Crystal Lattices, Interfaces, Matrices: An Extension of Crystallography
Crystal Lattices, Interfaces, Matrices: An Extension of Crystallography
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发表时间：
1982-06
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通讯作者：
W. Bollmann
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作者：
W. Bollmann
虽然这本书是由一位杰出的科学家私下出版的，因为商业出版商不愿意冒险，但潜在的买家不应该担心这本书的质量。这本质上是一本关于o晶格理论数学基础的教程。考虑两个完美的晶体，不一定是同一种类型，在一个界面相遇。晶格节点之间的几何失配为界面上的能量提供了最简单的指导，并可用于理解多晶金属和矿物共生的纹理。这本书发展的数学理论不适合几何之间的两个格，并提供问题和练习，以测试读者。这种味道可以从三段引文中获得：“初级o晶格之所以是o晶格，是因为偏离了初级PS（首选状态），即单晶状态。次级o晶格，由于偏离次级ps将在后面讨论。o晶格模型将边界描述为位错网络，边界内具有完整的Burgers矢量平衡。“这个晶体学的城镇有一个孪生城镇，一个镜像城镇，即互反晶格的城镇。在p能级（可能能级）上有双晶互穿的倒易晶格和倒易的o晶格，在r能级（实能级）上有由埃瓦尔德球与倒易晶格构型相交得到的实际衍射图。共110页，15章涵盖了晶体晶格和几何方面（点晶格、结构矩阵、倒易晶格、旋转、剪切、镜像、反演、平移等）；九章涵盖了界面，以及在139页的界面结构中的应用（主晶格、单元胞的选择等、次位错网络等）；13章涵盖矩阵和代数方法，（向量代数，矩阵运算，特征值等）在100页。这种风格是数学式的，但很容易理解，因为有充分的解释。次要的批评有：参考书目中没有Cottrell（1953）和Read (1953)；图14/1中缺少3、4、6；存在拼写和其他小错误。我没有在选择性阅读中发现数学错误。所有对界面理论感兴趣的科学家都希望查阅这本书，以便有可能购买。他们还希望将本书与计算应变能的相干和部分相干相边界的其他理论联系起来（例如，参考R. A. Yund在《长石矿物学》中的文章，P. H. Ribbe主编，1983）。
Although this book was published privately by a distinguished scientist because a commercial publisher would not take the risk, a potential buyer should not worry about the quality of the book. This is essentially a tutorial work-book on the mathematical basis of O-lattice theory. Consider two perfect crystals, not necessarily of the same type, meeting at an interface. The geometrical misfit between the lattice nodes provides the simplest possible guide to the energy at the interface, and can be used in understanding the textures of polycrystalline metals and of mineral intergrowths. This book develops the mathematical theory of the misfit geometry between two lattices, and provides questions and exercises to test a reader. The flavour can be obtained from three quotations: 'The primary O-lattice is the O-lattice due to the deviation from the primary PS (preferred state), the single crystal state. Secondary O-lattices, due to the deviation from secondary PSs will be discussed later.' 'The O-lattice models describe boundaries as dislocation networks with the complete Burgers vector balance within the boundary.' 'This town of crystallography has a twin town, a mirror town, namely that of the reciprocal lattices. On the P-level (possibility level) there are the interpenetrating reciprocal lattices of the bi-crystals and the reciprocal O-lattices, and on the R-level (real level) are the actual diffraction patterns, obtained by the intersection of the Ewald sphere with the reciprocal lattice configuration.' Fifteen chapters cover crystal lattices and geometrical aspects (point lattice, structure matrix, reciprocal lattice, rotation, shear, mirror imaging, inversion, translation, etc.) in 110 pages; nine chapters cover interfaces, and applications to interface structure (primary Olattice, choice of unit cells, etc., secondary dislocation networks, etc.) in 139 pages; thirteen chapters cover matrices and algebraic methods, (vector algebra, matrix operations, eigen values, etc.) in 100 pages. The style is mathematical but easy to follow because of full explanations. Minor criticisms are: absence of Cottrell (1953) and Read (1953) in the bibliography; absence of 3, 4, and 6 in Fig. 14/1; presence of spelling and other minor errors. I did not detect mathematical errors in selective reading. All scientists interested in interface theory will wish to consult this book for possible purchase. They wilt also wish to set the book in the context of other theories for coherent and partly coherent phase boundaries in which strain energies are calculated (e.g. references in R. A. Yund's articles in Feldspar Mineralogy, ed. P. H. Ribbe, 1983).