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106109 results in Materials Science

Page 4 of 5306

  • 9 - Superconductors

  • from Part II - Applications
  • Antoni Planes, University of Barcelona, Avadh Saxena, Los Alamos National Laboratory
  • Book:
    Phase Transitions
    Published online:
    01 May 2025
    Print publication:
    15 May 2025, pp 300-331

  • Summary

    Superconductivity is a quantum state of matter that occurs through a phase transition driven by thermal fluctuations. In this state, materials show ideal electric conductivity and ideal diamagnetism to a very good approximation. Two main classes of superconductors, type I and type II, can be distinguished with regards to flux penetration under an applied magnetic field. The properties of these two types are first discussed in detail. Next, the Ginzburg–Landau theory is developed and it is shown that in the presence of a magnetic field, when the ratio of penetration and coherence lengths is smaller than 1⁄√2 the superconductor behaves as type I, while it behaves as type II when this ratio is larger than 1⁄√2. In this second case, the flux penetrates through vortices that form a hexagonal lattice. Finally, in the last part, the microscopic BCS theory is discussed in order to provide an understanding of the physical origin of superconductivity.

  • 1 - Introduction to phase transitions

  • from Part I - General Aspects
  • Antoni Planes, University of Barcelona, Avadh Saxena, Los Alamos National Laboratory
  • Book:
    Phase Transitions
    Published online:
    01 May 2025
    Print publication:
    15 May 2025, pp 3-61

  • Summary

    The chapter is an introduction to basic equilibrium aspects of phase transitions. It starts by reviewing thermodynamics and the thermodynamic description of phase transitions. Next, lattice models, such as the paradigmatic Ising model, are introduced as simple physical models that permit a mechano-statistical study of phase transitions from a more microscopic point of view. It is shown that the Ising model can quite faithfully describe many different systems after suitable interpretation of the lattice variables. Special emphasis is placed on the mean-field concept and the mean-field approximations. The deformable Ising model is then studied as an example that illustrates the interplay of different degrees of freedom. Subsequently, the Landau theory of phase transitions is introduced for continuous and first-order transitions, as well as critical and tricritical behaviour are analysed. Finally, scaling theories and the notion of universality within the framework of the renormalization group are briefly discussed.

  • 2 - Dynamics of phase transitions

  • from Part I - General Aspects
  • Antoni Planes, University of Barcelona, Avadh Saxena, Los Alamos National Laboratory
  • Book:
    Phase Transitions
    Published online:
    01 May 2025
    Print publication:
    15 May 2025, pp 62-100

  • Summary

    The chapter starts by introducing the basic concepts of metastable and unstable states as well as time scales that control the occurrence of phase transitions. The limits for phase transitions taking place in equilibrium and out-of-equilibrium conditions are then established. In the latter case, thermally activated and athermal limits are distinguished associated with those situations where the transition is either driven or not driven by thermal fluctuations, respectively. Then the formal theory of the decay of metastable and unstable states in systems with conserved and non-conserved order parameters is developed. This general theory is in turn applied to the study of homogeneous and heterogeneous nucleation, spinodal decomposition and late stages of coarsening and domain growth.

Page 4 of 5306