Diffusion governs microstructure evolution in virtually every thermomechanical process of practical importance: carburizing, homogenization, heat treatment, welding, coating degradation, and solidification segregation. The physics is fundamentally well understood — Fick’s laws, chemical potential gradients, mobility. The challenge is applying this physics to real multicomponent engineering alloys with six, eight, or ten elements, where the diffusion of each element depends on the concentrations of all others, and where phase boundaries move as phases form and dissolve during the process.
DICTRA (DIffusion Controlled TRAnsformation) is Thermo-Calc’s answer to this challenge. It is the reference software for multicomponent diffusion-controlled transformation simulation — the tool materials scientists reach for when the question is not just “what phases are stable?” but “how fast do they form, and what concentration profiles result?”
This guide covers what DICTRA is, how it works, what problems it solves, and the mobility databases that make it function.
What Is DICTRA?
DICTRA is an Add-on Module to Thermo-Calc that simulates diffusion-controlled reactions in multicomponent alloys. It requires:
- A Thermo-Calc license (DICTRA is an add-on)
- At least one thermodynamic database (e.g., TCFE for steels, TCNI for nickel alloys)
- At least one mobility database (e.g., MOBFE for steels, MOBNI for nickel alloys) — the kinetic data DICTRA needs beyond thermodynamics
The thermodynamic database tells DICTRA what phases are stable and what their compositions are at local equilibrium. The mobility database tells it how fast atoms move through each phase. The combination — CALPHAD thermodynamics plus CALPHAD-assessed kinetics — is what enables DICTRA to simulate real industrial alloys without adjustable parameters.
Key principle: DICTRA is based on the numerical solution of the multicomponent diffusion equations coupled with CALPHAD thermodynamics at moving phase boundaries. It assumes local equilibrium at phase interfaces — each phase boundary adjusts its position so that the chemical potentials of all components are equal across it at every timestep. This is a physically sound assumption for most solid-state diffusion problems at elevated temperatures.
Geometric constraint: DICTRA simulations are one-dimensional. Three geometries are supported:
- Planar — an infinite plate (carburizing a flat specimen, concentration profile through a diffusion couple)
- Cylindrical — an infinite cylinder (diffusion through a tube wall, dissolution of a rod-shaped precipitate)
- Spherical — a sphere (dissolution of a spherical particle, growth of a spherical precipitate)
This one-dimensional constraint is sufficient for a large class of practically important problems, and the three geometry options extend coverage to many geometries that appear circular or spherical in cross-section.
The Physical Foundation: Multicomponent Diffusion
In a binary alloy A-B, diffusion of A relative to B is described by a single diffusion coefficient. In a multicomponent alloy with N components, the diffusion of each component depends on the chemical potential gradient of every other component — producing an N×N diffusion coefficient matrix.
The off-diagonal terms in this matrix — the cross-diffusion coefficients — physically represent the fact that a concentration gradient in element Cr can drive diffusion of Ni even in the absence of a Ni gradient. In the Darken experiment (the famous 1949 experiment with iron couples of different silicon content), carbon diffused up its own concentration gradient — from the lower-carbon piece to the higher-carbon piece — because the chemical potential gradient of carbon was reversed by the silicon. Cross-diffusion effects are real, quantitatively important in multicomponent alloys, and DICTRA captures them fully.
DICTRA formulates the problem in the lattice-fixed frame of reference, which correctly handles vacancy fluxes, Kirkendall drift, and the movement of phase boundaries due to molar volume differences between phases.
The diffusion coefficient matrix that DICTRA uses is not stored directly. Instead, mobility parameters for each element in each phase are stored in the mobility database. The diffusion coefficient matrix is computed from these mobilities combined with the thermodynamic factor (the second derivative of Gibbs energy with respect to composition) — the CALPHAD database supplies this thermodynamic factor. This is the key coupling that makes DICTRA fundamentally different from purely kinetic simulation tools: the thermodynamics and kinetics are treated consistently within the CALPHAD framework.
What DICTRA Simulates: Application Categories
1. Thermochemical Surface Treatment — Carburizing, Nitriding, Carbonitriding
Carburizing is the most historically important DICTRA application. The process involves exposing steel to a carbon-rich atmosphere at elevated temperature, allowing carbon to diffuse into the surface to increase hardness. What looks simple in a binary approximation becomes complex in a real alloy:
- The steel contains Cr, Mo, Mn, Ni, Si in addition to Fe and C
- Carbon diffusivity depends strongly on the alloying element concentrations
- Carbides (M₂₃C₆, M₇C₃, cementite) form and dissolve as carbon profiles evolve
- The positions of carbide/austenite boundaries move during the process
DICTRA handles all of this without adjustable parameters. Inputs are the steel composition, gas atmosphere (carbon activity), temperature profile, and time. Outputs are:
- Carbon concentration profile vs. depth vs. time
- Chromium depletion profile (Cr is consumed by carbide formation)
- Phase fraction profile (how much carbide at each depth, and which carbide)
- Position of phase boundaries as a function of time
Industrial impact: DICTRA carburization simulations have been validated against experimental measurements for a wide range of stainless steels, tool steels, and high-temperature alloys. The agreement is typically excellent because the model contains no fitted parameters beyond the thermodynamic and kinetic databases themselves. This allows DICTRA to be used predictively — designing carburizing cycles or alloy compositions for targeted case depth and hardness without experimental iteration.
Nitriding and carbonitriding follow the same computational approach. The chemistry differs (nitrogen atmosphere, formation of iron and alloy nitrides rather than carbides), but DICTRA handles both with the same framework provided the mobility database covers the relevant phases.
2. Homogenization of As-Cast Microstructures
Solidification produces microsegregation — regions enriched in late-solidifying elements (interdendritic regions) and regions depleted in them (dendrite cores). Homogenization heat treatment at elevated temperature allows solid-state diffusion to reduce these compositional gradients. DICTRA simulates this process.
Key questions DICTRA answers:
- How long must the homogenization hold at a given temperature to reduce the composition variation to within specification?
- What temperature optimizes the homogenization kinetics without causing incipient melting?
- How does the solute distribution evolve during slow cooling after the homogenization hold?
Setup: A unit cell representing the as-cast microstructure is defined — typically half a dendrite arm spacing in planar geometry, with the initial composition profile from a Scheil solidification calculation (which TC-Python or the Thermo-Calc graphical interface can provide as the starting condition for DICTRA). DICTRA then simulates solid-state diffusion from this initial state through the heat treatment cycle.
Application domains: Nickel superalloy ingots (homogenization before forging), aluminum alloy billets (homogenization before extrusion), duplex stainless steel slabs (eliminating δ-ferrite from solidification before hot rolling).
3. Diffusion-Controlled Phase Transformations
Austenite formation and decomposition in steels: The austenite/ferrite transformation in steel is diffusion-controlled when it occurs in the sub-critical temperature range where carbon and substitutional elements must redistribute between the two phases as the boundary moves. DICTRA simulates:
- Austenite growth into ferrite during intercritical annealing (for dual-phase or TRIP steel production)
- Ferrite growth into austenite during slow cooling
- Carbon profile in both phases as the boundary moves
- Effect of alloying elements (Mn, Si, Cr, Mo) on transformation kinetics
This is a moving boundary problem — the austenite/ferrite interface position changes as carbon redistributes, and DICTRA tracks this movement self-consistently.
Allotropic transformations in titanium: The α (HCP) / β (BCC) transformation in Ti alloys is handled analogously — DICTRA simulates the diffusion of stabilizing elements (Al, V, Mo, Cr) as the α/β boundary moves during heat treatment, providing composition profiles and transformation kinetics.
Pearlite growth: DICTRA can simulate pearlite growth from austenite — the coupled eutectoid transformation where carbon diffuses ahead of the advancing pearlite front to feed both the ferrite and cementite lamellae.
4. Coating-Substrate Interdiffusion
High-temperature coatings on metallic components — bond coats on turbine blades, diffusion barrier coatings, galvanizing on steel — degrade over time as elements interdiffuse between the coating and substrate. DICTRA quantifies this degradation.
MCrAlX bond coat / Ni superalloy substrate: The classic case: an MCrAlY coating (M = Ni, Co, or NiCo) on a Ni-based single crystal superalloy. Elements diffuse in both directions:
- Al diffuses from the coating into the substrate (Al needed for protective Al₂O₃ oxide formation is lost)
- Refractory elements (Re, W, Ta) diffuse from the superalloy into the coating, potentially forming brittle TCP (topologically close-packed) phases
DICTRA predicts:
- Al concentration profile in the coating and substrate vs. time at service temperature
- β-phase (NiAl) depletion rate in the coating (β → γ transition depletes the Al reservoir for oxidation protection)
- Interdiffusion zone composition and phase constitution
- Service lifetime estimate — when the β-phase is fully depleted
Galvanized steel: DICTRA simulates Fe-Zn interdiffusion during galvanizing annealing — the formation and growth of intermetallic phases in the Fe-Zn diffusion zone — guiding galvanizing temperature and time to achieve target coating microstructures.
Cemented carbide gradient sintering: DICTRA simulates the intentional creation of compositional gradients (binder-enriched surface zones) in WC-Co cemented carbides during sintering, enabling design of “dual property” cutting tools with a tough surface layer and a hard core.
5. Post-Weld Heat Treatment
When two dissimilar materials are joined by welding — austenitic stainless steel to ferritic steel, nickel superalloy to steel, dissimilar superalloy variants — the joint region contains steep composition gradients. During post-weld heat treatment (PWHT), elements diffuse across these gradients, potentially forming harmful phases.
What DICTRA calculates:
- Whether undesirable phases (brittle intermetallics, carbides) form at the joint during PWHT
- How long the PWHT must last to redistribute composition and reduce the risk
- Carbon migration — the Darken effect causes carbon to diffuse from the ferritic side to the austenitic side in steel-to-steel joints, leading to decarburization on one side and carburization on the other
6. Particle Growth and Dissolution
DICTRA simulates the growth or dissolution of individual precipitate particles — spherical geometry is typically used.
Applications:
- Carbide dissolution during austenitization of steel — how long at temperature until all carbides dissolve?
- γ’ dissolution in nickel superalloys during heat treatment
- Growth of coatings or intermetallic layers at interfaces
Stop criteria (added in Thermo-Calc 2024a, Console Mode): Instead of specifying a fixed simulation time, users can set a stop condition — for example, terminate the carburization simulation when the carbon content at 0.5mm depth reaches the target value. This makes DICTRA directly applicable to process optimization: find the time required to achieve a target profile, rather than simulating to a fixed time and inspecting the result.
Mobility Databases — The Kinetic Backbone
DICTRA requires a mobility database in addition to the thermodynamic database. The mobility database contains atomic mobility parameters — the CALPHAD-assessed kinetic equivalent of the thermodynamic Gibbs energy parameters.
How Mobility Data Is Organized
Atomic mobilities are assessed element-by-element for each phase in which they are relevant. For each element i in phase φ:
M_i^φ = M_i^φ(T, x) — a function of temperature and composition
The mobility is expressed in Arrhenius form: M_i = A × exp(−Q/RT), where Q is the activation energy for diffusion and A is a pre-exponential factor. Both Q and A may depend on composition in multicomponent systems, captured by Redlich-Kister polynomial expansions analogous to thermodynamic interaction parameters.
From atomic mobilities, the diffusion coefficient matrix D is computed at each point in the simulation as a combination of mobilities and thermodynamic factors:
D_ij = Σ_k (M_k × (δ_ik – x_i) × ∂μ_k/∂x_j)
where μ_k are chemical potentials from the thermodynamic database. This coupling is what makes DICTRA physically self-consistent: the mobility database provides atomic transport properties, and the thermodynamic database provides the driving forces.
Available Mobility Databases
| Database | Alloy system | Paired thermodynamic DB |
|---|---|---|
| MOBFE9 | Steel and Fe-alloys | TCFE15 |
| MOBNI (MOBNI6) | Ni-based superalloys | TCNI |
| MOBAL | Al-based alloys | TCAL |
| MOBTI6 (2026a) | Ti and TiAl alloys | TCTI7 |
| MOBHEA4 (2026a) | High entropy alloys | TCHEA |
| MOBMG | Mg-based alloys | TCMG |
| MOBCU | Cu-based alloys | Various |
Each mobility database is developed to correspond to a specific thermodynamic database. MOBFE9 is developed alongside TCFE15, MOBNI alongside TCNI. Using mismatched database versions can produce inconsistent results.
Database Coverage and Limitations
The mobility database specifies which phases have diffusion data. Phases not listed in the mobility database are treated as “diffusion NONE” — DICTRA includes them in the thermodynamic equilibrium calculation but treats them as immobile (no diffusion within them). This is physically reasonable for many applications — carbides in steels, for example, typically have very slow diffusion and their composition changes are dominated by the flux at their boundaries rather than internal diffusion.
A phase must be explicitly listed in the mobility database with assessed parameters for accurate simulation within that phase. The Fe-based system (MOBFE) covers BCC_A2 (ferrite), FCC_A1 (austenite), CEMENTITE, FE₄N, HCP_A3, and LIQUID. The Ni-based system (MOBNI) covers FCC_A1, L1₂ (γ’), BCC_A2, B2, and LIQUID.
Simulation Setup: Key Concepts
Regions and Cells
A DICTRA simulation is organized around regions — spatial domains with defined geometry and composition. A diffusion couple has two regions (the two alloys). A carburization simulation has one region (the steel specimen). Each region can contain multiple phases at local equilibrium.
A cell represents the 1D spatial extent of the simulation with defined boundary conditions and an initial composition profile.
Boundary Conditions
DICTRA boundary conditions specify what happens at the surfaces of the simulation domain:
Fixed composition boundary: The composition at the surface is fixed at a specified value. Used for carburizing (surface carbon activity fixed by gas atmosphere composition).
Zero flux boundary: No element crosses the boundary. Used for symmetry planes (centerline of a dendrite arm during homogenization) or sealed surfaces.
Fixed flux boundary: A specified flux of an element enters or leaves through the surface. Used when the transport rate in the gas phase is limited.
Activity boundary: Surface composition maintained at specified chemical potential (activity). Related to fixed composition but specified thermodynamically.
Temperature Profiles
Temperature in DICTRA can be specified as a constant or as a function of time using any combination of:
- Linear ramps (controlled heating or cooling)
- Isothermal holds
- Arbitrary time-temperature curves (for realistic industrial cycles)
This enables simulation of complete industrial heat treatment cycles: heat up → soak → cool → age — all in a single DICTRA simulation run.
Grid Refinement
DICTRA uses a finite volume method with user-configurable grid spacing. Grid points can be uniformly spaced or geometrically distributed (denser at phase boundaries where concentration gradients are steep). Correct grid refinement is important for accuracy, particularly near moving phase boundaries.
DICTRA Models for Different Physical Situations
Sharp Interface (Moving Boundary) Model
The default DICTRA model. Phases are separated by sharp, well-defined interfaces. The interface position moves as phases grow or shrink. Local thermodynamic equilibrium is assumed at the interface — compositions on both sides of the interface are determined by the thermodynamic database at each timestep. This model is physically appropriate when:
- Interfaces move by diffusion-controlled kinetics
- Phase boundaries are atomically sharp relative to the diffusion length scale
Applications: Austenite/ferrite transformation in steel, carburization with carbide formation, coating/substrate interdiffusion, particle growth and dissolution.
Homogenization Model
For multiphase regions where the phases are mixed on a scale smaller than the simulation resolution (e.g., a two-phase α+β region being homogenized), the moving boundary model cannot represent the geometry accurately. The homogenization model treats the multiphase mixture as a single effective medium:
- Local equilibrium holds within each volume element (phase fractions and compositions from CALPHAD)
- Diffusion is averaged over the mixture using locally averaged kinetic properties
- Computationally transforms a multiphase problem into an effective single-phase diffusion problem
This model is appropriate when the length scale of the two-phase mixture (e.g., dendrite arm spacing during homogenization, lamellar spacing in pearlite) is much smaller than the diffusion distances of interest.
Applications: Homogenization of as-cast microstructures (dendrite-scale two-phase structure), diffusion through cermet coatings, gradient sintering of cemented carbides.
Integration with TC-PRISMA and TC-Python
DICTRA and TC-PRISMA Together
DICTRA and TC-PRISMA (the Precipitation Module) address different length scales of kinetic behavior:
- DICTRA: Long-range diffusion — composition profiles over distances of microns to millimeters, moving phase boundaries, surface treatment profiles
- TC-PRISMA: Short-range kinetics — nucleation, growth, and coarsening of precipitates within a single-phase matrix
The two can be used sequentially: DICTRA calculates the composition profile after a heat treatment, and TC-PRISMA calculates how precipitates nucleate and grow within that profile. For example, in modeling the case of a carburized steel — DICTRA provides the carbon and chromium profiles, and TC-PRISMA models carbide precipitation kinetics at each depth.
DICTRA in TC-Python
All DICTRA calculations are accessible through TC-Python, enabling automated diffusion simulation in research and optimization workflows. Use cases include:
- Screening carburizing times across a range of steel compositions and temperatures
- Optimizing homogenization cycles for a new alloy by scanning temperature-time combinations
- Building DICTRA simulation results into machine learning training datasets
- Coupling DICTRA outputs with finite element models
Validation: Why DICTRA Can Be Trusted
DICTRA’s credibility rests on the same CALPHAD foundation as Thermo-Calc’s thermodynamics:
Database development methodology: Atomic mobility parameters in MOBFE, MOBNI, and other databases are assessed against experimental measurements — tracer diffusion coefficients, interdiffusion coefficients from diffusion couple experiments, and composition profile measurements. The assessment process is the same CALPHAD methodology applied to kinetics: optimize parameters to reproduce known experimental data, then extrapolate to multicomponent systems.
No adjustable parameters in applications: Once the databases are assessed, a DICTRA simulation of carburization or homogenization uses no free parameters — the databases provide all the physics. This is fundamentally different from simulation tools that require fitting parameters adjusted to match each new experimental dataset.
Extensive literature validation: DICTRA has been validated in hundreds of published studies against experimental measurements for:
- Carbon, nitrogen, and chromium profiles in carburized steels and high-temperature alloys
- Composition profiles in diffusion couples (Fe-Cr-Ni, Ni-Al-Cr, Ti-Al-V, and many others)
- Interdiffusion in MCrAlY / superalloy systems
- Homogenization kinetics in nickel superalloys and aluminum alloys
The agreement between DICTRA simulations and experiment is typically within measurement uncertainty when appropriate databases are used — a strong validation of the coupled CALPHAD thermodynamic/kinetic approach.
Limitations
Understanding where DICTRA is not appropriate:
One-dimensional only: DICTRA cannot simulate genuinely 2D or 3D diffusion fields — for example, diffusion around a corner, through a non-uniform weld geometry, or around an irregularly shaped precipitate. For 3D diffusion problems, phase-field methods (MICRESS, OpenPhase, MOOSE) or FEM codes with DICTRA-linked thermodynamics are required.
Local equilibrium assumption: DICTRA assumes thermodynamic local equilibrium at phase boundaries. This assumption breaks down for:
- Very rapid cooling rates (martensitic transformations)
- Massive transformations where interface migration is very fast
- Systems with significant solute trapping at high growth rates
For these cases, para-equilibrium or quasi-paraequilibrium models may be more appropriate.
Database coverage: DICTRA can only simulate phases and alloy systems for which mobility data has been assessed. A phase marked “diffusion NONE” has no kinetic description — DICTRA accounts for its equilibrium presence but cannot simulate diffusion within it.
No grain boundary diffusion: DICTRA models lattice diffusion. Grain boundary diffusion — typically 2-5 orders of magnitude faster than lattice diffusion — is not included in the standard model. For processes where grain boundary diffusion is important (e.g., low-temperature carburization of stainless steels), additional modeling approaches are needed.
Summary
DICTRA is the computational metallurgy tool for quantitative simulation of multicomponent diffusion-controlled transformations — from carburizing heat treatment to coating interdiffusion to solidification microsegregation homogenization. Its power comes from the rigorous coupling of CALPHAD thermodynamics (Gibbs energy databases) with CALPHAD-assessed kinetics (mobility databases), which enables no-adjustable-parameter simulations of real industrial alloys.
For any materials engineering problem where the question is not just “what phases are stable?” but “how do composition profiles evolve, and how fast do phase boundaries move?”, DICTRA is the tool of record. Its 30+ years of validation in the primary literature, coupled with Thermo-Calc’s continuously updated thermodynamic and mobility databases, make it the most trusted diffusion simulation package in computational materials science.
For DICTRA and Thermo-Calc licensing assistance, contact via Telegram: t.me/DoCrackMe
Also see: Thermo-Calc 2026a — What’s New: Complete Release Overview | TC-Python Guide — Automating Thermo-Calc with Python | Thermo-Calc vs FactSage vs Pandat — CALPHAD Software Compared
