Effect of alloying on the phase stability and elastic properties of L1 2 Cu 3 Pt crystal structure

. The alloying effect of three elements, namely Al, Cr and Zn, on the Pt site of L1 2 Cu 3 Pt phase was investigated using DFT (density functional theory) based first-principle calculations in attempt to stabilize it in the form of L1 2 Cu 3 Pt 1-x Y x ternary alloy. On the basis of phase stability and elastic properties, the substitution behaviour of all three alloying elements were compared with properties of thermodynamically sluggish Cu 3 Pt phase. The calculated heats of formation reveal that the thermodynamic phase stability is gradually enhanced with increasing content of aluminium alloying and diminished with increasing content of zinc and chromium. In this current work, the stress-strain approach was used according to Hooke’s law to calculate elastic properties such as elastic constants, Young’s modulus E, shear modulus G, bulk modulus B and Poisson’s ratio v, as they play an important role to investigate the resulting mechanical properties. The calculated results show that alloying with all three elements maintains the mechanical stability criteria of cubic crystals. Considered L1 2 Cu 3 Pt 1-x Y x ternary alloys exhibit the most ductile character with Al addition, followed by Cr, whereas introduction of Zn yielded lowest ductility at higher compositions.


Introduction
Lately, the alloys belonging to Cu-Pt system have received immense attention in research due to their importance in earmarked applications such as proton exchange membrane fuel cells (PEMFCs) as catalyst [1][2][3][4] as well as in smart thermoelectric generators (TEG) for harvesting waste energy [5]. It is reported that atomic ordering in Pt-M alloys (M: non-platinum group metals (PGMs) such as Cu, Ni, Fe, Co) improves catalytic performance and stability of the cathode through alteration of surface and electronic structure, resulting in efficient oxygen reduction reaction (ORR) and methanol oxidation reaction (MOR) in which the Pt poisoning resistance and durability is improved [3,6,7]. Recent successes in synthesis of Cu3Pt alloy nanoframes with a core-shell structure which further enhanced the ORR catalytic activity have sparked more interest in the study of bimetallic alloys comprised of PGM and non-PGM [8][9][10][11][12]. This interest stems from the potential applications of such novel materials in energy storage and conversion such as hydrogen storage, hydrogen production, and active fuel cell catalysts [13]. These developments are also positive towards addressing one of the stumbling blocks hindering industrial rollout of fuel cells that use pure Pt as a cathode catalyst, which is its high cost which accounts for at least half of the overall PEMFC manufacturing cost [14].
On the other hand, ordered intermetallics constitute a unique class of materials that form long-range ordered (LRO) crystal structure below a critical temperature that is generally referred to as the critical order-disorder phase transition temperature [15,16]. The interest in such materials emanate from their attractive properties such as high strength, stiffness, stability and oxidation resistance ideal for structural applications at elevated temperatures [15]. The thermodynamic stability of these compounds relates to their high bond strength brought about by ordering. As a result, the lower the thermodynamic stability corresponds to lower order-disorder phase transition temperature because it requires less amount of energy in the form of temperature to weaken the bond. Thus for L12 Cu3Pt alloy to be suitable for structural applications, its thermodynamic stability needs to be increased so that the ordering temperature can be higher than 735 °C, shown in Figure 1. This figure shows the Cu-Pt alloy phase diagram redrawn from Hansen [17]. The literature shows that the Cu-Pt alloy system consists of different phases, a continuous solid solution phase and several ordered intermetallic phases at low temperatures. The Cu-Pt system is the only platinum-based system which takes up a unique long-range ordered rhombohedral L11-CuPt superlattice near 50% wt.% from FCC cubic disordered lattice below 812 0 C Figure 1 [18]. L12-Cu3Pt and one dimensional long-period structure (LPS) have been observed at 30 wt.% Pt composition. The congruent point for the order-disorder transition of the L12-Cu3Pt phase appears around 16 wt.% Pt composition [18]. Additionally, the following phases were described, A1disordered phase, L12-Cu3Pt and L11-CuPt stable phases and L12-Cu3Pt and L10 CuPt metastable phases in the Pt-Cu alloy [18].  [17]. Therefore, the current work aims to investigate the effect of alloying on the phase stability and elastic properties of the L12 Cu3Pt phase using DFT (density functional theory) based first-principle technique. Three elements, namely Al, Cr and Zn were chosen for substitution on the Pt site of L12 Cu3Pt phase from a view-point of increasing stability, strength and 370, 02002 (2022) https://doi.org/10.1051/matecconf/202237002002 MATEC Web of Conferences 2022 RAPDASA-RobMech-PRASA-CoSAAMI Conference oxidation resistance in L12 Cu3Pt1-xYx ternary compositions. The focus is on understanding how alloying affects structural and mechanical properties and identify which alloying element promotes potential use as catalyst or structural material.

Methodology
First principles modelling of L12 Cu3Pt and ternary compositions was carried out using FCC supercells with space group #221(Pm-3m) consisting of 32 atoms and with the following structural compositions: Cu24Pt7Al1, Cu24Pt6Al2, Cu24Pt7Zn1, Cu24Pt6Zn2, Cu24Pt7Cr1 and Cu24Pt6Cr2 to represent 3.125 and 6.25 atomic percent (at. %) of the alloying element. All calculations in this work were performed using densify functional theory (DFT) based CASTEP code embedded in Materials Studio software package [19]. Robust Vanderbilt ultrasoft pseudopotentials [20] were used to describe the ion-electron interaction within the generalized gradient approximation (GGA) [21] of Perdew-Burke-Ernzerhof (PBE) [22]. A plane wave energy cutoff of 500 eV and k-points set of 6x6x6 were sufficient to converge the total energy of the considered systems. Effects of alloying on the phase stability and elastic properties of L12 Cu3Pt1-xYx (Y=Al, Zn, Cr) were determined from the ground-state structures optimized using the Brayden-Fletcher-Goldfarb-Shanno (BFGS) minimization scheme. The convergence criterion of less than 1×10 -5 eV/atom, the maximum residual forces of 0.03 eV/Å, maximum residual bulk stress of 0.05 GPa and maximum atomic displacement of 1×10 -3 Å were utilized.

Phase stability
In order to determine the thermodynamic stability, heats of formation were calculated from equation 1 below: where Cu3Pt1−xYx is the total energy of the alloy, , Cu and Y are the total energies of the ground-state structures of elemental Pt, Cu and corresponding alloying elements. Whereas x and 0.25-x refer to the fractional concentrations of the constituent elements, the total number of atoms in the superstructure is represented by n.

Elasticity properties
The stress-strain relation may be used to distinguish the elastic and plastic regimes of solid materials. The elastic moduli are the fundamental physical parameters which establish the stress-strain relation in the elastic regime. For an isotropic polycrystalline solid, the two independent elastic parameters are the bulk modulus (B) and the shear modulus (G). The ratio of B/G predicts the brittleness of metals depending on the threshold value of 1.75 (ductile if above 1.75). For the cubic structures, only three elastic constants, corresponding to C11, C12, and C44, are independent. The mechanical stability criteria of cubic crystals are given by expressions shown in equation 2, along side other mechanical property expressions in equation 3 with subscripts V, R, and H denoting Voigt, Reuss, and Hill averages, respectively.  Figure 2(b), it is evident that Cr addition leads to sharp reduction in thermodynamic stability while Al addition show the opposite trend in which stability increased. On the other hand, thermodynamic stability remains constant on introduction of Zn. The interpretation of the above stability trend is drawn on the basis that the heats of formation predict the phase to be thermodynamically stable when its value is negative (Hf<0), so a higher phase stability is indicated by the higher negative value. Formation energy of a binary Cu3Pt alloy was calculated to benchmark the formation of ternary alloys in order to determine the effect of doping elements on the platinum-site on the phase stability. Consequently, the current results predict Al addition to be most effective in increasing the thermodynamic stability of L12 Cu3Pt alloy with likelihood to increase the corresponding order-disorder phase transformation temperature [23], thus promoting its viability for being considered for structural applications provided the corresponding mechanical properties are also higher than those of unalloyed binary L12 Cu3Pt alloy.

Elastic properties
The response of a crystal structure to external force is determined by elastic constants, hence in this current work it was important to investigate elastic properties according to stress-strain approach. Figure 3 presents the predicted elastic constants C11, C12, and C44 of L12 Cu3Pt1-xYx compositions plotted against composition of respective alloying element Al, Zn and Cr in (a), (b) and (c), respectively. The effect of alloying trend on these elastic constants is similar for Al and Cr, where there is an initial increase of C11 and C12 at 3.125 at.% composition and a decrease thereafter at 6.25 at.%, whereas C44 increases gradually with increasing alloying elements for all three metals. As shown in Figure 3(b), both C11 and C12 decrease with Zn addition. Of importance is how these elasticity trends impact on the resulting elastic properties, as shown in Figure 4. It follows from Figure 4(a) that although the addition of all three alloying element maintains the mechanical stability criterion given in equation 2, the value of the tetragonal shear modulus (C'), which measures the degree of mechanical stability of a crystal, first drops at 3.125 at.% for all three alloying elements and increase thereafter at 6.25 at.% for Al and Zn while it continues to decrease in the case of Cr. These results suggest higher content of Al and Zn to be effective in increasing the mechanical stability of L12 Cu3Pt alloy. Furthermore, the above proposed ternary alloy compositions show highest Young's and Shear moduli amongst considered ternary compositions but these predicted elastic properties are much lower than those of unalloyed L12 Cu3Pt alloy, as shown in Table I. These moduli are directly linked to material strength. Thus the obtained inferior mechanical propeties of considered ternary compositions do not promote the potential use of these alloys in electrocatalytic applications. These moduli are directly linked to material strength. Therefore a combination as shown in Figure 4(a) and (b) for Al and Zn, the decrease and increase in C' 370, 02002 (2022) https://doi.org/10.1051/matecconf/202237002002 MATEC Web of Conferences 2022 RAPDASA-RobMech-PRASA-CoSAAMI Conference corresponds with increase and decrease in B/GH, which is a measure of ductility. However, this direct correlation is violated in the case Cr. Addition of Zn at 6.25 at.% results in embrittled material. Although the embrittlement noticed in Cu24Pt6Zn2 has a negative consequence on formability using conventional routes, the advent of additive manufacturing (AM) may presents an opportunity in terms of processing this alloy composition. Moreover, as shown in Table 1, this alloy possess the lowest Poisson's ratio, an indication of improved wear properties such as erosion resistance compared to unalloyed binary L12 Cu3Pt alloy. Therefore, despite Cu24Pt6Zn2 composition showing the highest stiffness amongst all considered ternary compositions, it is inferior to unalloyed L12 Cu3Pt, thus rendering studied ternary alloy compositions unsuitable for structural applications.  addition. As a result, current work predicted addition of at least 6 at.% Al to be most effective in increasing the thermodynamic stability of L12 Cu3Pt alloy with likelihood to increase the corresponding order-disorder phase transformation temperature. Alloying with 6 at.% Al and Zn on L12 Cu3Pt1-yXy ternary compositions yielded promising results in terms of mechanical properties, but these properties are inferior to those obtained for binary L12 Cu3Pt alloy. Therefore, since the predicted strength, drawn from Young's and Shear moduli, of all ternary compositions considered in this study is much lower than that of binary L12 Cu3Pt alloy, these ternary compositions are rendered unsuitable for both structural and electrocatalytic applications.