Crystal Structures of Biotite at High Temperatures and of Heat-Treated Biotite using Neutron Powder Diffraction
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Bibliographic record
Abstract
Abstract The crystal structure of biotite-1 M from Bancroft, Ontario, with the formula: <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mtext>K</mml:mtext><mml:mrow><mml:mn>1.96</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mtext>Na</mml:mtext></mml:mrow><mml:mrow><mml:mn>0.13</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mtext>Ca</mml:mtext></mml:mrow><mml:mrow><mml:mn>0.01</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mtext>Mg</mml:mtext></mml:mrow><mml:mrow><mml:mn>3.15</mml:mn></mml:mrow></mml:msub><mml:msubsup><mml:mrow><mml:mtext>Fe</mml:mtext></mml:mrow><mml:mrow><mml:mn>2.59</mml:mn></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msubsup><mml:msub><mml:mrow><mml:mtext>Ti</mml:mtext></mml:mrow><mml:mrow><mml:mn>0.17</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mtext>Mn</mml:mtext></mml:mrow><mml:mrow><mml:mn>0.09</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mtext>Si</mml:mtext></mml:mrow><mml:mrow><mml:mn>5.98</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mtext>Al</mml:mtext></mml:mrow><mml:mrow><mml:mn>1.92</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mtext>Ti</mml:mtext></mml:mrow><mml:mrow><mml:mn>0.10</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:msub><mml:mtext>O</mml:mtext><mml:mrow><mml:mn>20</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mtext>OH</mml:mtext></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mn>1.47</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mtext>F</mml:mtext><mml:mrow><mml:mn>1.98</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:math> , was determined by Rietveld refinement using high-resolution neutron powder diffraction at in situ temperatures ranging from 20 to 900°C. The room-temperature structure of the samples heated to between 400 and 900°C using an electric furnace in air was also refined. The crystal structures were refined to an R P of 2.98 — 5.06% and R wp of 3.84–6.77%. For the in situ heating experiments in a vacuum, the unit-cell dimensions increased linearly to 600°C. The linear expansion coefficient for the c axis was 1.65 × 10 −5 °C −1 , while those for the a and b dimensions were 4.44 × 10 −6 °C −1 and 5.21 × 10 −6 °C −1 , respectively. Accordingly, the increase in the unit-cell volume up to 600 C occurred mainly along the c axis, resulting from the expansion in the K coordination sphere along that direction. Results for all K−O bonds were analyzed in terms of the lattice component and an inner component of the structural strain. The ditrigonal distortion decreased (3.76 at 20°C to 1.95 at 600°C) with temperature, because the shorter bonds expanded and the longer bonds contracted. The increase in the interlayer separation and the decrease in the interlayer octahedral flattening angle confirmed that the c -dominated expansion occurred in the interlayer region. In the case of the ex situ -heated samples, the cell dimensions decreased sharply at temperatures over 400 C. The octahedral sheet thickness and mean < M −O> distance decreased linearly due to oxidation of octahedral Fe. However, the interlayer separation and mean <K−O> distance decreased at temperatures over 400°C. At 400°C, dehydroxylation began to increase and interlayer regions became more constricted. The overall cell parameters decreased rapidly with increasing temperatures due to dehydroxylation. The large inner strain components in the K−O bonds also resulted in an increase in the considerable ditrigonal distortion (3.57° at 400°C to 6.15° at 900°C).
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 it