A Thermodynamic Density Functional Theory for Predicting Properties of Complex Disordered Alloys Duane D. Johnson, NSF DMR Materials Science and Engineering, University of Illinois Urbana-Champaign After shearing, twinning is the dominate deformation mechanism in metals and alloys, as well as minerals, yet there is no theory that predicts twinning stresses and, hence, true mechanical response. Results: For the first time, we have predicted quantitatively the onset twinning stresses (  Crit ) for FCC metals and solid- solutions. The theory reveals that the unstable twin energy  ut, controls the twinning stress (  Crit   ut ), see figure, rather than stacking fault energy, as supposed experimentally. Approach: We combine DFT results in an analytic mesoscale dislocation model of twin nucleation to predict onset stresses for twinning. Directionality in twinning is also correctly described. Predicted Onset Twinning Stress: Twinning stresses (times Burger’s vector, in mJ/m 2 ) vs. unstable twin energy (in mJ/m 2 ) for elemental FCC metals from DFT-based analytic model. Dashed line is guide to eye. Experimental data are average reported stress and hi(low) stresses are given by ± bars. Theory results are given in red squares and calculated at expt. lattice constants. * Same relation holds plotting as MPa vs defect energy. Why it matters: Ideal stresses that occur when no dislocation defects are present are x larger than observed. For design of materials, we can now predict quantitatively what stress is required to alter the metal’s microstructure and how it will impact response. In collaboration with NSF DMR Quantitative Prediction of Onset Twinning Stresses

A Thermodynamic Density Functional Theory for Predicting Properties of Complex Disordered Alloys Duane D. Johnson, NSF DMR Materials Science and Engineering, University of Illinois Urbana-Champaign New theory and code were developed for direct prediction, characterization and design of real materials exhibiting chemical short-range order (SRO) that controls their technologically useful properties.. Results: In disordered alloys, we predicted temperature- dependent chemical SRO (see figure, denoted by  ) due to changes in free energy (controlling stability) and electronic structure (controlling properties). This was accomplished – for the first time – in a single first-principles calculation based on “dynamical mean-field theory” and “density functional theory” electronic-structure methods. Short-Range Order: Free energy change (mRy) of BCC disordered Cu 50 Zn 50 vs nearest-neighbor SRO parameter. At 816 K SRO of 0.21 agrees with value from neutron scattering. SRO changes optical, electronic, and mechanical properties. Why it matters: Technologically useful alloys, due to processing, and geophysical materials contain defects and chemical disorder that drive all critical properties. We can now directly predict properties of real-world alloys and analyze characterization experiments done at advanced synchrotron or neutron facilities. D. Biava and D.D. Johnson (to be published) Electronic effect, see publications prior to Direct Prediction of Alloy Short-Range Order: Effects on Electronic, Magnetic and Mechanical Properties New code (KKR-DCA) and theory for configurational averaging

A Thermodynamic Density Functional Theory for Predicting Properties of Complex Disordered Alloys Duane D. Johnson, NSF DMR Materials Science and Engineering, University of Illinois Urbana-Champaign Ruoshi Sun (2007) performed KKR-CPA calculations of defect energies that control magnetic properties and microstructure (e.g., antiphase boundaries, c-domain boundaries, and twins) in ferromagnetic (FM) state and paramagnetic (PM) state, where thermal processing is actually performed. Results: In L1 0 CoPt, FePt and FePd we find that the PM state profoundly alters the defect formation energies, now agreeing well with observation, and showed that calculations in the FM state yield wrong trends in properties needed for micromagnetics calculations. We also found that the assumption that defect energies measured in FePd are also good for CoPt and FePt is wrong. Defects in PM and FM states: Results for defect energies (mJ/m 2 ) show PM favors many APB’s in FePd (see figure), but not in CoPt, as is observed. Curie and order/disorder temperature is predicted. Why it matters: Micromagnetic simulations rely on input for defects that can form and their energies. For nanoparticles investigated experimentally as magnetic storage media, processing temperature and its effect on magnetism and defects should be addressed. J-B Liu, B. Kraczek, R. Sun, and D.D. Johnson (to be published) Summer REU project Magnetic Properties of Co-Pt-type Alloys: effects of processing temperature Layered-L1 0 (011) c-domain and antiphase boundary TEM of L1 0 FePd: the CDB (thick lines) and APB (wandering lines). [Soffa and Zhang, 1999] c-axis

A Thermodynamic Density Functional Theory for Predicting Properties of Complex Disordered Alloys Duane D. Johnson, NSF DMR Materials Science and Engineering, University of Illinois Urbana-Champaign Methods: We extended KKR-CPA methods and code developed by the PI using Korringa-Kohn-Rostoker (KKR) electronic-structure theory and the Coherent-Potential Approximation (CPA) for environmentally averaging. We added the k-space coarse-graining of Jarrell and Krishnamurthy (2001) – the Dynamical Cluster Approximation (DCA) – to calculate static disordered, i.e. atomic short-range order. We combined DFT results with mesoscale dislocation models of twin nucleation and cross-slip to predict quantitatively onset twinning stress and to provide design maps to predict yield- strength anomalies. What’s next?: Our primary objectives are: Extend the code to longer ranged SRO correlations and multi- sublattices for general applications. Improve efficiency of DCA via use of symmetry. Apply to more complex and important systems, e.g. energy or superconducting materials. Extend ideas to transformation pathways in alloys. PUBLICATIONS FROM RESEARCH ( ) S. Ghosh, D.A. Biava, W.A. Shelton, and D.D. Johnson, "Systematically exact, integrated density of states Lloyd's formula for disordered alloys with short-range order," Phys. Rev. B 73, (2006). S. Kibey, J.B. Liu, M.J. Curtis, D.D. Johnson, H. Sehitoglu, "Stacking Fault Energy and Stacking Fault Widths in High Nitrogen Steels," Acta Mater. 54, (2006). S. Kibey, J. B. Liu, D. D. Johnson and H. Sehitoglu, "Generalized Planar Fault Energies and Twinning in Cu-Al Alloys," Appl. Phys. Letts., 89, (2006). S. Kibey, J. B. Liu, D. D. Johnson and H. Sehitoglu, "Predicting twinning stress in fcc metals: linking twin-energy pathways to twin nucleation," Acta Mater. (2007), accepted. S. Kibey, J. B. Liu, D. D. Johnson and H. Sehitoglu, “Energy Pathways and Directionality in Deformation Twinning,” Appl. Phys. Lett. (2007) submitted. S. Kibey, L-L. Wang, J. B. Liu, D. D. Johnson, H.T. Johnson, and H. Sehitoglu, “Prediction of twinning stresses in fcc alloys: application to Cu- Al alloys,” Phys. Rev. B rapid comm. (2007), submitted. D.A. Biava, et al., ”First-principles prediction of short-range order and electronic properties of finite-temperature disordered alloys," in prep. J.B. Liu and D.D. Johnson, ”Solid-Solid Transformation Pathways in Iron: Coupled Shuffle and Shear Modes,” in prep. J.B. Liu, B. Kraczek, Ruoshi Sun, and D.D. Johnson, "Structural Defect Energies in Magnetic Co-Pt-type Alloys: Effect of Processing Temperatures," in prep. Graduate Students: D. Biava and S. Kibey* REU: Michael Curtis (Olins College, 2004); Joanne Wensley (Bristol, UK, 2006), and Ruoshi Sun (UIUC, 2007). Post-Doc: J-B. Liu and S. Ghosh † (former). *DMR , † DOE(BES) S. Kibey (Ph.D 2007) now staff member at ExxonMobil (UpStream Corp)

A Thermodynamic Density Functional Theory for Predicting Properties of Complex Disordered Alloys Duane D. Johnson, NSF DMR Materials Science and Engineering, University of Illinois Urbana-Champaign OUTREACH: Assist the Illinois Junior Academy of Science (IJAS) with the State Science Finals for all Junior High and High Schools. Professor Johnson is Chief Judge of Materials Science for grades 7-12 (now for 10 years). He recruits graduate students to act as judges and provide useful feedback to improve projects. He helps secure funding to support student mailings. Impact: Grades 7-12 students talk and receive comments from graduate students doing real research. It also acts as a recruitment tool and lets students know of educational opportunities. Graduate students get to provide constructive feedback and assessment to students, a wonderful learning opportunity for the graduate students. IJAS has 38 years helping grades 7-12!