Advances in Condensed Matter Physics

Volume 2018, Article ID 9383981, 8 pages

https://doi.org/10.1155/2018/9383981

## New Cr-Ni-Base Alloy for High-Temperature Applications Designed on the Basis of First Principles Calculations

^{1}Materials Center Leoben Forschung GmbH, Roseggerstraße 12, 8700 Leoben, Austria^{2}Joint-Stock Company “Kompozit”, Pionerskaya St. 4, Korolev, Moscow Region 141070, Russia

Correspondence should be addressed to V. I. Razumovskiy; ta.lcm@yiksvomuzar.dolovesv

Received 4 January 2018; Accepted 1 February 2018; Published 9 July 2018

Academic Editor: Yuxiang Ni

Copyright © 2018 V. I. Razumovskiy et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

We use ab initio calculations to analyze the influence of 4d and 5d transition metal alloying elements on cohesive properties of the bulk and a representative grain boundary in Cr within the framework of the Rice–Thomson–Wang approach. The results obtained for Cr are combined with the analogous results for Ni to select Ta and Nb as promising alloying additions to dual-phase () Cr-Ni-base high-temperature alloys. Ta and Nb are added to the alloying system of an existing alloy I (Cr-Ni-W-V-Ti) in an attempt to design a chemical composition of a new alloy II (Cr-Ni-W-V-Ti) + (Ta-Nb). Investigation of the microstructure of the Ta-bearing Cr-Ni-alloy reveals a Ta enrichment of large -areas near GBs in -matrix that we consider as potency to increase the cohesive strength of GBs and the cohesive energy of the bulk in -phase. Mechanical testing of alloys I and II demonstrates that the alloy II has improved tensile strength and creep resistance at high temperatures.

#### 1. Introduction

Traditional materials for production of critical components of gas-turbine engines, where significant resistance to loading at high temperatures is required, are Ni-base superalloys [1, 2]. One of the most important performance characteristics of Ni-base superalloys is their creep resistance. In the polycrystalline critical parts, for example, turbine disks [3, 4], one of the weakest elements of microstructure is grain boundaries (GBs). GBs are normally characterized by enhanced diffusivity [5], which leads to increased creep at high temperatures. One can include into the alloying system elements that segregate to GBs and increase their work of separation in order to strengthen GBs and improve their creep resistance. The is a fundamental thermodynamic quantity that controls the mechanical strength of an interface and allows one to study the problem of GB embrittlement from first principles using the Rice–Thomson–Wang model [6, 7]. In accordance with the* low alloying additions* concept [8, 9], the “useful” alloying addictions have to increase simultaneously the cohesive strength of GBs and the cohesive energy of the bulk. By such an approach, Ta, Nb, Zr, and Hf have been predicted to be beneficial alloying addictions to Ni-base alloys and used to design a new polycrystalline Ni-base superalloy for powder metallurgy applications [10].

The main weakness of Ni-base superalloys for high-temperature applications is insufficient corrosion resistance. One of the most effective approaches to improve this is alloying with Cr. Cr-Ni-base high-temperature alloys represent their own type of superalloys [11], which is of great practical importance, for instance, for manufacturing combustion chambers of thermocatalytic engines intended for correction of the orbit and orientation of a spacecraft [12]. Such alloys typically have the following chemical composition: Cr-(31–35)Ni-(1–3)W-(0.1–0.4)V-(0.05–0.3)Ti, wt.% (alloy I, [13]), and they consist of two major metallic phases: (solid solution based on Cr with bcc lattice) and (solid solution based on Ni with fcc lattice). A distinguishing feature of their microstructure is formation of large -phase areas near GBs in -matrix. The deformation behavior of the whole + microstructure in this type of alloys is controlled by -phase due to its high degree of ductility [14].

At first sight, it seems attractive to add the same elements that are beneficial for Ni-base alloys, which are Zr, Hf, Nb, and Ta, also into Cr-Ni-base alloys to obtain stronger GBs in the -phase. However, the influence of the aforementioned elements on the cohesive properties of -matrix remains unknown and data dealing with Zr, Hf, Nb, and Ta influence on mechanical properties of Cr-base alloys are controversial [17]. That is why it is important to investigate an embrittling potency of Zr, Hf, Nb, and Ta in Cr-base solid solutions as well.

In this paper, we investigate first the effect of a number of transition metals including Zr, Hf, Nb, and Ta on the cohesive properties of the bulk -phase and a representative GB in Cr alloys using ab initio calculations. Second, we determine the embrittling potency of 4d and 5d transition metals in Cr alloys in the framework of the* low alloying additions* concept [8, 9]. Finally, we introduce the elements acceptable for both and phases into a typical alloy to fabricate a new Cr-Ni-base alloy and investigate its microstructure and mechanical properties.

#### 2. Computational Details

##### 2.1. Electronic Structure Calculations

Electronic structure calculations have been performed using the projector augmented wave method [18] as implemented in Vienna ab initio simulation package (VASP) [19, 20] with generalized gradient approximation (GGA) [21]. Since the primary interest of the present study is in the cohesive properties of Cr-Ni-base alloys at elevated temperatures, all calculations have been performed at a relevant high-temperature bcc lattice constant of 2.92 Å [22]. As the magnetic moment of the high-temperature paramagnetic phase of chromium has been shown to be zero within the framework of the disordered local moment model (see for instance [23]), we have performed only non-spin-polarized calculations. The convergence accuracy of the total energy has been chosen as 10^{-5 }eV and 9 × 10^{−3} eV/A for the forces. The ionic relaxations have been included in the all types of calculations.

##### 2.2. Semiempirical Calculations

The semiempirical simulations made use of the second nearest neighbor modified embedded atom method (2NN-MEAM) potentials [24] within the LAMMPS environment [25, 26]. These potentials were developed specifically for bcc metals, for which the contribution of the second nearest neighbors is not to be neglected. The simulation cells were set up with the equilibrium lattice constant of the potential; that is, 0 = 2.88 Å. For the relaxations, the Hessian-free truncated Newton algorithm was selected, and the chosen convergence criterion for the relaxation was relative energy changes between iterations of less than 10^{−11} and a 2-norm of the global force vector of less than 10^{-13 }eV/Å.

##### 2.3. Grain Boundary and Free Surface Modeling

A special coincident site lattice (CSL) model GB Σ5 (210) and a free surface (FS) (210) have been used in all DFT calculations as a representative GB and the corresponding surface created after the GB cleavage. The GB has been modeled by a supercell containing 40 atomic layers of Cr (one atom per layer) separated by 7 Å of vacuum as shown in Figure 1. The same supercell, but without GB, has been used for the free surface (FS) calculations. Only substitutional sites have been considered for the GB and surface segregation of 4d and 5d impurities. The 8 × 4 × 2 Monkhorst-Pack [27] -point mesh has been used for GB and FS calculations, whereas the 6 × 6 × 6 mesh has been employed in pure bulk calculations with a 54-atom bcc supercell. The structure of Σ5 (210) GB has been additionally relaxed by shifting two grains in the slab with respect to each other. The found minimum energy structure (shown in Figure 1) has been used in all GB slab calculations.