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    1. The discovery a new fundamental effect in multicomponent
    nanoscaled systems related to their phase diagrams:
    the solubility curves in contrast to ones in bulk materials
    do not correspond to the condition of thermodynamic equilibrium
    and show only the beginning and the end of phase transformation.
    For example, solidus and liquidus curves in commonly accepted meaning of terms
    do not correlate to thermodynamic equilibrium.
    It is shown the "loop-like split path" of an equilibrium
    temperature-composition diagram for solidus and liquidus
    shifted in comparison to bulk infinite system.

    2. The construction of the size-dependent solubility curves
    and the solubility diagram of isolated nanosized Cu-Ni particle
    and the demonstration of the decrease and narrowing and
    vanishing of the two-phase zone.
    3. The reconsideration of such basic concepts as
    phase diagram, solubility curve, etc.
    The well-known concept of equilibrium state diagram has to be revised,
    due to the fact that the amount of matter is limited in a nanosystem.

    4. The introduction of the concept of "critical supersaturation"
    and prediction of the "split of the binodal curve"
    on the phase temperature-composition diagrams based on depletion effect
    - for the decomposition of supersaturated nanoalloys
    taking into account the number of coexisting solid phases
    and the compositional redistribution during the phase transitions.

    5. The demonstration of the size-dependent "thermodynamic” hysteresis
    for the volume fraction of the new phase in nanopowder
    under the thermal cycling as the function of the temperature
    and different phase transition mechanisms.
    It is shown that the thermal "thermodynamic” hysteresis arises
    due to the asymmetry of transforming paths of the nanosystem
    with respect to the initial conditions,
    kinetic constraints on the transition modes, different probabilities
    of forth and back transitions and multiple states
    separated by different energy barriers.
    It is argued that in nanosystems it is required to differentiate
    the "kinetic” hysteresis and "thermodynamic” hysteresis
    in the first order phase transition.

    6. First demonstration of fundamental effect of the superposition
    of "kinetic” hysteresis and "thermodynamic” hysteresis
    leading to the size-independent hysteresis of first order phase transition
    in nanomaterials for wide range of sizes and parameters.
    [Physics and Chemistry of Solid State, 2010, 11, 49;
    Doctorate thesis for scientific degree of doctor
    of physical and mathematical sciences by speciality
    01.04.07 – solid state physics, Kiev National University, 2012, 368p].

    7. The introduction of the notions of size-dependent ‘superheating limit’
    and ‘supercooling limit’ and discovery the logarithmic correlations
    for them as functions of nanosizes and temperature change rates.
    The description of the evolution of a transforming metal
    nanoparticle ensemble subjected to a temperature cycling
    with constant rates of temperature change.

    8. Demonstration of a size-induced thermal hysteresis
    in first order phase transitions and the invention of using
    of such hysteresis for the achievement of an alternative method
    of information (nonmagnetic) recording
    in present-day and future technologies.

    9. First demonstration of concentration ‘self-saturation’ effect in kinetics
    of phase separation of metastable mulicomponent alloy
    under the constant external conditions: at the end of the intermediate stage
    there takes place the "inverse behavior" of basic characteristics
    - the decrease of the mean size, critical size,
    and volume fraction of the new phase and the increase
    of the mole fraction of the component building the phase.
    The self-saturation effect can be considered as one of the simple criteria
    of the start of coalescence stage.

    10. A suggestion and thermodynamic validation the atomic hypothesis
    related to the size dependence of the atom-atom interaction energy:
    the nearest interactions and coordinated actions of atoms in the nanomaterial
    will be different depending on the size of a nanomaterial.
    Solid nanofilms of monoatomic metallic systems having an fcc structure
    are simulated by the molecular-statics method
    with the Morse and Sutton-Chen potentials.
    Bulletin of Kiev National University, Physical and Mathematical Series, 2011, 13, 34].

    11. Theoretical validation of the size dependence
    of diffusion coefficient of atoms in nanomaterials
    based on microscopic and phenomenological points of view.
    The result has been applied for the reactive diffusion problem
    of new nanosized phase growth kinetics in а binary diffusion couple.
    Depending on the type of diffusion coefficient dependence
    on the size of new nanophase layer
    the phase formation rate exponent can change nonmonotonically.
    Physics and Chemistry of Solid State, 2011, 12, 32].

    12. The development of the techniques of the thermodynamic calculations
    and designing temperature-composition diagrams of binary metallic nanophases
    based on the size dependence for potential energy of the interaction
    between neighbour atoms in nanomaterials at zero temperatures.

    13. The introduction of a notion "mesoentropy” in a thermodynamics
    of a new phase formation in the supersaturated binary solid solution,
    taking into account the depletion of the solution and
    the space distribution of new phase nuclei.
    It is shown the principal possibility of obtaining
    of the size distribution function for the new phase nuclei
    in the framework of a general variation procedure
    of the optimal crossover point determination
    for the first order phase transition,
    assigning the Gibbs free energy functional.

    14. The demonstration the competitive nucleation and growth
    of two intermediate phases in nanovolumes
    taking into account the mole fraction depletion
    of the parent phase and yielding situations:
    (i) total prohibition of separation,
    (ii) formation and total stabilization of metastable phase instead of a stable one,
    (iii) relative stabilization of metastable phase with the temporary delay
    of its transformation into the stable phase,
    (iv) formation and growth of stable phase
    when the metastable phase does not appear at all,
    (v) formation and growth of stable phase via the metastable phase.
    This was applied to the coherent precipitation of metastable
    Al3Li ordered phase in supersaturated solid solution Al(Li).

    15. The demonstration of the size-induced "freezing effect”
    in separation kinetics for the isolated nanoparticle
    with a coating shell of the third atoms
    by means of Monte-Carlo sampling and Ising-type model,
    where the species exchange positions due to vacancy mechanism:
    the rate of relaxation process depends on the size of a nanosystem.
    Depending on the shell properties, the nucleation of a new phase
    may be either heterogeneous (on the external surface)
    or homogeneous (in the core of the particle).
    Doctorate thesis for scientific degree
    of doctor of physical and mathematical sciences
    by speciality 01.04.07 – solid state physics,
    Kiev National University, 2012, 368p].

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