Direct and inverse design optimization of magnetic alloys with minimized use of rare earth elements AFOSR grant FA9550-12-1-0440 (started 10/2012) May 18-22, 2015 Arlington, VA AFOSR Program Manager: Dr. Ali Sayir
Prof. George S. Dulikravich MAIDROC Laboratory, Mechanical and Materials Engineering Department Florida International University, Miami, USA
Prof. Justin Schwartz and Prof. Carl C. Koch Department of Materials Science, North Carolina State University BH curve
{
(BH)max is a compromise between Br and Hc { (BH)max vs Selling Price
Kramer et al, Prospects for Non-Rare Earth Permanent Magnets for Traction Motors and Generators, JOM, Vol. 64, No. 7, 2012 Temperature sensitivity
Kramer et al, Prospects for Non-Rare Earth Permanent Magnets for Traction Motors and Generators, JOM, Vol. 64, No. 7, 2012
AlNiCo MAGNETS Discovered in 1931 by Mishima in Japan
(BH)max : 1 – 10 MGOe Hc : 600 – 2000 Oe Br : 0.5 – 1.5 T (High) Curie temperature: 700 – 860 C (highest) Excellent corrosion resistance High temperature stability (up to ~ 800 C)
Limited research after 1980’s. One of the most popular choices for the rare-earth free magnets
•Cullity, B.D. and Graham,C.D.: Introduction to Magnetic Materials, 2nd ed., New York, Wiley-IEEE Press, 2008. Rare earth replacement magnets Approach Maximize properties of AlNiCo magnets without REEs Use non-critical rare earth elements in small amounts
Rare earth free magnets (Sellmayer et al) Hf-Co and Zr-Co: Properties comparable to Alnico at 300K Fe-Pt nanocomposite and Mn-Bi based compounds: (BH)max: 15-54 MGOe at 300K
•Sellmyer et al, Advances In Rare-earth-free Permanent Magnets (edited by: Fernand Marquis), The 8 th Pacific Rim International Congress on Advanced Materials and Processing, TMS - The Minerals, Metals & Materials Society, 2013. Rare earth replacement magnets Improve AlNiCo magnets (Zhou et al) Ongoing research on AlNiCo alloy by experimental modeling Demonstrated scope of improvement by theoretical modeling Advantages Results are promising Limitations Predicted result is 3-5 times off the experiment. results
Hence, random experimentation can be misleading. Also, it may cost a fortune to arrive at a meaningful new permanent magnetic alloy.
•Zhou et al, Architecture and magnetism of alnico, Acta Materialia, 74, 224-233, 2014. AlNiCo magnets: Metallurgical aspects
Magnetic properties are attributed to two BCC alpha phases, α1 and α2
Separation of α1 and α2 is a result of “spinodal” decomposition
α1 is Fe-Co rich ferromagnetic phase while α2 is Ni-Al rich phase
α1 and α2 are stable up to 850 ºC (Curie temperature is about 860 ºC) AlNiCo magnets: Metallurgical aspects Above 850 ºC (up to 1175 ºC), FCC γ(gamma) phase is stable Gamma(γ) phase is detrimental for magnetic properties As a result, AlNiCo alloys are solution annealed at about 1200 ºC From literature, α-γ transformation has been reported for as low as 800 ºC A TASK FOR YEARS 4 & 5: Design heat treatment protocol so as to stabilize alpha phases and reduce/eliminate gamma phases Why using expensive experimental data instead of affordable computational predictions of physical properties? Because existing theoretical models for prediction and possible optimization of multiple physical properties of alloys are: 1. extremely complex, 2. not general (for small number of alloying elements only), 3. still not sufficiently reliable, 4. experimental data are more convincing to demonstrate the concept. AlNiCo magnets: Metallurgical aspects Limitations: Currently, Alnico alloys contains 8+ elements CALPHAD and ab-initio calculations can handle 3-4 elements Limited knowledge on composition property relationship Limited knowledge about influence of any particular element on any desired property for multi-component systems Hence, heat treatment protocol needs to be optimized for new composition
Suggested solution: Meta-modeling can be used for developing models to address composition – property relationship Statistical tools can be used for sensitivity analysis Multi-objective optimization will help in improving conflicting objectives like (BH)max, Hc and Br Motivation for present work Methodology successfully developed and implemented by Dulikravich et al. (since 2003) for direct and inverse design and optimization of arbitrary alloys. H-type steels Ni-base superalloys Hf-base BMGs Ti-base alloys Al-base alloys Can also use artificial neural networks in thermodynamic database such as ”Thermocalc” Publications available at: http://maidroc.fiu.edu/www/?page_id=28 How does it work?
Start with a set of reliable experimental data for the same type of arbitrary alloys or create such a data set using Sobol’s quasi-random sequences algorithm.
Create accurate multi-dimensional response surfaces that are based on these experimental data.
Use a multi-objective evolutionary optimization algorithm to search the response surfaces for Pareto optimal solutions.
WARNING: Classical single-objective optimization algorithms are incapable of performing this task!
WARNING: Artificial neural networks are fast interpolants and cannot give us out-of-box new solutions! Also, ANNs require very large experimental data sets to be trained. Proposed FIU Effort Development of knowledge base by coupling Experimental modeling: Experiments at NCSU Theoretical modeling: Experimental and ab initio computational data bases (FactSage, Thermocalc and Materials Project) Meta-modeling: Response surface methodology Multi-Objective Optimization: (MOHO, modeFRONTIER, IOSO, EvoNN, BioGP) Statistical modeling: Clustering and pattern recognition by using statistical tools like IBM SPSS, R-Programming Uncertainty quantification: To improve accuracy in prediction by meta-modeling. 5. RESEARCH PROBLEM PROPOSAL 1. Design and multi-objective optimization of chemical concentrations of each of the eight alloying elements in permanent magnetic Alnico type alloys 2. Experimental validation of Pareto-optimized predictions 3. Repeat 1 and 2 until the improvements are negligible 4. Statistical analysis of dataset, improvement of accuracy of response surfaces and relative importance of alloying elements 5. Replacement of the least performing alloying elements with rare-earth elements (only those that are relatively easily available) followed by multi- objective optimization of chemistry. Research questions 1. What is the importance of using computational tools? 2. What is the purpose of using multiple statistical tools? 3. What is the purpose of adding non-critical rare-earth elements? Approach 1. Sobol’s quasi-random number sequences generation algorithm for initial composition. 2. Response surfaces to understand system behavior. 3. Evolutionary algorithm for multi-objective optimization. 4. Analyze relative importance of alloying elements. 5. Abundant supply and presence of 4f shell electron. Quantities to be simultaneously extremized using multi-objective optimization
Properties Units Objective Magnetic energy density 1 kg m-1 s-2 Maximize ((BH)max) 2 Magnetic coercivity (Hc) Oersted Maximize 3 Magnetic remanence (Br) Tesla Maximize 4 Saturation magnetization (Ms) Emu/g Maximize 5 Remanence magnetization (Mr) Emu/g Maximize 6 (BH)max/mass m-1 s-2 Maximize 7 Magnetic permeability (m) kg m A-2 s-2 Maximize 8 Cost of raw material (cost) $/kg Minimize 9 Intrinsic coercive field (jHc) Am-1 Maximize 10 Density(ρ) Kgm-3 Minimize Response surfaces used No Properties Response Surface
1 Magnetic energy density ((BH)max) Radial Basis Function (Gaussian)
2. Magnetic coercivity (Hc) Radial Basis Function (Multi-Quadrics)
3. Radial Basis Function Magnetic remanence (Br) (Inverse Multi-Quadrics)
4. Saturation magnetization (Ms) Evolutionary Design
5. Radial Basis Function Remanence magnetization (Mr) (Inverse Multi-Quadrics)
6. (BH)max/mass Anisotropic Kriging (Gaussian)
7. Radial Basis Function Magnetic permeability (m) (Inverse Multi-Quadrics)
8. Cost of raw material (cost) Radial Basis Function (Multi-Quadrics)
9. Intrinsic coercive field (jHc) Anisotropic Kriging (Gaussian)
10. Density(ρ) Radial Basis Function (Multi-Quadrics) CURRENT STATE OF WORK Work has been carried out in cycles.
Table 1: Concentration bounds AlNiCo type alloys Variable bounds (Wt %) Alloying Alloys number elements 1 – 85 86 – 143 144-173 1 Cobalt (Co) 24 – 40 24 – 38 Variable bounds 2 Nickel (Ni) 13 – 15 13 – 15 relaxed by 5 % for 3 Aluminum (Al) 7 – 9 7 – 12 each of these 4 Titanium (Ti) 0.1 – 8 4 – 11 elements 5 Hafnium (Hf) 0.1 – 8 0.1 – 3 6 Copper (Cu) 0 – 6 0 – 3 7 Niobium (Nb) 0 – 2 0 – 1 8 Iron (Fe) Balance to 100 Table 2: Cycle and alloy number
Alloys Best alloy Cycle no. Designed 1 1-80 #30 2 81-85 #84 3 86-90 #86 4 91-110 #95 5 111-120 #117 6 120-138 #124 7 139-143 #139 8 144-150 #150 9 150-160 #157 10 160-165 #162 11 166-173 #169
Second quadrant of B-H curve: It can be seen that multi-objective optimization helped increasing the area under B-H curve Multi-objective optimization increased (BH)max from 8,600 to 12,000 and Hc from 760 to 1120 from alloy #84 to alloy #124.
Pearson’s correlation Principal component analysis
Top 10 alloys are marked on the figure; superior alloys are part of same clusters Single Variable Response (SVR)
Variable response # Properties Fe Co Ni Al Ti Hf Cu Nb Magnetic energy Mixed 1 Nil Nil Nil Nil Nil Nil Nil density ((BH)max) (+) Magnetic coercivity Mixed 2 Mixed Mixed Mixed Inverse Mixed Direct Direct (Hc) (+) Magnetic 3 Mixed Mixed Mixed Inverse Mixed Direct Direct Inverse remanence (Br) Saturation 4 Direct Inverse Direct Mixed Inverse Direct Mixed Mixed magnetization (Ms) Remanence 5 Nil Nil Nil Nil Nil Nil Nil Nil magnetization (Mr) 6 (BH)max/mass Nil Nil Nil Nil Nil Nil Nil Nil Magnetic Mixed 7 Mixed Mixed Mixed Mixed Inverse Mixed Mixed permeability (m) (+) Cost of raw 8 Inverse Inverse Inverse Direct Direct Direct Inverse Direct material (cost) Intrinsic coercive Mixed 9 Mixed Mixed Mixed Inverse Inverse Direct Mixed field (jHc) (+) 1 Density(ρ) Mixed Direct Mixed Inverse Inverse Mixed Mixed Direct 0 DISCUSSIONS 1.Current approach was able to recover from the error in the initial distribution of concentrations
2.Time frame using this alloy design methodology is about one year (significantly less than current alloy development cycle)
3.Additionally, time frame for alloys no. 81 – 173 was about 8 months (resulting in properties improved by an order of magnitude)
4.Linear correlation shows strong correlation between (BH)max, Hc and Br. Other correlations are quite weak. FUTURE WORK - (years 4 & 5) 1. Utilize limited phase stability data to generate heating/cooling curves 2. Optimize thermal treatment protocols of such alloys for improvements in magnetic properties 3. Improve accuracy of response surface predictions outside existing data sets 4. Quantify uncertainty and implement it in the present optimization approach 5. Evaluate advantages of non-critical REE addition PUBLICATIONS Journal articles 1. Jha, R.; Dulikravich, G.S.; Pettersson, F.; Saxen, H.; Chakraborti, N., Evolutionary Design of Nickel Based Superalloys Using Data-Driven Genetic Algorithms and Related Strategies. Materials and Manufacturing Processes http://dx.doi.org/10.1080/10426914.2014.984203. Conference papers 1. Jha, R.; Dulikravich, G.S.; Pettersson, F.; Saxen, H.; Chakraborti, N., A Combined Experimental-Computational Approach to Design Optimization of High Temperature Alloys. Paper ETS2014-1008, ASME Symposium on Elevated Temperature Application of Materials for Fossil, Nuclear, and Petrochemical Industries, Seattle, WA, March 25-27, 2014. 2. Jha, R.; Dulikravich, G.S.; Fan, M.; Shwartz, J.; Koch, C.; Egorov, I.N.; Poloni, C., A Combined Computational-Experimental Approach to Design of High-Intensity Permanent Magnetic Alloys, CONEM2014, Uberlandia, Brazil, August 10-15, 2014. 3. Dulikravich, G.S.; Jha, R.; Fan, M.; Shwartz, J.; Koch, C., Algorithms for Design Optimization of Hard Magnetic Alloys Using Experimental Data, ICMM4-International Conference on Material Modeling, Berkeley, CA, May 27-29, 2015.
4. Magnetic Alloys Design Using Multi-Objective Optimization (R. Jha, G.S. Dulikravich, M.J. Colaco, M. Fan, J. Schwartz, C.C. Koch), ACEX2015-9th International Conference on Advanced Computational Engineering and Experimenting, Munich, Germany, June 29 – July 2, 2015.
5. Multi-Objective Design and Optimization of Hard Magnetic Alloys Free of Rare Earths (R. Jha, G.S. Dulikravich, M.J. Colaco, I.N. Egorov, C. Poloni, N. Chakraborti, M. Fan, J. Schwartz, C.C. Koch), MS&T15-Materials science and Technology 2015 Conference, Columbus, Ohio, October 4-8, 2015.
6. Design and Optimization of Rare-Earth Free Hard Magnetic Alloys and Nickel-Based Superalloys for High Temperatures Applications (Jha, R., Dulikravich, G.S., Colaco, M.J.), COBEM- 2015, paper 1284, Rio de Janeiro, Brazil, December 6-11, 2015.
3 PC chosen, Cu-Hf and Ni- Al cluster can be observed in the figure 2 PC chosen, (BH)max, Mr and Br are clustered in the same region 40 alloys were chosen by MCDM. Top 10 alloys are marked in the figure. Superior alloys are part of same clusters 3 PC chosen, Cu-Hf and Ni- Al cluster can be observed in the figure 3 PC chosen, Mr and Br are clustered in the same region Microstructure analysis
Optical micrograph of Alloy # 95 showing white spots Microstructure analysis: BSE image
Table 4: Composition mapping by BSE imaging. Name Fe Co Ni Al Ti Hf Cu Nb C O Nominal 32.359 36.857 13.5449 7.2002 4.1162 2.0683 2.9385 0.9307 0 0 composition 5 4 Whole image 32.09 35.64 11.99 8.76 5.21 0.04 2.56 1.32 1.54 0.86 Microstructure analysis: SEM image
Table 5: Results from EDS analysis for alloy # 95 Name Fe Co Ni Al Ti Hf Cu Nb C O Nominal 32.359 36.857 13.544 7.2002 4.1162 2.0683 2.9385 0.9307 0 0 composition 5 4 9 Point 1(Grain) 32.5 35.45 14.32 9.67 4.3 0 3.32 0.44 0 0 Point 2(Grain 23.88 34.79 14.99 6.85 4.78 7.95 3.77 2.96 0.03 0 Boundary) Point 3(White 25.78 34.49 14.43 8.88 4.92 5.89 3.42 2.17 0.03 0 spots) Thermodynamic analysis
Fe - Co P=1.082 atm 1200
fcc fcc 1000
800
fcc
600 T(C) bcc + fcc
400 bcc
200 fcc + Co(s)
bcc + Co(s) 0 0 0.2 0.4 0.6 0.8 1 Fe/(Fe+Co) (mol/mol)
Phase Magnetic moment (μβ ) Magnetic ordering Decomposes to
Fe11Co5 37.273 Ferromagnetic Stable
Fe9Co5 36.356 Ferromagnetic Stable FeCo 4.463 Unknown Stable
Fe13Co3 37.556 Ferromagnetic Fe + Fe11Co5
Fe15Co 36.639 Unknown Fe + Fe11Co5
Fe3Co 9.354 Ferromagnetic Fe + Fe11Co5
AlFeCo2 4.974 Unknown Stable
Al9Co2 0.00 Unknown Stable
AlFe2Ni 4.502 Unknown AlNi +Fe AlNi 0.00 Unknown Stable
DISCUSSIONS 4. Variable response suggests a weak correlation between Ni and (BH)max. Current response surfaces were unable to detect any correlation between (BH)max and any other element. 5. Cu and Hf shows positive response for Hc and Br. Cu has positive effect on Hc and Br (from literature) 6. PCA and clustering analysis shows that top 10 alloys are clustered in 2-3 clusters. Hence, this demonstrates benefit of meta-modeling and multi- objective optimization 7. PCA and clustering analysis on elements shows Cu and Hf clustered in the complete dataset as well as dataset selected by MCDM. DISCUSSIONS 8. Optical micrograph shows presence of white precipitates which is expected (from literature) 9. BSE image shows that composition is homogeneous. 10. SEM (EDS analysis) on three points confirms precipitation of Hf at GB and its presence in the white precipitate. Cu content is a high at the GB and white precipitate. Hence, possibly Cu-Hf ppt. 11. Nb content is also high at the GB and white ppt. Hence, this can be further studied. 12. Thermodynamic analysis: Alloy # 124 is the most stable alloy. We cannot use Mn or B. 13. Ab-initio data on magetic moment demonstrates the need for improving heat treatment protocol. 6. 3. Uncertainty in ICME 1.Uncertainty: Identification and quantification of sources and develop mathematical representation I. Aleatory or irreducible uncertainty: Randomness of materials Represented by probability distribution Can be addressed by probability theory II. Epistemic or reducible uncertainty: Lack of knowledge due to idealization, approximation, numerical errors Bayes’s probability theory used by others, but limited success Alternate fuzzy set theory, possibility theory
Panchal et al, Key computational modeling issues in Integrated Computational Materials Engineering, Computer-Aided Design 45 (2013) 4–25 6. 3. Uncertainty in ICME 2. Uncertainty propagation or uncertainty analysis: From input of one model to its output From lower level models to higher level models From materials composition to structure Bayesian approaches can be used 3. Uncertainty mitigation: Reducing effect of uncertainty in materials design Multidisciplinary design and optimization (MDO) Surrogate modeling and statistical analysis 4. Uncertainty management: Decision on appropriate level of uncertainty based on tradeoff between effort and benefit 6. 4. Evaluate advantages of non-critical REE addition
Phase Magnetic Magnetic Decomposes to
moment (μβ ) ordering
Ce2Co17 46.262 Unknown CeCo2 +Co
CeCo3 6.023 Unknown CeCo2 +Co
CeCo5 5.749 Unknown CeCo2 +Co
CeCo2 0.00 Unknown Stable
Ce2Fe17 37.075 Unknown CeFe2 + Fe
CeFe5 9.864 Unknown CeFe2 + Fe
CeFe2 5.015 Unknown Stable Hence, there is scope of improvement, but the manufacturing protocol must be able to retain the desired phase 6. 5. Optimizing manufacture protocol
Planned approach: 1. Utilize limited phase stability data to generate heating/cooling curves 2. Work on microstructure-property relationship 3. Develop code for the most accurate response surface to incorporate modifications necessary for materials design 4. Incorporate uncertainty in the work 5. Design a heat treatment protocol or suggest modifications in the current approach 6. Design methodology that enables the experimentalist to predict chemical composition for desired property.
AlNiCo magnets: Metallurgical aspects Influence of alloying elements: Cobalt: It is a gamma stabilizer Increases Hc Increases Curie temperature Solutionization anneal temperature must be increased
Nickel: It is a gamma stabilizer Increases Hc (less than Cobalt) Decreases Br Solutionization anneal temperature must be increased
Aluminum: It is an alpha stabilizer Affects Hc positively Decreases solutionization anneal temperature
AlNiCo magnets: Metallurgical aspects Influence of alloying elements: Copper: It is an alpha stabilizer Increases Hc Increases Br Pure Cu precipitates out of α2 and increases phase separation between α1 and α2. (in Alnico 8 and 9) Decreases solutionization anneal temperature
Titanium: It is an alpha stabilizer Most reactive element; precipitates impurities S and N Eliminates Carbon(strong gamma stabilizer) Increases Hc Decreases Br Improves grain refining, assists columnar grain growth Decreases solutionization anneal temperature Alnico magnets: Metallurgical aspects Influence of alloying elements: Niobium: It is an alpha stabilizer Neutralizes effect of Carbon Increases Hc Decreases Br (less than Titanium) Assists columnar grain growth Decreases solutionization anneal temperature
Hafnium: It is added for high temperature properties Hf precipitates at the grain boundary Improves creep properties Apart from that, magnetic properties of Alnico are greatly influenced by final microstructure and texture, which is greatly influenced by heat treatment protocol Proposed FIU Effort MGI and ICME approach motivates research community for Use of computational tools: SATISFIED Use of experimental tools: SATISFIED Form Collaborative networks: SATISFIED Funding: AFOSR, USA: MAIDROC lab, NCSU team Brazil: Professor M.J. Colaco (UFRJ) Russia: Professor I.N. Igorov (IOSO) Italy: Professor C. Poloni (CEO: ESTECO) India: Professor N. Chakraborti (I.I.T. Kharagpur) Our group consists of a global network of professionals with proven expertise in handling complex problems in Materials modeling RESEARCH PROBLEM
1. Design and multi-objective optimization of chemical concentrations of each of the eight alloying elements in permanent magnetic AlNiCo type alloys 2. Experimental validation of Pareto-optimized predictions 3. Repeat 1 and 2 until the improvements are negligible 4. Statistical analysis of dataset, improvement of accuracy of response surfaces and relative importance of alloying elements 5. Replacement of the least performing alloying elements with rare-earth elements (only those that are relatively easily available) followed by multi- objective optimization of chemistry. Research questions 1. What is the importance of using computational tools? 2. What is the purpose of using multiple statistical tools? 3. What is the purpose of adding not-so-rare rare-earth elements? Approach 1. Sobol’s quasi-random number sequences generation algorithm for initial composition. 2. Response surfaces to understand system behavior. 3. Evolutionary algorithms for optimization. 4. Analyze relative importance of alloying elements. 5. Abundant supply and presence of 4f shell electron.