An internally consistent model for the thermodynamic properties of Fe−Mg-titanomagnetite-aluminate spinels
An internally consistent model for the thermodynamic properties of Fe−Mg-titanomagnetite-aluminate spinels
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DOI：
10.1007/bf00321989
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发表时间：
1991
影响因子：
3.5
通讯作者：
R. Sack;M. Ghiorso
中科院分区：
文献类型：
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作者：
R. Sack;M. Ghiorso
建立了一个Fd 3 m空间群的Fe 2 +− Mg 2 +-铝酸盐-钛酸盐-铁氧体尖晶石的热力学性质模型。该模型采用了一个表达式的构型熵的混合占长程有序四面体和八面体网站。不考虑短程有序或偏离立方对称。非构型吉布斯自由能被表示为六个线性独立的组成和排序变量的二阶泰勒展开式。校准模型参数以再现MgAl 2 O 4和MgFe 2 O 4中的有序-无序现象，以及橄榄石与以下材料之间的Fe 2 +− Mg 2+分配数据：（1）铝酸盐尖晶石;（2）铁氧体尖晶石;（3）钛酸盐尖晶石;（4）混合铝酸盐-铁氧体尖晶石。这种校准是在没有调用非构型的混合过剩熵的情况下进行的。该模型预测FeAl 2 O 4的有序状态比MgAl 2 O 4的有序状态更正常。它还成功地解释了二元组份中的溶解热测量和活度-组成关系。相平衡的限制要求的Fe 3 O 4的结构在所有温度下比随机更逆，Mg 2+具有较强的四面体位置的偏好相对于Fe 2+。分析表明，在钛酸盐中，八面体位置上的短程有序在高达1300° C的温度下可能是显著的。通过对Fe 2 +− Mg 2 +-铝酸盐钛酸盐-铁氧体尖晶石固溶体的热力学性质进行校准，得到了一些限制条件，这些限制条件允许扩展Berman（1988）的数据库，以包括对铁铝尖晶石（FeAl 2 O 4）、钛尖晶石（Fe 2 TiO 4）、MgFe 2 O 4和立方Mg 2 TiO 4的端元性质的估计。在构建这些估计，提供了低温磁熵的贡献和无序的铝酸盐和铁氧体的精力充沛的后果。这些估计是一致的，所有可用的低温绝热量热法，高温热含量，和热的解决方案的端员测量。分析表明，在300° ~ 900 ° C范围内，MgAl_2 O_4的结构出现了明显的无序化现象，而FeAl_2 O_4的无序化现象在700° C以上才变得明显。相同的热容量的铁氧体中的响应表明，有序/无序转变耦合到反铁磁-顺磁转变MgFe 2 O 4，但发生远高于磁铁矿中的亚铁磁-顺磁转变。该模型与其他文献中关于Fe 2 +− Mg 2+橄榄石和斜方辉石（Sack and Ghiorso 1989）、菱面体氧化物（Ghiorso 1990 a）以及Berman（1988）的剩余端元性质的溶液理论是一致的。
A model is developed for the thermodynamic properties of Fe2+−Mg2+-aluminate-titanate-ferrite spinels of space group Fd3m. The model incorporates an expression for the configurational entropy of mixing which accounts for long-range order over tetrahedral and octahedral sites. Short-range order or departures from cubic symmetry are not considered. The non-configurational Gibbs energy is formulated as a second degree Taylor expansion in six linearly independent composition and ordering variables. The model parameters are calibrated to reproduce miscibility gap constraints, order-disorder phenomena in MgAl2O4and MgFe2O4, and Fe2+−Mg2+partitioning data between olivine and: (1) aluminate spinels; (2) ferrite spinels; (3) titanate spinels; (4) mixed aluminate-ferrite spinels. This calibration is achievedwithoutinvoking non-configurational excess entropies of mixing. The model predicts that the ordering state of FeAl2O4is more normal than that of MgAl2O4. It also successfully accounts for heat of solution measurements and activity-composition relations in the constituent binaries. Phase equilibrium constraints require that the structure of Fe3O4is more inverse than random at all temperatures and that Mg2+has a strong tetrahedral site preference with respect to that of Fe2+. The analysis suggests that in the titanates short range order on octahedral sites may be significant at temperatures as high as 1300° C. Constraints developed from calibrating the thermodynamic properties of Fe2+−Mg2+-aluminatetitanate-ferrite spinel solid solutions permit extension of the database of Berman (1988) to include estimates of the end-member properties of hercynite (FeAl2O4), ulvöspinel (Fe2TiO4), MgFe2O4and cubic Mg2TiO4. In constructing these estimates, provision is made for low-temperature magnetic entropy contributions and the energetic consequences of disordering the aluminates and the ferrites. These estimates are consistent with all of the available low-temperature adiabatic calorimetry, high-temperature heat content, and heat of solution measurements on the end-members. The analysis implies that there is a substantial heat capacity anomaly in the range 300°–900° C associated with disordering of the MgAl2O4structure while that in FeAl2O4becomes significant at temperatures above 700° C. The same heat capacity response in the ferrites indicates that the order/disorder transformation is coupled to the antiferromagnetic-paramagnetic transition in MgFe2O4but takes place well above the ferrimagnetic-paramagnetic transition in magnetite. The proposed model is internally consistent with solution theory reported elsewhere for Fe2+−Mg2+olivines and orthopyroxenes (Sack and Ghiorso 1989), rhombohedral oxides (Ghiorso 1990a) and the remaining end-member properties of Berman (1988).