Abstract: We present two new interatomic potentials for platinum (Pt) in angular-dependent potential (ADP) and modified Tersoff (MT) formats. Both potentials have been trained on a reference database of first-principles calculations without using experimental data. The properties of Pt predicted by the ADP and MT potentials agree better with density functional theory calculations and experimental data than the potentials available in the literature. Future applications of the MT model to mixed-bonding metal-covalent systems are discussed.

Abstract: We present two new interatomic potentials for platinum (Pt) in angular-dependent potential (ADP) and modified Tersoff (MT) formats. Both potentials have been trained on a reference database of first-principles calculations without using experimental data. The properties of Pt predicted by the ADP and MT potentials agree better with density functional theory calculations and experimental data than the potentials available in the literature. Future applications of the MT model to mixed-bonding metal-covalent systems are discussed.

Abstract: We propose a simple parametric form for interatomic potentials of the Embedded Atom Method (EAM-X) for pure FCC metals, and study some of the basic properties as functions of input parameters. With this model, we deviate from the usual approach of fitting a set of functions to basic properties from experiments and/or density functional theory calculations, and then using those functions to investigate more complex properties. Instead, we illustrate here what we term the "inside out" approach, which seeks to understand generically how complex properties are dependent on the EAM-X parameters themselves. This method enables the identification of regions of parameter space that correspond to desirable attributes, and then the possibility of matching that neighborhood of parameters to real elements. A companion paper extends the model (and property studies) to FCC-based metal alloys.

Abstract: We extend our simple parametric form for Embedded Atom Method interatomic potentials for FCC metals [Daw & Chandross, "Simple Parameterization of Embedded Atom Method Potentials FCC Metals"] to treat alloys. Using this model, which we refer to as "EAM-X", we study the generic dependence of alloy properties on the model parameters. We introduce the idea of spread alloys, where the constituent elements are defined as parametric perturbations from a central, "average" FCC metal, and where different alloys are quantified by a measure of the magnitude of the perturbation. As an example, we consider a spread binary where the only differences between the constituent elements are lattice mismatch and the cross-interaction parameters and show that the model robustly describes the clustering and ordering tendencies of metal alloys. We use the model to prove a general theorem of "parametric simplicity" in random equimolar alloys: alloy properties differ from a simple rule of mixtures in a way that depends only on the standard deviation among the constituent parameters but are otherwise not dependent on the number of constituents, consistent with previous theoretical results.

Abstract: Recent molecular dynamics simulations of the growth of [Ni0.8Fe0.2/Au] multilayers have revealed the formation of misfit-strain-reducing dislocation structures very similar to those observed experimentally. Here we report similar simulations showing the formation of edge dislocations near the interfaces of vapor-deposited (111) [NiFe/CoFe/Cu] multilayers. Unlike misfit dislocations that accommodate lattice mismatch, the dislocation structures observed here increase the mismatch strain energy. Stop-action observations of the dynamically evolving atomic structures indicate that during deposition on the (111) surface of a fcc lattice, adatoms may occupy either fcc sites or hcp sites. This results in the random formation of fcc and hcp domains, with dislocations at the domain boundaries. These dislocations enable atoms to undergo a shift from fcc to hcp sites, or vice versa. These shifts lead to missing atoms, and therefore a later deposited layer can have missing planes compared to a previously deposited layer. This dislocation formation mechanism can create tensile stress in fcc films. The probability that such dislocations are formed was found to quickly diminish under energetic deposition conditions.

Abstract: Modified embedded atom method (MEAM) potentials for fcc elements Cu, Ag, Au, Ni, Pd, Pt, Al, and Pb have been newly developed using the original first nearest-neighbor MEAM and the recently developed second nearest-neighbor MEAM formalisms. It was found that the original MEAM potentials for fcc elements show some critical shortcomings such as structural instability and incorrect surface reconstructions on (100), (110), and/or (111) surfaces. The newly developed MEAM potentials solve most of the problems and describe the bulk properties (elastic constants, structural energy differences), point defect properties (vacancy and interstitial formation energy and formation volume, activation energy of vacancy diffusion), planar defect properties (stacking fault energy, surface energy, surface relaxation and reconstruction), and thermal properties (thermal expansion coefficients, specific heat, melting point, heat of melting) of the fcc elements considered, in good agreement with relevant experimental information. It has been shown that in the MEAM the degree of many-body screening (C_min) is an important material property and that structural stability at finite temperatures should be included as a checkpoint during development of semiempirical potentials.

Abstract: A detailed derivation of the simplest form of the effective medium theory for bonding in metallic systems is presented, and parameters for the fcc metals Ni, Pd, Pt, Cu, Ag and Au are given. The derivation of parameters is discussed in detail to show how new parameterizations can be made. The method and the parameterization is tested for a number of surface and bulk problems. In particular we present calculations of the energetics of metal atoms deposited on metal surfaces. The calculated energies include heats of adsorption, energies of overlayers, both pseudomorphic and relaxed, as well as energies of atoms alloyed into the first surface layer.

Abstract: The activation energies for self-diffusion of transition metals (Au, Ag, Cu, Ni, Pd, Pt) have been calculated with the Embedded Atom Method (EAM); the results agree well with available experimental data for both mono-vacancy and di-vacancy mechanisms. The EAM was also used to calculate activation energies for vacancy migration near dilute impurities. These energies determine the atomic jump frequencies of the classic "five-frequency formula," which yields the diffusion rates of impurities by a mono-vacancy mechanism. These calculations were found to agree fairly well with experiment and with Neumann and Hirschwald's "Tm" model.

Abstract: A consistent set of embedding functions and pair interactions for use with the embedded-atom method [M.S. Daw and M. I. Baskes, Phys. Rev. B 29, 6443 (1984)] have been determined empirically to describe the fcc metals Cu, Ag, Au, Ni, Pd, and Pt as well as alloys containing these metals. The functions are determined empirically by fitting to the sublimation energy, equilibrium lattice constant, elastic constants, and vacancy-formation energies of the pure metals and the heats of solution of the binary alloys. The validity of the functions is tested by computing a wide range of properties: the formation volume and migration energy of vacancies, the formation energy, formation volume, and migration energy of divacancies and self-interstitials, the surface energy and geometries of the low-index surfaces of the pure metals, and the segregation energy of substitutional impurities to (100) surfaces.

Abstract: Recent molecular dynamics simulations of the growth of [Ni0.8Fe0.2/Au] multilayers have revealed the formation of misfit-strain-reducing dislocation structures very similar to those observed experimentally. Here we report similar simulations showing the formation of edge dislocations near the interfaces of vapor-deposited (111) [NiFe/CoFe/Cu] multilayers. Unlike misfit dislocations that accommodate lattice mismatch, the dislocation structures observed here increase the mismatch strain energy. Stop-action observations of the dynamically evolving atomic structures indicate that during deposition on the (111) surface of a fcc lattice, adatoms may occupy either fcc sites or hcp sites. This results in the random formation of fcc and hcp domains, with dislocations at the domain boundaries. These dislocations enable atoms to undergo a shift from fcc to hcp sites, or vice versa. These shifts lead to missing atoms, and therefore a later deposited layer can have missing planes compared to a previously deposited layer. This dislocation formation mechanism can create tensile stress in fcc films. The probability that such dislocations are formed was found to quickly diminish under energetic deposition conditions.

Abstract: A detailed derivation of the simplest form of the effective medium theory for bonding in metallic systems is presented, and parameters for the fcc metals Ni, Pd, Pt, Cu, Ag and Au are given. The derivation of parameters is discussed in detail to show how new parameterizations can be made. The method and the parameterization is tested for a number of surface and bulk problems. In particular we present calculations of the energetics of metal atoms deposited on metal surfaces. The calculated energies include heats of adsorption, energies of overlayers, both pseudomorphic and relaxed, as well as energies of atoms alloyed into the first surface layer.

Abstract: We propose a simple parametric form for interatomic potentials of the Embedded Atom Method (EAM-X) for pure FCC metals, and study some of the basic properties as functions of input parameters. With this model, we deviate from the usual approach of fitting a set of functions to basic properties from experiments and/or density functional theory calculations, and then using those functions to investigate more complex properties. Instead, we illustrate here what we term the "inside out" approach, which seeks to understand generically how complex properties are dependent on the EAM-X parameters themselves. This method enables the identification of regions of parameter space that correspond to desirable attributes, and then the possibility of matching that neighborhood of parameters to real elements. A companion paper extends the model (and property studies) to FCC-based metal alloys.

Abstract: We extend our simple parametric form for Embedded Atom Method interatomic potentials for FCC metals [Daw & Chandross, "Simple Parameterization of Embedded Atom Method Potentials FCC Metals"] to treat alloys. Using this model, which we refer to as "EAM-X", we study the generic dependence of alloy properties on the model parameters. We introduce the idea of spread alloys, where the constituent elements are defined as parametric perturbations from a central, "average" FCC metal, and where different alloys are quantified by a measure of the magnitude of the perturbation. As an example, we consider a spread binary where the only differences between the constituent elements are lattice mismatch and the cross-interaction parameters and show that the model robustly describes the clustering and ordering tendencies of metal alloys. We use the model to prove a general theorem of "parametric simplicity" in random equimolar alloys: alloy properties differ from a simple rule of mixtures in a way that depends only on the standard deviation among the constituent parameters but are otherwise not dependent on the number of constituents, consistent with previous theoretical results.

Abstract: The activation energies for self-diffusion of transition metals (Au, Ag, Cu, Ni, Pd, Pt) have been calculated with the Embedded Atom Method (EAM); the results agree well with available experimental data for both mono-vacancy and di-vacancy mechanisms. The EAM was also used to calculate activation energies for vacancy migration near dilute impurities. These energies determine the atomic jump frequencies of the classic "five-frequency formula," which yields the diffusion rates of impurities by a mono-vacancy mechanism. These calculations were found to agree fairly well with experiment and with Neumann and Hirschwald's "Tm" model.

Abstract: A consistent set of embedding functions and pair interactions for use with the embedded-atom method [M.S. Daw and M. I. Baskes, Phys. Rev. B 29, 6443 (1984)] have been determined empirically to describe the fcc metals Cu, Ag, Au, Ni, Pd, and Pt as well as alloys containing these metals. The functions are determined empirically by fitting to the sublimation energy, equilibrium lattice constant, elastic constants, and vacancy-formation energies of the pure metals and the heats of solution of the binary alloys. The validity of the functions is tested by computing a wide range of properties: the formation volume and migration energy of vacancies, the formation energy, formation volume, and migration energy of divacancies and self-interstitials, the surface energy and geometries of the low-index surfaces of the pure metals, and the segregation energy of substitutional impurities to (100) surfaces.

Abstract: Interatomic potentials for Pt-M (M = Al, Co, Cu, Mo, Ni, Ti, V) binary systems have been developed on the basis of the second nearest-neighbor modified embedded-atom method (2NN MEAM) formalism. The parameters of pure Mo have also been newly developed to solve a problem in the previous 2NN MEAM potential in which the sigma and α-Mn structures become more stable than the bcc structure. The potentials reproduce various materials properties of alloys (structural, thermodynamic and order-disorder transition temperature) in reasonable agreements with relevant experimental data and other calculations. The applicability of the developed potentials to atomistic investigations for the shape and atomic configuration of Pt bimetallic nanoparticles is demonstrated.

Abstract: There has recently been a great deal of interest in employing immiscible solutes to stabilize nanocrystalline microstructures. Existing modeling efforts largely rely on mesoscale Monte Carlo approaches that employ a simplified model of the microstructure and result in highly homogeneous segregation to grain boundaries. However, there is ample evidence from experimental and modeling studies that demonstrates segregation to grain boundaries is highly non-uniform and sensitive to boundary character. This work employs a realistic nanocrystalline microstructure with experimentally relevant global solute concentrations to illustrate inhomogeneous boundary segregation. Experiments quantifying segregation in thin films are reported that corroborate the prediction that grain boundary segregation is highly inhomogeneous. In addition to grain boundary structure modifying the degree of segregation, the existence of a phase transformation between low and high solute content grain boundaries is predicted. In order to conduct this study, new embedded atom method interatomic potentials are developed for Pt, Au, and the PtAu binary alloy.

Abstract: Platinum-barium (Pt-Ba) alloy cathodes are promising for magnetron amplifiers due to their high electron emission coefficient and excellent work function. High-temperature deformation characteristics have the utmost importance with respect to these types of metal alloy cathodes. Molecular dynamics (MD) simulations have been carried out to study tensile and creep deformation characteristics of a single crystal BaPt₂ compound using a parameterized embedded-atom method (EAM) potential. The force-matching methodology and an optimization approach using converged density-functional theory (DFT) datasets have been used in this work to parameterize an EAM potential for the Pt-Ba alloy system. A list of fundamental properties, such as density, cohesive energy, and elastic properties, has been investigated via MD simulation, and these properties have been verified with the help of DFT analysis to examine the performance of the potential. Tensile deformation characteristics have been carried out at different temperatures from 300 K to 1600 K for strain rates of 10⁸/s, 10⁹/s, 10¹⁰/s, and 10¹¹/s. Ductile characteristics have been found, as supported by Pugh's criterion. In addition, creep characteristics have been studied at different loads ranging from 100 MPa to 400 MPa for temperatures 0.3 T_m, 0.6 T_m, and 0.8 T_m (i.e., T_m is the melting temperature), where no tertiary region has been observed. Additionally, X-ray diffraction spectra and radial distribution characteristics have also been visualized through MD simulation.

Abstract: The unavailability of embedded-atom method (EAM) potential for the Platinum-Barium (Pt-Ba) alloy system, which is an enticing choice as cathodes for magnetron amplifiers due to their high electron emission coefficient and excellent work function. The parameterization of an EAM potential for this alloy system has been described in part 1 portion. Studying different deformation mechanisms is crucial for these kinds of alloy systems in order to implement them in critical engineering applications. Tensile and creep characteristics have already been reported in part 1, along with the validation of density, cohesive energy, and elastic properties. Here, a list of other fundamental properties, such as lattice constant, surface energy, and lattice thermal conductivity, have been investigated via molecular dynamics (MD) simulation and compared with density-functional theory (DFT) analysis to concretize the accuracy of the potential. Thereafter, MD simulation has been used to study the deformation behavior of single crystal BaPt₂ compound under asymmetric cyclic loading having "R" (stress ratio) of -0.2, -0.4, and -0.6 at different temperatures ranging from 300 K to 1600 K using the parameterized EAM potential. A constant strain rate of 10⁸/s has been used in this present study. Although variations in strain axis are not significant, an increase in ratcheting strain with the increment in temperature and an increase in strain accumulation with the decrease in magnitude of stress ratio have been observed. Strain amplitude decreases and stabilizes at a terminal value, as observed from the strain cycle plot.

Abstract: Graphene-supported platinum (Pt) and palladium (Pd) nanoclusters have attracted attention as electrocatalysts for proton exchange membrane fuel cell (PEMFC) because of their high activity and resistance to CO poisoning. However, metal nanoparticles are weakly adsorbed to the graphene and easily migrate on the surface, causing sintering and loss of chemical activity. A thorough understanding of structure-adsorption relationship is important to design robust catalysts with high adsorption ability to stabilize metal nanoparticles, but this relationship is still not well understood, particularly in large scale systems (2–5 nm). Therefore, to investigate the structural evolution at atomic scale with atomistic simulations, we have developed interatomic potentials for the Pt-C and Pd-C binary systems, based on the second nearest-neighbor modified embedded-atom method (2NN MEAM) formalism. These potentials reproduce various fundamental properties of the alloy systems in reasonable agreement with the experimental data and first-principles calculations. Molecular dynamics simulations employing the 2NN MEAM potential were carried out to analyse structural factors that have decisive effect on the adsorption energy, by changing the symmetry of the nanoparticles and the configuration of the nanoparticles adsorbed to graphene. These factors were characterized via coordination numbers, number of Pt atoms in contact with the graphene and adsorption site. The results of our study suggest avenues for stabilizing and immobilizing metal clusters on graphene in large systems.

Abstract: We propose an analytical interatomic potential for modeling platinum, carbon, and the platinum-carbon interaction using a single functional form. The ansatz chosen for this potential makes use of the fact that chemical bonding in both covalent systems and d-transition metals can be described in terms of the Pauling bond order. By adopting Brenner’s original bond-order potential for carbon [Phys. Rev. B 42, 9458 (1990)] we devise an analytical expression that has an equivalent form for describing the C-C/Pt-Pt/Pt-C interactions. It resembles, in the case of the pure metal interaction, an embedded-atom scheme, but includes angularity. The potential consequently provides an excellent description of the properties of Pt including the elastic anisotropy ratio. The parameters for both the Pt-Pt interaction and the Pt-C interaction are systematically adjusted using a combination of experimental and theoretical data, the latter being generated by total-energy calculations based on density-functional theory. This approach offers good chemical accuracy in describing all types of interactions, and has a wide applicability for modeling metal-semiconductor systems.

Abstract: Interatomic potentials for Pt-M (M = Al, Co, Cu, Mo, Ni, Ti, V) binary systems have been developed on the basis of the second nearest-neighbor modified embedded-atom method (2NN MEAM) formalism. The parameters of pure Mo have also been newly developed to solve a problem in the previous 2NN MEAM potential in which the sigma and α-Mn structures become more stable than the bcc structure. The potentials reproduce various materials properties of alloys (structural, thermodynamic and order-disorder transition temperature) in reasonable agreements with relevant experimental data and other calculations. The applicability of the developed potentials to atomistic investigations for the shape and atomic configuration of Pt bimetallic nanoparticles is demonstrated.

Abstract: Interatomic potentials for Pt-M (M = Al, Co, Cu, Mo, Ni, Ti, V) binary systems have been developed on the basis of the second nearest-neighbor modified embedded-atom method (2NN MEAM) formalism. The parameters of pure Mo have also been newly developed to solve a problem in the previous 2NN MEAM potential in which the sigma and α-Mn structures become more stable than the bcc structure. The potentials reproduce various materials properties of alloys (structural, thermodynamic and order-disorder transition temperature) in reasonable agreements with relevant experimental data and other calculations. The applicability of the developed potentials to atomistic investigations for the shape and atomic configuration of Pt bimetallic nanoparticles is demonstrated.

Abstract: A semi-empirical interatomic potential formalism, the modified embedded atom method (MEAM), has been applied to obtain an interatomic potential for the Fe–Pt alloy system, based on the previously developed potentials for pure Fe and Pt. The potential can describe basic physical properties of the alloys (lattice parameter, bulk modulus, stability of individual phases, and order/disorder transformations), in good agreement with experimental information. The procedure for the determination of potential parameter values and comparisons between the present calculation and experimental data or high level calculation are presented. The applicability of the potential to atomistic studies to investigate structural evolution of Fe₅₀Pt₅₀ alloy thin films during post-annealing is also discussed.

Abstract: Interatomic potentials for Pt-M (M = Al, Co, Cu, Mo, Ni, Ti, V) binary systems have been developed on the basis of the second nearest-neighbor modified embedded-atom method (2NN MEAM) formalism. The parameters of pure Mo have also been newly developed to solve a problem in the previous 2NN MEAM potential in which the sigma and α-Mn structures become more stable than the bcc structure. The potentials reproduce various materials properties of alloys (structural, thermodynamic and order-disorder transition temperature) in reasonable agreements with relevant experimental data and other calculations. The applicability of the developed potentials to atomistic investigations for the shape and atomic configuration of Pt bimetallic nanoparticles is demonstrated.

Abstract: Interatomic potentials for Pt-M (M = Al, Co, Cu, Mo, Ni, Ti, V) binary systems have been developed on the basis of the second nearest-neighbor modified embedded-atom method (2NN MEAM) formalism. The parameters of pure Mo have also been newly developed to solve a problem in the previous 2NN MEAM potential in which the sigma and α-Mn structures become more stable than the bcc structure. The potentials reproduce various materials properties of alloys (structural, thermodynamic and order-disorder transition temperature) in reasonable agreements with relevant experimental data and other calculations. The applicability of the developed potentials to atomistic investigations for the shape and atomic configuration of Pt bimetallic nanoparticles is demonstrated.

Abstract: A new second nearest-neighbor modified embedded-atom model-based PtTi binary interatomic potential was developed by improving the pure Pt unary descriptions of the pre-existing interatomic potential. Specifically, the interatomic potential was developed focusing on the shape memory-associated phenomena and the properties of equiatomic PtTi, which has potential applications as a high-temperature shape memory alloy. The simulations using the developed interatomic potential reproduced the physical properties of the equiatomic PtTi and various intermetallic compound/alloy compositions and structures. Large-scale molecular dynamic simulations of single crystalline and nanocrystalline configurations were performed to examine the temperature- and stress-induced martensitic transformations. The results show good consistency with the experiments and demonstrate the reversible phase transformation of PtTi SMA between the cubic B2 austenite and the orthorhombic B19 martensite phases. In addition, the importance of anisotropy, constraint and the orientation of grains on the transformation temperature, mechanical response, and microstructure of SMA are presented.

Abstract: Interatomic potentials for Pt-M (M = Al, Co, Cu, Mo, Ni, Ti, V) binary systems have been developed on the basis of the second nearest-neighbor modified embedded-atom method (2NN MEAM) formalism. The parameters of pure Mo have also been newly developed to solve a problem in the previous 2NN MEAM potential in which the sigma and α-Mn structures become more stable than the bcc structure. The potentials reproduce various materials properties of alloys (structural, thermodynamic and order-disorder transition temperature) in reasonable agreements with relevant experimental data and other calculations. The applicability of the developed potentials to atomistic investigations for the shape and atomic configuration of Pt bimetallic nanoparticles is demonstrated.

Abstract: Interatomic potentials for Pt-M (M = Al, Co, Cu, Mo, Ni, Ti, V) binary systems have been developed on the basis of the second nearest-neighbor modified embedded-atom method (2NN MEAM) formalism. The parameters of pure Mo have also been newly developed to solve a problem in the previous 2NN MEAM potential in which the sigma and α-Mn structures become more stable than the bcc structure. The potentials reproduce various materials properties of alloys (structural, thermodynamic and order-disorder transition temperature) in reasonable agreements with relevant experimental data and other calculations. The applicability of the developed potentials to atomistic investigations for the shape and atomic configuration of Pt bimetallic nanoparticles is demonstrated.

Abstract: We propose a simple parametric form for interatomic potentials of the Embedded Atom Method (EAM-X) for pure FCC metals, and study some of the basic properties as functions of input parameters. With this model, we deviate from the usual approach of fitting a set of functions to basic properties from experiments and/or density functional theory calculations, and then using those functions to investigate more complex properties. Instead, we illustrate here what we term the "inside out" approach, which seeks to understand generically how complex properties are dependent on the EAM-X parameters themselves. This method enables the identification of regions of parameter space that correspond to desirable attributes, and then the possibility of matching that neighborhood of parameters to real elements. A companion paper extends the model (and property studies) to FCC-based metal alloys.

Abstract: We extend our simple parametric form for Embedded Atom Method interatomic potentials for FCC metals [Daw & Chandross, "Simple Parameterization of Embedded Atom Method Potentials FCC Metals"] to treat alloys. Using this model, which we refer to as "EAM-X", we study the generic dependence of alloy properties on the model parameters. We introduce the idea of spread alloys, where the constituent elements are defined as parametric perturbations from a central, "average" FCC metal, and where different alloys are quantified by a measure of the magnitude of the perturbation. As an example, we consider a spread binary where the only differences between the constituent elements are lattice mismatch and the cross-interaction parameters and show that the model robustly describes the clustering and ordering tendencies of metal alloys. We use the model to prove a general theorem of "parametric simplicity" in random equimolar alloys: alloy properties differ from a simple rule of mixtures in a way that depends only on the standard deviation among the constituent parameters but are otherwise not dependent on the number of constituents, consistent with previous theoretical results.

Abstract: We propose a simple parametric form for interatomic potentials of the Embedded Atom Method (EAM-X) for pure FCC metals, and study some of the basic properties as functions of input parameters. With this model, we deviate from the usual approach of fitting a set of functions to basic properties from experiments and/or density functional theory calculations, and then using those functions to investigate more complex properties. Instead, we illustrate here what we term the "inside out" approach, which seeks to understand generically how complex properties are dependent on the EAM-X parameters themselves. This method enables the identification of regions of parameter space that correspond to desirable attributes, and then the possibility of matching that neighborhood of parameters to real elements. A companion paper extends the model (and property studies) to FCC-based metal alloys.

Abstract: We extend our simple parametric form for Embedded Atom Method interatomic potentials for FCC metals [Daw & Chandross, "Simple Parameterization of Embedded Atom Method Potentials FCC Metals"] to treat alloys. Using this model, which we refer to as "EAM-X", we study the generic dependence of alloy properties on the model parameters. We introduce the idea of spread alloys, where the constituent elements are defined as parametric perturbations from a central, "average" FCC metal, and where different alloys are quantified by a measure of the magnitude of the perturbation. As an example, we consider a spread binary where the only differences between the constituent elements are lattice mismatch and the cross-interaction parameters and show that the model robustly describes the clustering and ordering tendencies of metal alloys. We use the model to prove a general theorem of "parametric simplicity" in random equimolar alloys: alloy properties differ from a simple rule of mixtures in a way that depends only on the standard deviation among the constituent parameters but are otherwise not dependent on the number of constituents, consistent with previous theoretical results.