Materials TheoryPub Date : 2017-06-21DOI: 10.1186/s41313-017-0005-1
Christopher S. R. Matthes, Nasr M. Ghoniem, Daniel Walgraef
{"title":"Stability and symmetry of ion-induced surface patterning","authors":"Christopher S. R. Matthes, Nasr M. Ghoniem, Daniel Walgraef","doi":"10.1186/s41313-017-0005-1","DOIUrl":"https://doi.org/10.1186/s41313-017-0005-1","url":null,"abstract":"<p>We present a continuum model of ion-induced surface patterning. The model incorporates the atomic processes of sputtering, re-deposition and surface diffusion, and is shown to display the generic features of the damped Kuramoto-Sivashinsky (KS) equation of non-linear dynamics. Linear and non-linear stability analyses of the evolution equation give estimates of the emerging pattern wavelength and spatial symmetry. The analytical theory is confirmed by numerical simulations of the evolution equation with the Fast Fourier Transform method, where we show the influence of the incident ion angle, flux, and substrate surface temperature. It is shown that large local geometry variations resulting in quadratic non-linearities in the evolution equation dominate pattern selection and stability at long time scales.</p>","PeriodicalId":693,"journal":{"name":"Materials Theory","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s41313-017-0005-1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4827446","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Materials TheoryPub Date : 2017-05-25DOI: 10.1186/s41313-017-0002-4
K. Y. Volokh
{"title":"Fracture as a material sink","authors":"K. Y. Volokh","doi":"10.1186/s41313-017-0002-4","DOIUrl":"https://doi.org/10.1186/s41313-017-0002-4","url":null,"abstract":"<p>Cracks are created by massive breakage of molecular or atomic bonds. The latter, in its turn, leads to the highly localized loss of material, which is the reason why even closed cracks are visible by a naked eye. Thus, fracture can be interpreted as the local material sink. Mass conservation is violated locally in the area of material failure. We consider a theoretical formulation of the coupled mass and momenta balance equations for a description of fracture. Our focus is on brittle fracture and we propose a finite strain hyperelastic thermodynamic framework for the coupled mass-flow-elastic boundary value problem. The attractiveness of the proposed framework as compared to the traditional continuum damage theories is that no internal parameters (like damage variables, phase fields, etc.) are used while the regularization of the failure localization is provided by the physically sound law of mass balance.</p>","PeriodicalId":693,"journal":{"name":"Materials Theory","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s41313-017-0002-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4981864","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Materials TheoryPub Date : 2017-05-25DOI: 10.1186/s41313-017-0003-3
Andrew A. Prudil, Michael J. Welland
{"title":"A novel model of third phase inclusions on two phase boundaries","authors":"Andrew A. Prudil, Michael J. Welland","doi":"10.1186/s41313-017-0003-3","DOIUrl":"https://doi.org/10.1186/s41313-017-0003-3","url":null,"abstract":"","PeriodicalId":693,"journal":{"name":"Materials Theory","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s41313-017-0003-3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4981863","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Materials TheoryPub Date : 2017-05-25DOI: 10.1186/s41313-017-0004-2
Markus Hütter, Bob Svendsen
{"title":"Formulation of strongly non-local, non-isothermal dynamics for heterogeneous solids based on the GENERIC with application to phase-field modeling","authors":"Markus Hütter, Bob Svendsen","doi":"10.1186/s41313-017-0004-2","DOIUrl":"https://doi.org/10.1186/s41313-017-0004-2","url":null,"abstract":"<p>The purpose of the current work is the formulation of models for conservative and non-conservative dynamics in solid systems with the help of the General Equation for the Non-Equilibrium Reversible-Irreversible Coupling (GENERIC: e.g., Grmela and ?ttinger, Phys. Rev. E 56(6), 6620 (1997); ?ttinger and Grmela, Phys. Rev. E 56(6), 6633 (1997)). In this context, the resulting models are inherently spatially strongly non-local (i.e., functional) and non-isothermal in character. They are applicable in particular to the modeling of phase transitions as well as mass and heat transport in multiphase, multicomponent solids. In the last part of the work, the strongly non-local model formulation is reduced to weakly non-local form with the help of generalized gradient approximation of the energy and entropy functionals. On this basis, the current model formulation is shown to be consistent with and reduce to a recent non-isothermal generalization (Gladkov et al., J. Non-Equilib. Thermodyn. 41(2), 131 (2016)) of the well-known phase-field models of Cahn and Hilliard (J. Chem. Phys. 28(2), 258 (1958)) for conservative dynamics and of Allen and Cahn (Acta Metall. 27(6), 1085 (1979)) for non-conservative dynamics. Finally, the current approach is applied to derive a non-isothermal generalization of a phase-field crystal model for binary alloys (see, e.g., Elder et al., Phys. Rev. B 75(6), 064107 (2007)).</p>","PeriodicalId":693,"journal":{"name":"Materials Theory","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s41313-017-0004-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4977491","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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