Authors: Maria A. Dias | Ralf Dohmen
Source: Contributions to Mineralogy and Petrology (article, 2024-04-01)
Field: Materials Science — Metals and Alloys

Experimental determination of Fe–Mg interdiffusion in orthopyroxene as a function of Fe content Abstract We have measured the dependence of the Fe–Mg interdiffusion coefficient, D Fe-Mg , on the ferrosilite component in orthopyroxene, which so far has not been experimentally calibrated. Diffusion couples, consisting of approximately 1 µm thin-films were deposited by pulsed laser ablation on orthopyroxene crystals of En 91 Fs 9 composition. Diffusion experiments were carried out at atmospheric pressure in vertical gas mixing furnaces (CO-CO 2 ) at temperatures between 950 and 1100 °C at constant f O 2 = 10 –7 Pa. Using a focused ion beam-scanning electron microscope (FIB-SEM), FIB-foils were cut from diffusion couples before and after annealing. Diffusion profiles were extracted by using combined backscattered electron (BSE) imaging and energy dispersive X-ray (EDXS) mapping on FIB-foils which allowed to resolve concentration gradients within 20 nm. The microstructure of the diffusion experiments was investigated using transmission electron microscopy (TEM). Using this method, we obtained the first experimentally determined data on the dependence of D Fe-Mg on the ferrosilite content in orthopyroxene at different temperatures, appearing to increase with increasing a temperature. For the temperature range (950 – 1100 °C), log f O 2 = -7 Pa, along [001] in the composition Fs9, the log D Fe-Mg yields the following Arrhenius equation: $$D_{Fe - Mg} [m^2 /s] = 3.8 \cdot 10^{ - 9} \exp [ - 261.07 \pm 24[kJ/mol]/(R/T[K])]$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi>F</mml:mi><mml:mi>e</mml:mi><mml:mo>-</mml:mo><mml:mi>M</mml:mi><mml:mi>g</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>[</mml:mo><mml:msup><mml:mi>m</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo>/</mml:mo><mml:mi>s</mml:mi><mml:mo>]</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mn>3.8</mml:mn><mml:mo>·</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn>9</mml:mn></mml:mrow></mml:msup><mml:mo>exp</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mo>-</mml:mo><mml:mn>261.07</mml:mn><mml:mo>±</mml:mo><mml:mn>24</mml:mn><mml:mrow><mml:mo>[</mml:mo><mml:mi>k</mml:mi><mml:mi>J</mml:mi><mml:mo>/</mml:mo><mml:mi>m</mml:mi><mml:mi>o</mml:mi><mml:mi>l</mml:mi><mml:mo>]</mml:mo></mml:mrow><mml:mo>/</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mi>R</mml:mi><mml:mo>/</mml:mo><mml:mi>T</mml:mi><mml:mrow><mml:mo>[</mml:mo><mml:mi>K</mml:mi><mml:mo>]</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:math> The effect of X Fe on D Fe-Mg, given by $$D(X_{Fe} ) = D(X_{Fe} = 0.09) \cdot {10}^{m (X_{Fe} - 0.09)},$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>D</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>Fe</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>D</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>Fe</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>0.09</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mo>·</mml:mo><mml:msup><mml:mrow><mml:mn>10</mml:mn></mml:mrow><mml:mrow><mml:mi>m</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>Fe</mml:mi></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:mn>0.09</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:msup><mml:mo>,</mml:mo></mml:mrow></mml:math> can be calculated by the following parameterization where m follows a linear regression of m on temperature: $$m = - 2.711 \cdot 10^4 /T(K) + 23.5408$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>m</mml:mi><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mn>2.711</mml:mn><mml:mo>·</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mn>4</mml:mn></mml:msup><mml:mo>/</mml:mo><mml:mi>T</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>K</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mn>23.5408</mml:mn></mml:mrow></mml:math> By considering the D Fe-Mg dependence on X Fe , the timescales of natural processes obtained from modelling the compositional zoning of natural crystal may considerably differ from previously estimated timescales. Geology ; Geochemistry ; Mineral resource classification ; Function (biology) ; Content (measure theory) ; Mineralogy ; Mathematics Hydrogen embrittlement and corrosion behaviors in metals ; Material Properties and Failure Mechanisms ; High-pressure geophysics and materials