The purpose of this work is to predict elastic and thermodynantie properties of chromium-based alloys based on first-principles calculations and to demonstrate an appropriate computational approach to develop new materials for high-temperature applications in energy systems. In this study, Poisson ratio is used as a screening parameter to identify ductilizing additives to the refractory alloys. The results predict that elements such as Ti, V, Zr, Nb, Hf, and Ta show potential as ductilizers in Cr while Al, Ge, and Ga are predicted to decrease the ductility of Cr. Experimental evidence, where available, validates these predictions. (ProQuest: ... denotes formula omitted.)

INTRODUCTION

In order to reduce environmental emissions in fossil power generation, more efficient energy-generating technologies such as oxy-fuel gas turbines, hydrogen turbines, and syngas turbines are being developed. One common barrier in the development of these different technologies for future energy generating systems is an insufficiency of existing materials at high temperatures (>1,150[degrees]C) and aggressive atmospheres (e.g., steam, oxygen, CO2). Even the highly alloyed and costly nickel-based superalloys do not have the desired properties for these applications since they soften at -1,100[degrees]C. To enable the development of these new technologies, new materials with high strength, good ductility and fracture toughness, and resistance against creep, high-temperature corrosion, wear, and thermal fatigue have been sought.

Alloys of body-centered cubic (bcc) refractory metals with high melting points1,2 are promising candidate materials for these structural applications. For example, the melting points (T^sub m^) of chromium, niobium, and molybdenum are 1,863[degrees]C, 2.469[degrees]C, and 2,623[degrees]C, respectively. In particular, chromium alloys are attractive because they have low density, high thermal conductivity, and high strength at elevated temperatures. Chromium generally forms a dense surface scale of Cr^sub 2^O^sub 3^ that possesses excellent corrosion resistance at high temperatures ( =1,000[degrees]C).3 More importantly, chromium is inexpensive compared to the other refractory metals because it is more abundant. However, its low-temperature (e.g., at room temperature) brittleness and embrittlement from nitrogen contamination at elevated temperatures have prevented it from major engineering applications.4 ("Low temperature" in this report refers to low homologous temperature [e.g., <0.3T^sub m^]). In fact, the lack of low- temperature ductility (e.g., high ductile-to-brittle transition temperature [DBTT]) is a common weakness of some refractory metals, such as chromium, molybdenum and tungsten, and their alloys.5 Therefore, studying how to improve the ductility of refractory metal alloys is important and yet challenging.

There are two main difficulties in developing refractory alloys: first, a lack of basic experimental data on the thermodynamics and mechanical and physical properties of most of these alloy systems, and second, difficulties associated with processing of these alloys. In order to avoid traditional trial-and-error experiments that are also time consuming and expensive, it has become essential to develop theoretical modeling to guide experimental alloy development. Such theoretical modeling can be multiscale in nature, which includes first-principles density functional theory (DFT) calculations, and atomistic, mesoscale, and continuum simulations. Due to their interpretative and predictive capacities, first- principles calculations are widely employed to study alloy lattice stability, interfacial energies, defect structures, etc.6-16 This report presents first-principles calculations on a series of chromiumbased binary alloys for initial screening of alloying elements to improve the intrinsic ductility of chromium.

It is well known that the Poisson ratio is well correlated with ductility of crystalline alloys17,18 and amorphous metals.19,20 The higher the Poisson ratio is, the better ductility the crystalline or amorphous metal has at low temperatures. For example, gold has a Poisson ratio of 0.42 and it has an elongation of 50%; niobium has a Poisson ratio of 0.40 and it has an elongation of 44% at room temperature. Other ductile metals (e.g., silver, palladium, and copper) also have high values of Poisson ratio. In contrast, commonly known brittle metals have low values of Poisson ratio. For example, beryllium has a Poisson ratio of 0.08 and its tensile elongation is only 1 %; chromium has a Poisson ratio of 0.21 and it is very brittle below its DBTT, which is about 150[degrees]C. Similar trends are also observed in wholly or partially amorphous metallic alloys.19,20 Therefore, Poisson ratio is chosen as the first screening tool to gauge ductility in this project. Moreover, it can be evaluated completely from first-principles calculations with virtually no empirical information.

A survey of established chromiumbased binary phase diagrams21 indicates that feasible alloying elements are Ti. V, Fe, Co, Ni. Zr. Nb. Mo, Ru, Rh, Pd, Hf, Ta, W. Re, Os. Ir, Pt. Al. Si, Ga, and Ge. These elements are soluble to varying extents in bcc chromium up to very high temperatures, whereas all other elements in the periodic table exhibit essentially negligible solubility. Therefore, all 22 elements were evaluated as potential substitutional alloying elements in this study. For comparison purposes, the elasticity of pure chromium with 6.25 at.% vacancies was also calculated.

COMPUTATIONAL DETAILS AND METHODOLOGY

The first-principles calculations use the plane-wave code VASP22,23 which solves for the electronic band structure using electronic density functional theory. Projector augmented-wave24 pseudopotentials are used as supplied with VASP. This study uses the PerdewBurke-Ernzerhof25 gradient approximation to the exchange- correlation functional.