DSIP Team Rohit Trivedi: Principal Investigator Alain Karma: Co-investigator

1. Dynamical Selection of Interface Patterns DSIP Team Rohit Trivedi: Principal Investigator Alain Karma: Co-investigator Richard Grugel: Project Scientist Members of the team: Shan Liu: Research Scientist Luis Fabietti: Visiting Scientist :

2. Outline of Presentation • Introduction • Background • Ground-Based Research • Ground-Bases Results, Experimental Plans and Objectives • Justification for Conducting Experiments in Space • Flight Experiment Plan • Flight Experiment Requirements • Principal Investigator’s Requirements

3. Introduction • Overview • Scientific and Technological Value of Knowledge Gained • Description and Objectives of ISS Experiments • Microgravity Justification • Summary of Ground-Based Experiments • Anticipated Advances • REMAP Priorities

4. Directional Solidification Apparatus

5. Microstructures

6. Dynamics of Pattern Evolution

8. Phase Field Simulation

9. Similarities: Physical Systems Saffman-Taylor finger Flame front Ensembled ave. DLA pattern Directional solidification

10. Similarities: Physical and Biological Systems Oxidation of Al mirror Electrodeposition Bacterial colony Etched sapphire crystal

11. Technological Importance

12. A Three-Dimensional Dendritic Structure A structure observed at a crack in the welding of a superalloy

13. Basic Questions • What physics governs the onset of instability and the initial • wavelength spectrum of instability? The understanding of complex pattern formation dynamics can be divided into the following questions: • What are the fundamental factors that subsequently lead to a complex wavelength selection process in the nonlinear growth regime and lead to the self assembly of patterns in the form of • different microstructures? • What physical principle controls the possible range of • stable steady-state growth structures? • What factors control the spatial arrangement of cells, • i.e. square or an hexagonal array?

14. Basic Questions (Cont.) • What fundamental physics dictates the formation of • ordered, disordered or chaotic patterns? • When does the sidewise instability occur and what controls its amplification or stability? • Are the multiple solutions observed for different cells in an • array random or governed by some fundamental laws? • Based on the benchmark results obtained on ISS, can we develop a realistic model of the complex pattern formation phenomenon that can be used to predict microstructures in different alloy systems under different growth conditions?

15. More Questions (Unifying Ideas) • What similarities are present for cellular and dendritic solutions • with similar patterns that form in other disciplines of sciences? • Although the governing physics may be different for patterns in different scientific fields, do they exhibit the following common features: • Can all patterns be described by the same • mathematical formulation? • Do they have analogous selection criterion? • Do they exhibit similar scaling laws?

16. Proposed Experiments • To answer these questions, we propose to carry out experiments in a transparent system in which the dynamics of pattern formation can be imaged in situ. • The experiments are proposed on ISS since low gravity conditions are required to obtain benchmark data that are not influenced by fluid flow. • The dynamics of pattern evolution will be examined under differnt growth and initial conditions to clearly establish the physics of pattern evolution in nonlinear growth regime where the selection of pattern occurs. • Complimentary ground-base measurements will also be carried out under the same conditions as the flight experiments

17. SCR Evaluation Charges 1. Significance of problem being investigated, including experimental and theoretical significance to materials science research community and industry 2. Maturity of overall scientific investigation 3. Scientific objectives of proposed flight experiments 4. Need for microgravity environment to achieve proposed scientific objectives 5. Priorities for theses scientific objectives 6. Rigor with which proposed experiment has been conducted terrestrially 7. Scientific specifications for proposed flight experiments as expressed in preliminary draft of Science Requirements Document (SRD) 8. Conceptual design of apparatus and whether this design could be expected to deliver performance that allows scientific objectives to be achieved 9. Technology issues that would prevent timely, successful achievement of scientific objectives

18. Charge # 1 Significance of problem • Development of fundamental quantitative understanding of microstructure evolution under dynamic growth conditions is crucially important for improving large scale industrial processes from casting to welding. • Results will provide the basis to predict reliably processing conditions that optimize microstructures and hence material properties and performance. • New knowledge of solidification dynamics has direct implications for understanding pattern formation in a wide range of physical and biological systems. • Corner stone for the validation of phase-field approach through unique quantitative comparison of model predictions and benchmark experiments in three dimensions.

19. Charge # 2 Maturity of scientific investigation • Large body of experimental and theoretical work over the last two decades (including the PI’s ground-based work) has identified key fundamental questions that can only be addressed through flight experiments. • Ground-based experiments have led to the selection and detailed characterization of an alloy system suitable for these experiments on ISS. • Ground-based work has established a well-defined experimental matrix and detailed procedures for flight experiments. • Modeling work has lead to the development of state-of-the-art quantitative phase-field models uniquely capable of making quantitative comparisons with experiments.

20. Charge # 3 Scientific objectives of proposed flight experiments • Initial morphological instability (rest to fixed V). When does it occur in time and what is the initial spatial pattern and its wavelength? • Nonlinear development of the structure after the initial instability until steady-state. • Dynamics of pattern reorganization following a change of growth condition (V1 to V2 > V1 or V2 < V1). • Identify widest possible range of stable steady-state growth structures • Identify the relative importance of different stages of morphological development for pattern selection, initial breakdown versus nonlinear coarsening.

21. Charge # 3 Scientific objectives (Cont.) • Probe the history dependence of dynamic pattern selection by different velocity ramps. • Understand the various stages of morphological development that select the final structure. • Design experimental pathways to the selection of new structures. • Measure tip positions => characterize spatial structure (square, hexagon or disordered). • Measure local primary spacing and tip radius of cell at low velocity. • Cell to dendrite transition: difference between 2-D and 3-D patterns.

22. Charge # 3 Scientific objectives (Cont.) • To understand quantitatively the detailed dynamics of complex interface pattern evolution through rigorous theoretical modeling and unambiguous results obtained from experiments on ISS. • Compare the model with the results in other pattern forming systems to extract the fundamental issues that are generic to all patterns in different fields of sciences.

23. Charge # 4 Need for microgravity • The evolution of cellular pattern from a planar front occurs under conditions where fluid flow effects are dominant under terrestrial conditions. Benchmark experimental data for 3D pattern formation under diffusive growth conditions can only be obtained under long duration low gravity environments. • Experiments and numerical modeling have shown a dominant effect of fluid flow in bulk samples under terrestrial conditions. A gravity level of 10-4 or smaller is required to have negligible fluid flow in 1.0 cm diameter sample under experimental conditions required in the present study.

24. Charge # 5 Priorities of Scientific Experiments • In decreasing order of priority: • The time evolution of interface pattern from an initially planar to the finally reorganized cellular/dendritic interface. • Extract the pattern selection process and the dominant physics leading to pattern selection. • Determine the condition for the development of sidebranches. • Test the model of amplification of thermal fluctuations on stable sidebranch formation.

25. Charge # 5 Priorities of Scientific Experiments (Cont.) • Dynamics of planar interface motion, conditions for initiation of instability, and initial wavelength selection under dynamical growth conditions. • Velocity-change experiments to study the history-dependent primary spacing selection • Develop relationships between microstructural scales and processing variables, during both the dynamical and steady state growth conditions • Develop an expression for the cell-dendrite transition condition

26. Charge # 6 Rigor of Terrestrial Experiments • Selection of alloy system and determination of phase diagram and relevant properties of the system. • Completed detailed studies in thin samples (i.e. diffusive growth conditions) to establish a well-defined experimental matrix and procedures for flight experiments. • Developed a booster heater concept to obtain flat isotherms in SCN-alloy system in high thermal conductivity quartz ampoule. • Developed theoretical models to analyze experimental data on spatio-temporal interface evolution that will be observed in ISS experiments.

27. Charge # 6 Rigor of Terrestrial Experiments (Cont.) • Completed theoretical and experimental studies to establish the need for low gravity environment for proposed studies. • Carried out experiments and used theoretical models to estimate the scales of microstructures that will be observed for the proposed matrix to establish the resolution of imaging techniques required.

28. Charge # 6 Rigor of Terrestrial Experiments (Cont.) • Developed theoretical models and carried out experiments to establish significantly different morphology and stability condition in 2D and 3D interface patterns. • Established new scaling laws for cellular patterns to explain the variation in cell microstructural scales in an array. • Showed that cell shapes with interdendritic eutectic can be described precisely by the 3D analog of the Saffman-Taylor equation, showing similarities among patterns that form in different disciplines of sciences. • Established the importance of spacing variation on the cell-dendrite transition.

29. Charge #7 Scientific Specification of ISS Experiments • Directional solidification apparatus with hot and cold stages, and a translation mechanism. • Imaging capabilities with two cameras and laser interference technique. • Appropriate thermocouples to characterize the thermal profile. • Precise measurements of sample translation rate and thermal profile in the sample as a function of time.

30. Charge # 8 Conceptual Design of Apparatus • DECLIC • - Designed and constructed by CNES • - Directional Solidification Insert (DSI) also designed by • CNES No Conceptual Design Problems

31. Charge # 9 Technology Issues that will Prevent Success None anticipated

32. Charge # 1 Biological Medical Physical REMAP: Topics of Top Priority Cell & Molecular Biology (Combined with Molecular Structures & Interactions and Cell Science & Tissue Engineering) Phase Transformation Fundamental Laws Physiology (Combine Integrated & Organ System) Clinical/ Operational Medicine Kinetics, Structure & Transport Energy Conversion Radiation Health Advanced Life Support (& parts of Gravitational Ecology) Fluid Stability & Dynamics Condensed Matter Propulsion & Power Behavior & Performance Organismal / Comparative Biology DSIP

33. Charge # 1 1a 1b 1d 1c 2b 2d 5a 5b 2c 2a 3b 4a 4b 4c 4d 3a Our Current Orbit – And Beyond:More Details on the Organizing Questions 1 2 3 4 5

34. Outline of Presentation • Introduction • Background • Ground-Based Research • Ground-Bases Results, Experimental Plans and Objectives • Justification for Conducting Experiments in Space • Flight Experiment Plan • Flight Experiment Requirements • Principal Investigator’s Requirements • Hardware: DECLIC with Directional Solidification Insert

35. Charges # 1,2,3 Background • Description of Scientific Field • Theoretical Studies on Steady-State Interface Patterns • Critical Questions to be Answered • Experimental Studies on Steady-State Interface Patterns • Dynamical Studies of Interface Pattern Evolution in Two-Dimensions

36. Charges # 1,2,3 Planar Interface Growth and Stability • Planar Interface growth models: • - Numerical Models • - Green function method (Caroli et al.) • - Boundary layer model (Warren and Langer) • Planar interface stability • - Constitutional supercooling (Tiller et al.) • - Linear stability analysis (Mullins and Sekerka) • - Weakly nonlinear analysis (Wollkind and Segel) The above Stability analyses assume initial steady state configuration, whereas interface instability occurs during the dynamical conditions of growth - Phase field method (Alain Karma, this project)

37. Charges # 1,2,3 Cellular Growth: Steady-state Growth Analytical model - Cell tip undercooling (Bower et al.) - Cell spacing model (Hunt, Kurz and Fisher) Numerical models - Cellular pattern (Coriell and McFadden) - Finite difference method (Hunt and Lu) Phase field model (Alain Karma)

38. Charges # 1,2,3 Numerically Predicted Cell Shapes Ag-Cu system (McFadden and Coriell)

39. Charges # 1,2,3 Dendrite Model • Analytical model (Ivantsov) • Boundary integral model (Many) • Numerical model (Hunt and Lu) • Phase field model (Karma and Rappel) Key conclusion from thee boundary integral and the phase field model is that the stability of cells and dendrites is governed by the anisotropy in interface properties.

40. Charges # 1,2,3 Pattern Evolution Dynamics • Theoretical models have been developed for two-dimensional patterns only. Two-dimensional models can not be validated since it is not possible to obtain true two-dimensional patterns in experiments due to surface energy effects at the walls • Dynamical evolution in three-dimensions is being modeled in our ground-based study and benchmark results from low gravity environment are needed to validate this model.

41. Charges # 1,2,3 Experimental Studies • Experimental studies on steady state patterns in thin samples of transparent materials have been carried out by several authors. • Experimental results have been obtained on cellular and dendritic tip radii and primary spacing. The finite thickness of the sample significantly influences primary spacing so that no reliable data are available. Experiments in bulk samples show that the patterns are significantly influenced by the presence of convection.

42. Charges # 1,2,3 Experimental Studies Cell/dendrite spacing variation with velocity History-dependence of primary spacing

43. Charges # 1,2,3 Anisotropy Effects on Microstructure (100) (111) (110) (Akamatsu et al.)

44. Charges # 1,2,3 Sidebranch Instability The sidewise instability of causing cell to dendrite transition has been modeled based on the amplification of thermal fluctuation at the tip. Cell to dendrite transition has been studied experimentally in thin samples within this project and will be described in the section on ground-based studies. Benchmark data in three-dimensional structures are needed to establish the physics that leads to sidewise instability.

45. Charges # 1,2,3 Unifying Models of Patterns in Different Fields of Sciences Basic approaches on pattern formation have been applied to patterns formed in different disciplines of sciences, and attempts have been made to obtain a unifying model. • Linear and weakly nonlinear stability analysis of a planar interface • instability is analogous to the stability of a fluid-fluid interface, and the • approach is similar to the one developed by Landau. • The sidebranch instability for dendrite formation has been examined by • using the concept of noise-induced amplification at the tip in flame fronts. • In our ground-based study we shall show that the shape of the cell, in • presence of an eutectic, can be described accurately by the Saffman- • Taylor equation developed for viscous fingering.These patterns, in • different disciplines of sciences, exhibit self-similarity.

46. Charges # 1,2 Outstanding Questions • What physics governs the onset of instability and the wavelength of • instability under dynamic conditions of growth? • What is the fundamental physics that leads to a complex wavelength • selection process in the nonlinear growth regime and lead to the self- • assembly of the pattern in the form of different microstructures? • What fundamental physics causes the initiation and amplification of • sidewise instability that lead to dendrite formation? • Based on the benchmark results obtained on ISS, can we develop a • realistic model of the complex pattern formation phenomenon that can • be used to predict microstructures in different alloy systems under • different growth conditions? • What fundamental principles of solidification patterns are common to • the broader area of pattern formation in other fields of sciences so that • a unifying theoretical models can be developed?

47. Outline of Presentation • Introduction • Background • Ground-Based Research • Ground-Bases Results, Experimental Plans and Objectives • Justification for Conducting Experiments in Space • Flight Experiment Plan • Flight Experiment Requirements • Principal Investigator’s Requirements • Hardware: DECLIC with Directional Solidification Insert

48. Directional Solidification Apparatus

49. Charges # 1,2,3 Ground-Based Research Science Related • Experimental Studies to Develop Critical Scientific Ideas on Interface Patterns • Establish Need for Low Gravity Experiments • Development of Theoretical Framework. Flight Related • Design of a Thermal Assembly to Obtain a Flat Interface. • Selection of Experimental Alloy System and Characterization of its Properties. • Experiments on Microstructural Scales of Cells and Dendrites for Designing Flight Experiments • Design Experimental Matrix for Reliable Analysis of the Results.

50. Charges # 1,2,3 Ground-Based Research (Sci. related) • ExperimentalStudiesto Develop Critical Scientific Ideas on Interface Patterns • Dynamical Evolution of Interface Patterns in Thin, Rectangular Samples • Dynamics of a planar interface motion • A comparison with the phase-field model results • Planar to cellular and cellular to dendritic transitions • Steady State Cellular Growth • Scaling relationship • Multiple solutions: order within disorder • Self-similarity with Saffman-Taylor finger shapes • Diffusive Growth in Thin Cylindrical Samples • Steady-state shapes of single-cells • Dynamical evolution of cells