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Abstract <p>Published experimental data were used in a new calibration of the dependence of the Ti<sup>4+</sup>/Ti<sup>3+</sup> ratio in silicate melts on temperature, oxygen fugacity, and melt composition. The standard error in determining <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({\text{log}}\left[ {{{{{X}_{{{\text{Ti}}{{{\text{O}}}_{{\text{2}}}}}}}} \mathord{\left/ {\vphantom {{{{X}_{{{\text{Ti}}{{{\text{O}}}_{{\text{2}}}}}}}} {\left( {{{X}_{{{\text{Ti}}{{{\text{O}}}_{{{\text{1}}{\text{.5}}}}}}}}} \right)}}} \right. \kern-0em} {\left( {{{X}_{{{\text{Ti}}{{{\text{O}}}_{{{\text{1}}{\text{.5}}}}}}}}} \right)}}} \right]\)</EquationSource> <!--PetrEng2670006Borisov-m1--> </InlineEquation> by the proposed equation <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({\text{log}}\left[ {{{{{X}_{{{\text{Ti}}{{{\text{O}}}_{{\text{2}}}}}}}} \mathord{\left/ {\vphantom {{{{X}_{{{\text{Ti}}{{{\text{O}}}_{{\text{2}}}}}}}} {\left( {{{X}_{{{\text{Ti}}{{{\text{O}}}_{{{\text{1}}{\text{.5}}}}}}}}} \right)}}} \right. \kern-0em} {\left( {{{X}_{{{\text{Ti}}{{{\text{O}}}_{{{\text{1}}{\text{.5}}}}}}}}} \right)}}} \right]\)</EquationSource> <!--PetrEng2670006Borisov-m2--> </InlineEquation> = 0.216log <i>f</i>O<sub>2</sub> – 0.280<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\({{X_{{{\text{Ti}}{{{\text{O}}}_{2}}}}^{2}} \mathord{\left/ {\vphantom {{X_{{{\text{Ti}}{{{\text{O}}}_{2}}}}^{2}} {X_{{{\text{Si}}{{{\text{O}}}_{2}}}}^{{}}}}} \right. \kern-0em} {X_{{{\text{Si}}{{{\text{O}}}_{2}}}}^{{}}}}\)</EquationSource> <!--PetrEng2670006Borisov-m3--> </InlineEquation> – 2.885<InlineEquation ID="IEq4"> <EquationSource Format="TEX">\({{{{X}_{{{\text{A}}{{{\text{l}}}_{{\text{2}}}}{{{\text{O}}}_{{\text{3}}}}}}}} \mathord{\left/ {\vphantom {{{{X}_{{{\text{A}}{{{\text{l}}}_{{\text{2}}}}{{{\text{O}}}_{{\text{3}}}}}}}} {{{X}_{{{\text{Si}}{{{\text{O}}}_{{\text{2}}}}}}}}}} \right. \kern-0em} {{{X}_{{{\text{Si}}{{{\text{O}}}_{{\text{2}}}}}}}}}\)</EquationSource> <!--PetrEng2670006Borisov-m4--> </InlineEquation> – 5.727<i>X</i><sub>MgO</sub>/<InlineEquation ID="IEq5"> <EquationSource Format="TEX">\({{X}_{{{\text{Si}}{{{\text{O}}}_{{\text{2}}}}}}}\)</EquationSource> <!--PetrEng2670006Borisov-m5--> </InlineEquation> – 5.997<i>X</i><sub>CaO</sub>/<InlineEquation ID="IEq6"> <EquationSource Format="TEX">\({{X}_{{{\text{Si}}{{{\text{O}}}_{{\text{2}}}}}}}\)</EquationSource> <!--PetrEng2670006Borisov-m6--> </InlineEquation> – 3.864<InlineEquation ID="IEq7"> <EquationSource Format="TEX">\({{{{X}_{{{\text{N}}{{{\text{a}}}_{{\text{2}}}}{\text{O}}}}}} \mathord{\left/ {\vphantom {{{{X}_{{{\text{N}}{{{\text{a}}}_{{\text{2}}}}{\text{O}}}}}} {{{X}_{{{\text{Si}}{{{\text{O}}}_{{\text{2}}}}}}}}}} \right. \kern-0em} {{{X}_{{{\text{Si}}{{{\text{O}}}_{{\text{2}}}}}}}}}\)</EquationSource> <!--PetrEng2670006Borisov-m7--> </InlineEquation> + 12 433(<i>X</i><sub>MgO</sub> + <i>X</i><sub>CaO</sub> + <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\({{X}_{{{\text{N}}{{{\text{a}}}_{{\text{2}}}}{\text{O}}}}}\)</EquationSource> <!--PetrEng2670006Borisov-m8--> </InlineEquation>)/(<InlineEquation ID="IEq9"> <EquationSource Format="TEX">\({{X}_{{{\text{Si}}{{{\text{O}}}_{{\text{2}}}}}}}\)</EquationSource> <!--PetrEng2670006Borisov-m9--> </InlineEquation><i>T</i>(K)) + 2.490 (where <i>X</i><sub><i>i</i></sub> is the mole fraction of component <i>i</i> in the melt) is 0.065, which is equivalent to an error of 0.24 in determining log <i>f</i>O<sub>2</sub>. It has been shown that in melts corresponding to the compositions of lunar glasses (Delano, 1986), the Ti<sup>3+</sup>/Ti<sub>tot</sub> ratio at 1300°C and oxygen fugacity at the iron–wüstite (IW) buffer level is only 0.03 on average. Even this small Ti<sup>3+</sup> content should be mostly oxidized to Ti<sup>4+</sup> during melt cooling/quenching into glass as a result of redox exchange with Fe<sup>3+</sup>.</p>

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New Calibration of the Ti4+/Ti3+ Ratio in Silicate Melts: From Simple Slags to Lunar Basalts

  • 期刊论文

  • 发表日期：

    2026年6月1日

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  • A. A. Borisov

摘要

Abstract

Published experimental data were used in a new calibration of the dependence of the Ti4+/Ti3+ ratio in silicate melts on temperature, oxygen fugacity, and melt composition. The standard error in determining \({\text{log}}\left[ {{{{{X}_{{{\text{Ti}}{{{\text{O}}}_{{\text{2}}}}}}}} \mathord{\left/ {\vphantom {{{{X}_{{{\text{Ti}}{{{\text{O}}}_{{\text{2}}}}}}}} {\left( {{{X}_{{{\text{Ti}}{{{\text{O}}}_{{{\text{1}}{\text{.5}}}}}}}}} \right)}}} \right. \kern-0em} {\left( {{{X}_{{{\text{Ti}}{{{\text{O}}}_{{{\text{1}}{\text{.5}}}}}}}}} \right)}}} \right]\) by the proposed equation \({\text{log}}\left[ {{{{{X}_{{{\text{Ti}}{{{\text{O}}}_{{\text{2}}}}}}}} \mathord{\left/ {\vphantom {{{{X}_{{{\text{Ti}}{{{\text{O}}}_{{\text{2}}}}}}}} {\left( {{{X}_{{{\text{Ti}}{{{\text{O}}}_{{{\text{1}}{\text{.5}}}}}}}}} \right)}}} \right. \kern-0em} {\left( {{{X}_{{{\text{Ti}}{{{\text{O}}}_{{{\text{1}}{\text{.5}}}}}}}}} \right)}}} \right]\) = 0.216log fO2 – 0.280 \({{X_{{{\text{Ti}}{{{\text{O}}}_{2}}}}^{2}} \mathord{\left/ {\vphantom {{X_{{{\text{Ti}}{{{\text{O}}}_{2}}}}^{2}} {X_{{{\text{Si}}{{{\text{O}}}_{2}}}}^{{}}}}} \right. \kern-0em} {X_{{{\text{Si}}{{{\text{O}}}_{2}}}}^{{}}}}\) – 2.885 \({{{{X}_{{{\text{A}}{{{\text{l}}}_{{\text{2}}}}{{{\text{O}}}_{{\text{3}}}}}}}} \mathord{\left/ {\vphantom {{{{X}_{{{\text{A}}{{{\text{l}}}_{{\text{2}}}}{{{\text{O}}}_{{\text{3}}}}}}}} {{{X}_{{{\text{Si}}{{{\text{O}}}_{{\text{2}}}}}}}}}} \right. \kern-0em} {{{X}_{{{\text{Si}}{{{\text{O}}}_{{\text{2}}}}}}}}}\) – 5.727XMgO/ \({{X}_{{{\text{Si}}{{{\text{O}}}_{{\text{2}}}}}}}\) – 5.997XCaO/ \({{X}_{{{\text{Si}}{{{\text{O}}}_{{\text{2}}}}}}}\) – 3.864 \({{{{X}_{{{\text{N}}{{{\text{a}}}_{{\text{2}}}}{\text{O}}}}}} \mathord{\left/ {\vphantom {{{{X}_{{{\text{N}}{{{\text{a}}}_{{\text{2}}}}{\text{O}}}}}} {{{X}_{{{\text{Si}}{{{\text{O}}}_{{\text{2}}}}}}}}}} \right. \kern-0em} {{{X}_{{{\text{Si}}{{{\text{O}}}_{{\text{2}}}}}}}}}\) + 12 433(XMgO + XCaO + \({{X}_{{{\text{N}}{{{\text{a}}}_{{\text{2}}}}{\text{O}}}}}\) )/( \({{X}_{{{\text{Si}}{{{\text{O}}}_{{\text{2}}}}}}}\) T(K)) + 2.490 (where Xi is the mole fraction of component i in the melt) is 0.065, which is equivalent to an error of 0.24 in determining log fO2. It has been shown that in melts corresponding to the compositions of lunar glasses (Delano, 1986), the Ti3+/Titot ratio at 1300°C and oxygen fugacity at the iron–wüstite (IW) buffer level is only 0.03 on average. Even this small Ti3+ content should be mostly oxidized to Ti4+ during melt cooling/quenching into glass as a result of redox exchange with Fe3+.