三次贝塞尔曲线拼接模型的折线式等值线曲线化应用

本文通过对曾广鸿等人[1]提出的利用三次Bezier曲线拼接模型实现满足拓扑关系的折线武等值线曲线化的理论方法进行编程实践后,发现仅仅根据文中的方法不能完全正确地实现等值线的绘制,为此作者通过编程实践对该方法进行了补充与完善,文中详细完整地介绍了能完全满足拓扑关系的折线式等值线全参数曲线化的具体实现方法.     

Oriented growth of garnet by topotactic reactions and epitaxy in high‐pressure,mafic garnet granulite formed by dehydration melting of metastable hornblende‐gabbronorite (Jijal Complex,Kohistan Complex,north Pakistan)

Garnet growth in high‐pressure, mafic garnet granulites formed by dehydration melting of hornblende‐gabbronorite protoliths in the Jijal complex (Kohistan palaeo‐island arc complex, north Pakistan) was investigated through a microstructural EBSD‐SEM and HRTEM study. Composite samples preserve a sharp transition in which the low‐pressure precursor is replaced by garnet through a millimetre‐sized reaction front. A magmatic foliation in the gabbronorite is defined by mafic‐rich layering, with an associated magmatic lineation defined by the shape‐preferred orientation (SPO) of mafic clusters composed of orthopyroxene (Opx), clinopyroxene (Cpx), amphibole (Amp) and oxides. The shape of the reaction front is convoluted and oblique to the magmatic layering. Opx, Amp and, to a lesser extent, Cpx show a strong lattice‐preferred orientation (LPO) characterized by an alignment of [001] axes parallel to the magmatic lineation in the precursor hornblende‐gabbronorite. Product garnet (Grt) also displays a strong LPO. Two of the four 〈111〉 axes are within the magmatic foliation plane and the density maximum is subparallel to the precursor magmatic lineation. The crystallographic relationship 〈111〉_Grt // [001]_Opx,Cpx,Amp deduced from the LPO was confirmed by TEM observations. The sharp and discontinuous modal and compositional variations observed at the reaction front attest to the kinetic inhibition of prograde solid‐state reactions predicted by equilibrium‐phase diagrams. The P–T field for the equilibration of Jijal garnet granulites shows that the reaction affinities are 5–10 kJ mol.^?1 for the Grt‐in reaction and 0–5 kJ mol.^?1 for the Opx‐out reaction. Petrographic and textural observations indicate that garnet first nucleated on amphibole at the rims of mafic clusters; this topotactic replacement resulted in a strong LPO of garnet. Once the amphibole was consumed in the reaction, the parallelism of [001] axes of the mafic‐phase reactants favoured the growth of garnet crystals with similar orientations over a pyroxene substrate. These aggregates eventually sintered into single‐crystal garnet. In the absence of deformation, the orientation of mafic precursor phases conditioned the nucleation site and the crystallographic orientation of garnet because of topotaxial transformation reactions and homoepitaxial growth of garnet during the formation of high‐pressure, mafic garnet‐granulite after low‐pressure mafic protoliths.     

透闪石,滑石拓扑定向反应—龙溪软玉的电子衍射研究

通过对龙溪软玉中矿物纤维所进行的电子衍射研究,发现了透闪石针状晶体中存在众多(010)多链层错,透闪石和滑石以(010)为晶界面形成连生,以及滑石晶体呈纤维状存在;探讨了透闪石退变质为滑石的反应运动学和反应动力学机制;提出了拓扑定向反应系列的理论。     

Oriented inclusions of pyroxene,amphibole and rutile in garnet from the Lüliangshan garnet peridotite massif,North Qaidam UHPM belt,NW China: an electron backscatter diffraction study

Oriented inclusions of clinopyroxene, orthopyroxene, sodic amphibole and rutile have been identified in garnet from the Lüliangshan garnet peridotite massif in the North Qaidam ultrahigh‐pressure metamorphic (UHPM) belt, northern Tibetan Plateau, NW China. Electron backscatter diffraction (EBSD) analyses demonstrate that nearly half of the measured intracrystalline clinopyroxene (8 out of 17) have topotactic crystallographic relationships with host garnet, that is, (100)_Cpx//{112}_Grt, (010)_Cpx//{110}_Grt and [001]_Cpx//<111>_Grt. One‐fifth of the oriented sodic amphibole (23 out of 110) inclusions of have topotactic crystallographic relationships with host garnet, that is, (010)_Amp//{112}_Grt, (100)_Amp//{110}_Grt and [001]_Amp//<111>_Grt. Over a third of rutile (36 out of 99) inclusions also show a close crystallographic orientation relationship with host garnet in that one <103>_Rt and one <110>_Rt parallel to two <111>_Grt while the axes of [001]_Rt exhibit small girdles centred the axes of <111>_Grt. But, no ‘well‐fit’ crystallographic relationship was observed between orthopyroxene inclusions and host garnet. Considering a very long and complex history for the Lüliangshan garnet peridotite, we suggest that the low fit rates for these oriented minerals may result from several possible assumptions including different generations or multi‐stage formation mechanisms, heterogeneous nucleation and growth under non‐equilibrium conditions, and partial changes of initial crystallographic orientations of some inclusions. However, the residual quantitative ‘well‐fit’ crystallographic information is sufficient to indicate that the nucleation and growth of many pyroxene, amphibole and rutile are controlled by the lattice of the host garnet. The revealed close topotactic relationships accompanied by clear shape orientations provide quantitative microstructural evidence demonstrating a most likely exsolution/precipitate origin for at least some of the oriented phases of pyroxene, sodic amphibole and rutile from former majoritic garnet and support an ultra‐deep (>180 km depth) origin of the Lüliangshan garnet massif.     

Pyroxene exsolution topotaxy in majoritic garnet from 250 to 300 km depth

We report here the detailed microstructure and chemistry of pyroxene exsolution from a polycrystalline garnet porphyroblast of the Western Gneiss Region (WGR) garnet peridotite, Otrøy, Norway. For both clinopyroxene (Cpx) and orthopyroxene (Opx), the same basic crystallographic relationship is found with the host garnet: (100)_py//{112}_grt, (010)_px//{110}_grt and (001)_px//{111}_grt for the majority (>90%) of its intracrystalline pyroxene rods. In addition, this pattern is also exhibited by some interstitial Opx and a subpopulation of both pyroxenes shows a different pattern or no discernible pattern. The results provide quantitative microstructural evidence demonstrating an exsolution (precipitation) origin of both the intracrystalline Cpx and Opx and the small interstitial Opx crystals. The reconstructed precursor majoritic garnet, taking into account both the intracrystalline pyroxenes and interstitial Opx, was characterized by Si = ～3.07 cation per formula unit that corresponds to a minimum pressure of 7.7 GPa (～250 km depth). We also deduce from the observation of Opx being the majority of intracrystalline precipitates and 100% of the interstitial ones that the precursor majoritic garnet probably originated from a pressure less than ～10 GPa (～300 km depth). A multistage decomposition hypothesis is proposed for this WGR majoritic garnet during exhumation of the peridotite from 250 to 300 km depth to explain the topotaxy and chemistry of the exsolved pyroxenes.     

斜方辉石筛状反应边的成因机制及其对岩石圈地幔性质转变的意义

本文利用电子背散射衍射(EBSD)技术对河北张家口大麻坪汉诺坝玄武岩橄榄岩捕虏体中斜方辉石与玄武岩反应结构的显微构造进行了详细研究。研究结果表明: ① 其反应边具有复杂的多层筛状结构特征,包括玄武岩层、富橄榄石层以及橄榄石和单斜辉石交生层;② 由外至内,橄榄石的Mg值逐渐升高,而单斜辉石的Mg值变化不大;③ 反应边结构中的单斜辉石与斜方辉石残斑之间存在很好的结晶学拓扑关系,即(100)_opx//(100)_cpx、(010)_opx//(010)_cpx、(001)_opx//(001)_cpx;④ 橄榄石的结晶学取向无序且与斜方辉石和单斜辉石均无关。这个反应过程可以用贫硅熔体先与斜方辉石反应形成单斜辉石,并导致熔体富硅,从而橄榄石从反应熔体中结晶出来合理地解释。相对富硅熔体与橄榄岩的反应,贫硅熔体与橄榄岩的反应过程由于筛状反应边的存在可能更容易进行,筛状结构反应边可以为熔体在橄榄岩中沿颗粒边界运移提供通道,并使橄榄岩主要组成矿物发生细粒化和岩石结构变得松散,可以有效保证熔体上升过程中对橄榄岩的持续侵蚀和破坏,从而可能导致岩石圈地幔性质的迅速转变。