Phase Textures of Metal-Oxide Nanocomposites Self-Orchestrated by Atomic Diffusions through Precursor Alloys

Metal-oxide nanocomposites (MON) are of pivotal importance as electrode materials yet lack a guiding principle to tune their phase texture. Here we report that the phase texture of MON can be tuned at the nanoscale by controlling the nanophase separation of precursor alloys. In-situ transmission electron microscopy ( in-situ TEM) has demonstrated that a MON material of platinum (Pt) and cerium oxide (CeO 2 ) is obtained through promoted nanophase separation of a Pt 5 Ce precursor alloy in an atmosphere containing oxygen (O 2 ) and carbon monoxide (CO). The Pt-CeO 2 MON material comprised an alternating stack of nanometre-thick layers of Pt and CeO 2 in different phase textures ranging from lamellae to mazes, depending on the O 2 fraction in the atmosphere. Mathematical simulations have demonstrated that the phase texture of MON originates from a balance in the atomic diffusions across the alloy precursor, which is controllable by the O 2 fraction, temperature, and composition of precursor alloys.


Introduction
][6][7][8][9][10] ] Indeed, nano-scaled particles of nickel (Ni) and yttria-stabilized zirconia (YSZ) materials are mixed with high-speed ball mills, pelletized, or spread over electrolyte membranes, and finally calcined at high temperatures to yield anodes for solid-oxide fuel cells (SOFCs).[ 11 ] The MON materials obtained in such bottom-up approaches however often suffer from poor transport performances that lead to increased power loss of the fuel cells and/or batteries.Each of the phases of MON is composed of a closed heterointerface between the different phases that terminates the flow of currents to increase the inherent impedance.
6][17] ] When subjected to an atmosphere containing oxygen (O 2 ), such precursor alloy is dissociated into metal and oxides as the result that the oxyphilic metal species are selectively converted into oxides.The infusion of oxygen atoms from the surface into the bulk of the precursor alloy develops a phase-connected MON comprising a nanometre-thick, interconnected network of metal and oxide (i.e., nanophase separation).9][20] The phase-connected MON materials are, despite the inherent priority of spatial connectedness of materials phases, still precluded from wide use in batteries or fuel cells due to the lack of a guiding principle to tune their phase texture toward maximized performances.
Herein, we report that a hybrid approach consisting of microscopic observations and mathematical simulations allows an understanding and even predictions of the mode of phase textures of MON.In-situ transmission electron microscopy (in-situ TEM) has demonstrated that a layer-bylayer, nanometre-thick (2 through 10 nm) lamella texture of platinum (Pt) and cerium oxide (CeO 2 ) spontaneously emerges out of a precursor alloy of Pt 5 Ce when subjected to an atmosphere consisting of O 2 and carbon monoxide (CO) at temperatures higher than 500 o C. The lower the O 2 fraction concerning the CO concentration, the more sluggish the texture formation and the more folded the phase texture that ranges from lamellae to mazes.Mathematical simulations based on a linearized reaction-diffusion model have shown that either a maze-or lamella pattern tends to emerge when Please do not adjust margins Please do not adjust margins the atomic diffusivity of one of the metal species is in the order of 1/50 or 4/50 compared to that of the counterpart metal species, respectively.This simulation result supports a picture that the atomic diffusion of Ce, which is much sluggish compared to that of Pt across the oxidating Pt 5 Ce alloy, plays a predominant role in the emergence of Pt-CeO 2 MON.This work opens up a route towards a tuned phase texture of MON by controlling the atomic diffusions of the constituent elements of precursor alloys through temperature, alloy composition, and/or the composition of the oxidative atmosphere.

Experimental Section
Pt 5 Ce alloy was obtained by melting ingots of Pt-and Ce metals at a mole ratio of Pt:Ce = 5:1 using an arc-torch in Argon atmosphere to avoid oxidation.The alloy ingot was crushed with a mortar and sieved to collect particles with an average diameter of 50 m.The Pt 5 Ce powder was then cut with a fieldion bombardment (FIB) apparatus down to a thickness of 80 nm.In-situ TEM observation was performed on the thinly cut sample of Pt 5 Ce using JEM-1000K RS TEM (JEOL) at Nagoya University, which was equipped with a specially designed atmosphere-controllable cell.The sample was exposed to a reactant gas consisting of CO and/or O 2 at 200 Pa while the sample temperature was set at 500 0 C throughout the experiments.
A. Turing proposed a mathematical model that mutual reactions between two diffusing components can lead to spatially uneven patterns (i.e., the Reaction-Diffusion (RD) model).[ [21][22] The RD model has been extensively applied to different systems including patterns on the skin of animals, an embryotic emergence of organs, and non-biological systems such as nanophase separation of high-tensile alloys.[ [23][24][25] ] The RD model is generally described as a set of non-linear, timedependent differential equations of two chemical species of u and v: This set of equations can be simplified in the form of a set of linear equations within a rational boundary condition to describe the pattern formation of nanophase-separated alloy systems as follows: where each of the parameters of , , , and is regarded         as constants in the vicinity of the origin of the (u, v) plane.See SI for the derivative of the linearized equation.
Numerical simulations were performed in cubic simulation boxes of 100 x 100 grids using a homemade software that was coded with C. The process of visualization of the simulation images from the mathematical model is described in detail in SI Fig. S1.An array of complex variables was executed to generate different 2-dimensional patterns.A periodic boundary condition was applied to the whole of the simulating area.Both u and v were assumed to depend on time (t) and coordinates (r), and monotonously depend on the concentrations of the chemical species.The coefficients of a v , and b u in eq. 2 denote a reaction of the two metal species comprising the precursor alloy: Pt-and Ce atoms, respectively.

Experimental Results
In-situ TEM has demonstrated that the Pt 5 Ce precursor alloy is separated into different phases when subjected to an oxidative atmosphere, leading to the formation of intricate patterns consisting of different nanophases of Pt metal and Please do not adjust margins Please do not adjust margins cerium oxide (CeO 2 ) (see supplementary videos S2(i) and S2(ii) in SI).Ce metal in Pt 5 Ce is oxidized to develop a CeO 2 phase due to its high oxygen affinity, driving the formation of intricate patterns consisting of Pt metal-and CeO 2 phases.This phenomenon was only observed at temperature 500 0 C and higher, no phase separation was observed at temperature lower than 500 0 C due to lack of energy to initiate oxidation.See supplementary video S2(iii) in SI.
A set of experiments was conducted to investigate the nanophase separation of the Pt 5 Ce alloy, one in a gas mixture of CO and O 2 at partial pressures of 200 Pa and 100 Pa, and the other at partial pressures of 0 Pa and 200 Pa.As can be seen from the snapshots of in-situ TEM in Fig. 1(a.2),lamella pattern emerged when the Pt 5 Ce alloy was exposed to a pure O 2 atmosphere.Continuous supply of O 2 further promoted the nanophase separation that led to a spatially ordered lamella pattern at an emergence rate of 20 nm/sec (Fig. 1(a.3)).In the gas mixture of CO and O 2 , an entangled, maze-like pattern emerged instead of the lamella pattern (Fig. 1(b.2)).CO here acts as an inhibitor and constraints the oxidation rate by intercepting some of the O species on the surface.[ 20 ] By increasing the CO concentration atmosphere, more O species were intercepted which results in a more sluggish, maze-like pattern.Note that the emergence rate of the maze pattern was much lower than that of the lamella pattern: an aliquot of 120 sec was necessary to accomplish the pattern formation, whereas the lamella pattern required only 5 sec (Fig. 1(a.2) and (b.2)).We observed the same trend in simulation where a longer iteration time required to generate maze pattern compared to lamella pattern (SI Fig. S3).eq. 3 Computational simulations were conducted on variable values of the off-diagonal terms of (a u , a v ) and the diffusion coefficients of (D u , D v ), setting the other parameters constant (SI, Fig. S4 and S5).First, we have noticed that the off-diagonal terms in the equation determine the nature of the "reaction" between the chemical species.When both a v and b u are the same in sign, the concentrations of the chemical species monotonously either diverge or converge with increasing time, being accompanied by no pattern formation.Only in the event the off-diagonal terms are different in sign (eq.3), spatially uneven patterns can spontaneously emerge out of a uniform medium due to a competition between the diffusions of mutually reacting chemical species.
We further computed the patterning evolution by considering the different parameters at the same time (Fig. 2).
Figure 2a corresponds to a v = 0.125 and D u = 0.02.With increasing a v from 0.125 while fixing D u , the pattern evolves from isolated spots to a lamella pattern that consists of a parallel array of stripes at a v = 0.150 (Fig. 2b).The warmcolored region diminishes with the increase in a v (Fig. 2c).As seen on the first column of figure 2 that corresponds to a v = 0.125, the spotty phase becomes more highly distributed with the decrease in D u (Fig. 2a, 2d, 2g).Another trend is recognized in the second column of figure 2 that corresponds to a v = 0.15.The lamella pattern (Fig. 2b) is folded (Fig. 2e) with the decrease in D u to develop a maze pattern when D u = 0.002 (Fig. 2h).A similar trend is recognized for the third column of figure 2 that corresponds to a v = 0.20, where the parallel array of broken stripes (Fig. 2c) is folded with decreasing D u values (Fig. 2f) to finally reach a maze pattern (Fig. 2i).
The results of computational simulation demonstrate that spatially connected patterns are generated in a limited range of a v and D u , where D u (0.02 to 0.002) is always 10 times or smaller than D v (0.5).It is acknowledged that Ce atoms diffuse much more slowly than Pt atoms across a given Pt-rich alloy matrix.Please do not adjust margins Please do not adjust margins of an inhibitor for the nanophase separation of Pt-Ce alloy precursor.Indeed, an increased Pt concentration can lower the concentration of the activator for the phase separation, namely, Ce.The diffusion of the fast-diffusing inhibitor, Pt, determines the distance between the two adjacent Pt phases that are separated by the activator, i.e., the Ce phase.
Figure 3 shows a similarity between the simulated patterns and the in-situ TEM images.The computational simulation has demonstrated that either lamella-or maze pattern is generated when the diffusivity ratio for the different chemical species is D u /D v = 0.02/0.50= 1/25 (Fig. 2b) or 0.002/0.50= 1/250 (Fig. 2h).Note that the lamella-and maze patterns emerged in the atmosphere of pure O 2 gas and a mixture gas of CO-O 2 , respectively.See SI Fig. S6 for Scanning Transmission Electron Microscope (STEM) image of lamella pattern formed over a micrometre-sized area.The Ce oxidation not only drives the nanophase separation but also can lead to a rise in the local temperature of the precursor alloy at the propagation front of the Pt-CeO 2 MON.Considering the reducing nature of CO, it is rational to presume that the rise in the local temperature at the propagating front can be in the CO-O 2 atmosphere, leading to slow atomic diffusions.This presumption is supported by the experimental fact that the emergence rate of the maze pattern, 3 nm s -1 , was much slower than that of the stripe pattern, 20 nms -1 (Fig. 1(b.3 and a.3)).The diffusivity ratio steeply increases with lowering temperature according to a widely acknowledged formula: , where   /  ∝ exp ( - , and correspond to the activation energy for the      diffusions of Ce, Pt, and temperature, respectively ( - ).We interpret the dramatic change in the mode of > 0 nanophase separation from the lamella-to maze patterns as a result of the increased diffusivity ratio, which is further attributed to the mitigated Ce oxidation in the CO-O 2 atmosphere.

Conclusions
Through a hybrid approach of computational simulations and in-situ transmission electron observations, we have successfully shed light to the emergence of metal-oxide nanocomposites (MON) from precursor alloys via nanophase separation.The in-situ TEM observation has allowed not only to monitor the emergence of MON but also to quantify the emergence rate of the MON with different phase textures.The simulation has shown that the phase texture of the MON such as a lamella-or maze pattern is predominantly determined by the ratio in the atomic diffusivity of the constituent atoms of the precursor alloy.The computational-experimental hybrid approach reported in this work has opened up a route to tailor the MON material by controlling the diffusivity of the constituent atoms of precursor alloys possibly through tuned temperature, alloy compositions, and/or atmospheres that promote nanophase separation of precursor alloys.

Figure 1 :
Figure 1: Snapshots of in-situ TEM images where lamellae and maze patterns were observed after Pt 5 Ce alloy was subjected to a) O 2 and b) CO: O 2 ; 2:1 environment.Wavefront of phase separation propagation indicated with white broken line.Close view of pattern formed as shown in (a.4) and (b.4) showing lamellae and maze respectively,

[ 26 ]
We assign D u and D v to the diffusion constants of Ce and Pt, and accordingly, the variables of u and v to the local concentrations of Ce and Pt, respectively.The driving force of the nanophase separation of the Pt-Ce alloy precursor is most likely the exothermic oxidation of Ce, which leads to positive feedback of the Ce concentration (u) to both the Ce-and Pt concentrations (v) through the positive parameters of a u and a v , respectively.Note that the feedback from the Pt concentration to the Ce-and Pt concentrations are negligibly small (b v = 0.0) or if any, negative (b u = -0.05),showing that Pt plays the role

Figure 2 :
Figure 2: Patterns obtained from simulation by triggering the reaction and diffusion terms.av value was set to (0.125, 0.15 and 0.2) and D u value was set to (0.002, 0.008, 0.02).All the other parameters were set to constant.

Figure 3 :
Figure 3: simulation images a, b) showing stripes and maze pattern which comparable to the experimental In-Situ TEM.Du = 0.02 and Du = 0.002 and snapshot images of in-situ TEM taken at different conditions c) in pure O 2 and d) CO-O 2 atmospheres.