摘要
为了克服矿物端员组分计算中先后分别计算不同端员的缺点,建立一个具广泛适用性的新方法,本文提出利用线性规划的方法同时求解所有端员组分。本方法得到的结果,均为非负值。在计算单斜辉石的例子中,引入艾斯科拉分子,以求接近化学计量系数。当固溶体中某些少量元素含量很显著时,在方程组内增加相应的端员组分向量并调整组成向量,可得到包括该端员的计算结果。文中并讨论了利用本计算方法估计矿物的电子探针分析结果的Fe^(3+)/Fe^(2+)的可能性。
Several schemes have been proposed for calculating the mineral end-members in solid-solutions such asclinopyroxene and garnet. These schemes show differences in the priority of calculation. Fbr example, Kushiro and Smyth calculate Na FeSi_2O_6 and LiAlSi_2O_6 prior to NaAlSi_2O_6 in their schemes; while Cawthorn and Collerson calculate NaFeSi_2O_6 after NaAlSi_2O_6, if any Na remains, in order to reduce the effect of Fe^(+3) on the calculation Obviously, substantially different results are obtained if different schemes of calculation are used. For the purpose of general comparison between data obtained by different workers, there must be a widely acceptable scheme which should be able to represent the end-members of the solidsolutions realistically. For this, the author proposes a new scheme for the calculation.
Consider a solid-solution system of the silicate components Na, Mg, Al, Si, K, Ca, Ti, Fe^(+3), Fe^(+2), Mn, Cr and Ni. For clinopyroxene there are common species, or endmembers, in the system: NaAlSi_2O_6(Jd), NaFeSi_2O_6(Ae), C_3Al_2SiO_6(CaTs), Ca_3Si_3O_9(Wl), Mg_2Si_2O_6(En) and Fe_2Si_2O_6(Fs). For clinopyroxene in eclogitic rocks, the Eskola molecule Ca_(0.5)□_(0.5)AlSi_2O_0(Es) often exists, consequently resulting in non-stoichiometry of the clinopyroxenes. Thus the author adds Es to the system Therefore this system can be written as:
By solving the equations simultaneously the mole fractions of the end-members can be obtained. If the least squares approximation is used, one sometimes cannot avoid a result with one or more negative values. The author therefore recommends the technique of linear programming to solve the equations, which always gives mole fractions≥0. If the mole fraction for a certain end-member is 0, this implies that the end-member does not exist. On the other hand, if there is a significant amount of Ti, Cr, K, Li, Ni, one simply adds extracolumns into the matrix at the left side of the equations, according to the cation numbers of appropriate new end-members, and separates the corresponding components in the vector at the right side, by which the extra end-members can be obtained.
When the mineral analysis is obtained by electron microprobe, an estimate of the ratio of ferric to ferrous iron must be made. This can be done by a trial-and-error procedure. Performing the computation several times with different ratios of Fe^(+3)/Fe^(+2) to reach a result with the minimum value of the objective function, one can obtain a result with a crystal-chemically possible ratio of Fe^(+3)/Fe^(+2). Such a ratio should be a reasonable estimate of the actual Fe^(+3)/Fe^(+2), if stoichiometry obtains.
The scheme outlined above proved successful in the end-member calculation of clinopyroxenes and garnets in some eclogites and ultrabasics of China. It must be emphasized that high-quality analytical results must be available in estimating the ratio of Fe^(+3)/Fe^(+2) and that meaningless values could result from erroneous analysis, as pointed out by Fleet et al. (1978).
出处
《地质学报》
EI
CAS
CSCD
北大核心
1991年第4期360-366,共7页
Acta Geologica Sinica
