6 Provenance & Formation
Part 1: Formation reservoirs/-locations of chondrite components (6.1 - 6.4)
Chondrule bulk compositions in individual chondrites have distinct distribution. Further, chondrules and matrix have different mean composition in individual chondrites. Learn about the relationship of chondrules and matrix in chondrites, and what we can learn from this about their formation and formation reservoirs. Describe the chondrule-matrix complementarity and explain – in conjunction with additional arguments – whether chondrules, as well as chondrules and matrix, respectively, formed from a common or from various reservoirs in the protoplanetary disk.
Learning Goals
Explain required parameters for chondrule-matrix complementarity. Explain and demonstrate whether and why chondrules and matrix either formed (i) together in a common reservoir, or (ii) in various reservoirs and were later mixed together. Further, explain and demonstrated if chondrules alone and of individual meteorites formed from a common or various reservoirs.
Part 2: Chondrule Formation (6.5 - 6.9)
Chondrules formed in brief, high-temperature events. While the conditions of chondrule formation are well known, the mechanism that formed chondrules are still rather speculative. Learn about chondrule formation conditions and familiarise yourself with the arguments behind these. Have a look at the suggested chondrule formation mechanisms. Describe what is currently known about chondrule formation.
Learning Goals
Demonstrate and argue why chondrules experienced only brief heating, and how we know this. Describe the ambient conditions of chondrule formation. Explain why there was a temperature limit during chondrule formation. Explain the meaning of the 2-component model, and where chondrules were likely formed. Recall, discriminate and describe the most important chondrule formation models.
Part 3: CAI formation (6.10 - 6.14)
Ca,Al-rich inclusions (CAIs) are a minor, but important component in chondrites, as they mark time zero for the dating of solar system events. Learn about the characteristics, abundances, formation and classification of CAIs, and discriminate these from similar components. Learning Goals
Describe the general appearance and characteristics of CAIs. Describe the classification and modal abundances of CAIs. Explain how CAIs formed and how we know this. Explain whether or not CAIs are xenoliths and how we know this. Discriminate CAIs, AOAs, and RIs.
Bonus 1: Structure and classification of chondrules (6.15 - 6.18)
Chondrules are one of the two major components in almost all chondrites. Their formation ranges among the most important questions in cosmochemistry. Solving this question should allow to understand one of the most important and wide spread processes in the protoplanetary disk. Chondrule textures provide ample evidence of the conditions during chondrule formation. Study the various chondrule textures and use this to describe what these tell us about the chondrule formation conditions. Learning Goals
Name and describe the various chondrule texture types and classifications. Explain and provide evidence for the formation of the various chondrule textures.
Bonus 2: Petrology and phase diagrams for chondrules (6.19 - 6.20)
Chondrules are ultramafic systems, resembling Earth’s mantle – plus metal and sulphides. Chondrule petrology and crystallisation are therefore best described in similar phase diagrams as used for basalts. Familiarise yourself with appropriate phase diagrams for chondrules and describe typical crystallisation paths for these, to explain their observed phases and phase relationships. Learning Goals
Name adequate ternary and binary phase diagrams to describe crystallisation and melting of chondrules. Explain the layout and details of these phase diagrams, as well as crystallisation whats for equilibrium and fractional crystallisation.
Bonus 3: Plot Types and Making of a Plot (6.21 - 6.27)
It is most sensible to present data in plots. It is of utmost importance to meaningfully present data, when constructing a plot. It is critical not to forget any of the key elements of a plot. It is equally important to be aware of which plot type one uses, or what plot type one is looking at, respectively. Inform yourself about the various plot types, describe their key elements, and produce a selection of the important plot types in MetBase. Learning Goals
Recall and name all required elements of a plot. Recall, present and apply all important plot types. Confident application of the various plot types in MetBase.
6.1 Chondrule-Matrix Complementarity
Bulk chondrites have CI chondritic compositions for a number of element ratios, e.g., Mg/Si. Chondrules and matrix in this same meteorite have, however, different element ratios. Combined, chondrules and matrix, of course, add up to the bulk chondrite’s CI chondritic Mg/Si ratio. Such complementarity relationships when the bulk chondrite has CI chondritic element ratios is seen for a number of element pairs and the various chondrite groups. It seems highly unlikely that the bulk chondrite element ratios were produced by fortuitous mixing of chondrules and matrix. Rather, chondrules and matrix of the same chondrite must have formed in the same chemical reservoir.
Chondrules and matrix need to have different compositions in the considered elements, while the bulk chondrite needs to be (close to) CI. More generally, any two or more components can be complementary. The main aspect is that the components have various compositions, while the bulk chondrite has CI chondritic compositions in the considered elements. It is finally helpful if the considered components have about similar modal abundances and/or element concentrations that in combination represent majority of the bulk chondrite element abundances of the considered elements.
Chondrule and matrix (or any other component fulfilling the requirements of complementarity) likely formed from a common, CI chondritic reservoir. It is unlikely that the complementary composition – while the bulk is (close to) CI chondritic in the considered elements – is the result from mixing the components from various, compositionally different reservoirs.
✗True
✓False
✓True
✗False
✗Only these have CI chondritic element compositions.
✗Not true, complementary relationships have also been frequently observed in many OC and EC.
✓They have about similar matrix and chondrule abundances.
✗Because these are the most primitive and experienced only miner parent body alteration.
6.2 Chondrule-Matrix Isotope Complementarity
Variations in the 183/184W ratio represent nucleosynthetic anomalies, i.e., variable additions of presolar material. Bulk planetary materials have identical 183/184W compositions. However, chondrules and matrix in CV chondrites have different 183/184W compositions. As chondrules and matrix are the major components, their combined 183/184W composition will likely represent the bulk CV 183/184W composition. The bulk CV composition has the planetary 183/184W composition, i.e., plots exactly on the intercept of the chondrule-matrix mixing line and the planetary 183/184W line. The most simple explanation for this is that chondrules formed from the same isotopic reservoir, which had the planetary 183/184W. Each component then incorporated variable amounts of 183/184W during component formation via variable addition of presolar carriers. Alternatively, it appears unlikely that chondrules and matrix formed in two isotopically different reservoirs and were subsequently mixed together in the right proportions to end up with the planetary 183/184W. Thereby, the isotope complementarity extends the chondrule-matrix complementarity observed for many elements in various chondrites.
Chondrules and matrix need to have different isotope compositions, and the bulk chondrite needs to plot on/close to the intercept of the mixing line between the chondrule and matrix compositions and the planetary mean value. This is the case for e.g., epsilon183/184W.
Matrix: ca. -2 to -0.8; Bulk -0.2 to 0.1; Chondrules: 0 to 2.2. Total range: ca. -2 to 2.
✗epsilon182/184W
✓epsilon183/184W
✗epsilon186/184W
✗epsilon187/184W
✗epsilon188/184W
✗CAIs
✓presolar grains
✗chondrules
✗matrix
✗IOM
✓… formed from a common reservoir.
✗… formed in chemically and isotopically separate reservoirs and were later transported and mixed together.
✗… formed in-situ on the parent body, with subsequent re-distribution of elements and isotope during parent bodz alteration.
✗… formed close to the Sun and were later transported into the chondrule forming region.
6.3 Comparing Mixing vs. Magmatic Origin for Bulk Chondrule Compositions
Bulk compositions of ordinary chondrite (OC) chondrules fall along mixing lines between olivine and SiO2. The magmatic evolution of terrestrial rocks as well as a calculated (MELTS) magmatic evolution with an OC starting composition deviate strongly from any olivine-SiO2 mixing line. Igneous clasts found in chondrites, as well as eucrites plot either on or close to the magmatic trends. Chondrules cannot have formed by magmatic process, and most likely formed by mixing of material, possibly by interacting with their surrounding gas during their formation. Mixing of thousands to millions of fine-grained precursor grains is not possible, as this would always result in the average composition of the precursors.
A first mineral to crystallise is Mg-rich olivine (Mg/Si of forsterite: 2), which is then removed from the melt. The Mg/Si ratio of the melt is thereby significantly reduced, while the Si-concentration in the is accordingly significantly increased.
By adding silica-rich material to chondrules. This is sensible, as chondrules fall on mixing lines between olivine and silica, whereas melt evolution trends deviate significantly from mixing lines. A possible process of adding silica is the material exchange between chondrules and surrounding gas during chondrule formation.
✓True
✗False
✓True
✗False
✗True
✓False
6.4 Possibilities of how to Mix Components
One of the key questions is whether components – in particular chondrules – in chondrites of one group (e.g., CV, H, L, …) originated from one, single parental reservoir, or whether these were mixed from multiple parental reservoirs. To address this question it is important to understand the various possibilities of how reservoirs can be mixed. There are four possibilities: (a) no mixing, the components/chondrules of all chondrites of one group come from one single reservoir; (b) no mixing, but components/chondrules in individual chondrites originate from separate, single parental reservoirs; (c) mixing, the components/chondrules of all chondrites of one group are mixed from the same set of parental reservoirs; (d) mixing, the components/chondrules of each individual chondrite of a group were mixed from a different set of parental reservoirs. Each of this possibilities to mix reservoirs leads to a different result. It is important to note, that this question only addresses chondrules from a same chondrite group, as chondrules from various chondrite groups could not have had the same parental reservoirs, as chondrule populations among chondrite groups are distinctly different.
- Single chondrule reservoir for all chondrites: all chondrites of a single group received all their chondrules from a single parental chondrule reservoir. (b) Single chondrule reservoir for each chondrite: each chondrite of a single group received its respective chondrules from a different parental chondrule reservoir. (c) Multiple chondrule reservoirs for all chondrites: Multiple parental chondrule reservoirs existed, and all chondrites of a single group received all their chondrules from a mix of all the various parental chondrule reservoirs. (d) Multiple chondrule reservoirs for each chondrites. Each chondrite of a single group received its respective chondrules from a different set of multiple parental chondrule reservoirs.
The currently competing models of chondrule formation postulate different origins for chondrules in a single chondrite. Considering the various possibilities where chondrules of individual chondrites originated might help decide which of the competing models is correct, or at least more plausible than the other.
✓True
✗False
✓True
✗False
✓True
✗False
6.5 Shock Wave Model of Chondrule Formation
Chondrule precursors likely consisted of up to millions of µm-sized dust grains. Millions of such chondrule precursors likely existed, surrounded by a reducing gas. A shock wave travelling through such a gaseous chondrule precursor regions compresses the gas and accelerates it and everything within it in its travelling direction. The massive compression and friction of the materials raises the temperature shortly behind the shock front within minutes or less from a few hundred K to more than 2000 K. This is above the liquidus of the mafic chondrule precursors, which start melting. This heating pulse is only brief – minutes at max. Farther away behind the shock front, the speed and gas density decelerates and decreases. The hot chondrules radiate away their heat, which together with the slowly relaxing gas density and speed leads to slow cooling over hours to days. This temperature profile allows the chondrule to crystallise large, porphyritic olivine and few pyroxene, surrounded by a glassy or fine-crystalline, Ca,Al-rich mesostasis. These conditions likely also facilitated material exchange between chondrules and the ambient gas to produce low-Ca pyroxene rims around most of the chondrules.
6.6 Asteroid Collision Model of Chondrule Formation
In the asteroid collision model two asteroids collide, of which at least one must be molten, but also having a thin, solid crust. In this model, the collision produces lots of melt that is splashed into sub-cm sized droplets that become the chondrules upon cooling. Additional dust might be present and envelop the droplets, later becoming the matrix. Problems with this model are e.g., how are metal and/or sulphides ending up in chondrules? These might have formed a core or similar in the molten asteroid. Further, REE in chondrules are typically flat, although fractionation patterns cold be expected from fractionation processes in the molten asteroid.
6.7 X-Wind Model
The X-wind is a theoretical, astrophysical model for dynamic processes in the early Solar System. The most interesting part for meteoriticists is the ›X-region‹ where magnetic fields have a cross-over. The X-region is close to the Sun (~0.06 AU), very hot, and has the potential to melt material for short time intervals. Further, material processed through the X-region is subsequently transported by winds above the protoplanetary disk (accretion disk) to distances a couple of AU away from the Sun, where it rains back down on the protoplanetary disk. It has therefore been proposed that chondrule precursor material might have been processed through the X-region and transformed into chondrules and then transported to the asteroid accretion regions further out. There, the chondrules mixed with fine-grained material, which forms the matrix of chondrites. Therefore, the X-wind model is a 2-component model and in conflict with considerations that chondrules and matrix formed in the same region, as interpreted from chondrule-matrix complementary relationships.
The X-region can potentially briefly melt chondrule precursor material, thereby forming chondrules. The X-wind model therefore a potential chondrule forming process. Chondrules could mix with CAIs in the X-region, and then together be transported by winds above the protoplanetary disk into the region of asteroid accretion.
In the 2-component model, the two main chondritic components are mixed togethere. This means, chondrules and matrix form in different regions of the protoplanetary disk, are then transported and mixed together. In the X-wind model, chondrules from the X-region are mixed with fine-grained matrix material in the region of asteroid accretion. The X-wind model therefore is a 2-component model.
The chondrule-matrix complementarity requires the Formation of chondrules and matrix in a single common region. This is in conflict with the 2-component model of the X-wind.
✗True
✓False
✗ca. 0.006 AU
✓ca. 0.06 AU
✗ca. 0.6 AU
✗ca. 6 AU
✗ca. 1-3 AU
✗ca. 2-3 AU
✓ca. 2-4 AU
✗ca. 3-5 AU
✗True
✓False
6.8 Additional Chondrule Formation Models
The actual chondrule formation mechanism remains enigmatic, unknown and controversial. The most popular, suggested mechanisms are: (i) schock waves – either travelling through the protoplanetary disk or bow shock in front of asteroids, (ii) asteroid collision, (iii) current sheets, (iv) lightning, (v) X-wind. The most popular models are described in more detail separately. In addition, there is a countless number of exotic models that are currently not seriously considered.
6.9 CAIs – Types & Classification with respect to Minerals
Ca,Al-rich inclusions (CAIs) commonly have irregular outlines, can be larger than chondrules and often show a mineralogical zonation from core to rim called ›Wark-Lovering rim‹. The sequence of minerals in such rims correspond to the condensation sequence of refractory minerals and together with the irregular outline of the CAIs indicate that CAIs directly condensed from a cooling gas. In few chondrites, CAIs were re-melted – likely during the chondrule forming process – and now have a similar, roundish appearance as chondrules. CAIs are classified according to various characteristics, one is based on mineralogy of the ternary diagram melilite–Al-rich pyroxene–remaining minerals. 3 types of CAIs (A, B, C) are discriminated in this diagram. Another classification is based on their texture, e.g., fine-grained, coarse-grained, or compact.
6.10 CAI Classification – REE patterns
One CAI classification scheme are their REE patterns. Six groups are discriminated, which are numbered ›Group I‹ to ›Group VI‹, although Group IV refers to ferromagnesian objects, not CAIs. Hence, this scheme only discriminates among 5 CAI groups, the sixths is called ›ultrarefractory‹. All groups are characterised by REE enrichments of typically at least about 20xCI. Three out of these six groups (I, III, VI) are characterised by the presence and/or absence of either positive or negative anomalie(s) in Eu and/or Yb, the two most volatile REE. The REE-pattern of Group V is entirely flat and unfractionated. Group II and the ultrarefractory group are generally characterised by fractionations of the HREE from the LREE. The ultrarefractory group is further highly enriched in the HREE, by orders of magnitude relative to CI. The Group II and ultrarefractory patterns might not only be volatility controlled, but also the result of mineral fractionation. This means, individual REE partition differently into minerals, and these are then variably included in the CAIs. Petrographic CAI types do not correlate with these REE patterns.
REE are typically enriched by a factor of >20 relative to CI. The group II and ultra refractory patterns are even enriched by 1 to 3 orders of magnitude. The REE patterns are characterised by enrichments and depletions in either volatile elements such as Eu and Yb, or enrichments and depletions between HREE and LREE.
Some patterns appear complementary to each other, e.g., group III and VI patterns, which are either depleted or enriched in the two volatile elements Eu and Yb. A similar complementarity is seen in the patterns of group II and ultrarefractory, which are depleted in LREE and enriched in HREE, or vice versa. In both cases, a genetic relationship might exist between the CAIs of the respective groups.
✗4
✗5
✓6
✗7
✗True
✓False
✗La
✗Ce
✗Pr
✗Nd
✗Pm
✗Sm
✓Eu
✗Gd
✗Tb
✗Dy
✗Ho
✗Er
✗Tm
✓Yb
✗Lu
6.11 CAI Abundances
Ca,Al-rich inclusions (CAIs) are a minor component with about 0.2-3 vol% in carbonaceous chondrites, and typically less than 0.1 vol% in all other groups, with exceptions of in cases maybe up to 1 vol%. Even in carbonaceous chondrites, the CAI abundances are mostly below 1 vol%, only CV chondrites have comparatively high abundances with about 3-4 vol%. These low abundances produce Poisson-distributions of CAI abundances, meaning that small, individual sections of chondrites might contain significantly lower or higher CAI abundances than the chondrite mean. To obtain accurate modal abundances, it is therefore mandatory to study sufficiently large sections.
6.12 CAIs are likely Xenoliths
It is possible to calculate an expected modal abundance of Ca,Al-rich inclusions (CAIs) and compare this to the measured CAI modal abundance in a given chondrite. It can be concluded from this comparison that CAIs are most likely xenolithic components, i.e., did not form together with chondrules, matrix, and opaque phases in the same reservoir. This is further evidence that CAIs are xenolihtic. Further, it can be concluded from the above mentioned comparison that the initial refractory element abundances in the formation location of carbonaceous chondrites might in fact have been similar to the refractory element abundances in the formation location of ordinary chondrites.
6.13 CAIs and AOAs are both Refractory Inclusions
There is sometimes a confusion with respect to what are refractory inclusions (RI). Ca,Al-rich inclusions (CAIs) are certainly a type of RI, with an abundance of about 0-3 vol%. However, there is another abundant type of RI, which are amoeboid olivine aggregates (AOAs). The AOAs also have a condensation signature, and despite being primarily composed of olivine, likely also formed similar to CAIs and with a signature of more refractory elements and minerals. The abundance of AOAs can be significantly higher than CAIs, with up to >5 vol%. Hence, RI is a summative term, comprising CAIs, AOAs, and other, minor components, which is why the RI content of a chondrite can be up to more than 10 vol%.
6.14 Chondrule Classification – Textural Types
Chondrules are classified into various textural types. Most abundant (typically >90%) are chondrules with large grains of olivine and/or pyroxene, and interstitial either fine-crystalline or glassy Ca,Al-rich, feldspathic like material, in cases an intergrowth of feldspar, pyroxene and maybe silica. This interstitial material is called mesostasis. Such chondrules are called porphyritic chondrules, because of their large crystals. Porphyritic chondrules are often mineralogically zoned, with olivine in the core and low-Ca pyroxene at the rim. These zoned chondrules are the dominant porphyritic type in almost all chondrites, and called mineralogically zoned porphyritic – or MZP – chondrules. Porphyritic chondrules that are unzoned are consequently called mineralogically unzoned porphyritic – or MUP – chondrules. Porphyritic chondrules likely formed from a melt with sufficient nuclei for the olivine and pyroxene grains to crystallise from. The next two most abundant types are barred olivine (BO) and radial pyroxene (RP) chondrules (ca. 5-10%). BO chondrules have about parallel olivine bars with interstitial mesostasis. The parallel olivine bars are a skeletal structure resulting from quick undercooling of a rather nuclei-free melt. BO chondrules further often have a magmatic rim surrounding the chondrule. RP chondrules likely also formed from an almost nuclei-free, more silica-rich melt. A seed crystal at the rim of the chondrule – that is in cases observable – triggered crystallisation, and fine pyroxene laths instantly crystallised radially from the seed crystal. There are many additional chondrule textural types that are either rare or restricted to certain chondrite groups. For example, CH and CB chondrites contain cryptocrystalline and skeletal chondrules, that are largely absent in other chondrite types. Further rare or sub-textural types are e.g., micro-porphyritic, granular olivine, or silica-rich chondrules.
These are porphyritic chondrules. These are mostly type I in carbonaceous chondrites (>95%), whereas the portion of type II is much higher in ordinary chondrites, with up to about half of the chondrules being type II. Enstatite chondrites almost exclusively contain type I chondrules. Porphyritic chondrules are often mineralogically zoned, with olivine in the core and low-Ca pyroxene at the rim. Olivine and pyroxene are the porphyritic minerals, sitting in a glassy to fine-crystalline, feldspar-like – i.e., Ca,Al-rich – mesostasis.
barred olivine (BO) chondrule, radial pyroxene (RP) chondrule, microporphyritic (MP) chondrule, cryptocrystalline (CC) chondrule, skeletal olivine (SO) chondrule, silica-rich chondrule (SRC), etc.
✓CI
✗CV
✗CK
✗CO
✗CM
✗CH
✗CB
✗True
✓False
✗True
✓False
6.15 Mineralogically Zoned Chondrules
Mineralogically zoned chondrules have olivine in the core, surrounded by low-Ca pyroxene. In very rare cases inverse zonation is also observed. The fraction of zoned chondrules relative to all chondrules is systematically different in the various chondrite groups: Carbonaceous: ca. 80%; Ordinary: ca. 50%; Enstatite: ca. 40%; R: ca. 40%; and K: ca. 7%. The pyroxene-rim most likely formed from the reaction of chondrule olivine with the ambient, SiO-rich gas. Hence, chondrules were open systems during their formation.
CC: 90%; OC, EC, R: 50%; K: 10%
Chondrules likely acted as open systems, i.e., exchanged material with the surrounding ambient gas. The chondrules might have started as olivine-rich materials. The ambient gas might have been SiO(g) rich due to fractional condensation processes. The chondrule olivine then reacted with the SiO, thereby forming low-Ca pyroxene, which is then naturally located at the border of the chondrule, and often poikilitically encloses relict olivine. This process might generally explain bulk chondrule compositional variations, as e.g., the surface/volume ratios or slightly variable temperature episodes of each individual chondrule might have resulted in variable amounts of material exchange, and, hence, bulk chondrule compositions.
✓… open systems
✗… closed systems
✗… a chondrule with low-Ca pyroxene in the core, surrounded by olivine.
✗… a section close to the chondrule equator with olivine in the core, surrounded by low-Ca pyroxene.
✗… a porphyritic chondrule with olivine in the core, surrounded by low-Ca pyroxene.
✓… a chondrule with olivine in the core, surrounded by low-Ca pyroxene.
✗True
✗False
6.16 Chondrule Classification – Type I and Type II
Chondrules are classified in two petrologic types based on their molar Fe-content in olivine and/or pyroxene. Type I have Fe-contents from 0 to 10 mol% Fe, and type II have Fe-contents from10 to 100 mol% Fe. Pyroxene should be used in chondrites that experienced significant metamorphism, as olivine exchange Mg-Fe faster than pyroxene. Ordinary chondrites contain a significant share of type II chondrules, whereas carbonaceous chondrites contain only a few, and enstatite chondrites nearly none.
Fe/(Fe+Mg), all in atomic, i.e., mol abundances.
Olivine or pyroxene in chondrules.
✗Mg2SiO4
✗(Mg,Fe)SiO3
✗Mg2SiO6
✗FeSiO4
✗(Mg,Fe)2Si2O6
✓Fe2SiO4
✓10 mol% Fe in ferrosilite.
✓10 mol% Fe in fayalite.
✓90 mol% Mg in enstatite.
✓90 mol% Mg in forsterite.
✓True
✗False
6.17 Chondrule Classification – Sub-Types A-AB-B
The petrologic chondrule type is in cases followed by one of 3 sub-types, designated by letters: A: olvine-rich (= Si-poor); AB: olivine/pyroxene (= intermediate Si); B: pyroxene-rich (= Si-rich).
at% = atom-%. Divide wt% by the mass of the element. For an entire analyses, first divide all element wt% by their respective masses, which will give at%. Then re-normalise the at% to 100 at%. The same applies to minerals, which are simply combinations of elements.
These are Fe-poor (type I) and Si-rich, which means, pyroxene-rich (sub-type B).
✗… 0.5
✗… 1
✗… 1.5
✓… 2
✗… Si-poor
✗… intermediate in Si
✓… Si-rich
✓… carbonaceous chondrites
✓… ordinary chondrites
✓… enstatite chondrites
✓… R & K chondrites
6.18 Mineral Crystallisation in Chondrules (An - SiO2 - Fo including binary systems)
Chondrules are mafic, magmatic systems. Chondrule crystallisation can be described in e.g., the petrologic ternary phase diagram Forsterite-Anorthite-Quartz. In brief, and only the most typical path: most chondrules start deep in the forsterite primary phase field. A melt then develops towards the peritectic line, where the peritectic reaction olivine + silica produces pyroxene from the olivine over-saturated melt. The melt develops along the peritectic line during this reaction and towards the peritectic point. There, the olivine and pyroxene are joined by anorthite, and the peritecic reaction plus anorthite crystallisation continues until all melt is consumed. This is equilibrium crystallisation, more likely is fractional crystallisation, in which the first formed olivine does not completely reacts to pyroxene druing the peritectic reaction. Then, also enstatite crystallises, and the melt develops to either the En+An or En+Qz cotecic, and finally crystallises either as glass or 3 phases, when the eutectic point is reached. Olivine is because of the fractional crystallisation also still present. Chondrules likely experienced fractional crystallisation, as their feldspar-like mesostases often is glassy or fine-crystalline, indicating fast cooling. The typically observed paragenesis of chondrules is olivine+pyroxene+feldspar, and in rare cases also silica. For a more complete description the ternary phase diagram Diopside-Anorthite-Forsterite should also be consulted.
6.19 Mineral Crystallisation in Chondrules (Di - An - Fo including binary systems)
Chondrules are mafic, magmatic systems. Chondrule crystallisation can be described in e.g., the petrologic ternary phase diagram Diopside-Anorthite-Forsterite. In brief, and only the most typical path: most chondrules start deep in the forsterite primary phase field. A melt then develops towards either the Fo+An or Fo+Di cotectic line, from where on the respective two minerals crystallise unit reaching the eutectic point. There, the 3 phases Fo+Di+An crystallise together until all melt is consumed. Fractional crystallisation is qualitatively identical. The final paragenesis is in accordance with typically observed parageneses of chondrules, which is olivine+pyroxene+feldspar, and the occasional spinel, indicating – at least in these cases – an initial melt closer to the Fo-An binary. For a more complete description, the ternary phase diagram Forsterite-Anorthite-Quartz should also be consulted.
6.20 Making a Plot
A brief guide outlining which important elements should or need to be included, i.e., need to appear in a plot.
Axes labelling, units, meaningful scaling with numbers, a legend.
Only information that could not sensibly be included in the figure itself. Resolving the used abbreviations. Alle explanations need to be placed in the text. Self-explanatories such as: ›The plot shows Mg vs. Ti‹ should not appear in the signature.
✓That the symbol colours are the same in all plots.
✗That both plots have a frame.
✗That both plots have similar figure captions.
✓That the symbols are the same.
✗That the plot is not unaesthetically ›open‹ in one direction.
✓It is easy to add specific lines.
✗A complete frame allows for more labelling-possibilities
✗The symbol names in alphabetic order from top to down.
✗All symbol names in the same colour.
✓The symbol names from top to down in the same sequence as the symbols themselves in the plot.
✓Heavy/dark colours more to the top.
6.21 Basics of Scatter Plots
The most typical plots to visualise data. Pairs of data ((x1,y1),(x2,y2),(…,…)) are required for this plot. Any dataset fitting this simple criteria can be presented in a scatter plot.
Both axes display a value, typically a simple value, a ratio, an inverse value, the logarithm of a value/ratio, etc.
It displays a static content. The displayed data show the current state of a system, for example the current composition of a rock.
✓… shows the composition of a rock with an element concentration or isotope composition on each axis (e.g., Mg vs. Al).
✗… shows REE compositions of rocks with various enrichment/depletion patterns.
✓… shows data an isochron plot.
✗… shows the isotope fractionation during evaporative loss from a melt.
✓… an element concentration
✓… normalised element concentration
✗… a sample name
✗… the time
✓… the isotope composition
✗… a chemical element
✓… an element concentration
✓… normalised element concentration
✗… a sample name
✗… the time
✓… the isotope composition
✗… a chemical element
6.22 Basics of Category Plots
This typical plot has categories along its x-axis, sometimes also along its y-axis. Sub-types are for example histograms, line-plots, bar-charts, Caltech Plots, or box-whisker charts. A category might be an element, e.g., the REEs or something like chondrule type, shock class, etc.
The y-axis displays a value, typically a simple value, a ratio, an inverse value, the logarithm of a value/ratio, etc. The category is typically, but not necessarily, a description and not a value. For example, a sample name, a location name, the name of a chemical element, a classification name, etc. The category is usually plotted along the x-axis. Isotope compositions are, however, often displayed the other way round, with the categories on the y- and values on the x-axis.
It displays a static content. The displayed data show the current state of a system, for example the current composition of a rock.
✓… shows REE compositions of rocks with various enrichment/depletion patterns.
✓… shows the composition of a rock with an element concentration or isotope composition on each axis (e.g., Mg vs. Al).
✗… is the ›Caltech‹ plot, i.e., an e.g., isotope composition on the x-axis and the samples stacked along the y-axis.
✓… is a normalised plot showing the bulk chondrite compositions with the various chondrite groups along the x-axis.
✓… an element concentration
✓… normalised element concentration
✗… a sample name
✗… the time
✓… the isotope composition
✗… a chemical element
✗… an element concentration
✗… normalised element concentration
✓… a sample name
✓… the time
✗… the isotope composition
✓… a chemical element
6.23 Basics of Function Plots
Functions are typically used for modelling. A function contains one free parameter plotted on the x-axis. This free parameter is used for modelling and might represent an abundance in mixing or amount of fractionated material from a melt or condensed from a vapour. It might represent an age in a reservoir evolution or the progession of time during element diffusion, and so on.
The y-axis displays a value that changes, i.e., is depended on the parameter plotted along the x-axis. The y-axis can be a simple value, a ratio, an inverse value, the logarithm of a value/ratio, …, while the parameter on the x-axis is typically a simple value that is often plotted across a limited interval (e.g., time or fraction).
It displays a dynamic content, as the variable on the x-axis changes. It is this dynamical change, what is usually the main interest of a function plot.
✓… is the compositional evolution of a reservoir over time.
✗… an isochron plot showing the chronological evolution of a reservoir over time.
✓… the compositional evolution of a reservoir relative to the amount of extracted material.
✓… the isotope fractionation in a reservoir relative to the amount of evaporative loss from a melt.
✗… the compositional evolution of a reservoir and over time, with a different element on each axis (e.g., Mg vs. Al).
✓… an element concentration
✗… the time
✓… the isotope composition
✗… a fraction (e.g., 0…1) of something that is added/removed
✓… an element concentration
✓… the time
✓… the isotope composition
✓… a fraction (e.g., 0…1) of something that is added/removed
✓True
✗False
6.24 Basics of Parametric Plots
Parametric plots are typically used for modelling. A parametric plot contains one free parameter, but two functions that use this same one parameter. The result of these functions, i.e., the respective y-values are plotted along the two axis of a x-y plot. Hence, the free parameter itself is not plotted. The two functions might in fact be the same, i.e., the equation for mixing two reservoirs, however, the two mixing equations will contain different elements. The result of this calculation is then plotted in a scatter plot with the two elements on the respective axes.
Both axes display the resulting value of a function. Both functions have the same parameter that changes. Formally, this looks as follows: y1 = f(x) and y2 = g(x). Then, y1 and y2 are displayed along the two axis. f and g are two functions, and x is the common value that changes. An example is the isochron equation. Here, the function for the x-axis is the decay equation for the parent isotope, and the function for the y-axis is the ingrowth equation for the daughter isotope. The common parameter that changes is the time t. Another example would be the mixing of reservoirs displayed in a scatter plot, e.g., with two element concentrations on the axes (e.g., Si vs. Na). Here the function would in both cases be the mixing equation, but with Si in it for one axis and Na in it for the y-axis. The common parameter that changes would be the fraction of the reservoirs involved in the mixing.
It displays a dynamic content, as the common variable changes. It is this dynamical change that is the main interest of a parametric plot. It is typically used to model various processes. It is also manly combined with the scatter plot.
✓… is the compositional evolution of a reservoir over time.
✓… an isochron plot showing the chronological evolution of a reservoir over time.
✓… the compositional evolution of a reservoir relative to the amount of extracted material.
✓… the isotope fractionation in a reservoir relative to the amount of evaporative loss from a melt.
✓… the compositional evolution of a reservoir and over time, with a different element on each axis (e.g., Mg vs. Al).
✓… an element concentration
✗… the time
✓… the isotope composition
✗… a fraction (e.g., 0…1) of something that is added/removed
✓… an element concentration
✗… the time
✓… the isotope composition
✗… a fraction (e.g., 0…1) of something that is added/removed
6.25 Basics of Combining Plots
For example, when data are combined with a model in a single plot, different types of plots need to be combined, e.g., a scatter plot with a parameteric plot.
Of course, any kind of values can be plotted. It is only important that when plots are combined that all the plots that are going to be combined have the same values on the same axes.
Combined plots are ideal to combine static and dynamic contents. For example, an x-y plot might display the static composition of a rock, and is then combined with a parametric plot showing e.g., a mixing or fractionation model. Another example would be a static x-y plot showing the isotope composition of many rocks, e.g., epsilon Hf vs. time, which is then combined with a dynamic evolution plot modelling the Lu-Hf system over time.
✓… is a static plot combined with another static plot.
✓… is a static plot combined with a dynamic plot.
✓… is a dynamic plot combined with another dynamic plot.
✗True
✓False
✓True
✗False
6.26 Basics of Ternary Plots
This is used when triples of data ((x1,y1,z1),(x2,y2,z3),(…,…,…)) are visualised in triangular plots. Phase diagrams of chemographic triangles use this kind of presentation.
In principle, any type of value. These values can be absolute concentrations, when e.g., elements are at the corners. But often, components such as minerals are plotted at the corners, in which case the fractions of these components are often plotted along the axes. This means, the absolute abundances of each component is first re-normalised to 1 or 100.
Of course this is possible. It is basically possible to construct a ternary parametric plot that would add dynamic content such as mixing, fractionation, or even radiogenic evolution.
✓… is a phase diagram.
✗… shows REE compositions of rocks with various enrichment/depletion patterns.
✗… is the ›Caltech‹ plot, i.e., an e.g., isotope composition on the x-axis and the samples stacked along the two other axes.
✓… is a chemographic representation.
✗True
✓False
✓a/(a+b+c)
✗a/(b+c)
✗a/a+b+c c/(a+b+c)
✓b/(b+c)