1. SURFACE SEGREGATIONS IN RANDOM ALLOYS FROM FIRST-PRINCIPLES THEORY Igor A. Abrikosov Department of Physics and Measurements Technology, Linköping University

2. ACKNOWLEDGEMENTS A. Ponomareva N. Skorodumova A. V. Ruban S. I. Simak L. Pourovski S. Shallcross

3. CONTENTS : Introduction: first principles calculations at T=0 and at T>0 Ordering effects in the bulk: multicomponent alloys Surface segregations in NiPt and NiPd. Segregation energies in Fe-Cr system. Cr-rich part of the diagram: importance of correlation effects.

4. Density Functional Theory (DFT)

5. FF C A B C D Structures: ABAB C D

6. 1111 1 11 11 11 111

7. Calculations of effective interatomic potentials The Connolly-Williams method 1. Choose structures fcc L1 2 L1 0 DO22 2. Calculate E tot : E(fcc) E(L1 2 ) E(L1 0 ) E(DO22) with predefined correlation functions

8. The Monte Carlo method Calculations of averages at temperature T: Create the Marcov chain of configurations: Balance at the equilibrium state: Atoms exchanged EE

9. Example: ordered phases in Cu 2 NiZn 21 concentration and volume dependent effective cluster interactions Electronic structure calculations using O(N) LSGF method 32 different atomic distributions at fixed concentration (144 atom supercell) V Ni-Zn (nn)=12.8mRy > V Cu-Zn (nn)=5.0 mRy > V Cu-Ni (nn)= 2.5 mRy V Ni-Zn (4nn)= -2.5mRy, all other ECI are small Cluster expansion represents total energy calculations with average accuracy better than 0.015 mRy, and with the maximal error 0.2 mRy (or 4% of the ordering energy)

10. Example: ordered phases in Cu 2 NiZn 21 concentration and volume dependent effective cluster interactions Electronic structure calculations using O(N) LSGF method 32 different atomic distributions at fixed concentration (144 atom supercell) V Ni-Zn (nn)=12.8mRy > V Cu-Zn (nn)=5.0 mRy > V Cu-Ni (nn)= 2.5 mRy V Ni-Zn (4nn)= -2.5mRy, all other ECI are small Cluster expansion represents total energy calculations with average accuracy better than 0.015 mRy, and with the maximal error 0.2 mRy (or 4% of the ordering energy)

16. Calculations of effective interatomic potentials The generalized perturbation method 1.Calculate electronic structure of a random alloy (for example, use the CPA): -determine a perturbation of the band energy due to small varioations of the correlation functions 2. where the effective interatomic interactions are given by an analytical formula:

17. Example: bulk ordering in NiPt Method  rnd (UR) (mRy/atom)  rnd (R) (mRy/atom)  ´L1 0 (UR) (mRy/atom) CPA-GPM 1.57-1.03-6.06 FP-CWM Lu et al. 1.72-2.23-5.71

18. The new surface Monte Carlo method In order to represent the bulk chemical potential, the obtained by bulk MC fixed reservoir of atoms is used: Bulk reservoir Surface sample Vacuum

19. The new surface Monte Carlo method Only one fixed bulk configuration of the reservoir is used. How do the results depend on the size of the reservoir? The dependence of the surface layer energy on size of reservoir in NiPd(100)

20. Configuration of the (111) surface of the Ni 49 Pt 51 substoichometric ordered alloy

21. Surface segregations in the NiPt and NiPd alloys 1.A segregation reversal phenomenon has been observed at the surfaces of NiPt random alloys: Pt segregates towards the (100) and (111) surfaces, Ni segregates towards the (110) surface. 2.No such effect has been found for the isoelectronic NiPd alloys. The strong Pd segregations have been observed on all low-indexed surfaces. There are bulk ordered phases NiPt(L1 0 ) and Ni 3 Pt(L1 2 ) in the Ni-Pt system No bulk ordering occur in NiPd down to T=400K

22. SGPM surface potentials for Ni 50 Pt 50 (Ni 50 Pd 50 ) in K (  Pt(Pd) =1) Layer 12345 V (1)  V (1) bulk 167(-1613)-883(-648)-265(-126)163(35)0(0) (110) V (2,1) 483(224)555(262)571(279)586(280)556(279) V (2,1)  2433(1017)2286(1097)2379(1132)2225(1116) V (2,1)  781(261)686(296)556(279) V (1)  V (1) bulk -705(-1118)231(2)-219(-60)0- (111) V (2,1) 1373(820)1852(854)1979(871)1668(837)- V (2,1)  1927(921)1857(861)1668(861)1668(837)-

23. Example: bulk ordering in NiPt Transition to L1 0 in Ni 50 Pt 50 : T c exp =917 K, T c teor =925 K

24. Segregation profiles in the Ni 50 Pt 50 and Ni 50 Pd 50 random alloys

25. Ni-Pt (111)

27. Configuration of the (111) surface of the NiPt stoichometric and substoichometric ordered alloys Ni 50 Pt 50 ordered alloyNi 49 Pt 51 ordered alloy (111) surface

30. 1111 1 11 11 11 111

34. EMTO vs Full-potential: c/a ratio in ordered alloys

43. CONCLUSIONS : There are problems. We are here to solve them!