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Complete classification of six-dimensional iso-edge domains. 六维等边域的完整分类。
IF 1.9 4区 材料科学
Acta Crystallographica Section A: Foundations and Advances Pub Date : 2025-01-01 DOI: 10.1107/S2053273324010143
Mathieu Dutour Sikirić, Wessel van Woerden
{"title":"Complete classification of six-dimensional iso-edge domains.","authors":"Mathieu Dutour Sikirić, Wessel van Woerden","doi":"10.1107/S2053273324010143","DOIUrl":"10.1107/S2053273324010143","url":null,"abstract":"<p><p>In this paper, we report on the full classification of generic iso-edge subdivisions of six-dimensional translational lattices. We obtain a complete list of 55083357 affine types of iso-edge subdivisions. We report on the use of the method of canonical forms that allows us to apply hashing techniques used in modern databases.</p>","PeriodicalId":106,"journal":{"name":"Acta Crystallographica Section A: Foundations and Advances","volume":" ","pages":"9-15"},"PeriodicalIF":1.9,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142589260","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A milestone for the solution to the lattice sphere covering problem in dimension n = 6. 求解n = 6维格球覆盖问题的里程碑。
IF 1.9 4区 材料科学
Acta Crystallographica Section A: Foundations and Advances Pub Date : 2025-01-01 DOI: 10.1107/S2053273324011513
Frank Vallentin
{"title":"A milestone for the solution to the lattice sphere covering problem in dimension n = 6.","authors":"Frank Vallentin","doi":"10.1107/S2053273324011513","DOIUrl":"10.1107/S2053273324011513","url":null,"abstract":"<p><p>The complete classification of (primitive, generic) parallelohedra in a given dimension is a challenging computational task. Nearly 50 years have passed since the classification for the last dimension, n = 5, was completed. One application of such a classification is in solving the lattice sphere covering problem for the corresponding dimension. The paper by Dutour Sikirić & van Woerden [Acta Cryst. (2025), A81, https://doi.org/10.1107/S2053273324010143] marks a milestone in the classification effort for dimension n = 6. It provides a complete classification of all primitive iso-edge domains; here primitive parallelohedra are identified based on their facet vectors.</p>","PeriodicalId":106,"journal":{"name":"Acta Crystallographica Section A: Foundations and Advances","volume":" ","pages":"5-8"},"PeriodicalIF":1.9,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142765042","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A computationally efficient quasi-harmonic study of ice polymorphs using the FFLUX force field. 基于FFLUX力场的冰多晶准谐波研究。
IF 1.9 4区 材料科学
Acta Crystallographica Section A: Foundations and Advances Pub Date : 2025-01-01 DOI: 10.1107/S2053273324010921
Alexandra Pák, Matthew L Brown, Paul L A Popelier
{"title":"A computationally efficient quasi-harmonic study of ice polymorphs using the FFLUX force field.","authors":"Alexandra Pák, Matthew L Brown, Paul L A Popelier","doi":"10.1107/S2053273324010921","DOIUrl":"10.1107/S2053273324010921","url":null,"abstract":"<p><p>FFLUX is a multipolar machine-learned force field that uses Gaussian process regression models trained on data from quantum chemical topology calculations. It offers an efficient way of predicting both lattice and free energies of polymorphs, allowing their stability to be assessed at finite temperatures. Here the Ih, II and XV phases of ice are studied, building on previous work on formamide crystals and liquid water. A Gaussian process regression model of the water monomer was trained, achieving sub-kJ mol<sup>-1</sup> accuracy. The model was then employed in simulations with a Lennard-Jones potential to represent intermolecular repulsion and dispersion. Lattice constants of the FFLUX-optimized crystal structures were comparable with those calculated by PBE+D3, with FFLUX calculations estimated to be 10<sup>3</sup>-10<sup>5</sup> times faster. Lattice dynamics calculations were performed on each phase, with ices Ih and XV found to be dynamically stable through phonon dispersion curves. However, ice II was incorrectly identified as unstable due to the non-bonded potential used, with a new phase (labelled here as II' and to our knowledge not found experimentally) identified as more stable. This new phase was also found to be dynamically stable using density functional theory but, unlike in FFLUX calculations, II remained the more stable phase. Finally, Gibbs free energies were accessed through the quasi-harmonic approximation for the first time using FFLUX, allowing thermodynamic stability to be assessed at different temperatures and pressures through the construction of a phase diagram.</p>","PeriodicalId":106,"journal":{"name":"Acta Crystallographica Section A: Foundations and Advances","volume":" ","pages":"36-48"},"PeriodicalIF":1.9,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11694218/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142851790","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On symmetries of higher-order elastic constants. 关于高阶弹性常数的对称性。
IF 1.9 4区 材料科学
Acta Crystallographica Section A: Foundations and Advances Pub Date : 2025-01-01 DOI: 10.1107/S2053273324011021
J D Clayton
{"title":"On symmetries of higher-order elastic constants.","authors":"J D Clayton","doi":"10.1107/S2053273324011021","DOIUrl":"10.1107/S2053273324011021","url":null,"abstract":"<p><p>In elastic crystals, a hyperelastic description is conventionally assumed, and the strain energy potential is idealized as a Taylor-series expansion in strain about an unstrained reference state. Coefficients of quadratic terms are second-order or linear elastic constants. Coefficients of higher-order terms are elastic constants of third order, fourth order, and so on. Recently published work by Telyatnik [Acta Cryst. (2024), A80, 394-404] extends prior knowledge of symmetry properties for anisotropic elastic constants of single crystals, as well as transversely isotropic and isotropic solids, to terms up to sixth order. Effective elastic constants for polycrystalline aggregates, with possible anisotropy, were reported by Telyatnik, in the same article, to the same order. A terse summary of nonlinear crystal elasticity and independent elastic constants of orders two and three are given in this commentary for context. Methods and results of Telyatnik, anticipated to be of great utility to crystal elasticity research, are then highlighted.</p>","PeriodicalId":106,"journal":{"name":"Acta Crystallographica Section A: Foundations and Advances","volume":" ","pages":"1-4"},"PeriodicalIF":1.9,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Simulation of reciprocal-space mapping using a new analytical solution of kinematical X-ray diffraction in a crystal. 用一种新的晶体运动x射线衍射解析解模拟往复空间映射。
IF 1.9 4区 材料科学
Acta Crystallographica Section A: Foundations and Advances Pub Date : 2025-01-01 DOI: 10.1107/S2053273324011422
Vasily Punegov
{"title":"Simulation of reciprocal-space mapping using a new analytical solution of kinematical X-ray diffraction in a crystal.","authors":"Vasily Punegov","doi":"10.1107/S2053273324011422","DOIUrl":"10.1107/S2053273324011422","url":null,"abstract":"<p><p>In the kinematical approximation, new analytical solutions are obtained that describe the diffraction of a restricted X-ray beam from a thin crystal. Calculation of the angular distribution of reflected X-ray beams within the framework of the developed approach significantly reduces the computational cost compared with numerical methods. For a thin silicon crystal, X-ray reciprocal-space mapping was simulated using analytical solutions, as well as calculated using numerical methods based on 2D recurrence relations and the Takagi-Taupin equations.</p>","PeriodicalId":106,"journal":{"name":"Acta Crystallographica Section A: Foundations and Advances","volume":" ","pages":"57-63"},"PeriodicalIF":1.9,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142779001","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An alternative method to the Takagi-Taupin equations for studying dark-field X-ray microscopy of deformed crystals. 研究变形晶体暗场 X 射线显微镜的高木-陶平方程替代方法。
IF 1.9 4区 材料科学
Acta Crystallographica Section A: Foundations and Advances Pub Date : 2024-11-01 Epub Date: 2024-09-26 DOI: 10.1107/S2053273324008295
Kun Lun Wang, Xu Kang, Xiao Ya Li
{"title":"An alternative method to the Takagi-Taupin equations for studying dark-field X-ray microscopy of deformed crystals.","authors":"Kun Lun Wang, Xu Kang, Xiao Ya Li","doi":"10.1107/S2053273324008295","DOIUrl":"10.1107/S2053273324008295","url":null,"abstract":"<p><p>This study introduces an alternative method to the Takagi-Taupin equations for investigating the dark-field X-ray microscopy (DFXM) of deformed crystals. In scenarios where dynamical diffraction cannot be disregarded, it is essential to assess the potential inaccuracies of data interpretation based on the kinematic diffraction theory. Unlike the Takagi-Taupin equations, this new method utilizes an exact dispersion relation, and a previously developed finite difference scheme with minor modifications is used for the numerical implementation. The numerical implementation has been validated by calculating the diffraction of a diamond crystal with three components, wherein dynamical diffraction is applicable to the first component and kinematic diffraction pertains to the remaining two. The numerical convergence is tested using diffraction intensities. In addition, the DFXM image of a diamond crystal containing a stacking fault is calculated using the new method and compared with the experimental result. The new method is also applied to calculate the DFXM image of a twisted diamond crystal, which clearly shows a result different from those obtained using the Takagi-Taupin equations.</p>","PeriodicalId":106,"journal":{"name":"Acta Crystallographica Section A: Foundations and Advances","volume":" ","pages":"414-421"},"PeriodicalIF":1.9,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142337535","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Lattice symmetry relaxation as a cause for anisotropic line broadening and peak shift in powder diffraction. 晶格对称性松弛是粉末衍射中各向异性线变宽和峰值移动的原因。
IF 1.9 4区 材料科学
Acta Crystallographica Section A: Foundations and Advances Pub Date : 2024-11-01 Epub Date: 2024-10-03 DOI: 10.1107/S2053273324008799
Miguel Gregorkiewitz, Alice Boschetti
{"title":"Lattice symmetry relaxation as a cause for anisotropic line broadening and peak shift in powder diffraction.","authors":"Miguel Gregorkiewitz, Alice Boschetti","doi":"10.1107/S2053273324008799","DOIUrl":"10.1107/S2053273324008799","url":null,"abstract":"<p><p>In powder diffraction, lattice symmetry relaxation causes a peak to split into several components which are not resolved if the degree of desymmetrization is small (pseudosymmetry). Here the equations which rule peak splitting are elaborated for the six minimal symmetry transitions, showing that the resulting split peaks are generally broader and asymmetric, and suffer an hkl-dependent displacement with respect to the high-symmetry parent peak. These results will be of help in Rietveld refinement of pseudosymmetric structures where an exact interpretation of peak deformation is required.</p>","PeriodicalId":106,"journal":{"name":"Acta Crystallographica Section A: Foundations and Advances","volume":" ","pages":"439-445"},"PeriodicalIF":1.9,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11532927/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142363543","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Symmetries and symmetry-generated averages of elastic constants up to the sixth order of nonlinearity for all crystal classes, isotropy and transverse isotropy. 所有晶体类别、各向同性和横向各向同性的非线性六阶以下弹性常数的对称性和对称性产生的平均值。
IF 1.9 4区 材料科学
Acta Crystallographica Section A: Foundations and Advances Pub Date : 2024-11-01 Epub Date: 2024-10-15 DOI: 10.1107/S2053273324007666
Rodion Sergeyevich Telyatnik
{"title":"Symmetries and symmetry-generated averages of elastic constants up to the sixth order of nonlinearity for all crystal classes, isotropy and transverse isotropy.","authors":"Rodion Sergeyevich Telyatnik","doi":"10.1107/S2053273324007666","DOIUrl":"10.1107/S2053273324007666","url":null,"abstract":"<p><p>Algebraic expressions for averaging linear and nonlinear stiffness tensors from general anisotropy to different effective symmetries (11 Laue classes elastically representing all 32 crystal classes, and two non-crystalline symmetries: isotropic and cylindrical) have been derived by automatic symbolic computations of the arithmetic mean over the set of rotational transforms determining a given symmetry. This approach generalizes the Voigt average to nonlinear constants and desired approximate symmetries other than isotropic, which can be useful for a description of textured polycrystals and rocks preserving some symmetry aspects. Low-symmetry averages have been used to derive averages of higher symmetry to speed up computations. Relationships between the elastic constants of each symmetry have been deduced from their corresponding averages by resolving the rank-deficient system of linear equations. Isotropy has also been considered in terms of generalized Lamé constants. The results are published in the form of appendices in the supporting information for this article and have been deposited in the Mendeley database.</p>","PeriodicalId":106,"journal":{"name":"Acta Crystallographica Section A: Foundations and Advances","volume":" ","pages":"394-404"},"PeriodicalIF":1.9,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142453746","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Structure of face-centred icosahedral quasicrystals with cluster close packing. 具有团簇紧密堆积的面心二十面体准晶体的结构。
IF 1.9 4区 材料科学
Acta Crystallographica Section A: Foundations and Advances Pub Date : 2024-11-01 Epub Date: 2024-09-30 DOI: 10.1107/S2053273324008568
Tsunetomo Yamada, Hiroyuki Takakura, Akiji Yamamoto
{"title":"Structure of face-centred icosahedral quasicrystals with cluster close packing.","authors":"Tsunetomo Yamada, Hiroyuki Takakura, Akiji Yamamoto","doi":"10.1107/S2053273324008568","DOIUrl":"10.1107/S2053273324008568","url":null,"abstract":"<p><p>A 6D structure model for face-centred icosahedral quasicrystals consisting of so-called pseudo-Mackay and mini-Bergman-type atomic clusters is proposed based on the structure model of the Al<sub>69.1</sub>Pd<sub>22</sub>Cr<sub>2.1</sub>Fe<sub>6.8</sub> 3/2 cubic approximant crystal (with space group Pa3, a = 40.5 Å) [Fujita et al. (2013). Acta Cryst. A69, 322-340]. The cluster centres form an icosahedral close sphere packing generated by the occupation domains similar to those in the model proposed by Katz & Gratias [J. Non-Cryst. Solids (1993), 153-154, 187-195], but their size is smaller by a factor τ<sup>2</sup> [τ = (1 + (5)<sup>1/2</sup>)/2]. The clusters cover approximately 99.46% of the atomic structure, and the cluster arrangement exhibits 15 and 19 different local configurations, respectively, for the pseudo-Mackay and mini-Bergman-type clusters. The occupation domains that generate cluster shells are modelled and discussed in terms of structural disorder and local reorganization of the cluster arrangements (phason flip).</p>","PeriodicalId":106,"journal":{"name":"Acta Crystallographica Section A: Foundations and Advances","volume":" ","pages":"422-438"},"PeriodicalIF":1.9,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11532924/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142337536","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the principle of reciprocity in inelastic electron scattering. 关于非弹性电子散射中的互易原理。
IF 1.9 4区 材料科学
Acta Crystallographica Section A: Foundations and Advances Pub Date : 2024-11-01 Epub Date: 2024-10-21 DOI: 10.1107/S2053273324009550
Budhika G Mendis
{"title":"On the principle of reciprocity in inelastic electron scattering.","authors":"Budhika G Mendis","doi":"10.1107/S2053273324009550","DOIUrl":"10.1107/S2053273324009550","url":null,"abstract":"<p><p>In electron microscopy the principle of reciprocity is often used to imply time reversal symmetry. While this is true for elastic scattering, its applicability to inelastic scattering is less well established. From the second law of thermodynamics, the entropy for a thermally isolated system must be constant for any reversible process. Using entropy and statistical fluctuation arguments, it is shown that, while reversibility is possible at the microscopic level, it becomes statistically less likely for higher energy transfers. The implications for reciprocal imaging modes, including energy loss and energy gain measurements, as well as Kainuma's reciprocal wave model are also discussed.</p>","PeriodicalId":106,"journal":{"name":"Acta Crystallographica Section A: Foundations and Advances","volume":" ","pages":"457-459"},"PeriodicalIF":1.9,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11532925/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142453744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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