Continuum Mechanics and Thermodynamics

, Volume 30, Issue 5, pp 1185–1199 | Cite as

Gradient and size effects on spinodal and miscibility gaps

  • Ioannis Tsagrakis
  • Elias C. AifantisEmail author
Original Article


A thermodynamically consistent model of strain gradient elastodiffusion is developed. Its formulation is based on the enhancement of a robust theory of gradient elasticity, known as GRADELA, to account for a Cahn–Hilliard type of diffusion. Linear stability analysis is employed to determine the influence of concentration and strain gradients on the spinodal decomposition. For finite domains, spherically symmetric conditions are considered, and size effects on spinodal and miscibility gaps are discussed. The theoretical predictions are in agreement with the experimental trends, i.e., both gaps shrink as the grain diameter decreases and they are completely eliminated for crystals smaller than a critical size.


Gradient elasticity Spinodal decomposition Miscibility gap Size effects Diffusion Coherency strains 


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Aristotle University of ThessalonikiThessalonikiGreece
  2. 2.Michigan Technological UniversityHoughtonUSA
  3. 3.Beijing University of Civil Engineering and ArchitectureBeijingChina
  4. 4.ITMO UniversitySt. PetersburgRussia
  5. 5.Togliatti State UniversityTogliattiRussia

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