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c system: A theoretical study from the alloys to the nanoalloys
Abir Hizia, Hedi Garbouj, Christine Mottet, Moncef Said
To cite this version:
Abir Hizia, Hedi Garbouj, Christine Mottet, Moncef Said. Chemical ordering and surface segregation
in Ni 1 - c Pt c system: A theoretical study from the alloys to the nanoalloys. Results in Physics,
Elsevier, 2019, 14, pp.102493. �10.1016/j.rinp.2019.102493�. �hal-02456589�
Contents lists available atScienceDirect
Results in Physics
journal homepage:www.elsevier.com/locate/rinp
Chemical ordering and surface segregation in Ni
1 cPt
csystem: A theoretical study from the alloys to the nanoalloys
Abir Hizi
a,b,⁎, Hedi Garbouj
a, Christine Mottet
b, Moncef Said
aaLaboratoire de la Matière Condensée et Nanosciences (LR11ES40), Faculté des Sciences de Monastir, Université de Monastir, 5019 Monastir, Tunisia
bAix-Marseille Université, CNRS, CINAM UMR 7325, Campus de Luminy, 13288 Marseille, France
A R T I C L E I N F O Keywords:
Tight-Binding Ising Model Alloys surfaces Nanoalloys Segregation
Order-disorder transition
A B S T R A C T
Monte Carlo simulations within a Tight-Binding Ising Model (TBIM) have been performed on bulk, surfaces, and nanoclusters ofNi1 cPtcalloys in order to describe and understand the competition between surface segregation and chemical ordering phenomena in nanoalloys. The effective pair interactions obtained from the DFT calcu- lations have been applied in Monte Carlo simulations to determine the bulk and alloy surfaces configurations.
The order-disorder transition temperatures in the bulk compare well with experimental data and the bulk phase diagram from the model have been compared to that determined experimentally to validate the fit. The (111), (100) and (110) crystallographic orientations surfacesNi1 cPtc are treated. The three driving forces for the segregation of surfaces have be studied in both diluted limits, together with the phenomenon of segregation at high temperature (in the disordered state) over the entire concentration range. Finally, we analyze the com- petition between superficial segregation and low temperature chemical order and conclude with a similar ap- proach on truncated octahedra of 1289 and 405 atoms.
1. Introduction
Nanoparticles have been used for several centuries, they are of particular interest because of their specific properties, different from that of the volume. If they have been studied for nearly a half a century, they have been unavoidable for fifteen years. They form the bricks of modern nanotechnologies[1]. Nanoparticles have attracted a great deal of interest in recent years, in particular for their optical, magnetic and catalytic properties, or in the context of the vectorization of medica- ments[2]. Pure metals have well known characteristics. Adding one or more other elements, then makes it possible to vary considerably their properties. In the context of binary alloys, a lot of theoretical and ex- perimental studies have been performed on systems with a tendency to order (NiPt[3–6], CoPt[7–11]or AuPd[12,13]) or systems with de- mixing tendency (AgPt [14–17], CuAg [18–22]). There are a large number of typical nanometric structures and morphologies of different sizes but also numerous chemical arrangements. Nanoalloys can therefore be studied according to their size, their structure, the tem- perature or the concentration of elements constituting them. If de- scribing a phase diagram of the alloy by temperature and composition is a well-known exercise of metallurgy, the objective of defining a phase diagram of nanoalloys is ambitious for more than one reason. The
nanoparticles phase diagram differs from that of the massive alloy on several points that must be taken into account: the size, the structure and the morphology of the cluster, the different crystallographic sites in equivalence, beside the temperature and the concentration as in bulk systems. It is in this long-term objective that this theoretical work takes place. There are many experimental studies of the Ni-Pt system where the surface segregation reversal is observed between the more compact surfaces, the (111) and (100), where Pt segregates[4,23]with an os- cillating profile and the (110) one where Ni segregates[24]forming a sandwich structure with a pure Ni surface, pure Pt subsurface and an almost pure Ni layer below. We are interested in Pt-Ni system with a tendency to order and we propose, using a simple Tight Binding Ising Model, to first explore the bulk phase diagram before to investigate the surface segregation and then to study the clusters of two sizes (405 and 1289 atoms) in the shape of a truncated octahedron.
2. Model and method 2.1. The TB-SMA potential
The interaction between metal atoms was modeled semi-empirically by means of the well-established second-moment approximation of the
https://doi.org/10.1016/j.rinp.2019.102493
Received 23 May 2019; Received in revised form 27 June 2019; Accepted 28 June 2019
⁎Corresponding author at: Laboratoire de la Matière Condensée et Nanosciences (LR11ES40), Faculté des Sciences de Monastir, Université de Monastir, 5019 Monastir, Tunisia.
E-mail address:hizi.abir1993@gmail.com(A. Hizi).
Available online 12 July 2019
2211-3797/ © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).
T
tight-binding (TB-SMA)[25] model where the attractive term re- produces the second moment of the density of state of the metal in- ducing a square root dependence with the neighboring atoms whereas the repulsive term is a pairwise Born Mayer term. The potential energy at site “i” for an atom of type A is then written as follows:
= +
< <
Ei exp Aexp
j r r
q r r
j r r
pr r ,
2 2 ( 1)
,
( 1)
ij c
ij
ij c
ij
0 0
(1) whererijis the distance between the atom at site “i” and its neighbors at site “j”,rcis the cut-off distance,r0is the nearest-neighbor distance in the pure metals (Pt and Ni), and p, q, A, are the parameters[6](listed inTable 1), which have been fitted to the DFT calculations.
2.2. The Tight Binding Ising Model (TBIM)
The Tight Binding Ising Model[26,27]is based on an effective Ising Hamiltonian for surface segregation and chemical ordering in alloys.
The Hamiltonian contains three terms: the effective pair interactions, the difference in surface energy, and the difference in size of the two elements, and writes as follows:
= + +
HTBIM p p V p ( h h )
n m n m nm
n
n n nsize
, (2)
2.3. Pt-Ni TBIM parameters
In order to distinguish the stability of the chemical ordering phases, it is necessary to consider the interactions of pairs up to the third neighbors. The choice of these pairs interaction parameters is so es- sential. We will chooseVito stabilize the phases observed experimen- tally at the expense of other phases theoretically existing at the same concentrations but essentially higher in energy. According to the ex- pression of the energies of formation of the ordered phases which one considers:
=
HLf10 4V1 8V3 (3)
=
HLf12 3V1 6V3 (4)
=
HLf11 3V1 3V2 3V3 (5) The effective pair interactions can be fitted to DFT (Density Functional Theory) calculations of the formation energies (Table 2) or to TB-SMA semi-empirical potential[6]. The DFT calculations were done using the VASP code with the GGA[28]exchange-correlation functional and the Projector Augmented Wave (PAW) method [29,30]. The electrons of valence ”s” and ”d” are considered for each species (Ni and Pt) with a cutoff energy of 600 eV for the plane waves. Cohesion energies, lattice parameters and formation energies were calculated for Ni, Pt, and Ni-Pt using spin polarized calculations (Table 2). The values of formation energy obtained in DFT are in good agreement with the experimental ones[38].
Effective pair interactions fitted either on DFT or on TB-SMA cal- culations are illustrated in theTable 3together with the order-disorder transition temperature (Tc) of the L10/A1transition. TheTcobtained by theVi fitted on TB-SMA potential respects the experimental order/dis- order transition temperature[38]. So we used in this work theVifitted on the TB-SMA potential.
The cohesive effect hnrepresents the difference between the sur- face energy of Pt and the surface energy of Ni. In the TB-SMA calcu- lations, it can be noted that the surface energy of Pt is lower than that of Ni, which is in favor of the surface segregation of Pt. The DFT calcu- lations are shown to be compared to the TB-SMA calculations but the TBIM parameters for the Ni-Pt system are calculated with the TB-SMA model and are presented inTable 4. For the edges we have taken the same values calculated for the (110) infinite surface and concerning the difference of energy in the vertex we found h= 0.08eV calculated with the TB-SMA model.
The last parameter to adjust is hsize, which takes into account the difference in size of the two elements in the segregation energy calcu- lated using quenched molecular dynamics simulations and TB-SMA potential. Here the impurity differs from the matrix only by its atomic radius. hsizeis calculated in both diluted limits for different surfaces (Table 5). For the edges we have taken the same values of hsizecal- culated for the (110) infinite surface and concerning hsizein the vertex we found hsize= −0.26 eV/at within the diluted limit Ni(Pt) and hsize Table 1
Parameters of the TB-SMA potential for Pt-Ni nanoalloys[6].
A (eV) (eV) p q
Pt-Pt 0.1602 2.1855 13.00 3.13
Ni-Ni 0.0845 1.405 11.73 1.93
Pt-Ni 0.1346 2.3338 14.838 3.036
Table 2
Lattice parameters (a), cohesive energy (Ecoh) and formation energy for alloys H
( f).
a(Å) Etot(eV/at) Hf(eV/at)
NiDFT 3.51 −5.467
TB-SMA 3.51 −4.65
Exp.[31,32] 3.52 −4.44
PtDFT 3.98 −6.097
TB-SMA 3.98 −5.53
Exp. 3.92[32,33] −5.84
NiPt3
DFT 3.88 −0.068
TB-SMA 3.88 −0.254
Exp. 3.89[34] −0.063[38]
NiPtDFT L10 3.84 −0.096
DFT L11 3.84 −0.058
TB-SMA L10 3.84 −0.368
TB-SMA L11 3.84 −0.276
Exp. L10 3.815[35] −0.096[38]
Ni3Pt
DFT 3.66 −0.072
TB-SMA 3.66 −0.276
Exp. 3.75[35] −0.07[38]
Table 3
Values of effective pair interactions,order/disorder transition temperature of the L10/A1transition fitted both on TB-SMA and DFT calculations and the ex- perimental order/disorder transition temperatures[38].
EPI fitted both on TB-SMA DFT Exp.
V1(meV) 88 24
V2(meV) 2 −5
V3(meV) 2
Tc(K) 940 430 940
Table 4
Relaxed surface energies for the pure metals.
Method Surface orientation/units Ni Pt h
DFT 100/eV/at 0.84[35] 0.91[37]
TB-SMA 100/eV/at 0.97 0.76 −0.03
DFT 111/eV/at 0.73[35] 0.64[37]
TB-SMA 111/eV/at 0.645 0.58 −0.06
DFT 110/eV/at 0.833[35] 1.31[37]
TB-SMA 110/eV/at 1.36 1.29 −0.07
Experimental (average face)/eV/at 0.94[36] 1.21[36]
= 0.16 eV/at within the diluted limit Pt(Ni) calculated with the TB- SMA model.
3. Monte Carlo simulations
The Monte Carlo simulations consist in atomic trials: permuting or exchanging the chemical nature of one or two atoms, keeping the same number of atoms in the simulation box. The Metropolis sampling[39]
ensures that we reach a Boltzmann distribution of the chemical con- figurations at equilibrium, this means the number of Monte Carlo trials is sufficient to get reliable averages of physical quantities. In the Me- tropolis Monte Carlo, a trial is accepted if it lowers the total energy of the system. If not, it can be still accepted with a probability equal to
E kT
exp( / ), where E is the energy difference between the configura- tions before and after the trial, k is the Boltzmann constant, and T, the temperature.
We realized Monte Carlo simulations in canonical and semi-grand canonical ensembles. In the first way, the concentration remains con- stant and the Monte Carlo simulations consist in exchanging the posi- tions of two atoms of Pt and Ni. In the second way, the difference of the chemical potential of the two elements remains constant but the trials consists in permuting the species of one atom, and we get the equili- brium concentration.
We realized twenty-thousand macrosteps. Each macrostep consists of proposing randomly to any atom of the box a Monte Carlo trial (exchange or permutation), repeated as many times as there are atoms in the box. For the canonical simulations, we performed either heating and cooling runs starting respectively from low-temperature ordered configurations and high-temperature disordered configurations. Then, at each augmentation of the temperature, we start with the last con- figuration. For the semi-grand canonical simulations, we started from pure systems, either Ni or Pt, and increased or decreased the chemical potential keeping the last configuration as a starting configuration.
4. TBIM Ni-Pt bulk phase diagram
The bulk is represented by a cubic box of 2304 atoms and periodic conditions. The order/disorder critical temperatures of the stoichio- metric phases have been characterized by canonical simulations. The results are shown inFig. 1where we can see the sublattices occupation.
The face centered cubic lattice is characterized by four simple cubic sublattices ( , , , ) as illustrated inFig. 1. The ordered phases are defined by an alternation of pure atomic planes in one direction for the L10and pure and mixed atomic planes for the L12 phase. The critical order/disorder temperature at equiconcentration is 940 K in our model, which is in good agreement with the experimental critical temperature of the NiPt phase [38]. The L12 of the NiPt3 andNi3Pt phases have equivalent critical temperature equal to 960 K, which is higher than the experimental critical temperature 830 K for the Ni3Pt and 790 K for NiPt3[38].
The presentation of the phase diagram is then performed using semi-grand canonical Monte Carlo simulations at constant temperature.
The isotherm at 100 K displays the ground states of the ordered phases as a function of the difference in the chemical potential µ=µPt µNi as illustrated onFig. 2with different plateaus of the Pt concentration as a function of µ. The three larger plateaus characterize the L12and L10
phases also defined by their short range order parameter (SROP). These phases result in our model from the extension of the effective pair in- teractions to the third-neighbor interactions and are illustrated in Fig. 2.
The isotherms at higher temperature are illustrated onFig. 3where the sublattice occupations are plotted as a function of the concentration of Pt in the box. We notice around the stoichiometric compositions the correspondingNi3Pt, NiPt and NiPt3 phases. There are concentration ranges (the hatched regions) where no phase is stabilized which re- presents a coexistence domain between the A1and the L12phases and between the L12and the L10phases. At low concentration of Pt, the four sublattices are equally occupied, which is characteristic of the dis- ordered A1phase. The L12phase is characterized by one sublattice po- pulated with Pt and the others three equally occupied by Ni. The next ordered phase obtained by increasing Pt concentration is the L10or- dered phase around the equiconcentration, which is characterized by the sublattices equally occupied two by two. Then the L12phase (NiPt3) is characterized by one sublattice populated with Ni and the others three equally occupied by Pt.
The complete bulk phase diagram is obtained from a series of iso- therms at different temperatures, as shown inFig. 4. The biphasic do- mains are depicted by hatched domains. The TBIM bulk phase diagram is in rather good agreement with the experimental one[40].
5. Surface segregation in Pt-Ni alloys
Experimentally, the most compact (111) and (100) Pt-Ni surfaces present an oscillating profile with Pt enrichment on top on the whole concentration range[4,23,41,42]. However, a wonderful switch of this concentration profile was observed on the (110) surface, at the equi- concentration[24], namely a ”sandwich” structure with an almost pure Ni plan at the surface, and a pure Pt plan on subsurface, then again Ni enrichment on the third plan. Knowing that all these experiments were performed at about 1200 K, in the disordered state, well above the maximum critical temperatureTc=940 K, we characterized the surface segregation in the disordered state to compare with experiments. Then we also characterized surface segregation and chemical ordering at low temperature.
5.1. (111), (100) and (110) surfaces at high temperature in the disordered state
We have taken into account three effects simultaneously in Eq.(2):
the cohesive effect (listed inTable 4), the size effect (listed inTable 5) and the effective pair interactionVnm(listed inTable 3). More precisely, limiting the summation in Eq.(2)to the third-neighbor interactions and referring to the pair interactionsVnmasV , V1 2andV3.
The oscillating behavior is shown for the (111), (100) and (110) surfaces inFig. 5 and 6. We obtain, in the whole range of concentrations and for all the otientations, a strong Pt enrichment of the surface plan, except on the (110) surface where in the Ni-rich domain we observe a slight Ni segregation, which is a small manifestation of the experi- mental segregation reversal observed on the (110) surface. Then, again for all the orientations, there is a significant Pt depletion (Ni enrich- ment) on the first underlayer and again a slight Pt enrichment on the second sublayer. The oscillation amplitude is much more pronouced in the (110) and (100) orientations than for the (111) one, where our theoretical prediction is much more damped than the experimental results. Our results are in qualitative agreement with the experimental results on the compact surfaces[4,23]for which an oscillating profile is observed at the surface with Pt segregation on the first plan. However, quantitatively, the experimental segregation on the (111) surface is much higher than in our model. We can wonder if the experimental samples are completly disordered or if there could be some ordering effects that could modify the quantity of segregated element as we will see in the next sections. However, on the (110) surface, the TBIM model Table 5
TBIM hsize parameters obtained by TB-SMA calculations of the segregation energies of one impurity differing from its matrix only by its atomic radius for a Pt impurity in Ni matrix: Ni(Pt) or a Ni impurity in Pt matrix: Pt(Ni).
hsize(eV/at) 100 111 110
Pt(Ni) 0.03 −0.05 0.10
Ni(Pt) −0.29 −0.27 −0.28
fitted on DFT calculations does not lead to the segregation inversion as in experiments[24]or with an other TBIM study[3]limited to first neigbors interactions and disordered state. In such case, the segregation inversion is obtained by varying the effective interactions at the sur- faces between (111) and (110). We will show in the next sections the influence of the chemical ordering at low temperature on the surface segregation.
5.2. (111), (100) and (110) surfaces at low temperature in the ordered state
5.2.1. Pt-Ni(100) Surface
For the (100) surface, the segregation isothem at 300 K is plotted in Fig. 7. In order to properly study the order in the surface slab we pre- sented the sublattices occupations in the core of the surface slab (all the plans except the two external ones), and compare them to that of the bulk at 300 K (Fig. 3). The comparison is excellent, showing a perfect chemical ordering of the interior of the surface slab. The ordered structures present a stacking of pure or mixed plans, parallel to the (100) surface. The different ordered phasesFig. 8(a), (b) and (c) cor- responding to different concentrations of the surface slab are shown.
The L12 (Ni3Pt and NiPt3) phases present an alternance of pure and mixed plans, and a mixed and pure Pt surfaces (respectively). The L10
phase at equiconcentration shows an alternate stacking of pure plans with a Pt termination at the surface.
InFig. 7, we plotted the first four plans near the surface (c0being the surface,c1the subsurface, etc…). We observe a pure Ni surface for the understoichiometric Ni3Pt alloy with an alternance of pure and mixed planes and Pt segregation with a mixed surface at the stoichio- metric alloy and for the overstoichiometric alloy up to the Pt con- centration in the slab equal to 0.5 where a pure Pt surface takes place.
The subsurface is rather Ni-rich until the NiPt3phase where it starts to be enriched in Pt.
The surface sublattices plotted inFig. 7 allow to characterize the surface ordered structure as the p(2x1) for theNi3Pt alloy with one surface sublattice filled by Pt atoms (c0orc0) whereas the other one is filled by Ni atoms in the L12phase. Then the two surface sublattices are filled with Pt in the range of concentration from c = 0.5 to 1. In the subsurface plan, we also observe a similar ordering in the NiPt3phase where the two sublattices (c1 andc1) are alternatly occupied one with Pt and the other one with Ni. In the disorded phases (Ni-rich and Pt- rich), the surface is respectively Ni-pure and Pt-pure and the 0 500 1000 1500 2000
Temperature(K) 0
0.2 0.4 0.6 0.8 1
c
α,β,γ,δPtNi
3Tc=960K
0 500 1000 1500 2000 Temperature(K) 0
0.2 0.4 0.6 0.8 1
T
PtNi
c=940K0 500 1000 1500 2000 Temperature(K)
0 0.2 0.4 0.6 0.8 1
cα cβ cγ cδ
Pt
3Ni
Tc=960K
α β
γ δ
Fig. 1.Order/disorder transitions obtained from canonical Monte Carlo simulations for stoichiometricNi3Pt, NiPt, and NiPt3alloys. the sublattice occupation ( , , , ) are represented as a function of temperature.
Fig. 2.Isotherm of bulk NiPt system at 100 K. The Pt concentration and SROP for the first ( 1) and second neighbors (2) are illustrated as a function of the chemical potential difference µ=µPt µNi.
subsurfaces are disordered.
To resume, at low temperature, the (100) orientation presents two important segregation profiles, depending on the composition. For the Ni3Pt alloys, the surface is composed of a mixed plane with stoichio- metry variations according to the alloy stoichiometry taking place in subsurface but the first subsurface plan is almost Ni-pure. For NiPt3 alloys, the surface is Pt pure and the first subsurface plane is mixed with stoichiometry variations according to the alloy stoichiometry.
5.2.2. Pt-Ni(111) surface
At low temperature, the (111) surface is simulated by a slab of
eighteen atomic planes with hundred atoms (ten by ten) per atomic layer as illustrated on theFig. 10, where the snapshots represent the top layer. The segregation isotherm at 300 K of the (111) surface plans and the core of the slab are plotted inFig. 9. The system is ordered as can be checked by the core sublattices occupations which are nicely compar- able to that of the bulk. Looking at the surface concentration and sur- face sublattices, we observe a linear variation corresponding to the variation of the composition of the disordered A1phase, which extends up to the L12(Ni3Pt) ordered phase. At c = 0.25 and beyond, the sublattice is filled by Pt atoms, whereas the other are equally filled with Ni atoms leading to the c(2 × 2)(111) surface structure which corre- sponds to any layer of the L12 (Ni3Pt) bulk structure (the top layer is illustrated onFig. 10(a)). Then at c = 0.5 and beyond, the and sublattices are filled by Pt atoms, whereas the other are equally filled with Ni atoms leading to the c(2 × 1)(111) surface structure which corresponds to any layer of the L10NiPt bulk structure (the top layer is illustrated onFig. 10(b)). Then the sublattice starts to be filled by Pt atoms and only the sublattice remains filled by Ni atoms, whereas the other are equally filled with Pt atoms leading to the c(2 × 2)(111) surface structure which corresponds to any layer of the L12(Pt3Ni) bulk structure (the top layer is illustrated onFig. 10(c)).
To conclude for the (111) surface, the bulk ordering drives the surface termination at the stoichiometry leading to the c(2 × 2) for the L12 (Ni3Pt and NiPt3) phases and the c(2 × 1)(111) for the NiPt L10
phase. The surface composition remains constant after reaching the stoichiometry (plateaus of the c0curve) whereas the underlayers adjust the variations of stoichiometry. For the L12(Ni3Pt) phase, surface seg- regation leads to the c(2 × 1)(111) surface structure before the L10
(NiPt) bulk phase domain. For theL10phase, the c(2 × 2)(111) surface structure occurs before the L12 (NiPt3) phase domain. In the end, the Fig. 3.Pt concentrations on the four sublattices ( , , , ) as a function of the nominal Pt concentration at different temperature.
Fig. 4.Ni-Pt bulk phase diagram.
(111) surface becomes pure in Pt in the overstoichiometric L12 (NiPt3) phase, whereas each bulk layer has the c(2 × 2)(111) structure. So that here also, the surface displays a Pt segregation as compared to the bulk ordered phase.
5.2.3. Pt-Ni(110) Surface
At low temperature, the (110) surface is simulated by a slab of sixteen atomic planes with hundred atoms (ten by ten) per atomic layer.
The segregation isotherm at 300 K of the (110) surface is plotted in Fig. 11. The surface concentration c0, plotted in the first graph of Fig. 11, starts with a Ni surface segregation in the Ni-rich domain. At the right limit of the miscibility gap, corresponding to 25% of Pt, the bulk is ordered according to the L12stoechiometricNi3Pt phase, and the
(110) surface layers concentrations oscillate between 0 and 0.5 ex- tending the L12phase up to the surface structure shown inFig. 12-a. The surface structure inFig. 12-a is the c(2 × 1)(110) which is well char- acterized by the surface sublattices (c0=1,c0=0,c1=0 andc1=0).
Increasing the Pt concentration from 25% to 37%, the surface con- centrationc0andc2remain constant equal to 0.5 with the c(2 × 2)(110) whilec1andc3follows the stoichiometric deviation of the L12phase. At 42% of Pt and up to 55%, the c(2 × 2) superstructure inFig. 12-b re- mains the same but the bulk phase underneath changes to the L10which is naturally stoechiometric atcPt=0.5 in which case the surface is made of the mixed variant of the L10 phase. From 55% up to pure Pt, the surface plan is Pt-pure as shown inFig. 12-c. At 75% of Pt, the bulk is ordered according to the L12stoechiometric NiPt3phase, which means Fig. 5.Variation of the Pt concentration at the (100), (111) and (110) surface at 1200 K as a function of the Pt concentration.
Fig. 6.(100), (111) and (110) surface profiles at 1200 K ofNi3Pt, NiPt, and NiPt3. The experimental results are drawn in blue square: (100) Surface[23], (111) Surface [4], and (110) Surface[24]. The experiments are generally performed on disordered single crystals at room temperature.
that the subsurface is mixed with an alternance of Pt-pure sublatticec1 and Ni-purec1.
To conclude on the three surface orientations, we can notice that the bulk ordering controls the global surface composition.
6. Ni-Pt nanoalloys with TBIM
6.1. Comparaison between infinite surface, facets and edges at high temperature in the disordered state
In this section we compared the segregation phenomenon at high temperature on the (100) facets, (111) facets and edges on the trun- cated octahedra (TOh) of 405 and 1289 atoms to the corresponding infinite surface in a semi-grand canonical ensemble. TOh is the equili- brium cluster morphology with the fcc structure. We consider two
different cluster sizes in order to study possible size effects. In the Fig. 13, we illustrated the segregation isotherms of the facets and the edges of the clusters and the one of the infinite surfaces to be compared at high temperature. The comparison is very good in the case of the (111) and (100) facets which have the same profile in the whole range of concentration with the (111) and (100) surfaces. In other way, the comparison is less good for the edges sites compared to the (110) sur- face orientation. The segregation in the (110) surface is almost what appears in the clusters except a slight shift for the clusters which have the tendency to start the steps at lower concentrations than in the in- finite system. This is due to the finite size effect of the edges on the cluster and because the (110) infinite surface is not fully equivalent to the edge sites.
To conclude, in the case of the facets, the correspondence with in- finite surface is very good at 1200 K. In the case of the edges, the (110) Fig. 7.Segregation isotherms at 300 K for the (100) surface with the surface plan and next planes Pt compositions, the sublattice occupations in the whole slab, and the sublattice concentrations for each layer parallel ( , , , ).
Fig. 8.Different (100) surface ordered structures are illustrated here with Ni atoms (in yellow) and Pt atoms (in blue).
Fig. 9.Segregation isotherms at 300 K for the (111) surface with the surface plan and next planes Pt compositions, the sublattice occupations in the whole slab, and the sublattice concentrations for each layer parallel ( , , , ).
Fig. 10.Different (111) surface ordered structures are illustrated here with Ni atoms (in yellow) and Pt atoms (in blue). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
infinite surface is not fully representative for describing the segregation phenomenon.
6.2. Ni-Pt nanoalloys at low temperature
We still concentrate on the same clusters: TOh of 405 and 1289 atoms. The concentration in Pt is determined for each type of surface site (vertex, edges, and facets). They are plotted as a function of the total Pt concentration of the nanoparticle.
The ordering of the clusters is illustrated inFig. 14where we can observe, by considering the occupation of the corresponding sublattice, that the cores of the two clusters of different size are ordered as in the bulk alloy. This is a nice verification that the cluster is well ordered at 300 K. But this is also a temperature allowing to get rid of the inter- mediate ordered phases found in the bulk below 300 K. By the way, we can notice that theTOh405andTOh1289clusters core, in the coexistence domain between the L10and L12(NiPt3) phases, is rather disordered. We also notice that forTOh405cluster, the ordered phase domains are much
more asymetric than in theTOh1289cluster where the order phases look like the ones in the bulk at the same temperature. This is in good agreement with the theoretical study of CoPt clusters[11]. With the segregation isotherms at 300 K shown in Fig. 14, we get a first de- scription of the global segregation tendency on the clusters. It is worth to point out that in this figure and in the following we plot the core concentration in Pt instead of the global concentration. We will see after how it can be sensible since the cluster is a finite object so that the nominal concentration in a cluster is divided between its surface and its core. However, we would like first to compare the segregation iso- therms to the one obtained in the infinite surfaces, for which there is an infinite reservoir corresponding to the nominal concentration of the alloy.
InFig. 15, we illustrated the segregation isotherms of the facets of the clusters and of the infinite surfaces to be compared at low tem- perature (300 K). The comparison is very good in the case of the (100) acets for which we recall that the (100) surface presents essentially three different superstructures at the surface, corresponding to the Fig. 11.Segregation isotherms at 300 K for the (110) surface with the surface plan and next planes Pt compositions, the sublattice occupations in the whole slab, and the sublattice concentrations for each layer parallel ( , , , ).
Fig. 12.Different(110) surface ordered structures are illustrated here with Ni atoms (in yellow) and Pt atoms (in blue). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
three stoichiometric ordered phases Ni3Pt, NiPt, and NiPt3. For the (111) orientation the comparison is not as simple as in the (100) or- ientation. The surface presents three plateaus corresponding to the three ordered phasesNi3Pt, NiPt, and NiPt3, in the same way for the clusters of sizes 405 atoms and 1289 atoms, but there is a slight shift for the clusters which have the tendency to start the steps at lower con- centrations than in the infinite system, especially in the Pt rich domain.
This is due to the finite size effect of the cluster given that the ordered NiPt3phase in the 405 atoms and 1289 atoms cluster is shifted to lower concentrations and the surface of the cluster is pure in Pt for core concentration of 70%, whereas it happens at the stoichiometry of the NiPt3phase of 75% for the (111) surface. We have the same profile of segregation compared with other theoretical works for the (111) facets [11].
In the case of the (110) infinite surface the comparaison is even worse. We notice that there is a sensible shift of the plateaus between the infinite surface and the edges, and the edges have the tendency to start the steps at higher concentrations than in the infinite system.
Finally inFig. 16we give an overview of the segregation isotherms at 300 K by plotting the surface concentration for each type of surface site (vertex, edges, (100) and (111) facets) and the core concentration together with the chemical potential difference µ=µPt µNi as a function of global concentration. We show the correspondance between the plateaus of the core concentration and the ordered phases which are illustrated by snapshots. The core is generally impoverished in Pt be- cause of the Pt surface segregation and the finite system effect. Only at low Pt concentration, below 25% of Pt, the (100) and (111) Pt segre- gations are compensated by Ni segregation on the edges and vertices. At
=
cPt 0.25, the core is ordered according to the L12 phase. The (111)
facets display a c(2×2) structure which is the same as their equivalent infinite surface. The ordering tendency leads to form mixed facets and pure facets in the same time whereas for the mixed case the ordering tendency of the alloy leads to alternate Ni and Pt rows inside the (100) facets (Fig. 16-a). Around the equiconcentration, there is a second plateau of the core concentration and of the chemical potential differ- ence corresponding to the L10ordered phase in the core. Some varia- tions of the (100) and (111) facet concentration display the c(2×1) superstructure (Fig. 16-b). AtcPt=0.62, the core remains ordered in L10, the (100) facets are saturated in Pt and the (111) facets display the c(2×1) superstructure (Fig. 16-c). AroudcPt=0.75and up tocPt=0.85 , the (100) facets remains saturated in Pt and the (111) facets display the c(2×2) superstructure with a core ordered in the L12phase (Fig. 16- d). BeyondcPt=0.85we show a total segregation in the shell of Pt with a core ordered in the L12phase.
7. Conclusion
We presented a theoretical study using a Tight Binding Ising Model fitted to TB-SMA calculations and Monte Carlo simulations in canonical and semi-grand canonical ensembles. We chose to focus on the case of alloys with a tendency to order as Co-Pt for which there are a lot of experimental developments and characterizations. The numerical si- mulations bring then a supplement to the understanding of these sys- tems. This work is a detailed theoretical study of Ni-Pt nanoalloys, surface segregation and core ordering. The objective was, by a simple method, on rigid lattice, to browse the system phase diagram and for a given cluster size, to study the competition between surface segregation and chimical ordering in the core of the clusters. We presented a study Fig. 13.(111) and (100) facets and edge segregation isotherms of theTOh405andTOh1289as compared to the infinite equivalent surfaces at 1200 K.
Fig. 14.Sublattice occupation and segregation isotherms on the different site at 300 K for the 405 and 1289 atoms TOh clusters.
Fig. 15.(111) and (100) facets and edge segregation isotherms of theTOh405andTOh1289as compared to the infinite equivalent surfaces at 300 K. In the case of the clusters, thecPtconcentration is the concentration of Pt in the core of the clusters to get a better comparison with the infinite surfaces.
of the three low indices surfaces ofNi1 cPtc alloys as an interesting study to forese the chemical arrangement of nanoalloys terminated by (111) and (100) facets and edges. In this model, we compared the Ni-Pt nanoalloys in the whole range of concentration with the bulk phase diagram and the order/segregation phenomena at the infinite surfaces (100), (110) and (111). We presented the relation between the core ordering and the cluster surface segregation. We showed that the clusters get ordered in their core as in the bulk phase diagram but the smaller size presents an asymmetry as a function of the Pt concentration in the core, which is typically a finite size effect. The segregation on the (111) and (100) facets is the same as in the (111) and (100) surfaces but their arrangement depends on the core ordering. The edges present either the mixed c(2×2) or the pure Pt configuration like the one on the (110) infinite surface.
Generally, all these chemical arrangements of Pt and Ni species at the vicinity of cluster surface are susceptible to important consequences for the catalytic properties of such systems, especially for the structures that are stable up to high temperatures. However, this study suggests new first principle calculations to investigate the stability of the 2D and
3D phases as compared to others and of course new experimental stu- dies for concentration ranges which were not investigated before.
A follow-up to this work would be to take into account many properties to introduce the effect of magnetism directly into the na- noalloys Pt-Ni model with an Heisenberg Hamiltonian[43].
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