Modal-Space Theory: A Study of the Mineralogical Expression of Tholeiitic Compositions At<i>T</i>> 850 °C In the Lithosphere and Mantle
Bibliographic record
Abstract
Abstract Modal-space illustrates changes in the volumes and compositions of minerals in a rock (Thompson 1991), for example, in response to P - T -sensitive, high-variance reactions. The method is applied to retrograded eclogite (Pl + Cpx + Grt + Qz + Hbl + Ep) in the Cuaba Unit of the Rio San Juan Complex in the Dominican Republic (Abbott & Draper 2007), where the issue is characterizing the highest-grade mineral assemblage (Omp + Grt + Coe ± Ky). For the purpose of comparing volumes, additive mineral components are normalized to one oxygen atom, such that grt = M 1/4 A 1/6 Si 1/4 O, px = M 1/3 Si 1/3 O, where M = Fe 2+ + Mg + Mn, A = Al + Fe 3+ ; an = Ca 1/8 Al 1/4 Si 1/4 O(anorthite), qz (quartz) = coe (coesite) = Si 1/2 O, and ky (kyanite) = Al 2/5 Si 1/5 O. A mole of each has approximately the same volume for all phases (10.6 ± 1.1 cm 3 /mole “O”). The error in the approximation is acceptable, given the error in estimating modal proportions, and especially given normal heterogeneity in a rock. Sodium in the form of an 1/3 ab 2/3 = csk 1/2 jd 1/2 ( an = 1 / 8 CaAl 2 Si 2 O 8 , ab = 1 / 8 NaAlSi 3 O 8 , csk = 1 / 6 Ca 1/2 □ 1/2 AlSi 2 O 6 , jd = 1 / 6 NaAlSi 2 O 6 ) is subtracted from the bulk composition. This works because the composition of any plagioclase can be expressed as a linear combination of an 1/3 ab 2/3 and an . The residual bulk-rock chemistry (after subtracting an 1/3 ab 2/3 = csk 1/2 jd 1/2 ) is in the CMAS system (M = Fe 2+ + Mg + Mn, A = Al + Fe 3+ ). Two CMAS exchange components are included, tk = A 2 M –1 Si –1 (tschermak) and cm = CaM –1 . The modal space is then defined by three independent vectors in CMAS: For a particular bulk composition, accessible parts of the modal space define a polyhedron. A point within the polyhedron is defined by a linear combination of V 1 , V 2 , and V 3 , and in CMAS relates to the modal proportions of the minerals and their compositions. The composition and total volume of plagioclase or pyroxene are easily corrected for the amounts of non-CMAS an 1/3 ab 2/3 or csk 1/2 jd 1/2 , respectively. For mafic compositions, different parts of the polyhedron correspond to basalt/gabbro, pyroxene granulite, garnet granulite, eclogite, and extremely high- P assemblages with majoritic garnet. The modal polyhedron can be calculated in two ways: (1) from the bulk composition, or (2) from mineral chemistry and observed modal proportions. When the description of the system is internally consistent, the two approaches converge on the same polyhedron.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".