Experimental grain growth of quartz aggregates under wet conditions and its application to deformation in nature

<p>Grain growth of quartz was investigated using two quartz samples (powder and novaculite) with water under pressure and temperature conditions of 1.0–2.5&thinsp;GPa and 800–1100&thinsp;<span class="inline-formula">^∘</span>C. The compacted powder preserved a substantial porosity, which caused a slower grain growth than in the novaculite. We assumed a grain growth law of <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M2" display="inline" overflow="scroll" dspmath="mathml"><mrow><msup><mi>d</mi><mi>n</mi></msup><mo>-</mo><msubsup><mi>d</mi><mn mathvariant="normal">0</mn><mi>n</mi></msubsup><mo>=</mo><msub><mi>k</mi><mn mathvariant="normal">0</mn></msub><msubsup><mi>f</mi><mrow class="chem"><msub><mi mathvariant="normal">H</mi><mn mathvariant="normal">2</mn></msub><mi mathvariant="normal">O</mi></mrow><mi>r</mi></msubsup><mi>exp⁡</mi><mo>(</mo><mo>-</mo><mi>Q</mi><mo>/</mo><mi>R</mi><mi>T</mi><mo>)</mo><mi>t</mi></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="150pt" height="17pt" class="svg-formula" dspmath="mathimg" md5hash="360eb1f1682d0a89fc56b42c8640a0cd"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="se-10-621-2019-ie00001.svg" width="150pt" height="17pt" src="se-10-621-2019-ie00001.png"/></svg:svg></span></span> with grain size <span class="inline-formula"><i>d</i></span> (<span class="inline-formula">µ</span>m) at time <span class="inline-formula"><i>t</i></span> (seconds), initial grain size <span class="inline-formula"><i>d</i>₀</span> (<span class="inline-formula">µ</span>m), growth exponent <span class="inline-formula"><i>n</i></span>, a constant <span class="inline-formula"><i>k</i>₀</span> (<span class="inline-formula">µ</span>m<span class="inline-formula">^<i>n</i></span>&thinsp;MPa<span class="inline-formula">^−<i>r</i></span>&thinsp;s<span class="inline-formula">⁻¹</span>), water fugacity <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M14" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>f</mi><mrow class="chem"><msub><mi mathvariant="normal">H</mi><mn mathvariant="normal">2</mn></msub><mi mathvariant="normal">O</mi></mrow></msub></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="22pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="1277ca9ea912fe61f0760abc7ed45444"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="se-10-621-2019-ie00002.svg" width="22pt" height="14pt" src="se-10-621-2019-ie00002.png"/></svg:svg></span></span> (MPa) with the exponent <span class="inline-formula"><i>r</i></span>, activation energy <span class="inline-formula"><i>Q</i></span> (kJ&thinsp;mol<span class="inline-formula">⁻¹</span>), gas constant <span class="inline-formula"><i>R</i></span>, and temperature <span class="inline-formula"><i>T</i></span> in Kelvin. The parameters we obtained were <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M20" display="inline" overflow="scroll" dspmath="mathml"><mrow><mi>n</mi><mo>=</mo><mn mathvariant="normal">2.5</mn><mo>±</mo><mn mathvariant="normal">0.4</mn></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="63pt" height="10pt" class="svg-formula" dspmath="mathimg" md5hash="7455d8bed57ba49d310f3cfabc573513"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="se-10-621-2019-ie00003.svg" width="63pt" height="10pt" src="se-10-621-2019-ie00003.png"/></svg:svg></span></span>, <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M21" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>k</mi><mn mathvariant="normal">0</mn></msub><mo>=</mo><msup><mn mathvariant="normal">10</mn><mrow><mo>-</mo><mn mathvariant="normal">8.8</mn><mo>±</mo><mn mathvariant="normal">1.4</mn></mrow></msup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="71pt" height="16pt" class="svg-formula" dspmath="mathimg" md5hash="468620545483b5b878aa790e21f79007"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="se-10-621-2019-ie00004.svg" width="71pt" height="16pt" src="se-10-621-2019-ie00004.png"/></svg:svg></span></span>, <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M22" display="inline" overflow="scroll" dspmath="mathml"><mrow><mi>r</mi><mo>=</mo><mn mathvariant="normal">2.3</mn><mo>±</mo><mn mathvariant="normal">0.3</mn></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="62pt" height="10pt" class="svg-formula" dspmath="mathimg" md5hash="6317045305de8e98b8397c3b72ea0395"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="se-10-621-2019-ie00005.svg" width="62pt" height="10pt" src="se-10-621-2019-ie00005.png"/></svg:svg></span></span>, and <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M23" display="inline" overflow="scroll" dspmath="mathml"><mrow><mi>Q</mi><mo>=</mo><mn mathvariant="normal">48</mn><mo>±</mo><mn mathvariant="normal">34</mn></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="59pt" height="10pt" class="svg-formula" dspmath="mathimg" md5hash="5d8d8344c5e9c84959f665b2c7a9ca35"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="se-10-621-2019-ie00006.svg" width="59pt" height="10pt" src="se-10-621-2019-ie00006.png"/></svg:svg></span></span> for the powder and <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M24" display="inline" overflow="scroll" dspmath="mathml"><mrow><mi>n</mi><mo>=</mo><mn mathvariant="normal">2.9</mn><mo>±</mo><mn mathvariant="normal">0.4</mn></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="63pt" height="10pt" class="svg-formula" dspmath="mathimg" md5hash="f37bba991e9203756c8a6fa553c2f786"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="se-10-621-2019-ie00007.svg" width="63pt" height="10pt" src="se-10-621-2019-ie00007.png"/></svg:svg></span></span>, <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M25" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>k</mi><mn mathvariant="normal">0</mn></msub><mo>=</mo><msup><mn mathvariant="normal">10</mn><mrow><mo>-</mo><mn mathvariant="normal">5.8</mn><mo>±</mo><mn mathvariant="normal">2.0</mn></mrow></msup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="71pt" height="16pt" class="svg-formula" dspmath="mathimg" md5hash="84337cf266827e3077f5edd66d7012cc"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="se-10-621-2019-ie00008.svg" width="71pt" height="16pt" src="se-10-621-2019-ie00008.png"/></svg:svg></span></span>, <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M26" display="inline" overflow="scroll" dspmath="mathml"><mrow><mi>r</mi><mo>=</mo><mn mathvariant="normal">1.9</mn><mo>±</mo><mn mathvariant="normal">0.3</mn></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="62pt" height="10pt" class="svg-formula" dspmath="mathimg" md5hash="6417f5160417f42ea64c7a2be22618d5"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="se-10-621-2019-ie00009.svg" width="62pt" height="10pt" src="se-10-621-2019-ie00009.png"/></svg:svg></span></span>, and <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M27" display="inline" overflow="scroll" dspmath="mathml"><mrow><mi>Q</mi><mo>=</mo><mn mathvariant="normal">60</mn><mo>±</mo><mn mathvariant="normal">49</mn></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="59pt" height="10pt" class="svg-formula" dspmath="mathimg" md5hash="2c9b29a1c4d49a23e5477ccfb185d677"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="se-10-621-2019-ie00010.svg" width="59pt" height="10pt" src="se-10-621-2019-ie00010.png"/></svg:svg></span></span> for the novaculite. The grain growth parameters obtained for the powder may be of limited use because of the high porosity of the powder with respect to crystalline rocks (novaculite), even if the differences between powder and novaculite vanish when grain sizes reach <span class="inline-formula">∼70</span>&thinsp;<span class="inline-formula">µ</span>m. Extrapolation of the grain growth laws to natural conditions indicates that the contribution of grain growth to plastic deformation in the middle crust may be small. However, grain growth might become important for deformation in the lower crust when the strain rate is &lt;&thinsp;10<span class="inline-formula">⁻¹²</span>&thinsp;s<span class="inline-formula">⁻¹</span>.</p>

Abstract licence: CC BY

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