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首页> 外文期刊>Contributions to Mineralogy and Petrology >Quantifying garnet-melt trace element partitioning using lattice-strain theory: new crystal-chemical and thermodynamic constraints
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Quantifying garnet-melt trace element partitioning using lattice-strain theory: new crystal-chemical and thermodynamic constraints

机译：使用晶格应变理论量化石榴石熔体中痕量元素的分配：新的晶体化学和热力学约束

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摘要

Many geochemical models of major igneous differentiation events on the Earth, the Moon, and Mars invoke the presence of garnet or its high-pressure majoritic equivalent as a residual phase, based on its ability to fractionate critical trace element pairs (Lu/Hf, U/Th, heavy REE/light REE). As a result, quantitative descriptions of mid-ocean ridge and hot spot magmatism, and lunar, martian, and terrestrial magma oceans require knowledge of garnet-melt partition coefficients over a wide range of conditions. In this contribution, we present new crystal-chemical and thermodynamic constraints on the partitioning of rare earth elements (REE), Y and Sc between garnet and anhydrous silicate melt as a function of pressure (P), temperature (T), and composition (X). Our approach is based on the interpretation of experimentally determined values of partition coefficients D using lattice-strain theory. In this and a companion paper (Draper and van Westrenen this issue) we derive new predictive equations for the ideal ionic radius of the dodecahedral garnet X-site, r_0(3+), its apparent Young's modulus E_X(3+), and the strain-free partition coefficient D_0(3+) for a fictive REE element J of ionic radius r_0(3+). The new calibrations remedy several shortcomings of earlier lattice-strain based attempts to model garnet-melt partitioning. A hitherto irresolvable temperature effect on r_0(3+) is identified, as is a pronounced decrease in E_X{3+) as Al on the garnet Y site is progressively replaced by quadruvalent cations (Si, Ti) as pressure and garnet majorite content increase. D_0(3+) can be linked to the free energy of fusion of a hypothetical rare-earth garnet component JFe_2Al_3Si_2O_(12) through simple activity-composition relations. By combining the three lattice-strain parameter models, garnet-anhydrous melt and majorite-anhydrous melt D values for the REE, Y and Sc can be predicted from P, T, garnet major element composition, and melt iron content at pressures from 2.5-25 GPa and temperatures up to 2,573 K, covering virtually the entire P-T range over which igneous garnets are stable in solar system compositions. Standard deviations of the difference between predicted and observed D_(REE,Y,Sc) range from 25 percent for Er to 70 percent for Ce, and are not correlated with trace element mass. The maximum error in D prediction (n > 300) is 218 percent for one measurement of D_(Dy). This is remarkably low considering the total spread in D values of over four orders of magnitude.
机译：地球，月球和火星上许多主要火成岩分化事件的地球化学模型都基于其分离关键痕量元素对（Lu / Hf，U和U）的能力，将石榴石或其高压主生等同物作为残留相存在。 / Th，重REE /轻REE）。结果，对中洋洋脊和热点岩浆作用以及月球，火星和陆地岩浆海洋的定量描述需要了解广泛条件下的石榴石融化分配系数。在这项贡献中，我们提出了石榴石和无水硅酸盐熔体之间稀土元素（REE），Y和Sc的分配随压力（P），温度（T）和成分（ X）。我们的方法基于使用晶格应变理论对分配系数D的实验确定值的解释。在本论文和伴随论文中（Draper和van Westrenen，本期），我们得出了十二面体石榴石X位置的理想离子半径r_0（3+），其表观杨氏模量E_X（3+）的新预测方程。离子半径为r_0（3+）的虚拟REE元素J的无应变分配系数D_0（3+）。新的校准方法弥补了早期基于晶格应变的石榴石融化分区建模方法的一些缺点。确认了迄今为止对r_0（3+）不可解决的温度影响，随着石榴石Y位点上的Al随着压力和石榴石主要成分含量的增加逐渐被四价阳离子（Si，Ti）取代，E_X {3+）的显着降低。 D_0（3+）可以通过简单的活性-成分关系与假设的稀土石榴石成分JFe_2Al_3Si_2O_（12）的融合自由能相连。通过结合这三个晶格应变参数模型，可以从P，T，石榴石主要元素组成和压力为2.5-1.5的铁水含量中预测出REE，Y和Sc的石榴石-无水熔体和主要矿物-无水熔体的D值。 25 GPa的温度和高达2,573 K的温度，几乎覆盖了整个PT范围，在此范围内火成石榴石在太阳能系统成分中稳定。预测和观察到的D_（REE，Y，Sc）之间差异的标准偏差范围为Er的25％至Ce的70％，并且与痕量元素质量无关。对于D_（Dy）的一次测量，D预测中的最大误差（n> 300）为218％。考虑到D值的总扩散超过四个数量级，这非常低。

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