Ternary Diagrams - Practice Problems
Solving earth science problems with ternary diagrams
Plotting data on ternary diagrams
Mineralogy - Plotting mineral compositions
Provenance: Ryan Kerrigan, University of Pittsburgh-Johnstown
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Many mineral groups can be plotted on ternary diagram with respect to three main components to differentiate between different mineral species.
Problem 1: A pyroxene mineral has the following geochemical oxide weight percents (wt.%) seen in the figure below. Plot the pyroxene with respect to the concentrations of CaO to MgO to FeO. When plotted, the data will plot within a labelled field which will allow for the determination of the pyroxene species name. Determine the pyroxene mineral name.
Step 1: Identify the three components of interest
Provenance: Ryan Kerrigan, University of Pittsburgh-Johnstown
Reuse: This item is in the public domain and maybe reused freely without restriction.
CaO, MgO, and FeO are the important variables present in the data set that will allow for plotting on the chosen ternary diagram. CaO, MgO, and FeO are the apices of the triangle and all other data can be ignored moving forward.
Step 2. Normalize the data into percentages of each component.
For each end-member component (CaO-MgO-FeO) divide its Wt.% by the sum of each of the end-member components
`((CaO)/(CaO+MgO+FeO))*100=CaO \%`
`((MgO)/(CaO+MgO+FeO))*100=MgO \%`
`((FeO)/(CaO+MgO+FeO))*100=FeO \%`
` CaO\% + MgO\% + FeO\% = 100\%`
`(18.31/(18.31+14.31+12.06))*100=41 \%`
`(14.31/(18.31+14.31+12.06))*100=32 \%`
`(12.06/(18.31+14.31+12.06))*100=27 \%`
` 41\% + 32\% + 27\% = 100\%`
Therefore, the values that will be plotted are:
$CaO = 41\%$
$MgO = 32\%$
$FeO = 27\%$
Step 3. Orient and Plot the normalized data on the specific ternary diagram.
Provenance: Ryan Kerrigan, University of Pittsburgh-Johnstown
Reuse: This item is in the public domain and maybe reused freely without restriction.
Plot the normalized values determined above on the ternary diagram. Plotting each percentage one at a time, insuring that the three plotted lines intersect at a point.
Provenance: Ryan Kerrigan, University of Pittsburgh-Johnstown
Reuse: This item is in the public domain and maybe reused freely without restriction.
Provenance: Ryan Kerrigan, University of Pittsburgh-Johnstown
Reuse: This item is in the public domain and maybe reused freely without restriction.
Step 4. Solve: read the plotted data to reveal the mineral name.
Provenance: Ryan Kerrigan, University of Pittsburgh-Johnstown
Reuse: This item is in the public domain and maybe reused freely without restriction.
Fully plotted, the data will be plotted as a point (represented as a star on the bottom). Based on these analyses, this pyroxene is an augite.
Sedimentology - Sediment classification
Shepherd sediment classification ternary diagram
Provenance: Kelly Deuerling, University of Nebraska at Omaha
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Sedimentologists have their own naming scheme based on grain size for sediments. These classifications are most often applied to offshore sediments or sediments with a minimal organic component.
Problem 2: You are given a sample from a core taken offshore in the Gulf of Mexico and asked to give the sample a name based on the Shepherd Classification (see ternary below). After sieving, the data you have gathered on grain size is in the table below. What is the name of this sample based on the Shepherd Classification?
Step 1: Identify the three components of interest
Provenance: Kelly Deuerling, University of Nebraska at Omaha
Reuse: This item is offered under a Creative Commons Attribution-NonCommercial-ShareAlike license http://creativecommons.org/licenses/by-nc-sa/3.0/ You may reuse this item for non-commercial purposes as long as you provide attribution and offer any derivative works under a similar license.
The relative abundance of sand, silt, and clay are the variables of interest for this ternary diagram. Gravel is not needed for the calculation of the ternary diagrams and will need to be set aside.
Step 2. Normalize the data into percentages of each component - for this example, sand, silt, and clay.
For each end-member component (sand, silt, clay) divide its mass by the total mass of the three end-member components.
`(("sand")/("sand"+"silt"+"clay"))*100="sand" \% =("35g"/("35g"+"63g"+"36g"))*100=26 \%"sand" `
`(("silt")/("sand"+"silt"+"clay"))*100="silt" \% =("63g"/("35g"+"63g"+"36g"))*100=47 \% "silt" `
`(("clay")/("sand"+"silt"+"clay"))*100="clay" \% =("36g"/("35g"+"63g"+"36g"))*100=27 \% "clay" `
Remember, the three percentages must add up to 100!
26% + 47% + 27% = 100%
Therefore, the values that will be plotted are: 26% sand, 47% silt, and 27% clay
Step 3. Orient normalized data on the specific ternary diagram.
The axes on this version of the Shepherd Classification increase counterclockwise.
Step 4: Plot the normalized data as a single point.
Plot the normalized values on the ternary diagram
Provenance: Kelly Deuerling, University of Nebraska at Omaha
Reuse: This item is offered under a Creative Commons Attribution-NonCommercial-ShareAlike license http://creativecommons.org/licenses/by-nc-sa/3.0/ You may reuse this item for non-commercial purposes as long as you provide attribution and offer any derivative works under a similar license.
Provenance: Kelly Deuerling, University of Nebraska at Omaha
Reuse: This item is offered under a Creative Commons Attribution-NonCommercial-ShareAlike license http://creativecommons.org/licenses/by-nc-sa/3.0/ You may reuse this item for non-commercial purposes as long as you provide attribution and offer any derivative works under a similar license.
Provenance: Kelly Deuerling, University of Nebraska at Omaha
Reuse: This item is offered under a Creative Commons Attribution-NonCommercial-ShareAlike license http://creativecommons.org/licenses/by-nc-sa/3.0/ You may reuse this item for non-commercial purposes as long as you provide attribution and offer any derivative works under a similar license.
Where the three lines cross (the star) represents the composition of the sediment sample on the Shepherd Classification ternary.
Step 5: Identify category, if applicable to the specific ternary diagram.
The fully plotted data (the star) lies within the "Sand-silt-clay" field on the Sherpherd Classification ternary diagram.
Reading ternary diagrams
Petrology - Extracting and interpreting plotted rock compositions
Problem 3. The ternary diagram below shows three plutonic igneous rocks plotted in the standard International Union of Geological Sciences (IUGS) ternary diagram. Rocks are plotted with respect to the abundance of quartz (Q) - alkali feldspar (AF) - plagioclase (P). These rocks have been collected from a field area that shows several different magmatic pulses making a composite intrusion. The relative rock ages are as follows: red circle - oldest; yellow square - middle; and blue triangle - youngest). Interpret the data plotted on this diagram.
Three rocks are plotted on the IUGS QAP diagram for the classification of plutonic igneous rocks
Provenance: This the IUGS standard diagram for this classification, it should be public domain
Reuse: This item is in the public domain and maybe reused freely without restriction.
Step 1: Identify the three components of interest (the apices of the ternary diagram) and the data associated with the components
The coarse-grained igneous rocks are plotted with respect to the abundance of quartz (Q) - alkali feldspar (AF) - plagioclase (P). There may be additional minerals in these rocks, however, only the abundance of quartz, alkali feldspar, and plagioclase are needed for this classification system. Based on where these rocks plot, the rocks are: red circle is a quartz monzonite, yellow square is a granodiorite, and blue triangle is a granite.
Step 2. Understand the relative abundances of each of the three components in each sample. Samples will have higher amounts/concentrations of the components they are plotted closest to and lower amounts/concentrations for those they are farther away from.
Which sample has the highest relative amount of quartz? - The blue triangle, the yellow square, or the red circle?
The blue triangle plots closest to the "quartz" and therefore has the highest relative amount of quartz compared to others. Additional examination shows the percentage of quartz.
Provenance: Ryan Kerrigan, University of Pittsburgh-Johnstown
Reuse: This item is in the public domain and maybe reused freely without restriction.
Which sample has the highest relative amount of plagioclase? - The blue triangle, the yellow square, or the red circle?
The red circle plots closest to the "plagioclase" and therefore has the highest relative amount of plagioclase compared to others. Additional examination shows the percentage of plagioclase of each (see below).
It should be noted that using this diagram requires a second normalization for the feldspars (alkali feldspar and plagioclase). While quartz is plotted as a normalized value with respect to all three (quartz-alkali feldspar-plagioclase), the feldspars are plotted as a normalized value with respect to only the feldspars (see figure).
Provenance: Ryan Kerrigan, University of Pittsburgh-Johnstown
Reuse: This item is in the public domain and maybe reused freely without restriction.
Which sample has the highest relative amount of alkali feldspar? - The blue triangle, the yellow square, or the red circle?
As this diagram plots feldspars normalized to each other, we can see that the blue triangle has the highest amount of alkali feldspar. A keen observer would notice that, if the samples were plotted with a standard normalization with respect to all three component, all of the samples have equal relative amounts.
Provenance: Ryan Kerrigan, University of Pittsburgh-Johnstown
Reuse: This item is in the public domain and maybe reused freely without restriction.
As mentioned above, these rocks represent multiple pulses of a magmatic body with the blue triangle sample as the youngest and the red square as the oldest. What can be said about the trend of the igneous body over time?
Provenance: From Wikipedia Commons
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Samples are becoming more quartz-rich and depleted in plagioclase. This type of enrichment in silica is seen in many igneous intrusions. As fractional crystallization progresses in the underlying magmatic body, the mafic component (including Ca-rich plagioclase) crystallizes early and settles to the bottom. Over time, more and more plagioclase is removed and the upwelling magmatic pulses become increasingly more felsic. The phenomena is seen in a wide range of igneous intrusions, including the igneous intrusions that make up Yosemite National Park.
Geomorphology - Dune types
There are many variables that can influence the shape of sand dunes but the ones most often cited by geomorphologists include vegetative cover, sand supply, and wind persistence.
Problem 4: The dunes shown in the left portion of the figure below are located in Oregon Dunes National Recreation Area. Most of the dunes are classified as parabolic dunes, particularly near the coastal forest, and that is reflected by the location of the dot on the dune morphology diagram below.
If the coastal forests are logged, what type of dune will likely establish?
Provenance: Oregon dunes picture: https://pixabay.com/photos/sand-dunes-dunes-national-park-52902/
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Step 1: Identify the three components of interest on the ternary diagram
On the dune morphology ternary diagram above supply of sand, wind, and vegetation are the three components of interest.
Step 2: Understand the relative abundances. Which of the components will change with deforestation and what will that mean for the dunes?
Logging removes vegetation, so the relative abundance of vegetation will decrease and dunes will trend toward transverse dunes
Provenance: Kelly Deuerling, University of Nebraska at Omaha
Reuse: This item is in the public domain and maybe reused freely without restriction.
Environmental Geochemistry - Water quality
Geochemists often look at what is dissolved in water to understand if the water is safe for human use and how water chemistry changes spatially and through time. Major ion composition (cations & anions) can be plotted on ternary diagrams to understand differences in major chemical composition.
Provenance: Kelly Deuerling, University of Nebraska at Omaha
Reuse: This item is offered under a Creative Commons Attribution-NonCommercial-ShareAlike license http://creativecommons.org/licenses/by-nc-sa/3.0/ You may reuse this item for non-commercial purposes as long as you provide attribution and offer any derivative works under a similar license.
Provenance: Kelly Deuerling, University of Nebraska at Omaha
Reuse: This item is offered under a Creative Commons Attribution-NonCommercial-ShareAlike license http://creativecommons.org/licenses/by-nc-sa/3.0/ You may reuse this item for non-commercial purposes as long as you provide attribution and offer any derivative works under a similar license.
Problem 5: The watersheds in the ice-free areas of western Greenland get their water from either ice melt (proglacial) or precipitation (nonglacial). As the ice melts, more nonglacial watersheds form. Proglacial and nonglacial watersheds have very different chemical composition as shown in the anion ternary below.
a) What is the dominant anion (Cl-, SO42-, or HCO3-) in proglacial and nonglacial watersheds?
b) What is the range of HCO3- relative abundances in the proglacial watersheds?
Step 1: Identify the three components of interest on the ternary diagram
The three end member components on this ternary diagram are chloride (Cl-), sulfate (SO42-), and bicarbonate (HCO3-). Note that the axes increase counterclockwise.
Step 2: Understand the relative abundances.
a) What is the dominant anion in proglacial (blue triangles) and nonglacial (red circles) watersheds?
The blue circles plot closer to the HCO3- point on the ternary diagram, so have relatively more HCO3-. The red nonglacial data points plot closer to the SO42- point of the triangle, so have relatively more SO42-
b) What is the range of HCO3- relative abundances in proglacial watersheds?
80-90% anions in the proglacial samples are HCO
3-.
Provenance: Kelly Deuerling, University of Nebraska at Omaha
Reuse: This item is offered under a Creative Commons Attribution-NonCommercial-ShareAlike license http://creativecommons.org/licenses/by-nc-sa/3.0/ You may reuse this item for non-commercial purposes as long as you provide attribution and offer any derivative works under a similar license.
Petroleum Geology - Shale reservoir quality & lithofacies classification
Petroleum geologists need to be able to understand whether a subsurface formation will produce enough oil to be worth the cost of implementation. They use lithofacies classification and carbon content of core samples to understand where productive reservoirs are located. Ternaries dealing with shale and mudstone lithofacies classification compare the abundance of siliceous primary minerals (quartz and/or feldspar, mica), clay minerals, and carbonate.
Problem 6: The data on the ternary diagram below are from Hou et al. (2023) and depict the mineralogical composition of a series of mudrocks from China. The color designation of each of the points is total organic carbon composition of the sample (related to oil content) and allows a fourth variable to be visualized as well. Answer the questions below with respect to this ternary diagram.
a) Which end-member are the majority of samples composed of?
b) What two mudrock classification names do the majority of samples fit?
Mudrock classification ternary diagram. Plotted data are from Hou et al. (2023) - https://doi.org/10.3390/en16062581
Provenance: Kelly Deuerling, University of Nebraska at Omaha
Reuse: This item is offered under a Creative Commons Attribution-NonCommercial-ShareAlike license http://creativecommons.org/licenses/by-nc-sa/3.0/ You may reuse this item for non-commercial purposes as long as you provide attribution and offer any derivative works under a similar license.
Step 1: Identify the three components of interest on the ternary diagram
The three end-members of this mudrock classification diagram are quartz, clay minerals, and carbonate minerals.
Note that the axes on this diagram are a bit different! The scales on ternary diagrams can be in percentages (0-100%) or decimal proportions (0-1) . These are essentially the same: the end-members on this diagram are 1, which means 100% of that end-member.
The axes also increase counterclockwise on this diagram.
Step 2: Understand the relative abundances.
a) Which end-member are the majority of samples composed of?
The majority of the samples plot closest to the quartz end-member, indicating that they are predominantly quartz.
b) What two mudrock classification names do the majority of samples fit?
The majority of samples plot in the C and D fields, which are mixed argillaceous mudstone and carbonate-rich argillaceous mudstone, respectively.
Next steps
If you feel comfortable with this topic, you can go on to the assessment.
Or you can go back to the Ternary Diagrams explanation page.