By E. Kraus
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The crystallography of aperiodic crystals employs many strategies which are many times utilized to periodic crystals. the current textual content has been written below the idea that the reader knows thoughts like house crew symmetry, Bragg reflections and vector calculus. This assumption is influenced via the popularity that readers drawn to aperiodic crystals will usually have a heritage within the sturdy kingdom sciences, and via the truth that many books can be found that take care of the crystallography of tronslational symmetric buildings at either introductory and complex degrees.
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Additional info for Essentials of Crystallography
5 Comments on the Uniqueness of the Models and Methods 43 distribution of the correlation function leads to a non-Gaussian and highly asymmetric distribution for the interaction parameters. There is a standing challenge to establish a more realistic Hamiltonian by taking into account the displacements in alloys. While the structural simulation of static displacements can already be performed by steepest descent methods or a straightforward energy minimization, establishing an appropriate Hamiltonian appears to be feasible as mentioned above but it requires one to include also the dynamical properties of the system.
25]) one achieves the most reasonable and stable solutions. This method imposes the least restrictions on the experimental procedure. In particular, this type of analysis is convenient if multiple-detectors are used, allowing for a straightforward measurement of intensities in planes and volumes of the reciprocal space. Quite often the quadratic displacement terms may be neglected in the analysis of elastic neutron data, since the thermal diffuse scattering is already separated experimentally. For instance, this is the case for all applications discussed in Chap.
5]. Monte Carlo simulations have been established as a useful tool to study order-disorder phenomena in alloys. g. 15]. The main advantages of the Monte Carlo method are that it can provide the most accurate results, and that it is straightforward to apply the method to complicated, realistic interaction models, which, for instance, may be of a longer range than the CVM is capable of handling. A brief description is given in Sect. 2. In this review, it will be of particular interest to discuss further the merits of Monte Carlo methods in relation to determinations of the structures (Sect.
Essentials of Crystallography by E. Kraus