Co-rich Decagonal Al-Co-Ni predicting structure, orientatio order, and puckering

Transcription

1 Co-rich Decagonal Al-Co-Ni predicting structure, orientatio order, and puckering Nan Gu, Marek Mihalkovič, and C.L. Henley, Cornell University ICQ9 poster, Monday May 23, 2005 Supported by DOE grant DE-FG02-89ER

2 Problem: structure prediction for d(al A fundamental problem: Given we can perfectly compute energy of a complex compound, what s the atomic arrange Brute-force Monte Carlo (MC) / Molecular Dynamics (MD typically get stuck in glassy states. Try this on d(alconi) which has many subphases [S. Rits Phil. Mag. Lett. 78: 67 (1998).] in particular, basic Ni ( Al 70 Co 10 Ni 20 ) and basic Co ( Al 70 Co 20 Ni 10 ). Input information: Quasilattice constant a 0 = 2.45Å, period (2 layers) c = Pair potentials 2

3 Pair potentials Derived using Moriarty s Generalized Potential Theory [ Al-Lehyani et al Phys. Rev. B 64, (2001)] Al-Al potential: just hardcore 2.7Å. Al-TM (esp. Al-Co): deep well 2.5Å. TM-TM potential: deep 2nd well Al-Al 0.3 Co-Co Al-Co Co-Ni Pair potential (ev) Al-Ni Pair potential (ev) Ni-Ni Distance (A) Distance (A) 3

4 Our recipe Multiscale Procedur Represent structures as decorations of Penrose rhombi 1 MC simulations with atoms as lattice gas on a fixed li sites, allowing atom swaps and tile-flips with a 0 = 2. rhombi. Lowest energy configuration in each run is vie identify common motifs. 2 Promote the observations [1] to rules for a larger scale with fewer degrees of freedom. 3 New MC simulations (fixed sites) on larger-scale tiling 4 Relaxation (and MD simulations) to find atoms true equilibrium positions. This method worked once for basic Ni [M. Mihalkovič e Phys. Rev. B 65, (2002). Will it work in general? 4

5 First stage rhombus edge a 0 = 2.45Å Two independent layers Tile flips and atom swaps. Simulations: Second stage rhombus edge τa 0 = One layer tiling // two-layer decor of candidate sit 2 flavors of fat rhom Atom swaps only We used tilings that maximize number of (nonoverlapping decagons. In effect, we really have a 10.4Å edge Binary broken down for decoration purposes into a 4.0Å edge De Hexagon-Boat-Star tiling 5

6 Simulation image Left side 2.45Å tiles... Right side 4.0Å ti Large and small circles indicate top and second layer. Gray = Al Black = Ni Blue= Co 6

7 Dominant motif 13Å Decagon (really 12.8Å): ring 2 ring 2.5 ring 3 ring 1 Cluster motifs Secondary motif Star c (fills spaces):!! " "!! " " Al Co Ni Concentric rings... some irregularities on rings 2.5/3. Circled: are puckering channels when relaxation allowed Co/Ni # # $ $ Ni/Al Ring of five TM site 30% TM (context dep erwise Al. 7

8 Decoration on 10.4A Binary tiling These clusters are centered respectively on rhombus vertic Binary Tiling with edge τ 3 a 0 = 10.4Å. Ni(s ) Co(1) Ni(3) Ni(s) Co(3) + - mark orientations σ i of TM s in centers. Other ings refer to a rule for TM decoration, which depends o orientations. Composition around Al 70 Co 21 Ni 9. 8

9 Another version of idealized decorat This image emphasizes a decomposition into 2.45Å He Boat, and Star tiles around 2.45Å Decagon tiles. The di possible tilings of the HBS tiles correspond to options for in rings 2.5/3, all of which maximize the number of Al-Co b 9

10 Orientational order Define σ i = ±1 on each cluster, like an Ising model s expresses the center s orientation (also controls in which lay TM s of ring 1 sit.) What is the pattern of orientations? For the (artificial!) case of fixed site list, the energy diff is delicately balanced. We often find a ferromagnetic ar ment, which means the point symmetry is pentagonal i pentagonal symmetry occurs in part of the Al-Co-Ni phas gram. This can be understood by matching the edges of th Decagon cluster: Al atoms alternate in which way they correlated with center orientation. At low and high densities, or in a approximant with Star clusters, antiferromagnetic arrangment is preferred can also be rationalized, because it avoids adjacent Ni-N forming a 72 angle in the Star cluster. 10

11 Relaxation and puckering Under relaxation, we found rearrangements of atoms in 2.5/3. Also, the period doubled to c = 2c = 8Å, the re riod for most d(alconi) subphases [when simulation was t a sample cell of that size]. Why? (a). TM Co τ a 0 4 A (b). z Al channel c 4 A ideal position U(z) 11

12 Explanation of Al in channels... We can define Al potential U Al (r) r V AlCo (r r ) + r V AlNi (r r ) given fixed positions of TM s. Isolated wells of this functi filled by a single Al, but there are also channels of po minima, running between columns of Co in the c direction. is just room to place three Al in every four layers, hence c = 2c. The placement of the atoms is determined by ( timum single-atom potential [plot (b) on previous sheet] in the atom layer with more TM s in distant locations (ii) to have maximum transverse displacement to satisfy Al-A core, since 2c/3 2.67Å is a little too close. 12

13 Al potential map Left plot shows Al potential map in the TM poor layer (at TM rich layer (at right). In middle is atom configuration layers (actual sites after relax - MD - relax). TM poor layer that will pucker) is larger circles. At right is a slice of the map along the c axis. Double lines show intersection of sli 13

14 Interaction of channels Adjacent channels pucker in opposite sense as shown, to avoid Al-Al contacts in mirror layers. The actual top view (rihgt) is a crooked cross of 2Al+2Al (in projection) around a column of Co. puckered mirror puckered mirror puckered 14

15 Global puckering pattern Puckering pattern in the Å cell. Key: black/u shows sign and size shows magnitude of displacements. rings of puckered atoms. 15

16 Simulated vs. actual W(AlCoNi) The top figure is a mirror layer; bottom is a puckered layer. Empty circles are experimentally determined sites: teeth = TM, smooth=al, large = mixed Al/TM. Filled circles are simulations: Dark gray = TM, light gray = Al. 16

17 Conclusions Methods of Mihalkovic et al (2002) for basic Ni d(al 70 successfully led to a structural understanding (at T = 0) o Co d(al 70 Co 20 Ni 10 : a completely different tiling (domina decagon clusters) despite a very similar nearest-neighbor o We have described the origin of puckering and orientati order. The fixed-site list simulations can lead to the wron conclusion for low-energy effects, unless relaxations are ap intelligently. When applied to a unit cell the same size as crystalline approximant W(AlCoNi) [Sugiyama K. Sugiyama et al J. Comp. 342: 65 (2002)] many details of our prediction agre not all. 17