideal phase diagram is a P,T plot of thermodynamically stable phases.  There is only one ideal phase diagram for any stoichiometric assembly of atomic species.  It is impossible to experimentally determine an ideal phase diagram since all experiments are dynamic, hysteresis is impossible to completely eliminate, and non-hydrostatic stresses and P,T gradients are impossible to eliminate.

b.     A phase diagram is a best estimate of the ideal phase diagram based on experimental and theoretical constraints.

c.      A dynamic phase diagram represents observed or predicted phases that can be produced.  A dynamic phase diagram can include metastable or transitional phases and must include descriptions of the conditions necessary; compression or decompression rate, cooling or heating rate, stress-strain conditions, etc.

d.     A transitional phase diagram represents the phase diagram including metastable states, … (Dr. Dziubek appears to only discuss transitional phase diagrams in molecular or multicomponent materials, the difference between dynamic and transitional phase diagrams and it needs to be clarified.)

e.     Such a set of definitions would clarify much of Dr. Dziubek’s arguments.

2.     In lines 147-183 Dr. Dziubek defines several definitions of phase stability, including thermodynamic stability, metastability, dynamic stability, mechanical stability, and elastic stability. 

a.     I cannot determine the difference between mechanical and elastic stability, as both seem to represent some aspect of Born’s stability criteria.  Elastic stability is defined by a positive definite second-order elastic stiffness tensor C, but mechanical stability is less well defined and appears nearly identical to elastic stability; it may be that this similarity is one of the ambiguities that Dr. Dziubek is highlighting and if so, that should be made more clear. 

b.     Dynamic stability, is defined as, “all of the atoms are trapped within local energy minima.”  Given equation 3, it is unclear why this definition is not the same as C being positive definite; this should be better explained.  Otherwise, the difference between dynamic stability, mechanical stability, and elastic stability needs to be further delineated.

c.      It would be nice to give examples of situations where a material is dynamically unstable, but mechanically stable, or mechanically unstable but elastically stable, etc..

3.     The phase diagram of carbon is used to illustrate the depiction of metastable phases in a transitional phase diagram (figure 3) and the recent NIF results by Jenei, et al. are mentioned in the discussion. I think it would be illustrative to include Jenei’s experimental result in figure 3 by extending the pressure scale to 10⁴ GPa along with a discussion in the caption of the differences between the hashed diamond metastability range (>years) and the proposed metastability above 1 TPa (>ns).  It should also be pointed out that that the high-pressure diamond phase is assumed to be metastable based on theoretical predictions alone since the BC8 phase of carbon has never been explicitly observed.

4.     Brief mention of three types of phase transitions at high pressure: pressure-induced, stress-induced, and strain-induced transformations is made (line 251), but the differences between these is not explained.  I assume that pressure-induced transitions are driven hydrostatically, and stress- and strain-induced transitions involve stress or strain gradients.  It is not clear how stress- and strain-induced transitions can be distinguished from each other.

5.     On line 297 reference is made to the metastability of multicomponent materials.  Does this refer exclusively to mechanical metastability, or has the discussion moved on to include chemical metastability as well?

6.     Section 2.4 (line 403) introduces the concept of a, dynamic phase diagram.  It is not clear whether or not Dr. Dziubek approves of such a description, and how it may differ from a transitional phase diagram.

7.     Section 3 (line 428) “In lieu of conclusions”, lists 6 “closing remarks, which may serve as a starting point for a further discussion”.  If Dr. Dziubek’s goal for this paper is to influence change in the current presentation of phase diagrams, this section is critical to the goal.  As such, I feel it should be much more precise and split into two lists, “issues” and “potential solutions”.  This section, as-written is a reasonable start, but it lacks clarity and feels a bit too vague to truly serve as a “starting point for a further discussion”.  Most importantly, Dr. Dziubek should include clear suggestions for addressing the various issues listed.

 

The issues raised by Dr. Dziubek are very topical and important and I am supportive of publishing Dr. Dziubek’s opinion, and I hope he will adopt some of my suggestions. 

 

 

Author Response

I thank the reviewer for their constructive comments and suggestions that significantly improved the quality of the manuscript.

I absolutely agree that the ideas contained in the opinion paper should be presented to the general reader as clearly as possible. It is a great recommendation to reshape the conclusions in an ordered fashion and include a list of suggestions for improvements. I followed the reviewer’s suggestions and completely reorganized the conclusions section, changing its title from “In lieu of conclusions” to the more direct “Conclusions and the call for actions”. I also explicitly suggested IUPAC, IUCr and AIRAPT as scientific organizations that may be interested in issuing official recommendations regarding the presentation of phase diagrams. Below please find my comments to the other issues raised by the reviewer, addressed in a point-by-point reply.

1. Following the reviewer’s suggestion, the key terms have been listed prior to the discussion in a new section 2 “Glossary of the key terms related to phase diagrams”.
2. My apologies for the earlier presentation on definitions of phase stability, which was not very clear and might have been ambiguous. I corrected this section by stating explicitly that the terms mechanical stability and elastic stability are synonymous. Besides, the definition of the dynamic stability is completely unrelated to the second-order elastic stiffness tensor and therefore the notions of mechanical stability and dynamic stability are independent. I also provided examples of structures which are dynamically unstable but mechanically stable and dynamically stable but mechanically unstable.
3. As requested, I extended the pressure scale in the transitional P–T diagram of carbon to 10⁴ GPa and revised the figure caption accordingly.
4. I included a quotation from the review article by Levitas on pressure-induced, stress-induced and strain-induced transformations. While some authors use slightly different definitions, I believe the detailed discussion of this issue is beyond the scope of my opinion paper.
5. I added a statement commenting on the metastability of multicomponent materials and its relationship to the concept of chemical metastability.
6. My view on the terms a dynamic P–T (phase) diagram and a transitional P–T (phase) diagram, including the denotation and semantic domain of both concepts is now clearly presented in the section 2 “Glossary of the key terms related to phase diagrams”, section 3.4. “Non-equilibrium studies and dynamic P-T diagrams”, and summarized in the conclusions (section 4).
7. I have rewritten and reorganized the conclusion section, changing its title to the more appropriate and straightforward “Conclusions and the call for actions”. I appreciate and completely agree with the reviewer’s suggestion to split the closing remarks into two list. They are now presented in a table containing two columns, “issues” and the related “potential solutions”.

Author Response File: Author Response.pdf

Reviewer 2 Report

Good work reviewing the literature.

Author Response

The author is grateful for the positive evaluation of the manuscript.