3D Growth Kinetics of Precipitates with Anisotropic Interfacial Free Energy: A Phase-Field Study

Roy, Arijit; Gururajan, M. P.

doi:10.1007/s12666-015-0558-0

Cited by 5 publications

(6 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, microstructure order parameter has evolved greater than 1 demonstrating its non-conserved behavior. This effect takes place due to the Gibbs-Thompson effect as described elsewhere [17]. In addition to IMC layer growth, multiple precipitates are grown independently in the Sn matrix with initial precipitates which have demonstrated low free energy that can be similarly observed in experimental results.…”

Section: Phase Field Modelmentioning

confidence: 85%

“…From our experiments, we observed that Ag in the Sn matrix of the solder joint has been transported towards the main IMC layer which was produced in the process of solder-joint and Cu bonding. We were able to successfully model this phenomena using the Zenner-Frank (ZF) phase field model only with considering the chemical contributions to FDF as discussed in this work [1], [17]. In addition, this work also served as a direct experimental verification of ZF PFM model which is challanging to observe in many direct experimental analysis [1].…”

Section: Introductionmentioning

confidence: 89%

“…We present the PFM model to simulate and analyze the uphill diffusion process observed in experimental results as below. Here with we incorporate Zenner-Frank (ZF) phase field model as presented by Mukherjee et al [1] and Roy and Gururajan [17] which is soundly demonstrated for precipitate growth and solid state transport phenomena. ZF model is developed based on Cahn-Hilliard equation to evolve the conserved order parameter which is the composition (𝑐).…”

Section: Phase Field Modelmentioning

confidence: 99%

See 2 more Smart Citations

Phase Field Modeling of Ghost Diffusion in Sn-Ag-Cu Solder Joints

2022

View full text Add to dashboard Cite

In this paper, we have introduced a phase field modeling technique to simulate ghost diffusion phenomena of intermetallic compounds in a bulk mettalic matrix phase. We used Zenner-Frank phase field approach to define free energy density functional which is to be evolved using Chan-Hilliard and Alan-Chan equations to simulate time evolution of the precipitates. We verified our simulation results with intermetallic compound growth of Sn-Ag-Cu solder joints in isothermal aging process attributing to the diffusion of Ag3Sn intermetallic compound. Herewith we present that Zenner-Frank model demonstrates sound validity and provides a best understanding of such phenomena.

show abstract

Section: Phase Field Modelmentioning

confidence: 85%

Section: Introductionmentioning

confidence: 89%

Section: Phase Field Modelmentioning

confidence: 99%

See 1 more Smart Citation

Phase Field Modeling of Ghost Diffusion in Sn-Ag-Cu Solder Joints

2022

View full text Add to dashboard Cite

show abstract

“…Using the fourth rank tensor terms (either P 4 or Q or both), it is possible to obtain cuboidal or octahedral shapes -that is, shapes which prefer (100) facets or (111) facets [41]. However, if the system prefers (110) facets over both (100) and (111), then, we have to necessarily use sixth rank tensors to obtain the equilibrium morphology (namely, dodecahedron: a shape with twelve facets) -which contains a term of the type c 2 1 c 2 2 c 2 3 which is missing in the fourth rank tensor.…”

Section: Cubic Symmetry: Dodecahedron In 3-dmentioning

confidence: 99%

Interfacial free energy anisotropy driven faceting of precipitates

Roy

Nani

Lahiri

et al. 2017

Philosophical Magazine

Self Cite

View full text Add to dashboard Cite

We use extended Cahn-Hilliard (ECH) equations to study faceted precipitate morphologies; specifically, we obtain four sided precipitates (in 2-D) and dodecahedron (in 3-D) in a system with cubic anisotropy, and, six-sided precipitates (in 2-D, in the basal plane), hexagonal dipyramids and hexagonal prisms (in 3-D) in systems with hexagonal anisotropy. Our listing of these ECH equations is fairly comprehensive and complete (upto sixth rank tensor terms of the Taylor expansion of the free energy). We also show how the parameters that enter the model are to be obtained if either the interfacial energy anisotropy or the equilibrium morphology of the precipitate is known. IntroductionProperties of crystalline materials are anisotropic due to the anistropy of the underlying continuum. In particular, the interfacial energy in crystalline systems is anisotropic and can have a strong influence on the formation and evolution of microstructures. Phase field models, which are best suited for the study of the formation and evolution of microstructures (see [1,2,3,4,5] for some recent reviews), have been used quite successfully to study the effect of interfacial energy anisotropy on microstructures and their evolution: see ] for some representative examples.The phase field models that incorporate interfacial energy anisotropy do so in one of two ways: (A) replace the gradient energy coefficient by an anisotropic function or polynomial, and (B) include higher order terms in the Taylor series expansion of the free energy functional. In this paper, we take the second approach -which is an extension of the original Cahn-Hilliard equation along the lines shown by Abinandanan and Haider [6] (hereafter referred to as ECHAH) and Torabi and Lowengrub [7] (hereafter referred to as ECHTL); this approach is argued to be advantageous in terms of the levels of anisotropy one can incorporate [6] and the kinetics remaining diffusionlimited [13]; in addition, the first method requires regularisation [22] for large anisotropies while ours does not.During solid-solid phase transformations interfacial energy anisotropy is known to lead to faceted precipitates: see for example, PbS precipitates in Na-doped PbTe system [31], Al 3 Sc precipitates in Al(Sc) alloys [32], Pt precipitates in sapphire [33], several metallic precipitates in internally reduced oxides [34], and Al 3 Ti precipitates in Al [35]. Our objective in this paper is to obtain, using phase field modelling, faceted precipitates in cubic systems that distinguish between 100 and 111 (for which one has to necessarily include fourth rank tensor terms [6]) and those that prefer 110 over both 100 and 111 (for which one has to necessarily include sixth rank tensor terms [8]); additionally, the sixth rank tensor terms can also be used to study

show abstract

“…Density functional theory (DFT), since it appeared, proved feasible to calculate some energy parameters in Al alloys at the atomic scale, such as interfacial energy [13,14], solubility energy [15], segregation energy [16,17], interaction energy [18] and free energy [19], even the lattice parameters [20,21] and elastic constants [20] as well. Based on these parameters, the phase-field models (PFMs) have been modified to study the evolutions of the microstructures, considering the anisotropies such as the interfacial energy anisotropy [22,23]. And PFMs have been applied to simulate the dendritic growth [24] and the solidification of Al-Cu alloys [25,26].…”

Section: Introductionmentioning

confidence: 99%