Equation of State for Bismuth at High Energy Densities

Round 1

Reviewer 1 Report

The paper provides results of the Equation of State for Bismuth at High Energy Densities. However, before publishing this manuscript, I have several comments for the revised version as following:

1. In the Abstract, the author should refine sentences for the purpose of better understanding the aim of this paper.

2. The authors should provide the particular computational details the particular computational details for EOS Model.

3. There is not complete enough list of present references, so I recommend considering the citation of the recent works, such as: Chin. Phys. B 31 (2022) 026101，Vacuum 195 (2022)110696.

4. I recommend publication. But the author should conduct the appropriate discussions for applications before publication.

Author Response

Comment 1.1

The paper provides results of the Equation of State for Bismuth at High Energy Densities. However, before publishing this manuscript, I have several comments for the revised version as following:

1. In the Abstract, the author should refine sentences for the purpose of better understanding the aim of this paper.

Reply 1.1

I have refined the following sentences in the abstract:

“The purpose of this work is to describe the thermodynamic properties of bismuth in a broad scope of mechanical and thermal effects. A model of the equation of state in a closed form of the functional relationship between pressure, specific volume and specific internal energy has been developed.”

Comment 1.2

2. The authors should provide the particular computational details the particular computational details for EOS Model.

Reply 1.2

A paragraph with Equations (17)–(19) is added, which explains the particular computational details for computing shock adiabats using the present EOS model.

Comment 1.3

3. There is not complete enough list of present references, so I recommend considering the citation of the recent works, such as: Chin. Phys. B 31 (2022) 026101，Vacuum 195 (2022)110696.

Reply 1.3

Thank you for the advice! The recommended papers ([24, 25] in the current list of references) are mentioned in Section 1 along with additional other recent papers:

“Interest in thermodynamic models is also associated, in particular, with the problems of studying the thermoelastic properties of various materials at high pressures [23–26].”

Comment 1.4

4. I recommend publication. But the author should conduct the appropriate discussions for applications before publication.

Reply 1.4

Many thanks! In addition to the first phrase in Section 4, the discussion of applications for the results of this work has been clarified in the Conclusions:

“The refined parameters of shock waves in air under the conditions of experiments on isentropic expansion of shock-compressed bismuth samples provide additional information that can be applied to study phase transitions in this metal. The developed EOS can be effectively used in numerical simulation of various processes in bismuth at high energy densities.”

Reviewer 2 Report

I have only a few minor points on the “Equation of State for Bismuth at High Energy Densities” that the authors should address before it is accepted for publication. Please, publish subject to the following revisions:

1-      There are a few grammatical mistakes. Please check the manuscript for grammar and English.

2-      Rewrite the novelty statement at the end of the introduction section.

3-      Authors should justify the importance of the current work of how this is different from earlier reports. So, it’s better to add comparison table material and its performance to show the importance of the manuscript.

4-      Abstract and conclusion should be rewritten and showed more clear results and novelty of this study.

Author Response

Comment 2.1

I have only a few minor points on the “Equation of State for Bismuth at High Energy Densities” that the authors should address before it is accepted for publication. Please, publish subject to the following revisions:

1-      There are a few grammatical mistakes. Please check the manuscript for grammar and English.

Reply 2.1

I have checked the manuscript for grammar and English. Everything that has been corrected in the manuscript is highlighted in the attached file.

Comment 2.2

2-      Rewrite the novelty statement at the end of the introduction section.

Reply 2.2

The novelty statement at the end of the introduction has been rewritten as follows:

“In contrast to the previously known EOSs (for bismuth) [32–41], a new expression is proposed for the internal energy of matter on the zero-temperature isotherm (cold curve) in a wide range of densities (ρ = V⁻¹), which has asymptotics to the Thomas–Fermi model with quantum and exchange corrections [42–45]. A new EOS has been developed for a body-centered cubic (bcc) solid phase and a melt of bismuth in the high-pressure region. The results of calculation of shock adiabats for samples of different initial density and release isentropes for shock-compressed samples using the new EOS are compared with the available experimental data for bismuth. Also, the relationship between the parameters of plane shock waves in the metal and in the air adjacent to it when the front of the first wave reaches the sample–gas interface is reconsidered.”

Comment 2.3

3-      Authors should justify the importance of the current work of how this is different from earlier reports. So, it’s better to add comparison table material and its performance to show the importance of the manuscript.

Reply 2.3

Thank you for this remark! Unfortunately, adding a comparison table goes too far beyond the scope of this work, as it seems to me the subject of a separate article. Nevertheless, in order to justify the importance of this work and to clearly show how it differs from previous works, I have added more curves (A3 and A4) from other works to the graph of Figure 1. I have also added the following to the text of Section 3:

“The cold compression curves of the bcc-phase of bismuth from EOSs [38,40] are in good agreement with the experimental data [53,54], but they deviate far from the results of calculations using the Thomas–Fermi model with corrections in the range of applicability of the latter (at compression ratios above 50).”

Comment 2.4

4-      Abstract and conclusion should be rewritten and showed more clear results and novelty of this study.

Reply 2.4

Many thanks! I have rewritten the abstract to show clearer results and novelty of this study:

“…A new expression is proposed for the internal energy on the zero-temperature isotherm in a wide range of compression ratios, which has asymptotics to the Thomas--Fermi model with corrections. Based on the new model, an equation of state for bismuth in the region of body-centered cubic solid and liquid phases is constructed. The results of calculating the thermodynamic characteristics of these condensed phases with the new EOS are compared with the available experimental data for this metal in waves of shock compression and isentropic expansion. The parameters of shock waves in air obtained earlier by unloading shock-compressed bismuth samples are reconsidered. The newly developed equation of state can be used in modeling various processes in this material at high energy densities.”

Also, I have slightly changed the conclusion:

“…The newly constructed EOS for the bcc and liquid phases of bismuth is in good agreement with the available experimental data, with the exception of the region of relatively low pressures achieved at low expansion velocities of the shock-compressed material into barriers with low dynamic impedance, where phase transitions (melting, evaporation) occur. The refined parameters of shock waves in air under the conditions of experiments on isentropic expansion of shock-compressed bismuth samples provide additional information that can be applied to study phase transitions in this metal…”