Potential Occurrence of Accessory Minerals in the Lower Mantle

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This manuscript revisits V.M. Goldschmidt's classical crystal-chemical approach to mantle composition using modern pressure-dependent ionic radii. The author proposes that the decrease in oxygen volume fraction (VO) at the transition zone–lower mantle boundary enhances the incompatibility of certain trace elements, leading to the formation of accessory minerals that could host elements like Nb, Ta, Zr, Hf, and others. The idea is novel and has significant implications for deep mantle geochemistry. While the manuscript is clearly written and the reasoning is logically structured, several key aspects require clarification and strengthening before the paper can be considered for publication.

Major points:

1. Conceptual Clarity and Justification of the VO Metric:

The author uses the volume fraction of O^2- (VO) as a proxy for trace element compatibility. While the correlation is intriguing, the physical or thermodynamic justification for why a decrease in VO should lead to trace element incompatibility is not sufficiently developed. Is this a steric effect? An electronic or bonding effect? The argument would benefit from a clearer physical model or reference to solid solution theory.

2. Treatment of Trace Elements:

The study focuses on the nine most abundant elements but makes conclusions about trace elements (Nb, Ta, REE, etc.). The author should explicitly address how the excluded 0.21% of elements (which include the very trace elements under discussion) influence the VO calculation, if at all. A supplemental calculation showing the sensitivity of VO to the inclusion of key trace elements would be helpful.

3. Observational or Experimental Support:

The hypothesis that accessory minerals form in the lower mantle is speculative. Both the multi-anvil  and DAC techiniques can easily cover the top lower mantle conditions. The author should discuss whether there is any experimental evidence that could support or refute this idea. For instance, are there high-pressure experiments showing saturation of Nb- or Zr-rich phases in lower mantle assemblages?

4. Mineralogical Predictions:

The list of possible accessory phases (sulfides, carbides, nitrides, etc.) is reasonable but very general. The author could narrow this down by discussing which phases are thermodynamically stable under lower mantle conditions and compatible with the geochemical behavior of the elements in question (e.g., Nb-Ta fractionation).

 

Minors:

1. The interpolation of O^2- radii at low pressures (Table 1) is pragmatic, but the method should be briefly justified (e.g., linear vs. power-law interpolation).
2. Reference formatting should be checked for consistency: some all the first character is captalized in the title (such as Tschauner, 2024). Some only the first character of the first word is capitalized (such as Corgne et al., 2005).

Author Response

This manuscript revisits V.M. Goldschmidt's classical crystal-chemical approach to mantle composition using modern pressure-dependent ionic radii. The author proposes that the decrease in oxygen volume fraction (VO) at the transition zone–lower mantle boundary enhances the incompatibility of certain trace elements, leading to the formation of accessory minerals that could host elements like Nb, Ta, Zr, Hf, and others. The idea is novel and has significant implications for deep mantle geochemistry. While the manuscript is clearly written and the reasoning is logically structured, several key aspects require clarification and strengthening before the paper can be considered for publication.

 

Response: I appreciate the detailed and thoughtful comments and question about this manuscript!

 

Major points:

1. Conceptual Clarity and Justification of the VO Metric:

The author uses the volume fraction of O^2- (VO) as a proxy for trace element compatibility. While the correlation is intriguing, the physical or thermodynamic justification for why a decrease in VO should lead to trace element incompatibility is not sufficiently developed. Is this a steric effect? An electronic or bonding effect? The argument would benefit from a clearer physical model or reference to solid solution theory.

 

Response: The discussion section has been extended to clarify these points: a) it is to first order steric effect (indeed), b) the relation to polyhedral compression andtrace element partitioning is further examined, c) the availability of polyhedra sites suitable for hosting incompatible elements as function of pressure/depth is examined. To the method section some background about the causes of ion compression has been added.

The following sections were added (and I apologize that only the text but not the formulas and figures are captured by the template here - please look at them in the revised paper):

"This is to first order a steric effect, illustrated in Figure 2.

 

 

 

Figure 2. Added

Caption: A simple 2-dimensional illustration of the steric effect of a marked reduction of the ionic volume of O^2-, such as it occurs at the 410- and 670 km boundaries. Red circles = O^2-, blue circles = cation. The radius of the cation is the same in both figures but in (a) the radius of O^2- is reduced by 2. Grey areas indicate the bond vectors (a square 4-fold coordination in this case, which may be taken for a cut through the base plane of an octahedron). Next it is assumed that cation is substituted by a larger ions (blue dashed circle, again of equal radius in (a) and (b)) – with bond distance constant O^2- is pushed further out (dashed red circles), thus increasing the polyhedral volume but significantly less for large than for small O^2-. In this illustration the effect is shown for an area only, but it is easily conceived that the effect is more pronounced in volume. This suggests that polyhedra with large contribution of the anions to the volume are more compatible with cation substitution than those with small anion contribution.

 

 

However, it is noted that the actual bond states, although only in spherical average, are incorporated in the crystal radii which allow for such volumetric assessments (otherwise the radius of, for instance, O^2- would be invariant under different coordination). Consequently, the volumetric effect is not purely geometric. This point will be further examined in the following section in context with established relations between partition coefficients and ionic radii and the compression of polyhedral volumes in general. According to the proposed steric effect (Figure 2), minor and trace elements are expected to become less compatible in the rockforming minerals if VO is reduced and the effect is expected to be noticeable when the change is VO is abrupt, such as at the 410 and 670 km discontinuities.

 

The proposed effects are the potential consequence of the steric effect of the change in VO on trace element substitution but it can be quantified better by looking at element partitioning and polyhedral volumes. This is attempted in the following section.

 

4.2.1 Geochemical Implications – polyhedral volumes

The logarithm of partition coefficients of trace elements is correlated to the square of the difference between the ionic radii of the element substituted and the element substituting [18,19]. This relation is quite well established for the partitioning of traces between solids and melts of compounds with O^2- as constituent and has originally been shown to hold for simple halides [16-19]. The slope of the correlation RT × lnD = const r₀(r_i-r₀)² involves the Young modulus of the crystal site at which the substitution takes place [18, 19]. Here the partition coefficient D is taken as the ratio of the concentration of an element in the solid phase over that in a liquid or fluid phase in equilibrium.

Further, it is known that polyhedral volumes compress along a general correlation B_poly/750 = n/d³, where B_poly is the polyhedral bulk modulus in GPa, n the formal valence of the cation, and d the cation-anion distance in Å [20]. The Young modulus of the sites where substitution takes place is expected to exhibit the same or similar compression behaviour: The sum of the Young moduli along all stress directions is not identical to but dominated by the elastic tensor components that constitute the bulk modulus.

Here, an average polyhedral bulk modulus áB_polyñ is calculated as the sum of the basic polyhedral building blocks of pyrolite in upper mantle-, transition zone-, and lower mantle rock as

for the upper mantle, for the transition zone as

 

 

and for the lower mantle as

, all in GPa, which gives a general increase in polyhedral elastic strength with pressure for all the mantle regions, as expected, but also shows a drop of 7% at the UM-TZ boundary and a drop of almost 19 % at the TZ-LM boundary (Figure 3).

 

 

Figure 3. Added

Caption: Evolution of <B_poly>, the average value of the polyhedral volume for pyrolitic mantle with blue = upper-, black = lower mantle, red = transition zone. Equivalent to the volumetric fraction of O^2- as function of pressure, the average polyhedral volume increases with pressure but drops markedly at both major mantle discontinuities (indicated by arrows).

 

 

For trace elements that show no preference for sites this drop signalizes a marked reduction of compatibility between TZ and LM.

The softening of B_poly with increasing geothermal temperature is not considered here, where we are concerned with a principal crystal chemical effect, in particular right at the two major mantle discontinuities where temperature is nearly constant. The present assessment is far from a quantitative forward modeling of mantle minor- and trace-element distributions that requires more information than we currently have (see below) and that would also involve actual geotherms (globally and regionally).

The drop in <B_poly> between UM and TZ is to first order caused by the increase in the anion bond coordination and radius. The marked drop at the TZ-LM boundary results in part from the change in Si-bond coordination, in part from the further increase in radius and bond coordination of O^2-. This finding about the averaged polyhedral volume is equivalent to above observations about the effect of the change in VO, because the cause of the discontinuities is the same: coordination changes of cat- and anion as function of pressure.

Most trace elements are expected to have preferences for specific sites. In fact, most of the incompatible elements concentrate in clinopyroxene in the shallow and in garnet in the deeper upper mantle and in the transition zone, whereas in the lower mantle they take refuge in the crystal lattice of davemaoite [16,17]. In the light of pressure-dependent ionic radii, this observation is further quantified: We take the percentage of large polyhedral sites, which are known to host the geochemically most important incompatible elements such as the rare earths, the large ionic lithophiles, and the heavier high-field-strength elements for upper mantle, transition zone, and lower mantle as

Formula added.

 

 

For the TZ, neglecting 8% of six-fold coordinated Si in majorite. For the UM the same formula is used but wit the radii of two-fold coordinated O^2- and a gradual increase of the fraction of MgX from 0 to 0.3. For the LM we use:

 

 

(neglecting that 8% of Si is bound to O also in sixfold coordination in davemaoite).

 

Figure 4. Added

Caption: Approximate percentage of large polyhedral sites in upper mantle (UM), transition zone (TZ), and lower mantle (LM). As in Fig. 1 continental crust (CC) is given for reference. UM + TZ exhibit the largest proportion of large polyhedra due to the high phase proportion of garnet. The 670 km boundary implies a significant drop in large crystal sites available for hosting mantle-incompatible elements. Interestingly CC is intermediate between UM and LM, owed to the high abundance of free silica in the upper, and pyroxene in the lower CC (which are not further discriminated here), which tentatively is consistent with the proposed general trend: The CC exhibits a large variety of minerals enriched in elements that are less compatible with the feldspar, amphibole, or clinopyroxene structures whereas the upper mantle hosts the bulk of incompatible elements in garnet.

Formula added.

 

The numerators in these two formulas well indicate what is depicted in Figure 4: The transformation of garnet to bridgmanite removes nearly 3/4^th of the polyhedral volume in potential host phases for incompatible elements. Although Mg in bridgmanite has ten-fold bond coordination [9], it is known to be incompatible for rare earths, the large ionic lithophiles, and the heavier high-field-strength elements [16,17]. In comparison, davemaoite possesses a larger A-site and O with higher bond coordination and, therefore, larger crystal radius than in bridgmanite, which observations bring us back to the initial argument that was made about the steric effect of VO (Figure 2). The change in available large polyhedral sites leaves davemaoite as host phase among the rock-forming minerals of the LM. However, davemaoite has been found not to be compatible (that is: with D < 1) for Li, Rb, Cs, Ba, Nb, Ta, Hf [16,17]. Having ‘no place to go’ these elements may still be hosted in davemaoite or, as suggested above, are enriched in accessory phases. It is not possible to make strong predictions which phases this might be but it is suggested here that it might be post-spinel phases of the maohokite-chenmingite- or xieite-tschaunerite series, which have suitably large crystal sites and also show in part noticeable solubility of alkaline elements [21]. This observation also holds for liuite [21] although the A-site in this perovskite is not as large as in the post-spinel oxides but it suggests that perovskite-type accessory phases similar to those of the isolueshite-goldschmidtite series are also plausible host phases. Notably goldschmidtite has been found as inclusion in a mantle diamond [22].

It is important to note that any such concentration of minor and trace elements in accessories requires their mobilization and local enrichment through partial melts or fluids, which ties the question of mineral variety and trace-element distribution to the amount and dept to which chemically bound water occurs within the lower mantle."

 

 and the Conclusions were modified accordingly, adding a summarizing Table.

 

1. Treatment of Trace Elements:

The study focuses on the nine most abundant elements but makes conclusions about trace elements (Nb, Ta, REE, etc.). The author should explicitly address how the excluded 0.21% of elements (which include the very trace elements under discussion) influence the VO calculation, if at all. A supplemental calculation showing the sensitivity of VO to the inclusion of key trace elements would be helpful.

Response: The influence of the remaining 0.21 % of elements is really neglectable. The following statement with an actual estimate was added:

"Only the nine most abundant elements of the mantle are considered which leaves out 0.21 % of the total element abundances and ionic volumes are normalized to those 99.79 %. The remaining 0.21 % of elements contribute to about 0.22 % of the ionic volume, well within the uncertainty of the volume assessment.  "

 

1. Observational or Experimental Support:

The hypothesis that accessory minerals form in the lower mantle is speculative. Both the multi-anvil  and DAC techiniques can easily cover the top lower mantle conditions. The author should discuss whether there is any experimental evidence that could support or refute this idea. For instance, are there high-pressure experiments showing saturation of Nb- or Zr-rich phases in lower mantle assemblages?

Response: Such experiments have not been conducted but there are observations (which ultimately counts more – as long as we know how to interpret them!). There is an additional aspect: Experiments, say, on MORB or pyrolite enriched in Nb or Zr by factor 10 or 100 may not yield separate phases in diamond cell experiments - perhaps not even in LVPs - because the surface free energy of accordingly very small, isolated grains is high and disfavours separation into free phases. This effect is observed in nature too: In pegmatites or carbonatites Nb- or Zr-rich phases occur usually as isolated grains within kg of rock, not as finely disseminated nano-grains everywhere (which is a huge issue in obtaining their average concentrations in such rocks).

Experiments should be done but the pathway should be a different one: a) Figure out which silicate/oxide phases rich in such elements form at LM pressures and temperatures, b) diffusion couple experiments of those phases combined with bridgmanite and davemaoite or c) mapping of the solid solution systems. This calls for an extensive project.

Two sections have been added in response to your comment:

To the Discussion:

"However, davemaoite has been found not to be compatible (that is: with D < 1) for Li, Rb, Cs, Ba, Nb, Ta, Hf [16,17]. Having ‘no place to go’ these elements may still be hosted in davemaoite or, as suggested above, are enriched in accessory phases. It is not possible to make strong predictions which phases this might be but it is suggested here that it might be post-spinel phases of the maohokite-chenmingite- or xieite-tschaunerite series, which have suitably large crystal sites and also show in part noticeable solubility of alkaline elements [21]. This observation also holds for liuite [21] although the A-site in this perovskite is not as large as in the post-spinel oxides but it suggests that perovskite-type accessory phases similar to those of the isolueshite-goldschmidtite series are also plausible host phases. Notably goldschmidtite has been found as inclusion in a mantle diamond [22].

It is important to note that any such concentration of minor and trace elements in accessories requires their mobilization and local enrichment through partial melts or fluids, which ties the question of mineral variety and trace-element distribution to the amount and dept to which chemically bound water occurs within the lower mantle. "

To Conclusions:  A Table that lists observed (!) accessory phases in mantle rocks and diamonds (and it is admitted that for the latter we have not yet a clear understanding what environments within the mantle they actually represent but the present paper intends to stimulate research with a broader perspective than assessing minor element effects on sound velocities of rock-forming minerals).

 

3. Mineralogical Predictions:

The list of possible accessory phases (sulfides, carbides, nitrides, etc.) is reasonable but very general. The author could narrow this down by discussing which phases are thermodynamically stable under lower mantle conditions and compatible with the geochemical behavior of the elements in question (e.g., Nb-Ta fractionation)

 

Response: Right! See above response. A list of candidate minerals has been added to the Discussion. Note, that their occurrences indicate stability under some conditions, not for the mantle in general. The question really is how much of local, regional, or global concentrations into accessories we have (- or none?). Presently, nobody can honestly state which Nb-Ta- hosting phases are stable under what conditions in the mantle. Compression of, say, ixiolite or tapiolite to 50 GPa and monitoring its potential phase transitions does not imply that these phases occur anywhere in the mantle (still, such experiments should be done!). Before assessing stability from thermodynamic calculations we need first of all know which phases occur and assess their properties. None of that is done for anything but the rock-forming minerals with little chemical variation (CMAS/CMFS)

 

Minors:

1. The interpolation of O^2- radii at low pressures (Table 1) is pragmatic, but the method should be briefly justified (e.g., linear vs. power-law interpolation).

Response: Good point. The following section was added to Methods:

'The interpolation is based on the assumption that the power of the pressure-dependent radius of O^2- between 0 and 5 GPa is intermittent between the previously reported ones and unity, warranting a continuous and monotonous contraction of the radius.

Generally, the ionic volume as stoichiometric sum of the cubes of the pressure-dependent crystal radii of the constituent ions [11] correlate with the difference of their pressure-dependent total ionization potentials [12] through a Morse-type functional relation (e.g. in [13]) which matches expectations from the general compression behaviour of solids over large ranges of pressure [14]. Hence, the linear compression of cations and the power-law pressure-dependence of anions appears to be intrinsic to compression of ionic solids while it does not directly explain the difference in cat- and anion compression. Upon compression overlap of bond orbitals increases and bonds generally become more covalent [15]. With the electron density around the anion, as the more electronegative ion, decreasing in this process more strongly than that around the cation the difference between cat- and anion compression over the pressure range of the Earth’s mantle [9] can be conceived as a series expansion in pressure of electron density along bond direction where the cations compress linearly and the anions compress with negative power > 1."

 

1. Reference formatting should be checked for consistency: some all the first character is capitalized in the title (such as Tschauner, 2024). Some only the first character of the first word is capitalized (such as Corgne et al., 2005).

Response: Thank you for catching this! I checked and adjusted reference formating.

Reviewer 2 Report

Comments and Suggestions for Authors

    The author revisits V.M. Goldschmidt’s classical geochemical concept—that Earth’s silicate mantle can be viewed as a packing of O²⁻ ions with interstitial cations—by applying modern mantle composition models and pressure-dependent crystal radii. He systematically analyzes the volume fraction of O²⁻ (VO) as a function of depth and compares its behavior across the continental crust, upper mantle, transition zone, and lower mantle. His study suggests that a significant amount of accessory minerals containing less-common elements, which are undetectable by seismic observations, may exist beneath the mantle transition zone and the lower mantle (TZ-LM) boundary. This work provides important insights into understanding the differences in the occurrence forms of trace elements across various regions of the mantle.

I would like to raise two points for the author's consideration:

1. The logical foundation of this paper rests on the assumption that there exists a significant chemical composition difference between the crust and the upper mantle as a whole, while the chemical composition (elemental abundances) of the upper mantle, transition zone, and lower mantle is generally consistent, meaning no substantial differences exist. Therefore, the variations in VO among the upper mantle, transition zone, and lower mantle are unrelated to overall chemical composition differences between these regions. Although many early mantle chemical composition models have defaulted to this assumption (as reflected in the cited references), and it is widely accepted among researchers studying deep Earth composition, there is, in fact, no definitive or irrefutable evidence to conclusively prove this point. While lower-mantle mineral inclusions have been found in deep-source diamond inclusions, compared to the direct access we have to upper-mantle rock samples in nature, these inclusions offer limited constraints on the overall chemical composition of the transition zone and lower mantle. Indeed, high-pressure and high-temperature studies support that the 410 km, 520 km, and 660 km discontinuities controlled by phase transitions of major constituent minerals, but this does not rule out the possibility of differences in elemental abundances among the upper mantle, transition zone, and lower mantle. I simply invite the author to provide his perspective on this issue, though any response will not affect the assessment of the paper's suitability for publication.
2. The author suggests that the mineralogical composition is particularly rich at the TZ–LM boundary and within the upper quarter of the lower mantle, where less common elements may become components of accessory phases. These accessory phases would not produce observable seismic features but could influence mantle geochemical signatures through element partitioning. Could the author further speculate on whether there might be other methods or approaches to validate this conclusion, given that seismic observations cannot confirm the existence of such accessory minerals? Again, I merely invite the author to share his views on this matter, and the response will not impact the evaluation of the paper's publishability.

Author Response

The author revisits V.M. Goldschmidt’s classical geochemical concept—that Earth’s silicate mantle can be viewed as a packing of O²⁻ ions with interstitial cations—by applying modern mantle composition models and pressure-dependent crystal radii. He systematically analyzes the volume fraction of O²⁻ (VO) as a function of depth and compares its behavior across the continental crust, upper mantle, transition zone, and lower mantle. His study suggests that a significant amount of accessory minerals containing less-common elements, which are undetectable by seismic observations, may exist beneath the mantle transition zone and the lower mantle (TZ-LM) boundary. This work provides important insights into understanding the differences in the occurrence forms of trace elements across various regions of the mantle.

 

Response: Thank you for the positive comment and the helpful suggestions!

 

I would like to raise two points for the author's consideration:

1. The logical foundation of this paper rests on the assumption that there exists a significant chemical composition difference between the crust and the upper mantle as a whole, while the chemical composition (elemental abundances) of the upper mantle, transition zone, and lower mantle is generally consistent, meaning no substantial differences exist. Therefore, the variations in VO among the upper mantle, transition zone, and lower mantle are unrelated to overall chemical composition differences between these regions. Although many early mantle chemical composition models have defaulted to this assumption (as reflected in the cited references), and it is widely accepted among researchers studying deep Earth composition, there is, in fact, no definitive or irrefutable evidence to conclusively prove this point. While lower-mantle mineral inclusions have been found in deep-source diamond inclusions, compared to the direct access we have to upper-mantle rock samples in nature, these inclusions offer limited constraints on the overall chemical composition of the transition zone and lower mantle. Indeed, high-pressure and high-temperature studies support that the 410 km, 520 km, and 660 km discontinuities controlled by phase transitions of major constituent minerals, but this does not rule out the possibility of differences in elemental abundances among the upper mantle, transition zone, and lower mantle. I simply invite the author to provide his perspective on this issue, though any response will not affect the assessment of the paper's suitability for publication.

 

Response: This point is well chosen. I have added a complementary calculation of VO for the enstatite-chondrite model by Javoy et al. (2010) – ref. 6 in the revised manuscript – because it gives the largest deviation of upper- and lower mantle composition. The overall conclusions hold with that model as well but Javoy’s model provides a bracket for the quantitative effect of potential large scale chemical differentiation in the mantle. The following sections were added:

To Methods:

"In this work, mantle composition is based on the pyrolite model in [3] and an enstatite-chondrite model [6] that predicts marked differences between upper- and lower mantle composition."

 

To Discussion:

."VO as function of depth is shown for the pyrolitic mantle composition from [3] and for an enstatite chondrite model of Earth ([6], henceforth: EC model) that reports a the markedly different LM composition.

Figure 1 shows the pressure-dependence of VO for all three regions of the mantle. Two principal observations can be made: 1) VO increases with depth, 2) at each of the major mantle discontinuities VO drops markedly.

Figure 1: Modified.

Caption: Dependence of the fractional volume of O^2- in Earth as function of depth. Red dot: Continental crust in average [6], UM = upper mantle, TZ = transition zone, LM = lower mantle. Dark colours based on mantle composition from [3], bright ones from [13]. Vertical bars indicate uncertainties.

The reduction of VO at the two major mantle discontinuities at 410- and 670 km is much more pronounced than that between CC and UM, despite the equal bulk composition of UM, TZ, and LM, or, with the EC model [6] for the LM even so more. Thus, the changes in coordination, that is: chemical bonding, at each of these discontinuities, dominates over a change in bulk rock composition as distinct as that between CC and UM. Yet, Goldschmidt’s statement about the dominance of VO over the volumes of all cations [1] is quite well confirmed for BSE over its whole range of depth of the mantle.

4. Discussion

More quantitatively, the following observations are made:

91. VO, the volume fraction of O^2- ions of the total ionic volume of BSE, increases monotonously with pressure for each of the three mantle zones, such that in extrapolation from the top to the bottom of the whole mantle VO gains by 6-7% to 91.0 ±0% (Figure 1).
92. VO drops at the UM-TZ boundary by between 2.6 and 4.7 % and at the TZ-LM boundary by another 2.5 -7.2 %. These values compare to a 5.1 and 9.6 % increase in rock density at the 420 and 670 km discontinuities [4]. Thus, the reduction of VO is a substantial component of the densification at both discontinuities but at 670 km the change in cation coordination accounts for at least a third of the density increase. The enstatite chondrite model [6] remains within uncertainties for UM and TZ, but for the LM it gives values of VO slightly higher than the initial assessment of uncertainties which, therefore are adjusted to encompass the EC model.
93. The comparison between the results for pyrolitic and enstatite chondritic mantle shows that differences between upper and lower mantle affect VO, which, however, does not respond sensitively to compositional differences less marked than those between these two models, at least not with the given uncertainties."

 

1. The author suggests that the mineralogical composition is particularly rich at the TZ–LM boundary and within the upper quarter of the lower mantle, where less common elements may become components of accessory phases. These accessory phases would not produce observable seismic features but could influence mantle geochemical signatures through element partitioning. Could the author further speculate on whether there might be other methods or approaches to validate this conclusion, given that seismic observations cannot confirm the existence of such accessory minerals? Again, I merely invite the author to share his views on this matter, and the response will not impact the evaluation of the paper's publishability.

Response: This is also an important point, also made by another reviewer. Trace-/isotope-geochemical data are one source of information – the issue is the interpretation of these data: The come from igneous rocks such as OIBs or from xenoliths which both deviate from a potential deep source composition – there is much work to do. There are inclusions in diamonds, but they may not be representative over geochemically relevant volumes (they may reflect local conditions during the growth of the very diamond – we need more statistics). In order to respond to this point, I give a list of candidate minerals in the Discussion and added a tabular overview to the Conclusions that lists accessory phases that actually have been observed in xenoliths or as inclusions in diamond (excluding inferred higher pressure precursors of some of the inclusions, without prejudice). The following sections were added:

To the Discussion:

"However, davemaoite has been found not to be compatible (that is: with D < 1) for Li, Rb, Cs, Ba, Nb, Ta, Hf [16,17]. Having ‘no place to go’ these elements may still be hosted in davemaoite or, as suggested above, are enriched in accessory phases. It is not possible to make strong predictions which phases this might be but it is suggested here that it might be post-spinel phases of the maohokite-chenmingite- or xieite-tschaunerite series, which have suitably large crystal sites and also show in part noticeable solubility of alkaline elements [21]. This observation also holds for liuite [21] although the A-site in this perovskite is not as large as in the post-spinel oxides but it suggests that perovskite-type accessory phases similar to those of the isolueshite-goldschmidtite series are also plausible host phases. Notably goldschmidtite has been found as inclusion in a mantle diamond [22].

It is important to note that any such concentration of minor and trace elements in accessories requires their mobilization and local enrichment through partial melts or fluids, which ties the question of mineral variety and trace-element distribution to the amount and dept to which chemically bound water occurs within the lower mantle."

To Conclusions:

"A Table that lists observed (!) accessory phases in mantle rocks and diamonds (and it is admitted that for the latter we have not yet a clear understanding what environments within the mantle they actually represent but the present paper intends to stimulate research with a broader perspective than assessing minor element effects on sound velocities of rock-forming minerals)."

Reviewer 3 Report

Comments and Suggestions for Authors

The manuscript is very interesting for the geological community  and potentially for a broader audience. The topic is well developed and looks from  a new  viewpoint  to the mineralogy of the Earth mantle outlining a possible distribution of elements in high pressure mineral phases.

In my opinion this approach could also be interesting to understand the behaviour of materials. The manuscript is well written and clear.

Please check the Angstrom symbols at line 89.

In my opinion it deserves to be published as it is

 

Author Response

The manuscript is very interesting for the geological community  and potentially for a broader audience. The topic is well developed and looks from  a new  viewpoint  to the mineralogy of the Earth mantle outlining a possible distribution of elements in high pressure mineral phases.
In my opinion this approach could also be interesting to understand the behaviour of materials. The manuscript is well written and clear.

Response: Thank you for the positive, supportive comment!

 

Please check the Angstrom symbols at line 89.

Response: Thank you for catching this – it’s corrected!

In my opinion it deserves to be published as it is.

 

Response: Thank you for your positive comments!

Reviewer 4 Report

Comments and Suggestions for Authors

This is a very interesting manuscript that reports the occurrence of minerals in the lower mantle and their suggested elemental composition, based on the updated list of pressure-dependent crystal radii. I believe this is a great contribution that deserves to be published, as it addresses many important questions about deep mantle mineralogy. I have a few general questions and comments:

1. How were the uncertainties assessed? The VO uncertainties for UM and TZ, as shown in Figure 1, are around 1%, while the error bars for LM appears to be twice as long. Do the uncertainties vary with depth? Perhaps the confidence bands could be represented as shaded areas around the UM, TZ, and LM curves.

2. How do the pressure-dependent crystal radii determined from experimental data compare to the radii based on theoretically predicted crystal structures for typical deep mantle minerals?

3. What is the influence of temperature on the crystal radii, and was this considered when drawing conclusions about the high-pressure-high-temperature conditions of the lower mantle?

Author Response

This is a very interesting manuscript that reports the occurrence of minerals in the lower mantle and their suggested elemental composition, based on the updated list of pressure-dependent crystal radii. I believe this is a great contribution that deserves to be published, as it addresses many important questions about deep mantle mineralogy.

Response: Thank you for the supportive, encouraging comment!

 

 I have a few general questions and comments:

1. How were the uncertainties assessed? The VO uncertainties for UM and TZ, as shown in Figure 1, are around 1%, while the error bars for LM appears to be twice as long. Do the uncertainties vary with depth? Perhaps the confidence bands could be represented as shaded areas around the UM, TZ, and LM curves.

Response: Yes, this point was not sufficiently clear in the original manuscript. 1bar radii give volume uncertainties of ~ 1% but the uncertainties of their pressure-dependencies propagate to a total of ~ 5%. In addition, the margins change with depth because the volume contributions change not strictly linearly. Following a suggestion by another reviewer I added the enstatite-chondrite model by Javoy et al. (2010), ref. 6 in the revised paper, to the calculations of VO. This model predicts a markedly different lower mantle composition. The uncertainties in Figure 1 has been changed to a) give full error propagation at the lowest depth of each region (UM,TZ, LM) b) incorporate Javoy’s model – this model is not an uncertainty but it defines a margin, which is actually better for geochemical/geophysical modeling than uncertainties of starting parameters. The Discussion has been modified as follows:

" VO as function of depth is shown for the pyrolitic mantle composition from [3] and for an enstatite chondrite model of Earth ([6], henceforth: EC model) that reports a the markedly different LM composition.

Figure 1 shows the pressure-dependence of VO for all three regions of the mantle. Two principal observations can be made: 1) VO increases with depth, 2) at each of the major mantle discontinuities VO drops markedly.

Figure 1. Modified.

Caption: Dependence of the fractional volume of O^2- in Earth as function of depth. Red dot: Continental crust in average [6], UM = upper mantle, TZ = transition zone, LM = lower mantle. Dark colours based on mantle composition from [3], bright ones from [13]. Vertical bars indicate uncertainties.

The reduction of VO at the two major mantle discontinuities at 410- and 670 km is much more pronounced than that between CC and UM, despite the equal bulk composition of UM, TZ, and LM, or, with the EC model [6] for the LM even so more. Thus, the changes in coordination, that is: chemical bonding, at each of these discontinuities, dominates over a change in bulk rock composition as distinct as that between CC and UM. Yet, Goldschmidt’s statement about the dominance of VO over the volumes of all cations [1] is quite well confirmed for BSE over its whole range of depth of the mantle.

4. Discussion

More quantitatively, the following observations are made:

91. VO, the volume fraction of O^2- ions of the total ionic volume of BSE, increases monotonously with pressure for each of the three mantle zones, such that in extrapolation from the top to the bottom of the whole mantle VO gains by 6-7% to 91.0 ±0% (Figure 1).
92. VO drops at the UM-TZ boundary by between 2.6 and 4.7 % and at the TZ-LM boundary by another 2.5 -7.2 %. These values compare to a 5.1 and 9.6 % increase in rock density at the 420 and 670 km discontinuities [4]. Thus, the reduction of VO is a substantial component of the densification at both discontinuities but at 670 km the change in cation coordination accounts for at least a third of the density increase. The enstatite chondrite model [6] remains within uncertainties for UM and TZ, but for the LM it gives values of VO slightly higher than the initial assessment of uncertainties which, therefore are adjusted to encompass the EC model.
93. The comparison between the results for pyrolitic and enstatite chondritic mantle shows that differences between upper and lower mantle affect VO, which, however, does not respond sensitively to compositional differences less marked than those between these two models, at least not with the given uncertainties."

 

2. How do the pressure-dependent crystal radii determined from experimental data compare to the radii based on theoretically predicted crystal structures for typical deep mantle minerals?

Response: i assume you refer to a Baader-charge separation of ab initio calculated crystal structures.

There is a nice study by the late V. Gibbs et al. where this was done and that matches the empirical pressure-dependent radii (reference is given in this manuscript, see also discussion in https://doi.org/10.3390/solids4030015).  In fact, derivation of crystal radii (ambient or at any pressure) require a fiducial value, which for Goldschmidt were the values of O2- and F- from Wasastjerna’s work (Comm. Phys.-Math., Soc. Sci. Fenn. 1 (38), 1). Following his footsteps I used O2-radii from a Baader charge separation of ab initio calculated silica phases and corrected for the systematic offset of these radii at 1bar from Shannon’s. The offset comes from the general overestimation of volume in GGA-based ab initio calculations. To my surprise it turned out that the ab initio calculation based pressure-dependence of O2- cannot be quite correct – based on testing it for simple known structures at various pressures: MgO, stishovite, akimotoite, bridgmanite (endmember) etc. over several 10 to 100 GPa. This is described and discussed in more detail and with references  in https://doi.org/10.3390/geosciences12060246. Whether this is a general issue (match at low pressure - deviation over several 10 - 100 GPa) or specific to the references that I used i cannot tell.

Alternatively, one could use computed interatomic distances as one uses empirical ones, but either one uses the empirical P-dependent O2- radii as fiducial - then the calculational results are no longer an independent set, or the Baader approach - but that does not give good results for pressures in the range of 10 - 100 GPa, at least not in all cases.

In sum: the systematic volume offsets from ab initio calculations carry over to radii that are derived from interatomic distances – this can be corrected. However, a Baader charge separation is a tedious procedure. It would definitely be worth conducting for ultrahigh pressure phases where no empirical structure analyses of high quality are possible, e.g. postperovskite.

A section has been added to Methods that shows consistency between the observed P-dependent radii and ab initio (!) calculated P-dependent electronegativities and potential-based equations of state:

"The interpolation is based on the assumption that the power of the pressure-dependent radius of O^2- between 0 and 5 GPa is intermittent between the previously reported ones and unity, warranting a continuous and monotonous contraction of the radius.

Generally, the ionic volume as stoichiometric sum of the cubes of the pressure-dependent crystal radii of the constituent ions [11] correlate with the difference of their pressure-dependent total ionization potentials [12] through a Morse-type functional relation (e.g. in [13]) which matches expectations from the general compression behaviour of solids over large ranges of pressure [14]. Hence, the linear compression of cations and the power-law pressure-dependence of anions appears to be intrinsic to compression of ionic solids while it does not directly explain the difference in cat- and anion compression. Upon compression overlap of bond orbitals increases and bonds generally become more covalent [15]. With the electron density around the anion, as the more electronegative ion, decreasing in this process with pressure more strongly than that around the cation the difference between cat- and anion compression over the pressure range of the Earth’s mantle [9] can be conceived as a series expansion in pressure of electron density along bond direction where the cations compress linearly and the anions compress with negative power > 1."

 

3. What is the influence of temperature on the crystal radii, and was this considered when drawing conclusions about the high-pressure-high-temperature conditions of the lower mantle?

Response: Right! There is a very nice paper about this effect by Hazen and Prewitt: American Mineralogist, 62,309, 1977. Since geothermal evolution is rather smooth and slightly superadiabatic (in PREM average), the correction for the temperature-effect is gradual and of 2^nd order compared to the effect of pressure. In particular, it does not change the sudden drop of VO at the mantle discontinuities. In the revised manuscript a statement has been added to the paper in the Discussion section (in relation to polyhedral volumes and their pressure-dependence). This statement is part of a newly added section that places VO into context of trace element partitioning and available polyhedral sites – and their changes with pressure:

"The softening of B_poly with increasing geothermal temperature is not considered here, where we are concerned with a principal crystal chemical effect, in particular right at the two major mantle discontinuities where temperature is nearly constant. The present assessment is far from a quantitative forward modeling of mantle minor- and trace-element distributions that requires more information than we currently have (see below) and that would also involve actual geotherms (globally and regionally)."