Laboratory for 4D Interface Control & Engineering

Enabling controllability in microstructure processing …

Our Vision

Recent advances in high-throughput experimental and computational techniques have led to an accelerated discovery of new materials. On the contrary, the development of processing routes required for sustainable manufacturing of advanced materials is lagging behind.

At 4D ICE, we aim to fill this gap by developing computational tools for rapid and systematic discovery of time-, energy- and cost-efficient processing routes for the synthesis of materials with tailored functionality. Our work, which lies at the triple-point of phase-field modeling, machine learning, and high-performance computing aims at enabling controllability in advanced materials processing.

We welcome collaborations with other computational and experimental researchers in universities, national labs, and industries.


Kumar Ankit, Ph.D.
Associate Professor of Materials Science and Engineering
School for Engineering of Matter, Transport and Energy
Arizona State University, Tempe

MateriAlZ Seminar Series

We are excited to announce a new remote lecture series in the broad field of Materials Science and Engineering (MSE) jointly organized by the Arizona State University and the University of Arizona.

Thanks to our sponsors



October 3, 2023: Big News! Dr. Ankit is a co-PI on the newly announced $ 5 million U.S. Department of Energy (DOE) ‘Earthshots’ grant which will develop a cutting-edge technology to make steel production carbon-free, paving the way for a more sustainable future. More on ASU News.

June 22, 2023: In our recent work published in Computational Materials Science, we demonstrate how Neural Networks can be employed to emulate microstructural evolution.

Link to the manuscript: https://doi.org/10.1016/j.commatsci.2023.112330

February 2, 2023: Machine Learning algorithms employed to emulate defect formation in interconnects. Article published in the Journal of Electronic Materials.

Link to the manuscript: https://doi.org/10.1007/s11664-023-10237-9

January 11, 2023: Phase-field (PF) models are one of the most powerful tools to simulate microstructural evolution in metallic materials, polymers, and ceramics. However, for accuracy, existing PF approaches rely on rigorous mathematical model development, sophisticated numerical schemes, and high-performance computing. Our recent work published in MRS Bulletin demonstrates how a Machine Learning algorithm, that is able to circumvent the above-noted challenges, can emulate materials’ microstructure evolution. Financial support from the National Science Foundation (NSF) is gratefully acknowledged.

Link to the manuscript: https://doi.org/10.1557/s43577-022-00443-x


Capillary-mediated solid-liquid interface energy fields

Our recent theoretical analyses of the Isothermal Dendritic Growth Experiment (IDGE) archived in the NASA PSI system reveals the presence of a 4th-order interfacial scalar field, termed the bias field, that works in the background and dynamically couples with interface normal motion. Solid-liquid interfaces support such scalar perturbation fields by adding or withdrawing small amounts of thermal energy. However, our current understanding of the factors that govern the intensity of capillary-mediated fields is limited to pure melts and to two spatial dimensions. Moreover, any quantitative understanding of the intensity threshold beyond which such capillary-mediated fields can potentially modulate pattern formation is all together, absent.

At 4D-ICE, motivated by our recent detection of perturbation fields on grain boundary grooves (GBGs), which also appear to explain the anomaly reported in the IDGE data, we adopt the phase-field modeling approach to explore this fascinating autogenous mechanism of pattern formation. It is anticipated that the technological developments borne out of this project will enable us to develop novel processing methods to improve microstructure-level control in alloy castings.

This project is currently funded by NASA and the College of Engineering at ASU.

Electromigration-induced defects in electronic materials

With a continuous downscaling of very large-scale integrated circuits, metallic conductors or interconnects are subject to increasingly high current densities. However, a sufficiently large electric current density can impart momentum to the metal ions triggering atomic diffusion, known as electromigration (EM), leading to the generation of microdefects, for e.g. voids and hillocks and ultimately causing circuit failure. Current safety measures adopted in the electronics industry to mitigate EM-induced damage are unreliable as they are typically framed based on limited insights provided by 2D imaging of the microstructural degradation process.

The aim of this research project is to devise an integrated experimental and computational approach to achieve a fundamental understanding of the underlying mechanisms that accompany microstructural degradation in Sn- and In-based, Pb-free interconnects and solders. At 4DICE, we adopt the phase-field modeling approach to predict the onset and growth of EM-mediated defect patterns in multiphase, multicomponent electronic materials. The new knowledge gained from this work will enhance our capabilities to accurately predict the onset of EM damage and at the same time enable us to devise strategies for controlling EM-mediated failure of soldered components and interconnects, efficiently.

This project is currently funded by NSF and the College of Engineering at ASU.

Nanostructural self-assembly in vapor-deposited films

Nanostructured thin films are used in a wide range of applications due to their superior structural and functional properties, both of which are dependent on their morphology. The mechanisms by which morphological evolution occurs in thin films has been a perennial topic of fundamental interest, however, recent prospects of varying deposition conditions to fabricate films with tailored functionality have leveraged their technological relevance. Experiments and TEM characterization have demonstrated a rich variety of self-organized nanoscale concentration modulations in physical vapor deposited films of phase separating alloys. However, a comprehensive model capable of predicting an entire spectrum of such self-organized nanostructures as a function of material and processing parameters is yet to be formulated.

At 4D-ICE, we adopt a 3D phase-field approach to numerically investigate the role of deposition rates and separation kinetics, on the morphological self-structuring in vapor-deposited alloy films. By analyzing and predicting the nanoscale self-organization of vapor deposited binary alloy films through phase-field modeling, we will lay the foundation for synthesizing multi-component metallic films with enhanced properties.

This project is currently funded by the College of Engineering at ASU.


 Kumar Ankit, Ph.D.

Kumar Ankit, Ph.D.

Principal Investigator

Rahul Raghavan

Rahul Raghavan

Graduate Research Associate, Ph.D. student

William Farmer

William Farmer

Graduate Research Associate, Ph.D. student

Peichen Wu

Peichen Wu

Graduate Research Associate, Ph.D. student

Ziming Zhong

Ziming Zhong

Graduate Research Associate, Ph.D. student

Kumar Ankit, Ph.D.

Principal Investigator


Kumar Ankit is an Associate Professor of Materials Science and Engineering (MSE) in the School for Engineering of Matter, Transport and Energy at the Arizona State University. He received an integrated dual bachelor’s/master’s degree in metallurgical engineering from the Indian Institute of Technology (BHU) in 2010 and obtained a doctorate (2015) in mechanical engineering from the Karlsruhe Institute of Technology (KIT), Germany, where he graduated summa cum laude. Following graduation, he was appointed as Group Leader at KIT where his group specialized in Quantitative Phase-field Modeling. Prior to his appointment at ASU, he was a postdoctoral research associate at Texas A&M University where he worked in the area of modeling and simulations of pattern formation in vapor-deposited films.

Dr. Ankit is a recipient of the 2018 Robert Cahn prize which is jointly awarded by Springer Nature and the Journal of Materials Science, the 2016 German Research Foundation’s (DFG) Young Investigator award, and the 2022 National Science Foundation’s (NSF) CAREER award. In 2020, he, along with his collaborators at ASU and the University of Arizona – Tucson, co-founded the MateriAlZ Seminar series to promote student engagement in MSE through interactive sessions, increase the nationwide and international visibility of the Arizona universities and provide a platform for active discussions in different areas of MSE.

Dr. Ankit’s group, 4D ICE, specializes in the development and application of mesoscopic modeling approaches and their integration with continuum approaches for both fundamental and applied research in microstructure science and engineering. His group is currently interested in deciphering computational pathways to optimally design microstructure processing routes. Target areas include solidification, solid-state transformations and grain coarsening in multicomponent alloys and geomaterials, electromigration-induced damage, and self-organization in polymers and vapor-deposited films.


  • Ph.D. (Dr.-Ing.) Mechanical Engineering, Karlsruhe Institute of Technology, Germany (2015).
  • Integrated Dual Degree Metallurgical Engineering, Indian Institute of Technology BHU (2010).

Research Interests

Phase-field method, Pattern formation, Machine learning, Phase Transformations, Electromigration, Self-organization in soft matter, Vapor deposition.

Honors and Awards

  • 2022 Editors’ choice award, Journal of Phase Equilibria and Diffusion
  • 2022 NSF CAREER Award
  • 2018 Robert W. Cahn prize of Springer Nature and the Journal of Materials Science
  • 2016 Early Career Investigator Award of the German Research Foundation (DFG)

Rahul Raghavan 

Graduate Research Associate (Ph.D. student)


  • Master of Science, Materials Science and Engineering at Arizona State University
  • Bachelor of Technology, Metallurgical and Materials Engineering at National Institute of Technology, Trichy

Work experience

  • Materials Engineer at Materials and Electrochemical Research Corporation, Tucson (2014-2016)
  • Research Assistant at SEMTE, ASU (2012-2013)


  • Tau Beta Pi Honor Society Initiate (2016)
  • International Climate Champion, India award (2009)


  • Wagner, N. A., Raghavan, R., Zhao, R., Wei, Q., Peng, X. and Chan, C. K. (2013), “Electrochemical Cycling of Sodium-Filled Silicon Clathrate”, ChemElectroChem.
  • Li, Y., Raghavan, R., Wagner, N. A., Davidowski, S. K., Baggetto, L., Zhao, R.,  & Chan, C. K. (2015). Type I Clathrates as Novel Silicon Anodes: An Electrochemical and Structural Investigation. Advanced Science.
William Farmer 

Graduate Research Associate (Ph.D. student)


  • Bachelors of Science, Chemistry/Biochemistry at University of West Florida

Work experience

  • NASA – FSGC Scholar at University of West Florida (2016-2018)
  • Summer Intern at Intelligent Retinal Imaging Systems; Pensacola, FL (2015)


  • 2017 American Institute of Chemists Award.


  • Hamilton, H. S. C., Farmer, W. M., Skinner, S. F., ter Haar, L. W. (2018) “Metal organic framework Cu9Cl2(cpa)6as tunable molecular magnet”AIP Adv. 8.
  • Farmer, W. M., Skinner, S. F., ter Haar, L. W. “Heat capacity of the highly frustrated triangulated Kagome lattice Cu9Cl2(cpa)6” AIP Adv. (Submitted).
Peichen Wu 

Graduate Research Associate (Ph.D. student)


  • Master of Science, Mechanical Engineering at University of Florida (2017-2019)
  • Bachelor of Science, Manufacturing System Engineering at the University of Shanghai for Science and Technology (2013-2017)

Work experience

  • Summer intern at Zhengzhou Weisheng Mechanical Equipment Company, Henan, China (2016)
  • Research student at Atomistic and Multiscale Mechanics Laboratory, University of Florida, United States (2018-2019)


  • University of Florida Engineering achievement award (2017)
  • Undergraduate Academic Excellence Scholarship (2013-2017)


  • Graphene/Hexagonal Boron Nitrite in Plane Hetero-structures Simulations (Master thesis at the University of Florida)

Ziming Zhong 

Graduate Research Associate (Ph.D. student)


  • Master of Science, Mechanical Engineering at Arizona State University
  • Bachelor of Science, Mechanical Engineering at Arizona State University

Work experience

  • Graduate Service Assistant at HVAC Lab, ASU (2022-2023)



Materials Structures and Defects

Materials Structures and Defects

MSE 355

Materials Kinetics

Materials Kinetics

MSE 335

Microstructure Modeling & Simulations

Microstructure Modeling & Simulations

MSE 494/598


Journal articles 

43. Wu, P., Farmer, W., Iquebal, A., and K. Ankit (2023). Emulating microstructural evolution during spinodal decomposition using a tensor decomposed convolutional and recurrent neural network. Computational Materials Science, 224, 112187. doi: 10.1016/j.commatsci.2023.112187.

42. Mukherjee, A., Ankit, K., Selzer, M., and Nestler, B. (2023). Phase-field modelling of electromigration-induced intergranular slit propagation in metal interconnects. Computational Materials Science, 228, 112330. doi: 10.1016/j.commatsci.2023.112330.

41. Wu, P., Farmer, W., Iquebal, A., Sarfraz, A., and K. Ankit (2023). A novel data-driven emulator for predicting electromigration-mediated damage in polycrystalline interconnects. Journal of Electronic Materials, 1–16. doi: 10.1007/s11664-023-10237-9.

40. Iquebal, A. S., Wu, P., Sarfraz, A., & Ankit, K. (2023). Emulating the evolution of phase separating microstructures using low-dimensional tensor decomposition and nonlinear regression. MRS Bulletin, 1-12. doi: 10.1557/s43577-022-00443-x.

39. Raghavan, R., Wu, P., & Ankit, K. (2022). Phase-field modeling of nanostructural evolution in physical vapor deposited phase-separating ternary alloy films. Modelling and Simulation in Materials Science and Engineering, 30(8), 084004. doi: 10.1088/1361-651X/aca03f.

38. Glicksman, M. E., Ankit, K., & Wu, P. (2022). Capillary effects on curved solid–liquid interfaces: An overview. Journal of Crystal Growth 602, 126871. doi: 10.1016/j.jcrysgro.2022.126871.

37. Glicksman, A, Wu, P., and Ankit, K. Periodic Grain Boundary Grooves: Analytic Model, Formation Energies, and Phase-Field Comparison. Journal of Phase Equilibria and Diffusion 43. 781-737 (2022). doi: 10.1007/s11669-022-00967-4

36. Roy, A, Luktuke, A., Chawla, N., and Ankit, K. Predicting the Cu6Sn5 Growth Kinetics During Thermal Aging of Cu-Sn Solder Joints Using Simplistic Kinetic Modeling. Journal of Electronic Materials 51, 4063-4072 (2022). doi: 10.1007/s11664-022-09643-2

35. Chen, P.-E., Raghavan, R., Zheng, Y., Li, H., Ankit, K. and Jiao, Y. Quantifying microstructural evolution via time-dependent reduced-dimension metrics based on hierarchical n-point polytope functions. Physical Review E 105, 025306 (2022). doi: 10.1103/PhysRevE.105.025306 

34. Glicksman, M.E., Wu, P. and Ankit, K. Surface Laplacian of interfacial thermochemical potential: its role in solid-liquid pattern formation. Nature Microgravity 7, 41 (2021). doi: 10.1038/s41526-021-00168-2

33. Raghavan, R., W. Farmer, L. Mushongera and K. Ankit (2021). Multiphysics approaches for modeling nanostructural evolution during physical vapor deposition of phase-separating alloy films. Computational Materials Science 199, 110724. doi: 10.1016/j.commatsci.2021.110724

32. Raghavan, R., P.-E. Chen, Y. Jiao, and K. Ankit (2021). Phase-field modeling and n-point polytope characterization of nanostructured protuberances formed during vapor-deposition of phase-separating alloy films. Journal of Applied Physics 129, 245301. doi: 10.1063/5.0047928.

31. Raghavan, R., A. Mukherjee, and K. Ankit (2020). Nanostructural evolution in vapor deposited phase-separating binary alloy films of non-equimolar compositions: Insights from a 3D phase-field approach. Journal of Applied Physics 128, 175303. doi: 10.1063/5.0007385.

30. Farmer, W. and K. Ankit (2020). Phase-field simulations of electromigration-induced defects in non-columnar grain microstructures. Journal of Applied Physics 127(17) 175301. doi: 10.1063/1.5145104.

29. Glicksman, M. and K. Ankit (2020). Thermodynamic behavior of solid-liquid grain boundary grooves. Philosophical Magazine 100(14), 1789-1817. doi: 10.1080/14786435.2020.1740340.

28. Ankit, K. and M. Glicksman (2020). Growth competition during columnar solidification of seaweed microstructures. The European Physical Journal E 43 (14). Selected for Journal cover page: February 2020. doi: 10.1140/epje/i2020-11940-5.

27. Laxmipathy, V.P., F. Wang, M. Selzer, B. Nestler, K. Ankit (2019). Influence of melt convection on the morphological evolution of seaweed structures: Insights from phase-field simulations. Computational Materials Science 170, 109196. doi: 10.1016/j.commatsci.2019.109196.

26. Ankit, K., B. Derby, R. Raghavan, A. Misra, and M. Demkowicz (2019). 3-D phase-field simulations of self-organized composite morphologies in physical vapor deposited phase-separating binary alloys. Journal of Applied Physics 126 (6). doi: 10.1063/1.5110410.

25. Glicksman, M. and K. Ankit (2019). Capillary-mediated solid-liquid energy fields: their detection with phase-field method. IOP Conference Series: Materials Science and Engineering 529, 012027.doi: 10.1088/1757-899x/529/1/012027.

24. Amos, P.G.K., A. Bhattacharya, B. Nestler, K. Ankit (2018), Mechanisms of pearlitic spheroidization: Insights from 3D phase-field simulations, Acta Materialia 161, 400–411. doi: 10.1016/j.actamat.2018.09.043

23. Nani, E.S., B. Nestler, K. Ankit (2018), Analyzing the cooperative growth of intermetallic phases with a curved solidification front, Acta Materialia 159, 135-149. doi: 10.1016/j.actamat.2018.08.017

22. Prajapati, N., M. Selzer, B. Nestler, B. Busch, C. Hilgers, and K. Ankit (2018). Three‐Dimensional Phase‐field Investigation of Pore space Cementation and Permeability in Quartz Sandstone, Journal of Geophysical Research-Solid Earth, 123. doi: 10.1029/2018JB015618.

21. Glicksman, M. and K. Ankit (2018). Measuring Solid-Liquid Interfacial Energy Fields: Diffusion-Limited Patterns. Journal of Materials Science 53 (15), 10955-10978.

20. Mukherjee, A., K. Ankit, M. Selzer, and B. Nestler (2018). Electromigration-induced surface drift and slit propagation in polycrystalline interconnects: Insights from phase-field simulations. Physical Review Applied 9, 044004.

19. Mushongera, L.T., P.G.K. Amos, B. Nestler, K. Ankit (2018). Phase-field simulations of pearlitic divergence in Fe-C-Mn steels, Acta Materialia 150, 78-87.

18. Glicksman, M. and K. Ankit (2017). Detection of Capillary-Mediated Energy Fields on a Grain Boundary Groove: Solid-Liquid Interface Perturbations. Metals 7, 547.

17. Xing, H., K. Ankit, X. Dong, H. Chen, and K. Jin (2018). Growth direction selection of tilted dendritic arrays in directional solidification over a wide range of pulling velocity: A phase-field study. International Journal of Heat and Mass Transfer 117, 1107-1114. 

16. Bhattacharya, A., K. Ankit, and B. Nestler (2017). Phase-field simulations of curvature-induced cascading of Widmanstätten-ferrite plates. Acta Materialia 123, 317–328.

15. Ankit, K., H. Xing, M. Selzer, B. Nestler, and M. Glicksman (2016). Surface rippling during solidification of binary polycrystalline alloy: Insights from 3-D phase-field simulations. Journal of Crystal Growth 457, 52–69.

14. Meller, C., J. Bremer, K. Ankit, and 33 others (2016). Integrated research as key to the development of a sustainable geothermal energy technology. Energy Technology (invited review) 5(7), 965-1006.

13. Mukherjee, A., K. Ankit, R. Mukherjee, and B. Nestler (2016). Phase-field modeling of grain-boundary grooving under electromigration. Journal of Electronic Materials 45 (12), 6233–6246. 

12. Mukherjee, A., K. Ankit†, A. Reiter, M. Selzer, and B. Nestler (2016). Electric-field-induced lamellar to hexagonally perforated lamellar transition in diblock copolymer thin films: Kinetic pathways. Physical Chemistry Chemical Physics 18, 25609–25620.

11. Mukherjee, A., R. Mukherjee, K. Ankit†, A. Bhattacharya, and B. Nestler (2016). Influence of substrate interaction and confinement on electric-field-induced transition in symmetric block-copolymer thin films. Physical Review E 93(3), 032504.

10. Ankit, K., T. Mittnacht, R. Mukherjee, and B. Nestler (2015). Evolution of mixed cementite morphologies during non-cooperative eutectoid transformation in Fe-C steels. Computational Materials Science 108 (B), 342–347.

9. Ankit, K., R. Mukherjee, and B. Nestler (2015). Deviations from cooperative growth mode during eutectoid transformation: Mechanisms of polycrystalline eutectoid evolution in Fe-C steels. Acta Materialia 97, 316–324.

8. Ankit§, K., M. Selzer, C. Hilgers, and B. Nestler (2015). Phase-field modeling of fracture cementation processes in 3-D. Journal of Petroleum Science Research 4 (2), 79–96.

7. Ankit, K., J. Urai, and B. Nestler (2015). Microstructural evolution in bitaxial crack-seal veins: A phase-field study. Journal of Geophysical Research B: Solid Earth 120(5), 3096–3118.

6. Ankit, K., R. Mukherjee, T. Mittnacht, and B. Nestler (2014). Deviations from cooperative growth mode during eutectoid transformation: Insights from a phase-field approach. Acta Materialia 81, 204–210.

5. Ankit, K., A. Choudhury, C. Qin, S. Schulz, M. McDaniel, and B. Nestler (2013). Theoretical and numerical study of lamellar eutectoid growth influenced by volume diffusion. Acta Materialia 61(11), 4245–4253.

4. Ankit, K., B. Nestler, M. Selzer, and M. Reichardt (2013). Phase-field study of grain boundary tracking behavior in crack-seal microstructures. Contributions to Mineralogy and Petrology 166(6), 1709–1723.

3. Ankit, K. and N. Prasad (2011). Simulation of creep cavity growth in Inconel 718 alloy. Materials Science and Engineering A 528(12), 4209–4216.

2. Fleck, M., L. Mushongera, D. Pilipenko, K. Ankit, and H. Emmerich (2011). On phase-field modeling with a highly anisotropic interfacial energy. European Physical Journal Plus 126(10), 1–11.

1. Ankit, K. (2009). Remaining creep life assessment techniques based on creep cavitation modeling. Metallurgical and Materials Transactions A 40(5), 1013–1018.


Ankit, K. (2016). Phase-field modeling of microstructural pattern formation in alloys and geological veins. Vol. 58. Series of Institute of Applied Materials, Karlsruhe Institute of Technology. KIT Scientific Publishing, 242 pages.





Graduate student positions

Prospective Ph.D. students should apply for admission to the Materials Science and Engineering program at ASU before contacting us. Please see instructions here. Applications are solely evaluated by the graduate admissions committee.

After a successful acceptance in the program, Ph.D. students who are interested in working at 4D ICE may send a copy of their CV and accomplishments to Prof. Kumar Ankit for consideration as Graduate Research Assistant. We are interested in hiring hard-working, motivated, and enthusiastic students with backgrounds in computational materials science, or physics with an inclination towards microstructure modeling.

Students interested in pursuing their Masters’ thesis research may contact Prof. Kumar Ankit along with their CV and transcripts.

Undergraduate student positions

Current undergraduates at ASU who are interested in working on a research project may contact Prof. Kumar Ankit by email. We are interested in enthusiastic, hard-working students with any science or engineering major. You are also encouraged to apply for a FURI project. Here is an advertisement.

Postdoctoral positions

A Postdoctoral Associate position is available starting January 2019 at the School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, United States. The position will be based in the Laboratory for 4D Interface Control and Engineering (4D-ICE) which is headed by Prof. Kumar Ankit.

Candidates need to have a strong background in Phase Field Modeling (PFM) with a demonstrated experience in parallel code development (MPI). Experience with implementation of multiphase-field, and phase-field crystal models is desirable. The research opportunity will help the successful candidate to strengthen his/her skills in computational modeling for materials and manufacturing design and will enable future career development.

    Qualified applicants must have a doctoral degree in materials science, metallurgical engineering, physics, computer engineering or similar field prior to beginning employment. Salaries will be commensurate with relevant experience and based on the prevailing wage for postdoctoral fellows set by the Arizona State University. The Arizona State University is an Affirmative Action/Equal Opportunity Employer and values equality of opportunity, human dignity and diversity.

    To apply, please submit the application documents to Prof. Kumar Ankit (kumar.ankit[at]asu.edu) with an email titled as “Postdoc Application by Your_Full_Name.” The application package should include a complete CV, transcripts of all degrees, at least three reference contact with their email and phone number, and a cover letter (less than 2-page) summarizing your previous work and career goals. Review of applicants will begin immediately and will continue until the position is filled. Applicants are encouraged to learn the research lab and the Arizona State University through the website before application: http://www.kumarankitresearch.com.


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