Research

High-temperature alloys

Goal. Predict how the microstructure of structural alloys evolves at high temperature: oxide scales that form on surfaces, and bond lines that heal or fail during diffusion bonding.

Significance. Alloys in power plants and compact heat exchangers often fail at surfaces and interfaces. Multiphase, multicomponent phase-field (MPMF) models place grains, voids, carbides, oxides and the diffusing elements in one simulation, so alloy compositions and processing schedules can be screened before furnace trials.

Alloy oxidation at high temperature
Competing oxides: NiO and Al₂O₃
Diffusion bonding of Alloy 617
Diffusion bonding of 316H stainless steel

Alloy oxidation at high temperatureA phase-field model of oxidation in multicomponent alloys. It predicts whether an alloy forms a protective
external oxide scale or internal oxide particles, as a function of alloy composition and the size and shape of
the oxide nuclei, and it is validated against Wagner’s classical theory.
Own code In-house code, written from scratch in Fortran with MPI; no commercial software.
Internal oxidation of a Ni-Al alloy, surface at the left. Top: Al2O3 particles (blue) nucleate where inward-diffusing oxygen (middle) meets outward-diffusing aluminium (bottom), then grow and coarsen.Internal Al2O3 rods grow inward; their tips spread laterally and merge into a continuous front, the onset of the internal-to-external oxidation transition.
The physicsOxygen diffuses inward from the surface and aluminium diffuses outward. Where the local driving force for oxide
formation is positive, Al2O3 nucleates. Phase fields follow Allen–Cahn kinetics and species
follow multicomponent diffusion, both derived from one free-energy functional. The transition from internal
particles to a protective external layer follows Wagner’s criterion,
NAl > NAlcrit ∝ (NOs DO / DAl)1/2
which the model reproduces without assuming it.
Papers: Acta Mater. 2023 · JOM 2022
Model and code: R. Wang (Ph.D. research, Penn State, with NETL). Co-authors: Y. Ji, T.-L. Cheng, F. Xue, L.-Q. Chen, Y.-H. Wen.
Competing oxides: NiO and Al₂O₃in preparationThe same framework with two competing oxides on a Ni-Al alloy: fast-growing NiO and protective
Al2O3. The simulations follow the competition between the two as a function of the alloy’s
aluminium content.
Own code In-house code, written from scratch in Fortran with MPI; no commercial software.
XAl = 0.06: an external NiO scale (orange) grows while Al2O3 (blue) remains as discontinuous internal particles.XAl = 0.15: Al2O3 nuclei merge into a continuous external layer and the NiO nuclei dissolve.
Model and code: R. Wang. Co-author: Y. Ji. Manuscript in preparation.
Diffusion bonding of Alloy 617in preparationDiffusion bonding joins metal plates in the solid state and is used to manufacture compact heat exchangers for
advanced reactors. A sound joint requires the interface voids to close and grains to grow across the original
interface; in Alloy 617, carbides and oxides can pin the bond line. The MPMF model predicts the bond-line
microstructure for a given temperature, pressure and surface-roughness schedule.
Own code In-house code, written from scratch in Fortran with MPI; no commercial software.
Bond line heated to 1150 °C under 16 MPa: interface voids close, M23C6 carbides (orange) dissolve, Al2O3 particles (blue) remain on the original plane, and a grain boundary migrates across it.Voids, carbides, oxide, grain growth and diffusion in one model: the bond line at an intermediate time, with the simulated element distributions (Ni, Cr, C, Al, O) in the boxed region.Mechanisms resolved by the model: (c) rough contact under pressure, (d) voids and carbides during the ramp, (e) carbide pinning and boundary depinning during the hold, (f) the bond line after cooldown.A 100 × 50 µm window of a 200 × 100 µm simulation. Top: during heating, with interface voids and carbides. Bottom: after a 59 min hold at 1150 °C, with grains grown across the original plane (dotted).
The physicsOne free-energy functional couples the grain order parameters, the void, M23C6 carbides and
α-Al2O3 with C, Cr, Al and O on CALPHAD sublattices. Phases evolve by Allen–Cahn equations and
species by Cahn–Hilliard-type diffusion. Gap closure under load follows a creep-type rate,
Ġ ∝ (P / σy(T))n exp(−Q / RT)
Model and code: R. Wang, F. Gao group, U. Michigan. DOE NEUP Integrated Research Project on diffusion bonding for compact heat exchangers. Manuscript in preparation.
Diffusion bonding of 316H stainless steelThe first version of the bonding model, developed for 316H stainless steel. It relates processing conditions
(temperature, pressure, surface roughness) to void closure and grain morphology at the bond line, and to the
resulting bonding ratio.
Own code In-house code, written from scratch in Fortran with MPI; no commercial software.
Bond line during bonding. Top: grains (grey boundaries) and interface voids (orange). Bottom: vacancy concentration around the shrinking voids.Three modeling stages: initialization with an initial gap, surface contact under applied stress, and diffusion bonding with voids evolving together with the grains.Model validation (1050 °C, 8 MPa, Ra = 0.1 µm): simulated bond line at 0, 1800 and 3600 s (a–c), compared with an optical micrograph of a bonded joint from the project (d). Mater. Sci. Eng. A 2025, Fig. 9.Effect of hold temperature (950, 1050, 1150 °C; 8 MPa, Ra = 0.3 µm; t = 2000 s). Mater. Sci. Eng. A 2025, Fig. 12.Effect of surface roughness (Ra = 0.1, 0.3, 0.5 µm; 1050 °C, 8 MPa; t = 2000 s). Fig. 14.Effect of bonding pressure (2, 4, 16 MPa; 1050 °C, Ra = 0.3 µm; t = 2000 s). Fig. 16.
The physicsGrain order parameters evolve by Allen–Cahn kinetics, and a void phase interacts with a vacancy-concentration field
that diffuses toward grain boundaries and free surfaces (Cahn–Hilliard type). The applied pressure adds a driving
force for gap closure, and temperature enters through the mobilities and diffusivities.
Papers: Mater. Sci. Eng. A 2025 · AM-EPRI 2024
Model and code: R. Wang, F. Gao group, U. Michigan, with Argonne National Laboratory.