Pressure-Dependent Crystal Radii

Round 1

Reviewer 1 Report

Comments on the manuscript solids-2465470 of Oliver Tschauner:

Title:

“Pressure-Dependent Crystal Radii”

 

The manuscript reports the pressure dependent crystal radii of several cations and the anions O^2-, Cl^- and Br^-. The most important elements building up the earth's mantle were investigated within this report, and the results provide important foundations for both high-pressure chemists and geoscientists.

The work was written with great care and can be published as it is, except for a few minor details which will be discussed below.

 

Abstract:

Line 6: Please ad an space between Mg,Si

Introduction:

There is an excellent paper by Grochala et al. published in Angewandte Chemie (DOI: 10.1002/anie.200602485) that describes the hierarchy of responses to pressure in crystals, which I should be cited in the introduction.

 

Text:

The indication of coordination numbers in square brackets and italic numbers is very confusing because citations are shown in the same way except for the italics. In addition, there are always coordination numbers in the manuscript that are not italicised. See in particular Table 2 and l.339.

 

Table 1 occurs twice and table 2 is missing

Table 1 line 6: two open brackets

 

Figure 2:

The cross-over to a different linear compression can be referred to the pressure coordination rule and a phase-transformation

 

Figure3:

Please add the coordination numbers of the rare earth elements in the graphic.

 

Question:

To what extent does the known pressure homologue rule fit into the picture of radii decreasing under pressure? If one compares known high-pressure phase transformations with the corresponding radii under pressure, are they comparable?

 

Author Response

Title:

 

“Pressure-Dependent Crystal Radii”

 

 

 

The manuscript reports the pressure dependent crystal radii of several cations and the anions O2-, Cl- and Br-. The most important elements building up the earth's mantle were investigated within this report, and the results provide important foundations for both high-pressure chemists and geoscientists.

 

The work was written with great care and can be published as it is, except for a few minor details which will be discussed below.

 

• Thank you for the positive assessment!

My responses to these very useful comments are indicated by arrows.

 

 

 

Abstract:

 

Line 6: Please ad an space between Mg,Si

 

• Done!

 

Introduction:

 

There is an excellent paper by Grochala et al. published in Angewandte Chemie (DOI: 10.1002/anie.200602485) that describes the hierarchy of responses to pressure in crystals, which I should be cited in the introduction.

 

• Yes, this is a very useful paper, indeed – we add the reference and the following statement to the introduction:

‘More recently, these concepts were reexamined, confirmed, and extended to molecular solids by Grochala et al. [8] by means of concepts of theoretical chemistry and by relating them to a large set of experimental and computational studies that had been carried out since the publication of Prewitt and Downs paper [6].’

 

 And in the discussion, section 4.1, page 10 of the manuscript: ‘Hence, the transition from the metastable to the stable valence electron configuration in decompressed bridgmanite is sterically hindered (see section 9 in Grochala et al. [8])’

 

 

Text:

 

The indication of coordination numbers in square brackets and italic numbers is very confusing because citations are shown in the same way except for the italics. In addition, there are always coordination numbers in the manuscript that are not italicised. See in particular Table 2 and l.339.

 

• I agree, this is an issue. There is a conflict with the citation format. Hence, coordinations are changed to roman numbers in square brackets.

 

 

 

Table 1 occurs twice and table 2 is missing

• Table 2 was mislabeled, corrected to Table 2. – Thank you!

 

Table 1 line 6: two open brackets

 

• Corrected, thanks!

 

Figure 2:

 

The cross-over to a different linear compression can be referred to the pressure coordination rule and a phase-transformation

 

• Yes! I add this point, it is good to state this explicitely. It is noted that data from the regime of observed spontaneous lattice deformation (to the orthorhombic phases) were not included here, already because actual interatomic distances were not measured in those phases However, it is true that a change in (ionic) compression is a phase transformation (let it be in the formal sense of Ehrenfest’s criteria). In the case of the alkalhalides the physical meaning of these transitions may be a change towards multicenter bonding (such as discussed for other materials in Grochala et al.’s paper) possibly in correlation with minor displacement of the ions within the cubic lattice (e.g. from sites 1a and 1b to partially occupied sites of higher multiplicity 6f, 8g etc.). However, an electronic transition with rebalance of valence electron orbital states would cause the same or similar structural response. A combination of structure analysis and X-ray spectroscopy is needed to solve this issue.

 

Figure3:

 

Please add the coordination numbers of the rare earth elements in the graphic.

 

 

• Done!

 

 

Question:

 

To what extent does the known pressure homologue rule fit into the picture of radii decreasing under pressure? If one compares known high-pressure phase transformations with the corresponding radii under pressure, are they comparable?

 

 

• This is an interesting point. First of all, with the pressure-dependent radii high-pressure polymorphs plot into the field of their structure types, at least for perovskites. I added a paragraph to the Discussion section that examines the pressure-effect on radii with respect to tolerance fields of ABO3-structures. Structure fields that are based on cation ratios only are less useful for assessing pressure effects because the compression of the anion is quite important. For ABO3 the r_A versus r_B plot still places bridgmanite and davemaoite into the field of perovskites but the evolution of structures with pressure in not properly accounted for without anion contraction. Hence, I abstain from discussing ABO4 etc. – it is certainly possible to reassess the structure fields of ABX4 etc. with tolerance factors that involve the anion.
• The point about structure-tolerances is rather matter of fact, but there may be a more fundamental explanation: Section 4.1 ( 4.2 in the revised version) provides a tentative explanation of the relation between dr/dP and 1/(Z-S) with Z = nuclear charge number and S. where increasing electron repulsion is suggested to favour shifting electron density into orbitals with higher azimuthal quantum number, which then also allows for increased coordination. If this explanation points in the right direction, elements of a given principal quantum number exhibit valence electron states at high pressure that correspond to those of elements of the same row but higher principal quantum number – which is basically the homology rule.
• Grochala et al. emphasize the role of multicenter bonding as a cause of increased coordinating at high pressure. They mention but they do not much discuss the pressure effect on valence electrons from s- and p – towards p- and d-states which also could cause increasing coordination (and homology). The more recent work by Rahm, Hoffmann, Cammi and others (papers are cited) indicate that such changes occur – and for metals we know already that this effect is real (see the XANES studies by Fabbris et al.and Iota et al., also the correlation between phase transition volumes, -pressures, and outer electron states as proposed in: Crystals 12, 1698. https://doi.org/10.3390/cryst12121698).

Reviewer 2 Report

 

Tschauner studied the radii of some elements with increasing pressure from ambient to above 100 GPa. The cation radii present a linear response with pressure, while anions display a nonlinear relationship. This study provides a systematic study on the radii of Earth’s elements with pressure, and the deviations are well discussed based on the change in electronegativity. The result is significant in understanding the change in element behavior with increasing Earth depth. The manuscript is also well written. I suggest accept with minor revision.

 

The radii of ions can be used to predict solid solution. A solid solution can be formed if two elements have similar ionic radii in a lattice, such as K+ and Na+ in liebermannite and Mg2+ and Ca2+ in bridgmanite. Based on the author’s study, is it possible to make some further discussions on some possible hosts for specific elements in deep Earth? It may have a significant influence on the distribution of these elements in Earth.

 

In Figure 2, symbols for Cs[6] and Cs[8] are not clear for me.

 

In Figure 5, it is better to explain the meaning of different symbols in the caption.

Author Response

Tschauner studied the radii of some elements with increasing pressure from ambient to above 100 GPa. The cation radii present a linear response with pressure, while anions display a nonlinear relationship. This study provides a systematic study on the radii of Earth’s elements with pressure, and the deviations are well discussed based on the change in electronegativity. The result is significant in understanding the change in element behavior with increasing Earth depth. The manuscript is also well written. I suggest accept with minor revision.

 

• Thank you very much for your comments and your positive assessment!

My responses are indicated by arrows.

 

 

 

The radii of ions can be used to predict solid solution. A solid solution can be formed if two elements have similar ionic radii in a lattice, such as K+ and Na+ in liebermannite and Mg2+ and Ca2+ in bridgmanite. Based on the author’s study, is it possible to make some further discussions on some possible hosts for specific elements in deep Earth? It may have a significant influence on the distribution of these elements in Earth.

 

• This is correct, this is a very good point and it is the purpose of this study to provide a basis exactly for this kind of work.

Without nearly doubling its length it is not possible to expand the present paper by serious modeling of source rock compositions and element partitioning and by comparing such models to geochemical signatures. This work will certainly be done very soon! For now, a statement is added to the Summary: ‘The pronounced pressure effect on heavier alkaline- and alkaline earth elements, K, Ca and beyond, is potentially relevant for identifying potential deep mantle signatures in geochemical trace element patterns. In particular, the present results confirm the role of davemaoite as host of elements that are geochemically incompatible in the upper mantle and, therefore, are compatible in deep mantle rock, where this mineral is stable and solidus phase.’

 

 

In Figure 2, symbols for Cs[6] and Cs[8] are not clear for me.

 

• Thank you for pointing this out! The figure has been modified for consistency of coordination labels and the issue of crossover in coordination is now briefly discussed in section 3.2. I also moved the labels for Cs VI and –VIII to make the relation to the two fits more clear. Note that the data which show crossover from VI to VIII coordination come from two different Cs salts but agree within small uncertainties , hence data points largely overlap and this is what we wanted to see.

 

 

In Figure 5, it is better to explain the meaning of different symbols in the caption.

 

• I agree, it is better to explain as much in the caption, not just the text. The Figure caption is modified to

‘Overview and systematics of the pressure dependencies of the examined ions: correlation between –dr/dP in 1/ GPa and ambient pressure crystal radii r₀ in Å. Left side: dr/dP as function of r₀. Fit through filed symbol data, hollow symbols are for the following ions: Li[IV], Na[VI], Na[VII] Na[VIII], Cs[VI], Ca[VIII],[X], Ba[VI],[VIII], La,Pr,Gd. Filled symbols are for all other ions that represent the ‘mail trend’ (as explained in secion 4.2). Right side: dr/dP as function of electronegativity c in eV, at 0 GPa [74]. The fits are for the data that are represented as filled symbols, the same is true for the left panel.’