Pauling's Rule #1 (Radius Ratio) would suggest that Mg2+ should not be happy in tetrahedral coordination. Assuming that's the case, are there any thoughts on spinel stability given this situation?
Thanks.Steve Feldman

On Friday, February 2, 2024 at 11:39:17 AM EST, Barry Bickmore via MSA-talk <msa-talk@minlists.org> wrote:  

In case anyone is interested, a few years ago we came up with a model to estimate bond dissociation energies based on 1) bond valence, 2) bond ionic character (using Pauling’s formula that depends on the difference in atomic electronegativities), and 3) bond covalency vs. metallicity (estimated using the average electronegativity of the two bonded atoms).  The model wasn’t all that accurate, but it was great for hand-waving about periodic trends.

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On Feb 1, 2024, at 2:50 PM, Hummer, Daniel R daniel.hummer@siu.edu wrote:

I think Barry is right on the nose – going back to Pauling’s rules, we can even predict that ionic bonds involving more highly charged ions in lower coordination numbers are going to be particularly strong and resistant to cleaving, and this is what we exclusively find in the spinel structure (and also minerals like quartz, rutile, corundum, Al-oxyhdroxides, etc.).  Dan  From: Barry Bickmore bbickmore1970@gmail.com 
Sent: Thursday, February 1, 2024 2:06 PM
To: Denton Ebel debel@amnh.org
Cc: Ayers, John C john.c.ayers@Vanderbilt.Edu; Pilar Lecumberri-Sanchez lecumber@ualberta.ca; MSA-talk@minlists.org; Hummer, Daniel R daniel.hummer@siu.edu
Subject: Re: [MSA-talk] Polymerization, composition, melting point and weathering of silicates  
[EXTERNAL EMAIL ALERT]: Verify sender before opening links or attachments.
Hi Denton,  I will take a stab at this.  Spinel has a sort of framework structure of Al octahedra. The Al-O bonds would be relatively strong, and Al-oxyhydroxides tend to be a lot of what’s left over after really intense weathering of soils.  In the gaps of the octahedral framework you have Mg in tetrahedral coordination, so the Mg-O bonds would be stronger than those in phases where Mg is 6-coordinated.  
Barry Bickmore
Professor of Geological Sciences
Brigham Young University

On Feb 1, 2024, at 12:00 PM, Denton Ebel via MSA-talk msa-talk@minlists.org wrote:  Thanks Pilar, John, Dan - Fascinating discussion. In my world, it is the spinel family that is of great interest. 1) In CV chondrites e.g. Allende, the MgAl2O4 in CAIs retains its O-16 rich character but the melilite, "fassaites" and anorthite equililibrate with the parent body. This effect is subdued in the less-hydrated CV-reduced (e.g. Vigarano) class (e.g., MacPherson 2014). 2) In the K-Pg boundary clay, the surviving condensates from the impact plume are magnesio-wustite spinels with wt% levels of NiO, the rest of the spherules were Ca-rich glass which is long altered everywhere (Ebel & Grossman 2005). 3) In fossil meteorites in Swedish quarries ~480 Ma we see the L chondrite textures, but the only surviving minerals are... spinels! And we can then tell the L typology from Cr-Mn isotope systematics in spinel (Alwmark & Schmitz 2009; Heck et al. 2010). Ideas about why spinels are so persistent?ThanksDreferences:MacPherson G.J. (2014) Calcium-aluminum-rich inclusions in chondritic meteorites. In Meteorites, Comets and Planets (A.M. Davis, ed.), pp. 201-246. Volume 1 of Treatise on Geochemistry, (H.D. Holland and K.K. Turekian, eds.), Elsevier. 10 volumes.Ebel, D.S., and L. Grossman (2005) Spinel-bearing spherules condensed from the Chicxulub impact-vapor plume. Geology 33: 293-296.Alwmark, C. and Schmitz, B. (2009) The Origin of the Brunflo Fossil Meteorite and Extraterrestrial Chromite in Mid-Ordovician Limestone from the Gärde Quarry (Jämtland, Central Sweden), Meteoritics and Planetary Science, v. 44, p. 95-106.Heck, P. R., Ushikubo, T., Schmitz, B., Kita, N. T., Spicuzza, M. J., and Valley, J. W. (2010) A single asteroidal Source for extraterrestrial Ordovician chromite grains from Sweden and China: High-precision oxygen three-isotope SIMS analysis,Geochimica et Cosmochimica Acta, v. 74(2), p. 497-509.---------------------------------------------------------------Denton S. Ebel, Curator, Dept. of Earth and Planetary Sciences
Chair, Division of Physical Sciences, American Museum of Natural History 200 Central Park West, New York, NY  10024(212) 769-5381     http://research.amnh.org/~debelspace show VI: https://www.amnh.org/exhibitions/permanent/hayden-planetarium/worlds-beyond-earth“Historically, pandemics have forced humans to break with the past and imagine their world anew. This one is no different. It is a portal, a gateway between one world and the next. We can choose to walk through it, dragging the carcasses of our prejudice and hatred, our avarice, our data banks and dead ideas, our dead rivers and smoky skies behind us. Or we can walk through lightly, with little luggage, ready to imagine another world. And ready to fight for it.” -- Arundhati RoyFrom: Hummer, Daniel R via MSA-talk msa-talk@minlists.org
Sent: Thursday, February 1, 2024 11:18 AM
To: Ayers, John C john.c.ayers@Vanderbilt.Edu; Pilar Lecumberri-Sanchez lecumber@ualberta.ca; MSA-talk@minlists.org msa-talk@minlists.org
Subject: [MSA-talk] Re: Polymerization, composition, melting point and weathering of silicates EXTERNAL SENDER  Pilar and friends, This is a fantastic question, and really gets one thinking about the underlying behavior of the bonds that hold together our favorite Earth materials. Here is my take: One important difference is that olivine and other mafic minerals contain Fe2+, which is susceptible to oxidation in the high fO2 environment of Earth’s surface. That difference basically boils down to electrochemistry. But for a moment, let’s ignore the redox sensitivity of Fe, because I think there’s an even more fundamental concept at work…. the unique chemistry of water and how it reacts to ionic vs. covalent bonds. Olivine is composed of primarily ionic bonds between cations and anions, and the more covalent-natured Si-O bonds don’t play a very large role because the silica component is unpolymerized (i.e., the SiO4 units just behave as their own “ions”). The highly polar water molecule is therefore able to rip cations and anions away from each other very effectively via electrostatic attraction. Whereas, in the absence of water, it takes a LOT of heat to overcome the attraction of the ionic bonds, because you’re trying to do it by brute force (rather than with the help of such a highly effective molecular scalpel). Contrast this with K-spar and other network silicates, which are held together mostly by bonds with much more covalent nature, where electrons sit directly between the atoms. In the absence of water, these bonds will more easily get “mushy” (like a limp rope) when heated and soften the silica framework to the point where it can squish and slide, forming a melt (where bonds are weakened but still present). You don’t even have to break all the bonds, you just need to break enough for bond angles to slide and twist around… just enough to soften the silica network. But at room temperature, even in the presence of water, the covalent bonds will keep Si and O atoms tethered to each other tightly because they don’t care whether the water molecular is polar or not. There is not enough separation of charge for those bonds to be susceptible to the + or – end of a H2O molecule, so the Si-O framework just sits there, and at best you get a little bit of incongruent dissolution of components like K and Na, as pointed out by John Ayers. Both olivine and K-spar could probably sit happily in equilibrium with air for millions of years with very little change, but water will make a tremendous difference. So in my view, we need to think beyond just “strong” vs. “weak” bonds, we also have to think about how different the nature of the bonding is at each end of Bowen’s reaction series. Each style of bonding reacts very differently to heat vs. reactive molecules like H2O and O2, and I suspect that’s the key to understanding these trends on a molecular level. Of course, there is sure to be much more nuanced thermodynamics at play than what I’ve outlined here, but hopefully this is a useful way to frame the issue from a broad perspective. Very interested to hear other thoughts on this. Best,Dan   From: Ayers, John C via MSA-talk msa-talk@minlists.org 
Sent: Wednesday, January 31, 2024 9:16 AM
To: Pilar Lecumberri-Sanchez lecumber@ualberta.ca; msa-talk@minlists.org
Subject: [MSA-talk] Re: Polymerization, composition, melting point and weathering of silicates [EXTERNAL EMAIL ALERT]: Verify sender before opening links or attachments.When I teach this material to my students, I do not use bond strengths to explain the stabilities of the minerals, but rather the conditions at which they formed. Minerals like olivine that are stable in the mantle are less likely to be stable at the Earth’s surface. This is due to differences in temperature, pressure, oxygen fugacity, and water activity/availability.  Minerals like K-feldspar that crystallize at the lowest temperatures in Bowen’s reaction series can be stable in equilibrium with water, but only after the K-feldspar dissolves incongruently to form clays and the fluid composition evolves until it becomes saturated in K-feldspar. Hope this is helpful. Professor John C. AyersDept. of Earth & Environmental Sciences
Vanderbilt University
PMB 351805
2301 Vanderbilt Place
Nashville, TN 37235-1805
Tel 1-615-973-1879https://my.vanderbilt.edu/johncayers   From: Pilar Lecumberri-Sanchez via MSA-talk msa-talk@minlists.org 
Sent: Tuesday, January 30, 2024 10:32 PM
To: msa-talk@minlists.org
Subject: [MSA-talk] Polymerization, composition, melting point and weathering of silicates Hi all, In explaining silicates and the Bowen reaction series in class and I have realized that I don’t understand how this works. I can sort of figure out melting behavior, but then I struggle with weathering behavior. I think of melting temperature of a mineral as a function of the strength of the weakest bonds present in a mineral (what holds them together) and the repulsion between the cations occupying their sites (what pulls them apart). Because the bonds formed between Fe/Mg-O are shorter and can have lower coordination numbers than those formed between Na/K-O, it makes sense that nesosilicates have stronger “weakest” bonds than tectosilicates and melt at higher temperatures. In addition, with increasing polymerization, more silicons are forced into close proximity to each other causing repulsion between the tetrahedrally occupied sites. Therefore more polymerized silicates will have internal repulsion forces that will further facilitate bond breakage (again lower melting temperatures). Here comes where I struggle. If the strength of the weakest bond is highest in nesosilicates, why do nesosilicates minerals weather easier than felsic ones (i.e., why are nesosilicates further from theromdynamic equilibrium at room temperatures than tectosilicates)? I know that we are now putting the minerals in a different solvent and that phase equilibrium predicts that forsterite is not stable at environmental conditions in the presence of water, the question is why is that more so for forsterite than for K-feldspars. Since dissolution into water also requires bond breakage intuitively it would make sense that olivine, which has stronger bonds and less internal repulsion forces, would survive better than feldspar. I can try to think about it in terms of the bonds formed by the elements in aqueous solution and whether the way in which sodium dissolves in pure water is more competitive than magnesium, but it is not clear to me that that would be the case.  So here is my question, why at the atomic structure level and not just from a descriptive perspective is forsterite more readily weathered than K-feldspar given that the bonds in olivine are significantly stronger and the internal repulsion forces between atoms weaker? Thank you everyone, Pilar ————————————————
Pilar Lecumberri-SanchezAssociate ProfessorDept. of Earth & Atmospheric Sciences
1-26 Earth Sciences Building
University of Alberta
Edmonton, Alberta, T6G 2E3Phone: 780-492-5071

https://cms.eas.ualberta.ca/lecumberri/
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Fair point(s), Barry.  I also note that determining ionic radii is like trying catch a moving target.Cheers.
Steve

On Friday, February 2, 2024 at 02:41:23 PM EST, Barry Bickmore <bbickmore1970@gmail.com> wrote:  

On Feb 2, 2024, at 9:46 AM, Steve ekozoe@yahoo.com wrote:
Pauling's Rule #1 (Radius Ratio) would suggest that Mg2+ should not be happy in tetrahedral coordination. Assuming that's the case, are there any thoughts on spinel stability given this situation?
Thanks.Steve Feldman

Hi Steve,
Here are a few arguments on this point.

1. Spinel is formed in metamorphic environments, so relatively high pressure. Sometimes that forces cations into coordination environments they wouldn’t adopt if they formed at STP. A classic example of this is the high-pressure SiO2 polymorph, stishovite, which has 6-coordinated Si. You can pretty much just assume Si will be 4-coordinated in almost any other circumstance.
2. If you get a good table of ionic radii, it will have different radii for different coordination numbers. I typically use the one on p. 44 of Klein and Dutrow’s Manual of Mineralogy, 23rd ed., which says that the ionic radius of Mg(2+) is 0.57 in 4-coordination, and 0.72 in 6-coordination. In spinel, the O(2-) is 4-coordinated, so its ionic radius is listed as 1.38 Å. This means that the radius ratio of Mg/O in spinel is 0.413, which is slightly below the critical radius ratio for 6-coordination (0.414).  TADA!!!! Pauling’s First Rule “works” in this situation, “predicting” the coordination number as long as you already know the coordination number. The key to understanding this is that the rationale for the 1st Rule is all about treating atoms as if they are hard spheres, but in reality they are squishy, so to make the rule work more consistently we have to make the number representing the “radius” squishy, as well.
3. If I stare at Fig. 5b in that paper I linked before, taking into account that the fraction ionic character of Mg-O bonds would be about 0.68, I can convince myself that it is more energetically favorable for Mg to be 6-coordinated (bond valence = 0.33), but it actually doesn’t take much of a hit if it’s 4-coordinated (bond valence = 0.5).  The energetics of the individual bonds isn’t the only factor in play, however.  In order to adopt a particular coordination number, the cation needs bonds of a particular length (assuming a regular polyhedron) to satisfy the valence of the cation, and while a particular length (or bond valence) may be energetically favorable, adopting such a configuration might force the anions too close together. So even if the anions are a bit squishy, there are limits. This means that, even if we can’t take the actual numbers representing “ionic radii” all that seriously, we can at least recognize that the ions involved do need to take up (at least roughly) a certain amount of space. 
   The moral of the story is that Pauling’s First Rule represents an easy way to think about why cations adopt certain coordination numbers preferentially, but you can’t really expect it to be quantitatively accurate in all situations.
   Barry