Polytypism is common in micas, and the frequency of polytype occurrence is believed to be related closely to the crystallization conditions and chemical compositions of the corresponding fluids and melts. Coexisting multiple standard and complex/disordered polytypes in igneous rocks generally reflect a complicated magma evolution history. The purpose of the current study was to clarify the origin of coexisting biotite polytypes and their growth mechanism. Micro-X-ray diffraction (μXRD) and transmission electron microscopy (TEM) were used to investigate Fe-rich biotite phenocrysts in rhyolite from the Long Valley Caldera, California, USA. The μXRD analyses characterized various polytypes, and TEM observations revealed that common polytypes (e.g. 1M, 2M1, and 3T) and rare polytypes (e.g. 4M2 and 4A8) coexist within biotite monocrystals. The two 4-layer polytypes of Fe-rich biotite, 4M2 and 4A8, were identified via selected-area electron diffraction (SAED) and high-resolution scanning transmission electron microscopy (HRSTEM) at the atomic resolution, with unique stacking sequences ([0222] for 4M2 and [002$\overline{2}$] for 4A8). Energy-dispersive X-ray spectroscopy (EDS) results showed differences in their chemical compositions, especially Fe and K. The 4A8 polytype is reported for the first time. The present study suggested that environmental changes, such as rapid cooling and inhomogeneous compositional distribution, led to chemical and structural oscillations and complex nucleation of the two 4-layer polytypes. Screw dislocations producing spiral growth enhance polytype stability and form ordered long-period/complex polytypes. These results are useful to understand the origin of long-period/complex polytypes and the intergrowths of diverse polytypes formed in non-equilibrium crystallization environments.

On the basis of the linear magnetoelectroelasticity, the interaction problem between a generalized screw dislocation and a fibrous three-phase magnetoelectroelastic composite penetrated by a semi-infinite wedge crack is investigated in this paper. The fibrous magnetoelectroelastic composite is composed of three dissimilar materials bonded along two concentric circular interfaces. The magnetoelectroelastic materials are assumed to be transversely isotropic and have the same poling direction. The analytical derivations are based on the complex variable, conformal mapping, analytical continuation and image singularity methods. Numerical calculations are given graphically for studying the effects of material combinations, geometric models, wedge angles and the load type on the generalized stress fields, the generalized stress intensity factors, and the forces on the dislocation.

In this paper, the interaction of a generalized screw dislocation with multiple circular inclusions perfectly bonded to an unbounded matrix under remote magnetoelectromechanical loadings is dealt with. The analytical solutions of electric field, magnetic field and displacement field either in the inclusions or the matrix are obtained by use of the complex variable method. The image force acting on the magnetoelectric screw dislocation is calculated by using the generalized Peach-Koehler formula. Finally, the influence of material combinations on the image force is examined for several practical examples. The obtained solutions can be used as Green's functions for the analysis of the corresponding magnetoelectric crack problem.