PhasePot has been used for the simulation of various material processes and microstructures. Here is a selection of examples.

Surface melting and re-solidification

Surface melting, e.g. by laser, is widely used for cutting, welding and surface modification of metallic materials. PhasePot can be used to simulate grain structure, phase change and solute distribution in the re-solidified region and the heat affected zone.

Simulated temperature field (left) and grain structure (right) during surface melting and re-solidification of nickel using pulsed laser.

Dendritic growth

Dendritic growth is a most common and widely-studied feature in solidification of materials. By combining the phase-field and the Monte-Carlo Potts models, PhasePot provides a unique capacity for the simulation of dendritic patterns that may form in alloys and compounds under different solidification conditions.

Simulation of the transition from regular dendrite to irregular dendrite (seaweed) in an undercooled B2 intermetallic-forming system. Undercooling increases from left to right.

Rapid solidification

Rapid solidification of alloys and compounds can be associated with kinetic effects, such as solute trapping, disorder trapping, inverted partitioning and formation of non-equilibrium microstructures, e.g. consisting of anti-phase domains. PhasePot uses a special phase-field formulation for quantitative simulation of these kinetic effects and non-equilibrium microstructures.

Simulation of a complex (invertible) solute partitioning behaviour in intermetallic forming systems. The left diagram shows the kinetic phase boundaries for a B2 system; the right diagram shows the corresponding concentration profiles across the solid-liquid interface for different values of growth velocity (normalized with respect to the 'diffusive speed').

Simulation of characteristic anti-phase domains that may form during rapid solidification of intermetallic forming systems.

Diffusion bonding 

Transient-liquid-phase diffusion bonding with non-planar bond lines, which are favourable in terms of bond strength, can be achieved by imposing a temperature gradient upon the sample. PhasePot can be used to simulate unique features of this process, e.g. formation of morphological instabilities on the retreating melting front because of the so-called 'constitutional superheating' effect.

Simulation of formation of morphological instabilities on both solidifying and melting fronts during transient-liquid-phase diffusion bonding of aluminium with copper interlayer.

Self-Propagating High-Temperature Synthesis (SHS)

SHS is used as a technique for the synthesis and processing of a wide variety of materials, such as intermetallic compounds, ceramics and composites. PhasePot can be used to simulate the process kinetics and also the reaction mechanism at the microstructure level.

Simulation of SHS of NiAl, showing the reaction between solid nickel particles and liquid aluminium matrix at micro- (left) and macroscopic (right) levels.

Grain boundary segregation

Mechanical properties of polycrystalline materials are to a large extent influenced by the nature of grain boundaries, which can be manipulated through controlled segregation. PhasePot can be used to simulate segregation and the associated nano-scale phase transformation at grain boundaries of polycrystalline materials, and thus, help with the design of alloys of superior properties.

Simulation of segregation and phase transformation (re-austenitisation) at grain boundaries of martensitic Fe-9 at. % Mn. The left map shows distribution of austenite (red) in a martensite (green) matrix, and the right map shows the crystal orientation of the initial martensite.


Electro-deoxidation is an electrochemical process that can be used for direct reduction of metals from their oxides in a simple step. PhasePot can be used to simulate the underlying mechanism and kinetics of electro-deoxidation, and thus, help with the optimisation of this process, e.g. in terms of geometry and porosity level of the cathode.

Simulation of electro-deoxidation in molten salt, showing different stages of phase change in cathode. The oxide is shown in grey and the metallic phase in white.



  • H. Assadi (2004): A phase field model for crystallization into multiple grain structures, chapter 3 in Solidification and Crystallization, ed. D.M. Herlach, Wiley-VCH, Weinheim, pp. 17-26.

  • H. Assadi (2006): Phase-field modelling of electro-deoxidation in molten salt, Modelling & Simulation in Mater. Sci. & Eng. 14, pp. 963-974.

  • H. Assadi (2007): A phase-field model for non-equilibrium solidification of intermetallics, Acta Materialia 55, pp. 5225-5235.

  • H. Assadi, M. Oghabi, D.M. Herlach (2009): Influence of ordering kinetics on dendritic growth morphology, Acta Materialia 57, pp. 1639-1647.

  • M.A. Jabbareh, H. Assadi (2009): Modelling of microstructure evolution in transient-liquid-phase diffusion bonding under temperature gradient, Scripta Materialia 60, pp. 780-782.

  • I. Hadi, M.A. Jabbareh, R. Nikbakkht, H. Assadi (2012): Modelling of microstructure evolution during thermal processes – A hybrid deterministic-probabilistic approach, Materials Science Forum 704-705, pp. 63-70.

  • M. Ojaghi-Ilkhchi, H. Assadi (2012): Modelling of electrodeoxidation of porous oxides in molten salt, Computational Materials Science 53, pp. 1-5.

  • R. Nikbakkht, H. Assadi (2012): Phase-field modelling of self-propagating high-temperature synthesis of NiAl, Acta Materialia 60, pp. 4041-4053.

  • M.A. Jabbareh, H. Assadi (2013): Modeling of grain structure and heat-affected zone in laser surface melting process, Metallurgical and Materials Transactions 44B, pp. 1041-1048.

  • D. Raabe, S. Sandlöbes, J. Millán, D. Ponge, H. Assadi, M. Herbig, P.-P. Choi(2013): Segregation engineering enables nanoscalemartensite-to-austenite phase transformation at grain boundaries: a pathway to ductile martensite, Acta Materialia 61, pp. 6132-6152.