Structure-property maps and optimal inversion in configurational thermodynamics

Physical Review B - Condensed Matter and Materials Physics

Volumn 81, Issue 9, 2010, Pages

  Arnold, Björn ^a   Díaz Ortiz, Alejandro ^a,d   Hart, Gus L W ^b   Dosch, Helmut ^c  

^a MAX PLANCK INSTITUTE FOR INTELLIGENT SYSTEMS   (Germany)

^b Brigham Young University   (United States)

^c DESY   (Germany)

^d UNIVERSITY OF ULM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77954916644     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.81.094116     Document Type: Article

References (52)

1. M. E. Eberhart and D. P. Clougherty, Nature Mater. 3, 659 (2004). 10.1038/nmat1229
2. S. Curtarolo, D. Morgan, K. Persson, J. Rodgers, and G. Ceder, Phys. Rev. Lett. 91, 135503 (2003). 10.1103/PhysRevLett.91.135503
3. C. C. Fischer, K. J. Tibbetts, D. Morgan, and G. Ceder, Nature Mater. 5, 641 (2006). 10.1038/nmat1691
4. O. A. von Lilienfeld, R. D. Lins, and U. Rothlisberger, Phys. Rev. Lett. 95, 153002 (2005). 10.1103/PhysRevLett.95.153002
5. M. Wang, X. Hu, D. N. Beratan, and W. Yang, J. Am. Chem. Soc. 128, 3228 (2006). 10.1021/ja0572046
6. E. Borges, N. Lemes, and J. Braga, Chem. Phys. Lett. 423, 357 (2006). 10.1016/j.cplett.2006.03.090
7. J. M. Sanchez and D. de Fontaine, in Modulated Structures, edited by, J. Cowley, J. Cohen, M. Salamon, and, B. Wuensch, (American Institute of Physics, New York, 1979), Vol. 53, pp. 133-145.
8. J. M. Sanchez, F. Ducastelle, and D. Gratias, Physica A 128, 334 (1984). 10.1016/0378-4371(84)90096-7
9. J. M. Sanchez, Phys. Rev. B 48, 14013 (1993). 10.1103/PhysRevB.48.14013
10. D. de Fontaine, Solid State Phys. 47, 33 (1994). 10.1016/S0081-1947(08) 60639-6
11. A. Zunger, in Statics and Dynamics of Alloy Phase Transitions, NATO Advanced Studies Institute, Series B:, edited by, P. E. A. Turchi, and, A. Gonis, (Plenum Press, New York, 1994), pp. 361-419.
12. A. Franceschetti, S. V. Dudiy, S. V. Barabash, A. Zunger, J. Xu, and M. van Schilfgaarde, Phys. Rev. Lett. 97, 047202 (2006). 10.1103/PhysRevLett.97. 047202
13. A. Díaz-Ortiz, R. Drautz, M. Fähnle, H. Dosch, and J. M. Sanchez, Phys. Rev. B 73, 224208 (2006). 10.1103/PhysRevB.73.224208
14. A. van de Walle, Nature Mater. 7, 455 (2008). 10.1038/nmat2200
15. Notice that in this case, the f α above represent the many-body configuration averages of the potential V.
16. K. Kawasaki, in Phase Transitions and Critical Phenomena, edited by, C. Domb, and, M. S. Green, (Academic, New York, 1973), Vol. 2, p. 465.
17. A. Franceschetti and A. Zunger, Nature (London) 402, 60 (1999). 10.1038/46995
18. M. d'Avezac and A. Zunger, J. Phys.: Condens. Matter 19, 402201 (2007). 10.1088/0953-8984/19/40/402201
19. M. Stone, J. R. Stat. Soc. Ser. B (Methodol.) 36, 111 (1974).
20. J. Shao, J. Am. Stat. Assoc. 88, 486 (1993). 10.2307/2290328
21. A. Díaz-Ortiz and H. Dosch, Phys. Rev. B 76, 012202 (2007). 10.1103/PhysRevB.76.012202
22. A. Díaz-Ortiz, H. Dosch, and R. Drautz, J. Phys.: Condens. Matter 19, 406206 (2007). 10.1088/0953-8984/19/40/406206
23. G. L. W. Hart, V. Blum, M. Walorski, and A. Zunger, Nature Mater. 4, 391 (2005). 10.1038/nmat1374
24. V. Blum, G. L. W. Hart, M. J. Walorski, and A. Zunger, Phys. Rev. B 72, 165113 (2005). 10.1103/PhysRevB.72.165113
25. T. Saito, T. Furuta, J.-H. Hwang, S. Kuramoto, K. Nishino, N. Suzuki, R. Chen, A. Yamada, K. Ito, Y. Seno, T. Nonaka, H. Ikehata, N. Nagasako, C. Iwamoto, Y. Ikuhara, and T. Sakuma, Science 300, 464 (2003). 10.1126/science.1081957
26. T. Li, J. W. Morris, Jr., N. Nagasako, S. Kuramoto, and D. C. Chrzan, Phys. Rev. Lett. 98, 105503 (2007). 10.1103/PhysRevLett.98.105503
27. V. Blum and A. Zunger, Phys. Rev. B 72, 020104 (R) (2005). 10.1103/PhysRevB.72.020104
28. R. Drautz, A. Díaz-Ortiz, M. Fähnle, and H. Dosch, Phys. Rev. Lett. 93, 067202 (2004). 10.1103/PhysRevLett.93.067202
29. G. L. W. Hart and R. W. Forcade, Phys. Rev. B 77, 224115 (2008). 10.1103/PhysRevB.77.224115
30. G. L. W. Hart and R. Forcade (unpublished).
31. R. L. Graham, D. E. Knuth, and O. Patashnik, Concrete Mathematics: A Foundation for Computer Science (Addison-Wesley, London, 1994).
32. See also, E. W. Weisstein, "Floor Function," from MathWorld-A Wolfram Web Resource, http://mathworld.wolfram.com/FloorFunction.html
33. D. B. Laks, L. G. Ferreira, S. Froyen, and A. Zunger, Phys. Rev. B 46, 12587 (1992). 10.1103/PhysRevB.46.12587
34. N. A. Zarkevich and D. D. Johnson, Phys. Rev. Lett. 92, 255702 (2004). 10.1103/PhysRevLett.92.255702
35. M. H. F. Sluiter and Y. Kawazoe, Phys. Rev. B 71, 212201 (2005). 10.1103/PhysRevB.71.212201
36. R. Kikuchi, Phys. Rev. 81, 988 (1951). 10.1103/PhysRev.81.988
37. J. A. Barker, Proc. R. Soc. London, Ser. A 216, 45 (1953). 10.1098/rspa.1953.0005
38. T. Morita, J. Phys. Soc. Jpn. 12, 753 (1957). 10.1143/JPSJ.12.753
39. J. M. Sanchez and D. de Fontaine, Phys. Rev. B 17, 2926 (1978). 10.1103/PhysRevB.17.2926
40. D. A. Vul and D. de Fontaine, Mater. Res. Soc. Symp. Proc. 291, 401 (1993).
41. In practice, we have determined the number of validation sets used in Eq. by a random construction from the leave-one-out set, i.e., to warrant that all structures are at least once out. To avoid that ill-defined sets spoil the estimation of the prediction error, several random runs are taken at each step. For all cases studied here, this proved to be enough for both the variational and evolutionary approaches to the CE.
42. A. J. Miller, Subset Selection in Regression (Chapman and Hall, London, 1990).
43. C. R. Rao and Y. Wu, Inst. Math. Stat. Lecture Notes Monogr. Ser. 38, 1 (2001). 10.1214/lnms/1215540960
44. R. Drautz and A. Díaz-Ortiz, Phys. Rev. B 73, 224207 (2006). 10.1103/PhysRevB.73.224207
45. A. van de Walle and G. Ceder, J. Phase Equilib. 23, 348 (2002). 10.1361/105497102770331596
46. A. van de Walle, M. Asta, and G. Ceder, CALPHAD: Comput. Coupling Phase Diagrams Thermochem. 26, 539 (2002). 10.1016/S0364-5916(02)80006-2
47. A. Seko, Y. Koyama, and I. Tanaka, Phys. Rev. B 80, 165122 (2009). 10.1103/PhysRevB.80.165122
48. J. U. Hjorth, Computer Intensive Statistical Methods (Chapman and Hall/CRC, London/Cleveland, 1994).
49. S. M. Weiss and C. A. Kulikowski, Computer Systems That Learn: Classification and Prediction Methods from Statistics, Neural Nets, Machine Learning, and Expert Systems, Machine Learning (Morgan Kaufmann, San Mateo, CA 1991).
50. S. Curtarolo, AFLOW: Software for High Throughput Calculation of Material Properties, 2009, http://materials.duke.edu/aflow.html
51. S. Curtarolo, D. Morgan, and G. Ceder, CALPHAD: Comput. Coupling Phase Diagrams Thermochem. 29, 163 (2005). 10.1016/j.calphad.2005.01.002
52. O. Levy, R. V. Chepulskii, G. L. W. Hart, and S. Curtarolo, J. Am. Chem. Soc. 132, 833 (2010). 10.1021/ja908879y