Analysis of P-V-T data: Constraints on the thermoelastic properties of high-pressure minerals
Analysis of P-V-T data: Constraints on the thermoelastic properties of high-pressure minerals
复制标题
DOI：
10.1016/0031-9201(96)03143-3
复制
发表时间：
1996-08-01
影响因子：
2.3
通讯作者：
Rigden, SM
中科院分区：
文献类型：
--
作者：
Jackson, I;Rigden, SM
利用同步加速器X射线衍射仪精确测定地幔矿物的晶胞体积作为压力和温度的函数，促使人们重新评估这些数据约束各种高阶热弹性参数的能力。基于热力学恒等式(偏导数P/偏导数T)(V)=αK-T的积分和简单的振动能的Mie-Gruneisen-Debai模型，通过应用最近公布的β-(Mg，Fe)(2)SiO_4和MgSiO_3钙钛矿的P-V-T数据，比较了不同的热压参数。这些方法中的每一种都提供了可用P-V-T数据的适当表示。然而，由于Mie-Gruneisen-Debai状态方程明确包含了振动能量的近似模型，因此更受欢迎，因为它更真实地描述了热膨胀的温度相关性，并允许在等温实验条件和与了解地球深处更相关的绝热条件之间进行内部一致的转换。对具有β-(Mg，Fe)(2)SiO4性质的相的合成数据集的热力学最小二乘拟合所获得的热弹性性质的形式误差的评估表明，对于最先进的P-V-T数据，(偏导数K-T/偏导数T)(P)和偏导数(2)K(T)/偏导数P偏导数T的值应该分别在10%和50%内可分辨。由热力学和Mie-Gruneisen-Debai两种方法得到的(偏导数K-T/偏导数T)(P)和偏导数(2)K(T)/偏导数P的偏导数T之间有很好的一致性，特别是当比较适当温度范围内的平均值时。在300K~1600K温度区间(等化学模式地幔中下地幔绝热的潜在温度)，β-(Mg，Fe)(2)SiO4和MgSiO_3钙钛矿的择优α平均值分别为3.6×10~(-5)K~(-1)和2.6×10~(-5)K~(-1)。对于(K-T/T)(P)和(K-S/T)(P)，β-(Mg，Fe)(2)SiO4的优选平均值为-0.028 GPaK(-1)和-0.019GPaK(-1)，而镁钙钛矿的首选平均值为-0.027GPaK(-1)和-0.017GPaK(-1)，这与对一系列氧化物和硅酸盐矿物的偏导数(2)K(T)/偏导数P的偏导数T的独立估计一致。贝塔相和钙钛矿相的分析结果分别接近2×10(-4)K-1和1×10(-4)K-1。然而，似乎更具地震学相关性的参数[偏导数(偏导数K-S/偏导数P)(S)/偏导数T](P)对于这两个阶段几乎都小一个数量级。
The availability of precise determinations of unit cell volumes of mantle minerals as functions of both pressure and temperature through synchotron-based X-ray diffraction has motivated a re-evaluation of the capacity of such data to constrain various higher-order thermoelastic parameters. Alternative parameterisations of the thermal pressure, based upon integration of the thermodynamic identity (partial derivative P/partial derivative T)(V) = alpha K-T and upon the simple Mie-Gruneisen-Debye model for the vibrational energy have been compared through application to recently published P-V-T data for beta-(Mg,Fe)(2)SiO4 and MgSiO3 perovskite. Each of these approaches provides an adequate representation of the available P-V-T data. However, the Mie-Gruneisen-Debye equation-of-state, with its explicit incorporation of an approximate model for the vibrational energy, is preferred because it describes more faithfully the temperature dependence of thermal expansion, and allows internally consistent conversion between isothermal experimental conditions and the adiabatic conditions more relevant to understanding the Earth's deep interior. Evaluation of formal errors in thermoelastic properties obtained from 'thermodynamic' least-squares fits of a synthetic dataset for a phase with the properties of beta-(Mg,Fe)(2)SiO4 indicates that values of (partial derivative K-T/partial derivative T)(p) and partial derivative(2)K(T)/partial derivative P partial derivative T should be resolvable within 10% and 50% respectively for state-of-the-art P-V-T data. Excellent agreement is obtained between values determined for (partial derivative K-T/partial derivative T)(p) and partial derivative(2)K(T)/partial derivative P partial derivative T from the two thermodynamic and Mie-Gruneisen-Debye methods, particularly when average values over an appropriate temperature range are compared. For the temperature interval between 300 K and 1600 K (the potential temperature appropriate for the lower-mantle adiabat in an isochemical model mantle), preferred average values of alpha are 3.6 x 10(-5) K-1 and 2.6 x 10(-5) K-1 for beta-(Mg,Fe)(2)SiO4 and MgSiO3 perovskite, respectively. For (K-T/T)(p) and (K-S/T)(p) the preferred average values are -0.028 GPaK(-1) and -0.019GPaK(-1) for beta-(Mg,Fe)(2)SiO4 and -0.027GPaK(-1) and -0.017GPaK(-1) for MgSiO3 perovskite, In agreement with independent estimates of partial derivative(2)K(T)/partial derivative P partial derivative T of (1-3) x 10(-4) K-1 for a range of oxide and silicate minerals, this analysis yields values near 2 x 10(-4) K-1 and 1 x 10(-4) K-1 for the beta-phase and perovskite, respectively. It appears likely, however, that the more seismologically relevant parameter [partial derivative(partial derivative K-S/partial derivative P)(S)/partial derivative T](p) is almost an order of magnitude smaller for both phases.