Nanoscale Patterning of Chemical Order in Irradiated ...• Potential applications for...
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Materials Computation Center, University of Illinois Nanoscale Patterning of Chemical Order in Irradiated Metallic Alloys Jia Ye and Pascal Bellon Introduction Kinetic Monte Carlo Simulations Kinetic Monte Carlo simulations are employed to study the effect of the size of displacement cascades in an ordered alloy. A particular binary A 1-x B x model alloy undergoing L1 0 ordering is selected. The forced mixing and disordering produced in displacement cascades is introduced by forcing exchanges of atoms in the cascade. In the present model, four parameters are used to specify this forced mixing. - Γ c the rate of introduction of cascade per atom. - b the cascade size. - ¶— cascade density: set to 80% in this work in order to create fully or near fully disordered zones in L10 phases. - R the relocation distance: forced exchanges are here performed between nearest neighbor atoms, in order to isolate cascade size effects from relocation range effects on patterning reactions. Finally, for comparison purposes, it is useful to introduce the ballistic jump frequency, Γ b = b* Γ c , which is a measure of the disordering rate. 2 Γ b is the number of replacements par atom per second. The simulation temperature is set at 60% T c . Simulation results are analyzed using complementary methods, encompassing direct visualization of the configurations in 2D and 3D, determination of the size and number of ordered clusters belonging to any variant, and calculation of the spherically averaged structure factor, centered on an L1 0 superlattice position • A new steady state, patterning of chemical order, is predicted under irradiation with large and dense cascades. • A dynamical phase diagram is built that yields the stable steady states as a function of the cascade size and the irradiation flux. • KMC results are supported by analytical model (see PRB 70,094105(2004)). • Patterning of chemical order is a general phenomenon. It can be used to rationalize previous experimental results by Nelson et al and Schmitz et al for Ni 88 Al 12 alloy. • Direct synthesis of nano-composites by large and dense cascades (heavy ion irradiation) is possible. • Potential applications for exchange-spring magnets (Kneller and Hawig, 1991). Summary T = 103 K T = 170K Materials under irradiation are dissipative systems, and as such, they are susceptible to self-organize (SO). There are twofold interests: - Fundamental: excellent test bed of the theory driven systems since microscopic mechanisms are well identified and can be varied in a controlled manner experimentally. - Practical: self-organization can be used to synthesize functional nanocomposites with tunable scales Objective: study the effect of cascade size b on self-organize. Main results: we identify a new patterning reaction in the case of ordered alloys: when the cascade size b is large enough, the degree of chemical order develops nanoscale patterns, under appropriate irradiation flux and temperature. (100) cut of instantaneous configuration after the introduction of one large dense cascade (b=8000, density=80%) in an initially long-range ordered phase; Only B atoms are displayed. Three colors correspond to three rotational L1 0 variants. Steady states of AB alloy under irradiation with large dense cascade (b=4002, density=80%) at increasing disordering frequency: (a) _ b =1000s -1 ; (b) _ b =3000s -1 ; (c) _ b =30000s -1 . Three steady states under sustained irradiation Three distinct steady-states are identified. Besides the expected long-range ordered (LRO) and disordered states, for large enough cascade, there is a new state in the sense that the alloy is well ordered, but all six variants are present in domains of finite size; this is a state of patterning of the chemical order. 1) there is a minimum cascade size for patterning of degree of order to be possible. This threshold value is around b=100. 2) The patterning-disorder boundary is almost independent of the cascade size. 3) At small b, I domain obeys scaling with _ b /_ b,c . At large b, it obeys scaling with _ b /_ b,s . Schematic drawings illustrating the characteristic lengths introduced by irradiation: the relocation range R and the cascade size L (In this study, the number of forced pair exchanges in one cascade b is used to represent the cascade size). Cascade model used in the simulations Dynamical steady-state phase diagram This work is supported in part by MRL-Materials Computation Center (NSF-DMR), by DOE- CESP “Nano-magnets”, by MRL-CFC, and by Intel. Acknowledgement Irradiation with energetic ions creates displacement cascades, resulting in disordered zones in chemically ordered alloys. At finite temperatures, this disorder competes with thermally activated reordering. 3D view of atomic configuration of patterning of chemical order steady state. All six variants of L1 0 structure are present in domains of finite size. Domains from same variant form connected structure in 3D. Simulation parameters: b=4002, _ b =3000s -1 . Identification of Patterning-disordered boundary ) 2 ln exp( 2 ln 1 ) ( 2 2 2 2 k l l I k I k I D SRO − + + = π ξ ξ Two components of structure factor: 1. Gaussian: Ordered domain, approximation of dynamical scaling function. 2. Lorentzian: SRO, exponential decay of fluctuation of order. Low _ b Long-Range Ordered Intermediate _ b Patterning of order High _ b Disordered Decomposed structure factors of two steady state: patterning of chemical order and disordered. It is clearly shown that the domain intensity is much higher than the SRO intensity in patterning state. Simulation parameters are as marked. • Two different regions: Constant I D,max at small b region and abnormal I D,max value at large b region • Consistent with direct observation of the atom configurations. • Threshold for patterning at crossover. With small cascade size b (b=1,5,17 and 35), all I domain vs. normalized _ b /_ b,c curves can be rescaled to one curve. For large b (b=394 and 4002), the behaviors of the system are different. Rescaling requires the introduce of new flux, _ b,s . (a) (b) (a) Sketch of exchange-spring magnet. (b) KMC result of patterning state from c B =37.5%, b=4002. White region: soft magnet (L1 2 phase). Dark region: hard magnet (L1 0 phase). Materials Computation Center, University of Illinois Duane D. Johnson and Richard M. Martin (PIs), Funded by NSF DMR 03-25939 For simplicity, the volume of the cascade is assumed to be spherical, and only one cascade size is used during each KMC run. Critical b for patterning
Transcript of Nanoscale Patterning of Chemical Order in Irradiated ...• Potential applications for...
Materials Computation Center, University of Illinois
Nanoscale Patterning of Chemical Order in Irradiated Metallic AlloysJia Ye and Pascal Bellon
Introduction
Kinetic Monte Carlo Simulations Kinetic Monte Carlo simulations are employed to study the effect of thesize of displacement cascades in an ordered alloy. A particular binaryA1-xBx model alloy undergoing L10 ordering is selected.
The forced mixing and disordering produced in displacement cascades isintroduced by forcing exchanges of atoms in the cascade. In the presentmodel, four parameters are used to specify this forced mixing.
- Γc the rate of introduction of cascade per atom.
- b the cascade size.
- ¶—cascade density: set to 80% in this work in order to create fully or nearfully disordered zones in L10 phases.
- R the relocation distance: forced exchanges are here performed betweennearest neighbor atoms, in order to isolate cascade size effects fromrelocation range effects on patterning reactions.
Finally, for comparison purposes, it is useful to introduce the ballistic jumpfrequency, Γb = b* Γc, which is a measure of the disordering rate. 2 Γb isthe number of replacements par atom per second.
The simulation temperature is set at 60% Tc.
Simulation results are analyzed using complementary methods,encompassing direct visualization of the configurations in 2D and 3D,determination of the size and number of ordered clusters belonging to anyvariant, and calculation of the spherically averaged structure factor,centered on an L10 superlattice position
• A new steady state, patterning of chemical order, is predicted under irradiation withlarge and dense cascades.
• A dynamical phase diagram is built that yields the stable steady states as a function ofthe cascade size and the irradiation flux.
• KMC results are supported by analytical model (see PRB 70,094105(2004)).
• Patterning of chemical order is a general phenomenon. It can be used to rationalizeprevious experimental results by Nelson et al and Schmitz et al for Ni88Al12 alloy.
• Direct synthesis of nano-composites by large and dense cascades (heavy ion irradiation)is possible.
• Potential applications for exchange-spring magnets (Kneller and Hawig, 1991).
Summary
T = 103K
T =170K
Materials under irradiation are dissipative systems, and as such, they aresusceptible to self-organize (SO). There are twofold interests:- Fundamental: excellent test bed of the theory driven systems sincemicroscopic mechanisms are well identified and can be varied in acontrolled manner experimentally.- Practical: self-organization can be used to synthesize functionalnanocomposites with tunable scales
Objective: study the effect of cascade size b on self-organize.
Main results: we identify a new patterning reaction in the case ofordered alloys: when the cascade size b is large enough, the degree ofchemical order develops nanoscale patterns, under appropriateirradiation flux and temperature.
(100) cut of instantaneousconfiguration after theintroduction of one largedense cascade (b=8000,density=80%) in an initiallylong-range ordered phase;
Only B atoms are displayed.Three colors correspond tothree rotational L10 variants.
Steady states of AB alloy under irradiation with large dense cascade (b=4002, density=80%) atincreasing disordering frequency: (a) _b =1000s-1; (b) _b =3000s-1; (c) _b =30000s-1.
Three steady states under sustained irradiation
Three distinct steady-states are identified. Besides the expected long-range ordered (LRO) anddisordered states, for large enough cascade, there is a new state in the sense that the alloy is wellordered, but all six variants are present in domains of finite size; this is a state of patterning ofthe chemical order.
1) there is a minimum cascade sizefor patterning of degree of orderto be possible. This thresholdvalue is around b=100.
2) The patterning-disorderboundary is almost independentof the cascade size.
3) At small b, Idomain obeys scalingwith _b/_b,c. At large b, it obeysscaling with _b/_b,s.
Schematic drawings illustrating thecharacteristic lengths introduced byirradiation: the relocation range R andthe cascade size L (In this study, thenumber of forced pair exchanges in onecascade b is used to represent thecascade size).
Cascade model used in the simulations
Dynamical steady-state phase diagram
This work is supported in part by MRL-Materials Computation Center (NSF-DMR), by DOE-CESP “Nano-magnets”, by MRL-CFC, and by Intel.
Acknowledgement
Irradiation with energetic ions creates displacement cascades, resulting indisordered zones in chemically ordered alloys. At finite temperatures, thisdisorder competes with thermally activated reordering.
3D view of atomicconfiguration of patterning ofchemical order steady state.All six variants of L10structure are present indomains of finite size.Domains from same variantform connected structure in3D.
Simulation parameters:
b=4002, _b =3000s-1.
Identification of Patterning-disordered boundary
)2lnexp(2ln1
)( 2222 kllIk
IkI DSRO
−++
= πξξ
Two components of structure factor:1. Gaussian: Ordered domain, approximation of dynamical scaling function.2. Lorentzian: SRO, exponential decay of fluctuation of order.
Low _bLong-Range Ordered
Intermediate _bPatterning of order
High _bDisordered
Decomposed structure factors of two steady state: patterning of chemical order anddisordered. It is clearly shown that the domain intensity is much higher than the SROintensity in patterning state.
Simulation parameters are as marked.
• Two different regions: ConstantID,max at small b region andabnormal ID,max value at large bregion
• Consistent with direct observation ofthe atom configurations.
• Threshold for patterning atcrossover.
With small cascade size b (b=1,5,17and 35), all Idomain vs. normalized_b/_b,c curves can be rescaled to onecurve. For large b (b=394 and 4002),the behaviors of the system aredifferent. Rescaling requires theintroduce of new flux, _b,s.
(a) (b)
(a) Sketch of exchange-spring magnet. (b) KMC result of patterning state from cB=37.5%, b=4002.White region: soft magnet (L12 phase). Dark region: hard magnet (L10 phase).
Materials Computation Center, University of Illinois Duane D. Johnson and Richard M. Martin (PIs), Funded by NSF DMR 03-25939
For simplicity, the volume of the cascade is assumed to be spherical,and only one cascade size is used during each KMC run.
Critical b forpatterning
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