<p>With the chemical composition, you can calculate the <a href="https://en.wikipedia.org/wiki/Normative_mineralogy" rel="nofollow noreferrer">normative mineralogy</a> of the rock. This gives you the (idealized) mass fractions of the minerals. Then it's easy to convert these into volume fractions (or modes), knowing mineral densities from the literature. Be careful, there are some limitations with normative mineralogy, which can't be applied to all types of rocks.</p>
<p>There is another way, but you'd need a thin section rather than a chemical composition. By looking at the minerals in a thin section, you can determined there proportion in a 2D plane. Then there are formulas to convert these proportion in 3D (i.e., to get a volume fraction) depending on the aspect ratio of the grains of each mineral species.</p>

CC BY-SA 4.0
2024-11-21T01:44:01.897Z
You can do it (estimating volumetric composition by-mineral) using polished sections too. Or even just by careful examination of, say, a fractured surface. It takes a deal of practice though, so you'd probably do better to fabricate a 1% grid of holes punched in opaque sheet, 5%, 10% etc sheets if you want to be able to justify your volumetric estimates.
Rockdoctor
CC BY-SA 4.0
2024-11-21T09:32:17.930Z
@Rockdoctor You're right! I did something similar during my PhD, but it was just to estimate the phenocryst content. It was quite easy, because it was lava with a dark matrix and only white sanidine phenocrysts. I took photos of rock sections, then with a binarization of the images it was fairly easy to get an estimate of the phenocryst content (in surface area). One has to be careful with crystal orientation though, there was no fabric like in a metamorphic rock, but still, some sanidine tabular crystals were oriented, so it's better to do this in several sections with different orientations.
Jean-Marie Prival
CC BY-SA 4.0
2024-11-22T15:28:50.573Z
What? No overlaying the specimen cut surface with a sheet of 1mm graph paper, and counting squares? That's how we had to do it. you're right about (ideally) needing multiple sections, preferably orthogonal, to counteract fabric issues. but you'll probably be needing to check for oriented fabrics for your structural assessment - at least in the metamorphics I was more interested in.
Rockdoctor
CC BY-SA 4.0
2024-11-20T08:39:39.140Z
2024-11-20T08:39:39.140Z
Jean-Marie Prival
<p>As Jean-Marie says, your question is about re-inventing the wheel known as &quot;normative mineralogy&quot;. There are a variety of different calculations, which <em>norm</em>ally (sorry!) will give moderately different answers. I would strongly advise against re-inventing that wheel, but instead using one of the existing systems. Preferably using several different systems, then combining the results to the nearest 10% or so. If you want higher precision, you've just guaranteed yourself several days of work at the microscope, &quot;point-counting&quot; all your relevant thin sections, then all your flat surfaces of the appropriate rock. You may well still struggle to be able to justify, statistically, claiming a +/-10% confidence limit on a mineral proportion. You'd need to have point-counted dozens to hundreds of slides to get enough independent samples into the rock unit. No, you can't measure the same slide 3 times to get 3 samples, because your data sets would then not be <strong>independent</strong>, and you statistics have just got horribly more complicated.</p>
<p>To précis the <a href="https://en.wikipedia.org/wiki/Normative_mineralogy" rel="nofollow noreferrer">Wiki article on normative mineralogy</a>, they were developed from melting lots of glasses of various compositions, to see which minerals crystallised first, at which compositions, then extracting (mathematically) the atomic components of those first minerals to get a new composition for the melt, and seeing what minerals solidify from glass of that composition, at what mineral compositions themselves. Lather rinse repeat. 15 years may be an under estimate.</p>
<p>The best-known &quot;normative&quot; scheme is the &quot;CIPW norm&quot; (Cross, Iddings (of Iddingsite?), Pearson and Whoever), based on Bowen (and Cross? I forget) 1910~1925 series of melt-quenching experiments to determine crystallisation sequences from &quot;picrite&quot; through &quot;gabbro&quot; to &quot;granite&quot;. I've got a spreadsheet somewhere that automates converting a composition (atom-% or gravimetric oxides) into a CIPW-norm. [noise of electronic searching] I *<em>had</em> a spreadsheet, which I found by searching a couple of years ago, and only took a <em>little</em> massaging to get it to work. Ah, that link on the Wiki page looks familiar.</p>
<p>There is a scheme named for a Continental (Italian?) geologist &quot;Niggli&quot;, which I literally never used. I think it may be more associated with metamorphism - where metasomatism is always going to be the 363 kg gorilla in the room, waiting to invalidate you with false assumptions. I never found a clear discussion of it the last time I looked (and found the CIPW spreadsheet).</p>
<p>There's at least one other scheme which my Mantle Petrology lecturer liked for rocks which weren't &quot;crustal ephemera&quot; (anything that has been at 100km depth for 100 Myr, and <em>may</em> be <em>approaching</em> equilibrium - his pet phrase). Dunites, lherzolites and eclogites have their own chemistry, far removed from Bowen/ CIPW's mundane gabbro-to-granite range. Seeing kyanite (aluminium silicate ; &quot;disthene&quot;) come out of his &quot;normative&quot; calculation to match the 3cm crystal in the kimberlite xenolith was a particular favourite of his.</p>
<p>A <a href="https://duckduckgo.com/?q=Niggli%20norm%20&amp;t=newext&amp;atb=v453-2&amp;ia=web" rel="nofollow noreferrer">search for &quot;Niggli norm&quot; will</a> uncover various links to Researchgate, Springerlink and (ghods help us!) YouTube about Niggli's later (mid-30s vs late-20s) variation on CIPW norms ; again based on igneous petrology, but ... my memory is niggling (sorry!!) me that my metamorphic petrology and mantle petrology lecturers used Niggli &quot;components&quot; more often than either of my Igneous petrology lecturers did. But that may be more to do with one group working with Norwegian and Swiss colleagues and the other group going transatlantic and Canadian. As significant as the &quot;DH&amp;Z versus Dana&quot; wars of the text books.</p>
<p>Typically, &quot;normative&quot; schemes <strong>assume</strong> that minerals are of uniform composition throughout each grain, and from grain to grain in the rock unit. As you'll know from probably the very first thin section you ever examined, that's an unrealistic (if necessary) assumption. Which is fundamentally why a normative calculation is at best an approximation to the actual composition of a rock. For a metamorphic (or even sedimentary!) rock, the whole concept of a mineralogical norm becomes really hard to justify. At which point, slave labour at the petrological microscope is probably looming in your future.</p>
<p>Do you remember spending many hours in your &quot;ore mineralogy&quot; practical sessions, inspecting every one of the Department's set of gold ore polished sections to establish if the ore body was 5ppm, 10ppm or 15ppm? You know, from your question, I rather think you didn't do that exercise. Pity - it was very educational. My undergrad thesis involved point-counting <em>every one</em> of my allocation of thin sections (6, total), plus a dozen or so cut surfaces. The point counts disagreed with the normative mineralogy (which itself was a whole afternoon of calculation with the log tables). And that was the data I had to work with.</p>
<p>Checking your original Q ... you go to some effort to convert weight or atomic percentages to volumetric percentages. That's probably wasted effort. Very few &quot;rock forming minerals&quot; (to quote the title of my badly worn microscope-side reference book) have a density outside the 2~3 gm/cc (tonne/ cu.m) interval, and you're not likely to get data that is meaningful at the single percent level. By the time you've checked your theoretical &quot;normative&quot; calculation against your actual point counts, you're probably going to be suspicious about the 5% differences, let alone the 1% differences.</p>
<p>What instrumentation do you have access to? I could envisage a stage-shifter attachment for an SEM/ electron backscatter/ XRF device that would effectively automate &quot;point counting&quot;. You'd need to train it with &quot;this grain [zap] is a mica ; this grain [zap] is a k-feldspar ; this grain is a plagioclase [zap] ...&quot; But that might be quicker and a lot cheaper (in human hours) than point-counting by hand. That wouldn't differentiate, of course, between say calcite and aragonite, and would probably struggle to differentiate anhydrite and gypsum. But depending on your actual task, that may be acceptable.</p>

CC BY-SA 4.0
2024-11-21T03:30:22.787Z
2024-11-21T04:42:38.433Z
2024-11-21T04:42:38.433Z
Rockdoctor
<p>I would like to trim some data by making rough estimations of the possible volume percent muscovite in a sample given pXRF data which provides a wt% potassium. Muscovite and K-feldspar are the only significant K bearing phases in the rock and, given that they can hold about 9 and 14 wt% K respectively at end-member compositions, I'd like to calculate which samples can <em>possibly</em> contain &gt;10% muscovite. This might come out to nothing, but I would also just simply like to know how a calculation like this might be done. Would the following procedure provided by Chatgpt work (example values used)? My instinct says the weight fraction is not correct.</p>
<p>Calculate the weight fraction of the mineral</p>
<p>Weight fraction of mineral = Potassium in the rock (% by weight)/
Potassium in the mineral (% by weight)​</p>
<p>For example:</p>
<p>Potassium in the rock = 5%</p>
<p>Potassium in the mineral = 9%</p>
<p>So:</p>
<p>Weight fraction of mineral=5/9≈0.556(or 55.6% by weight)</p>
<p>Convert weight fraction to volume fraction:
To find the mineral’s volume fraction, adjust for differences in density between the mineral and the rock.</p>
<p>Use this formula:</p>
<p>Volume fraction of mineral= Weight fraction of mineral
×(Density of rock/Density of mineral)</p>
<p>For example, if:</p>
<p>Density of the rock = 2.8g/cm^3
Density of the mineral = 2.6g/cm^3
Then:
Volume fraction of mineral=0.556×(2.8/2.6)≈0.599 (or 59.9% by volume)</p>
<p>Express volume fraction as a percentage
Multiply the volume fraction by 100 to express it as a volume percent:</p>
<p>Volume percent of mineral=59.9%</p>

CC BY-SA 4.0
2024-11-20T06:14:10.317Z
I am sure, that some parts of the calculation didn't copy well die to Formating getting lost. At least i cannot quite follow the math or reasoning there. Can you check?
planetmaker
CC BY-SA 4.0
2024-11-20T06:31:34.290Z
You're right, sorry about that. I should have checked that before submitting the post. I think this accurately represents chat gpt's reasoning.
Josiah
CC BY-SA 4.0
2024-11-20T08:28:45.663Z
By your logic, the proportion of K-feldspar would be 38.5% =(9/14)(2.8/2.6). Thus the proportion of the minerals in the sample that have no K would be 1.6% (100-59.9-38.5). Does this seem logical to you?
Fred
CC BY-SA 4.0
2024-11-20T10:13:58.097Z
One issue I have with "estimating the volume % of (e.g.) potassium" is that (nearly) no single element is in its pure form, but always withing a mineral. It's comparatively easy to estimate the volume % of the mineral - but the *volume* % of an element in a mineral? Sure, somewhat feasible, but not sure that makes too much sense anymore. Weight % is something different and still makes sense.
planetmaker
<geology><geochemistry><mineralogy><petrology>
What is a reasonable method of estimating the volume percent of a mineral in a rock given some composition data?
Josiah
# What is a reasonable method of estimating the volume percent of a mineral in a rock given some composition data?

(Asked by: username_0 on 2024-11-20)

I would like to trim some data by making rough estimations of the possible volume percent muscovite in a sample given pXRF data which provides a wt% potassium. Muscovite and K-feldspar are the only significant K bearing phases in the rock and, given that they can hold about 9 and 14 wt% K respectively at end-member compositions, I'd like to calculate which samples can *possibly* contain >10% muscovite. This might come out to nothing, but I would also just simply like to know how a calculation like this might be done. Would the following procedure provided by Chatgpt work (example values used)? My instinct says the weight fraction is not correct.

Calculate the weight fraction of the mineral

Weight fraction of mineral = Potassium in the rock (% by weight)/
Potassium in the mineral (% by weight)​

For example:

Potassium in the rock = 5%

Potassium in the mineral = 9%

So:

Weight fraction of mineral=5/9≈0.556(or 55.6% by weight)

Convert weight fraction to volume fraction:
To find the mineral’s volume fraction, adjust for differences in density between the mineral and the rock.

Use this formula:

Volume fraction of mineral= Weight fraction of mineral
×(Density of rock/Density of mineral)

For example, if:

Density of the rock = 2.8g/cm^3
Density of the mineral = 2.6g/cm^3
Then:
Volume fraction of mineral=0.556×(2.8/2.6)≈0.599 (or 59.9% by volume)

Express volume fraction as a percentage
Multiply the volume fraction by 100 to express it as a volume percent:

Volume percent of mineral=59.9%

**Tags:** geology, geochemistry, mineralogy, petrology

> **Comments:**
> **username_1**: I am sure, that some parts of the calculation didn't copy well die to Formating getting lost. At least i cannot quite follow the math or reasoning there. Can you check?  
> **username_0**: You're right, sorry about that. I should have checked that before submitting the post. I think this accurately represents chat gpt's reasoning.  
> **username_2**: By your logic, the proportion of K-feldspar would be 38.5% =(9/14)(2.8/2.6). Thus the proportion of the minerals in the sample that have no K would be 1.6% (100-59.9-38.5). Does this seem logical to you?  
> **username_1**: One issue I have with "estimating the volume % of (e.g.) potassium" is that (nearly) no single element is in its pure form, but always withing a mineral. It's comparatively easy to estimate the volume % of the mineral - but the *volume* % of an element in a mineral? Sure, somewhat feasible, but not sure that makes too much sense anymore. Weight % is something different and still makes sense.  

---

## 2 answers

### Answer by username_3 on 2024-11-20. Score: 3

With the chemical composition, you can calculate the [normative mineralogy](https://en.wikipedia.org/wiki/Normative_mineralogy) of the rock. This gives you the (idealized) mass fractions of the minerals. Then it's easy to convert these into volume fractions (or modes), knowing mineral densities from the literature. Be careful, there are some limitations with normative mineralogy, which can't be applied to all types of rocks.

There is another way, but you'd need a thin section rather than a chemical composition. By looking at the minerals in a thin section, you can determined there proportion in a 2D plane. Then there are formulas to convert these proportion in 3D (i.e., to get a volume fraction) depending on the aspect ratio of the grains of each mineral species.

> **Comments:**
> **username_4**: You can do it (estimating volumetric composition by-mineral) using polished sections too. Or even just by careful examination of, say, a fractured surface. It takes a deal of practice though, so you'd probably do better to fabricate a 1% grid of holes punched in opaque sheet, 5%, 10% etc sheets if you want to be able to justify your volumetric estimates.  
> **username_3**: @username_4 You're right! I did something similar during my PhD, but it was just to estimate the phenocryst content. It was quite easy, because it was lava with a dark matrix and only white sanidine phenocrysts. I took photos of rock sections, then with a binarization of the images it was fairly easy to get an estimate of the phenocryst content (in surface area). One has to be careful with crystal orientation though, there was no fabric like in a metamorphic rock, but still, some sanidine tabular crystals were oriented, so it's better to do this in several sections with different orientations.  
> **username_4**: What? No overlaying the specimen cut surface with a sheet of 1mm graph paper, and counting squares? That's how we had to do it. you're right about (ideally) needing multiple sections, preferably orthogonal, to counteract fabric issues. but you'll probably be needing to check for oriented fabrics for your structural assessment - at least in the metamorphics I was more interested in.  

---

### Answer by username_4 on 2024-11-21. Score: 1

As username_3 says, your question is about re-inventing the wheel known as "normative mineralogy". There are a variety of different calculations, which *norm*ally (sorry!) will give moderately different answers. I would strongly advise against re-inventing that wheel, but instead using one of the existing systems. Preferably using several different systems, then combining the results to the nearest 10% or so. If you want higher precision, you've just guaranteed yourself several days of work at the microscope, "point-counting" all your relevant thin sections, then all your flat surfaces of the appropriate rock. You may well still struggle to be able to justify, statistically, claiming a +/-10% confidence limit on a mineral proportion. You'd need to have point-counted dozens to hundreds of slides to get enough independent samples into the rock unit. No, you can't measure the same slide 3 times to get 3 samples, because your data sets would then not be **independent**, and you statistics have just got horribly more complicated.

To précis the [Wiki article on normative mineralogy](https://en.wikipedia.org/wiki/Normative_mineralogy), they were developed from melting lots of glasses of various compositions, to see which minerals crystallised first, at which compositions, then extracting (mathematically) the atomic components of those first minerals to get a new composition for the melt, and seeing what minerals solidify from glass of that composition, at what mineral compositions themselves. Lather rinse repeat. 15 years may be an under estimate.

The best-known "normative" scheme is the "CIPW norm" (Cross, Iddings (of Iddingsite?), Pearson and Whoever), based on Bowen (and Cross? I forget) 1910~1925 series of melt-quenching experiments to determine crystallisation sequences from "picrite" through "gabbro" to "granite". I've got a spreadsheet somewhere that automates converting a composition (atom-% or gravimetric oxides) into a CIPW-norm. [noise of electronic searching] I \**had* a spreadsheet, which I found by searching a couple of years ago, and only took a *little* massaging to get it to work. Ah, that link on the Wiki page looks familiar.

There is a scheme named for a Continental (Italian?) geologist "Niggli", which I literally never used. I think it may be more associated with metamorphism - where metasomatism is always going to be the 363 kg gorilla in the room, waiting to invalidate you with false assumptions. I never found a clear discussion of it the last time I looked (and found the CIPW spreadsheet).

There's at least one other scheme which my Mantle Petrology lecturer liked for rocks which weren't "crustal ephemera" (anything that has been at 100km depth for 100 Myr, and *may* be *approaching* equilibrium - his pet phrase). Dunites, lherzolites and eclogites have their own chemistry, far removed from Bowen/ CIPW's mundane gabbro-to-granite range. Seeing kyanite (aluminium silicate ; "disthene") come out of his "normative" calculation to match the 3cm crystal in the kimberlite xenolith was a particular favourite of his.

A [search for "Niggli norm" will](https://duckduckgo.com/?q=Niggli%20norm%20&t=newext&atb=v453-2&ia=web) uncover various links to Researchgate, Springerlink and (ghods help us!) YouTube about Niggli's later (mid-30s vs late-20s) variation on CIPW norms ; again based on igneous petrology, but ... my memory is niggling (sorry!!) me that my metamorphic petrology and mantle petrology lecturers used Niggli "components" more often than either of my Igneous petrology lecturers did. But that may be more to do with one group working with Norwegian and Swiss colleagues and the other group going transatlantic and Canadian. As significant as the "DH&Z versus Dana" wars of the text books.

Typically, "normative" schemes **assume** that minerals are of uniform composition throughout each grain, and from grain to grain in the rock unit. As you'll know from probably the very first thin section you ever examined, that's an unrealistic (if necessary) assumption. Which is fundamentally why a normative calculation is at best an approximation to the actual composition of a rock. For a metamorphic (or even sedimentary!) rock, the whole concept of a mineralogical norm becomes really hard to justify. At which point, slave labour at the petrological microscope is probably looming in your future.

Do you remember spending many hours in your "ore mineralogy" practical sessions, inspecting every one of the Department's set of gold ore polished sections to establish if the ore body was 5ppm, 10ppm or 15ppm? You know, from your question, I rather think you didn't do that exercise. Pity - it was very educational. My undergrad thesis involved point-counting *every one* of my allocation of thin sections (6, total), plus a dozen or so cut surfaces. The point counts disagreed with the normative mineralogy (which itself was a whole afternoon of calculation with the log tables). And that was the data I had to work with.

Checking your original Q ... you go to some effort to convert weight or atomic percentages to volumetric percentages. That's probably wasted effort. Very few "rock forming minerals" (to quote the title of my badly worn microscope-side reference book) have a density outside the 2~3 gm/cc (tonne/ cu.m) interval, and you're not likely to get data that is meaningful at the single percent level. By the time you've checked your theoretical "normative" calculation against your actual point counts, you're probably going to be suspicious about the 5% differences, let alone the 1% differences.

What instrumentation do you have access to? I could envisage a stage-shifter attachment for an SEM/ electron backscatter/ XRF device that would effectively automate "point counting". You'd need to train it with "this grain [zap] is a mica ; this grain [zap] is a k-feldspar ; this grain is a plagioclase [zap] ..." But that might be quicker and a lot cheaper (in human hours) than point-counting by hand. That wouldn't differentiate, of course, between say calcite and aragonite, and would probably struggle to differentiate anhydrite and gypsum. But depending on your actual task, that may be acceptable.


---

