前言

以结晶学矿物学和地球化学为主要内容的专辑,可以说,这又是一件从无到有的事。在今天说,这是一个新芽。 在一切事物中,为什么能从无中生有呢?这是由于某些旧因素的破灭,新因素的兴     

群论在结晶矿物学中的应用

群论是高等代数的一个分支,在量子化学和矿物物理学中早已广泛应用。本文重点介绍群论在结晶学和矿物学中的应用:结晶学中的点群、空间群均为群论中的群;对称要素组合定理与群的乘法;以对称要素的矩阵表象证明对称要素的组合定性。进而讨论了如何划分群中的类以及类在结晶学中的用途和意义。最后简略介绍了原子轨道的对称变换和特征标的概念。     

海南文昌二辉橄榄岩中辉石出溶结构的结晶学取向分析

本文用电子背散射衍射技术(electron backscatter diffraction,EBSD)测试了海南文昌玄武岩中二辉橄榄岩包体中的辉石主晶与其出溶片晶的结晶学取向关系。结合电子探针成分测试,得出:单斜辉石(透辉石)主晶中出溶了两组不同方向的片晶,一组为斜方辉石(顽火辉石-易变辉石)片晶,另一组为单斜辉石(普通辉石)片晶。由于出溶片晶在EBSD测试切面上体现为以线状体,因此需要找到一种方法将线状体所代表的片晶的晶面符号推算出来。本文介绍了一种利用吴氏网进行坐标系旋转的"晶带相交法",该方法可以作图推算出溶片晶的晶面符号。根据"晶带相交法"得出,斜方辉石(顽火辉石-易变辉石)出溶片晶为(100),单斜辉石(普通辉石)出溶片晶为~(401)。根据前人的研究资料,出溶片晶~(401)可能指示最小出溶压力为9.5~12.5GPa。出溶片晶的结晶学取向涉及到主晶与出溶体的晶体结构匹配关系,并且与出溶温度-压力有关,因此出溶片晶的结晶学取向分析具有晶体化学理论意义和反映地质温压过程的实际意义。这种"晶带相交法"可以推广应用于其他矿物出溶结构的结晶学取向研究中。     

小波变换与地震奇异性属性

地震属性是由地震数据提取的有关地震波的几何形态、运动学特征、动力学特征和统计学特征等组成。这里主要讨论了一种新的地震属性(奇异性属性)计算方法。由于地震数据携带着大量的奇异性信息,因此,这一新的地震属性是在偏移地震数据的小波变换和奇异性分析的基础上形成的。小波变换使检测数据中的局部奇异程度成为可能。为能够估计出偏移地震数据每一采样点的局部奇异规律,从小波变换系数的角度来提取地震信号的奇异指数。这种新属性实行单道处理,不需要子波和速度信息,它给出了地下分层情况和断层位置。在地震数据奇异性属性的基础上,用小波变换来划分地层旋回,从而提高了小波变换在地震解释中的应用。     

晶面腐蚀像与晶面对称及晶面结构的关系

综合分析了石英、石榴子石、橄榄石、锆石、红柱石的各不同结晶学意义的晶面腐蚀像特点,总结了晶面腐蚀像与晶面对称性及晶面结构特点之间的关系.腐蚀像不仅可以揭示晶面及晶体的对称性,还可以揭示晶面的结晶学意义,即同一晶体上的不同结晶学意义的晶面,尽管对称性相同,也具有不同的腐蚀像;不同晶体之间的具有相同对称性的晶面可能会有相同的腐蚀像;腐蚀像类似于一种宏观晶体形态,主要与晶面的对称性有关,与晶面上原子、离子排列的结构细节关系不大;同一晶体的同一晶面在不同的腐蚀剂中所得的腐蚀像也可能完全不同;有些晶面的腐蚀像可以用晶体生长形态的常见晶面与被腐蚀面的交棱来解释.该研究在揭示晶体溶解形态机理、将溶解形态与晶体生长形态对比、用溶解形态来反映晶体曾经经历的酸-碱环境等方面具有理论与实际意义.      

水文系统的鉴别讲座(第四讲)

七、用矩和累积量进行鉴别1959年,纳希(J.E.Nash)对瞬时单位线的计算,首先采用了矩法。在水文系统中,使用矩或累积量与数理统计中的意义相同。1.特征函数,矩和累积量设g(t)为概率密度函数,其相应的特征函数定义为下列变换式对照傅里叶变换式(3-2),特征函数相当于傅里叶逆变换,仅差一常数1/(2π)。将式(7-1)中的e~(ist)进行级数展开,得已知数理统计中的r阶原点矩为及r阶中心矩为     

矿物晶体腐蚀像的新应用

矿物晶体腐蚀像是一种研究晶体对称、晶格缺陷等传统的方法。对腐蚀像提出了一个全新的研究思路,建立各种不同矿物晶体的腐蚀像立体模型,从而可以在这个模型上进行：①腐蚀像的晶体对称理论意义及其在岩石中矿物晶体定向作用的研究;②腐蚀像所反映的晶格缺陷与定向及其地质意义的研究;③腐蚀像所反映的晶体溶解机理的结晶学各向异性特征的研究。这些研究充分挖掘了腐蚀像在地质学、矿物学中的新的研究意义。     

数学变换方法在地震勘探中的应用

数学变换是地震勘探资料处理方法中的重要手段之一,从数学模型的求解到地震数据压缩的很多方面都离不开数学变换。着重概述了现今地震勘探方法中几种常用数学变换的基本原理及方法,包括傅立叶变换、小波变换、K-L变换及R adon变换等,并介绍了各种方法在地震勘探领域的应用及发展趋势。     

岩浆岩成因类型REE判别

本文根据REE丰度特征与对数真数特征的关系以及REE燕式曲线的物理定义 (化学内涵 )和数学关系 ,引入了丰度坐标系———双对数坐标系 (一种准四维坐标系 )定量模型 ,按照岩浆岩系的数据点在丰度坐标系中的分布情况 ,对岩浆岩系REE丰度结构进行分类 ,并探讨岩浆岩系的REE演化类型和演化运动特征 ,据此对岩浆岩成因的类型进行判别     

一种新类型的辉闪石切面的结晶学方位研究

本文提出了斜交c轴但平行b轴或垂直(100)面的第三种类型的特殊切面,并通过数学运算建立其上的解理夹角与结晶学方位之间的关系,致使据已知的辉闪石的光性方位,可计算得知该类切面的光学性质。     

K-Space symmetry rules and their application to ordering behaviour in non-stoichiometric (metal-enriched) chalcopyrite

Electron-optical study of the transformation behaviour in metalenriched chalcopyrite indicates that several metastable ordered variants occur in short term cooling experiments (Putnis and McConnell, 1976). The implications of this behaviour are discussed in relation to the theory of symmetry point ordering. This permits one to distinguish between three types of ordering transformation which differ markedly, both in the nature of the structural changes involved, and in their kinetics. A brief account of the theory of symmetry point ordering, based on a group-theoretical treatment by Landau and Lifshitz, is included. Analysis of the experimental results obtained on metal-enriched chalcopyrite indicate that metastable transformation behaviour in this system is associated with symmetry point ordering, and that partially ordered structures are produced.     

含五次对称的准晶体的点群与单形

应该把有关准晶体的研究纳入晶体学领域,扩大晶体学的内容与涵义。作者把含有五次对称的准晶体的点群与单形作了推导,与经典结晶学相比,增加了14种新点群和24种新单形。此外,作者根据准晶态的构筑原理,又推导出4种准晶格。     

岩浆岩中石英晶体的对称性连生

矿物晶体连生是岩浆岩中晶体生长及岩石结构形成过程中的一个重要现象，可以提供岩浆演化过程信息.用电子背散射衍射技术(EBSD)分析了天堂寨花岗岩和梅川花岗闪长岩中石英晶体的结晶学取向关系.这2种岩石中石英的道芬双晶和交生(两晶体以某个相同的面重合连生)出现概率非常高.除了道芬双晶和交生外，还发现了一种特殊的石英晶体对称性连生现象.在这种特殊的对称性连生体中，考虑石英的劳埃群3 2/m(而不是石英的点群32)，两晶体形成的道芬双晶的双晶面(0001)或(1010)与第3个晶体的对称面(1120)重合.这样的重合使得这3个晶体的连生体保留了道芬双晶的某些对称性.这种双晶面与第3个晶体的对称面重合的现象在我们以前报道的NH₄Cl晶体聚集体和透辉石枝晶聚集体中也出现过.这种现象说明晶体的连生受控于对称性，即:晶体连生会选择对称性高的形式.由于劳埃群是与晶体空间格子的对称性相关而并不是与晶体结构的对称性相关的，所以，空间格子的对称性可能是控制晶体对称性连生的主要因素.      

Stereographic Projections of Symmetry Elements and Single Forms on Quasicrystals

INTRODUCTIONThe stereographic projection of symmetry ele ments and the single forms of crystals is very system atic in classical crystallography. Shechtman et al.( 1984 ) reported the existence of a metallic solidwhich diffracted electro…     

Generalized solution to the anisotropic Mandel's problem

Existing solutions to Mandel's problem focus on isotropic, transversely isotropic, and orthotropic materials, the last two of which have one of the material symmetry axes coincide with the vertical loading direction. The classical plane strain condition holds for all these cases. In this work, analytical solution to Mandel's problem with the most general matrix anisotropy is presented. This newly derived analytical solution for fully anisotropic materials has all the three nonzero shear strains. Warping occurs in the cross sections, and a generalized plane strain condition is fulfilled. This solution can be applied to transversely isotropic and orthotropic materials whose material symmetry axes are not aligned with the vertical loading direction. It is the first analytical poroelastic solution considering mechanical general anisotropy of elasticity. The solution captures the effects of material anisotropy and the deviation of the material symmetry axes from the vertical loading direction on the responses of pore pressure, stress, strain, and displacement. It can be used to match, calibrate, and simulate experimental results to estimate anisotropic poromechanical parameters. This generalized solution is capable of reproducing the existing solutions as special cases. As an application, the solution is used to study the responses of transversely isotropic and orthotropic materials whose symmetry axes are not aligned with the vertical loading direction. Examples on anisotropic shale rocks show that the effects of material anisotropy are significant. Mandel-Cryer's effects are highly impacted by the degree of material anisotropy and the deviation of the material symmetry axes from the vertical loading direction.     

影象线性体密度-中心对称度综合统计分析方法及其在古火山岩区地质研究中的应用

本文探讨通过遥感影象线性体统计分析预测古火山机构的方法及效果。首先,作者提出并详细讨论了一种新的统计变量——线性体空间分布中心对称度。然后,又根据研究区已知火山机构的典型局部构造为环状、放射状断裂系统而设计采用了一套线性体密度-中心对称度综合统计分析方法,并对区内火山岩地质研究取得初步成功。     

Albite crystallographic preferred orientation and grain misorientation distribution in a low-grade mylonite: implications for granular flow

Crystallographic orientation data from pure albite domains in a low-grade sheared metagabbro from the Combin Zone of the western Italian Alps were measured by electron backscatter diffraction. Crystallographic preferred orientations (CPOs) in four high-strain domains are non-random and have a triclinic symmetry. The clusters of [100], [010] and [001] show an angular relationship that corresponds to that of the albite crystal lattice. However, the orientations of axis clusters to the kinematic axes vary from domain to domain. CPOs from a low-strain domain also show clustered axes with triclinic symmetry, but with more intense clustering than those in the high-strain domains. Grain misorientation distributions are presented both for the low-strain domain and one of the high-strain domains. In the high-strain domain, the distribution of misorientation angles between neighbouring grains displays a peak at about 70°. The equivalent distribution in the low-strain domain has a peak at 30°. For both domains, the misorientation axis distributions, between neighbouring and non-neighbouring grains, are random, except for some of axes with 160–180° misorientation that exhibit a slight concentration around [010]. The diversity of CPOs among the domains suggests that these CPOs could not be produced by dislocation creep. They are likely to have been inherited from plagioclase parents, as a result of host control on the nucleation of the new albite grains. These CPOs do not contain any direct information about the deformation kinematics. We interpret that deformation of these domains occurred by granular flow. Crystallographic axis dispersion due to grain boundary sliding (GBS) caused weakening of CPOs, modification of misorientation angle distributions and randomisation of misorientation axis distributions. The fact that a CPO can survive GBS even after a high strain indicates that CPO is not always a sensitive indicator of deformation mechanisms. Misorientation distribution may provide a complementary, and possibly a more sensitive indicator of deformation mechanisms.     

矿物光率体主轴-晶轴-弹性张量的数学转换和计算机实现的方法

以往是通过手工转图由光率体主轴获取晶轴和应力主轴的,把手工操作变为计算机运算和成图,是一个重要的附加课题．主要介绍了计算机实现轴与轴以及坐标系和投影面之间的各种转换方法,具体步骤有：（１）把费氏台下读数转换为地理坐标系下的数据;（２）已知任意两个光率体主轴求第三个光率体主轴;（３）投影面的旋转;（４）由光率体主轴获取晶轴;（５）把弹性张量从与晶轴相关的坐标系转到地理坐标系中．由此编制的处理程序和绘图软件已在应用中．