Elemental site occupancy in the L12 A3B ordered intermetallic phase in Co-based superalloys and its influence on the microstructure

Accepted Manuscript Elemental site occupancy in the L12 A3B ordered intermetallic phase in Co-based superalloys and its influence on the microstructure P. Pandey, S.K. Makineni, A. Samanta, A. Sharma, S.M. Das, B. Nithin, C. Srivastava, A.K. Singh, D. Raabe, B. Gault, K. Chattopadhyay PII:

S1359-6454(18)30761-4

DOI:

10.1016/j.actamat.2018.09.049

Reference:

AM 14858

To appear in:

Acta Materialia

Received Date: 30 May 2018 Revised Date:

23 September 2018

Accepted Date: 23 September 2018

Please cite this article as: P. Pandey, S.K. Makineni, A. Samanta, A. Sharma, S.M. Das, B. Nithin, C. Srivastava, A.K. Singh, D. Raabe, B. Gault, K. Chattopadhyay, Elemental site occupancy in the L12 A3B ordered intermetallic phase in Co-based superalloys and its influence on the microstructure, Acta Materialia (2018), doi: https://doi.org/10.1016/j.actamat.2018.09.049. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Mo atoms distribution across the γ/γ′ interface

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[100]

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Spatial Distribution Maps (SDMs)

γ/γ′ Lattice mismatch = +0.48%

[100]

γ/γ′ Lattice mismatch = +0.19%

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Elemental site occupancy in the L12 A3B ordered intermetallic phase in Co-based superalloys and its influence on the microstructure P. Pandey1*, S. K. Makineni2*, A. Samanta3, A. Sharma1, S. M. Das1, B. Nithin1, C. Srivastava1, A. K. Singh3, D. Raabe2, B. Gault2, K. Chattopadhyay 1*

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1

Department of Materials Engineering, Indian Institute of Science, Bangalore 560012, India. Department of Microstructure Physics and Alloy Design, Max-Planck-Institute für Eisenforschung, 40237 Düsseldorf, Germany 3 Materials Research Center, Indian Institute of Science, Bangalore 560012, India 2

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*Corresponding Authors: [email protected] (SKM), [email protected] (PP), [email protected] (KC)

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Abstract

We explore the effects of the elemental site occupancy in γ'-A3B (L12) intermetallic phases and their partitioning across the γ/γ' interface in a class of multicomponent W-free Co-based superalloys. Atom probe tomography and first principles density functional theory calculations (DFT) were used to evaluate the Cr site occupancy behavior in the γ' phase and its effect on the

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γ/γ' partitioning behavior of other solutes in a series of Co-30Ni-10Al-5Mo-2Ta-2Ti-xCr alloys, where x is 0, 2, 5, and 8 at.% Cr, respectively. The increase in Cr content from 0 to 2 to 5 at.% leads to an inversion of the partitioning behavior of the solute Mo from the γ' phase (

into the γ matrix (

> 1)

< 1). At 5 at.% Cr, the Cr also has a preference to replace the excess anti-

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site Co atoms from the B-sites. At 8 at.% Cr, the Cr develops an additional preference to replace

Co atoms from the A-sites. These compositional changes in the phases and the site partitioning behavior in the γ' phase are accompanied by an overall decrease in the lattice misfit (δ) across the

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γ/γ' interfaces as measured by high-resolution X-ray diffraction at room temperature. The reduction in misfit triggers a change in morphology of the γ' phase from cuboidal (δ ~ +0.48 % at 0 at.% Cr) to round-cornered (δ ~ +0.34% at 5 at.% Cr) to spheroidal shaped (δ ~ +0.19% at 8 at.% Cr) precipitates. We also observed an increase in the solvus temperature from 1060°C to 1105°C when adding 5 at.% Cr to the alloy. These results on the effects of Cr in Co-base superalloys enables tuning the microstructure of these alloys and widening the alloy spectrum for designing improved high temperature alloys.

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Keywords: L12 A3B Compound; Co-based superalloys; Site occupancy; Partition coefficient; Lattice misfit. 1. Introduction

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Interfaces play a critical role in the mechanical behavior of high-temperature Ni-based superalloys that are used for components in gas turbines and plane engines [1–5]. These often have characteristic γ/γ' microstructures with a low interface energy, coherent interfaces between a solid solution face-centered cubic (fcc)-γ matrix phase and block-shaped L12 ordered γ'

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precipitates [1,2]. The elastic misfit stresses across the γ/γ' interface often controls their high temperature mechanical and coarsening behavior. Suitable alloying and the resulting partitioning

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behavior across these interfaces tunes the lattice misfit between γ and γ' [6–9]. In Ni-based superalloys, the generally observed lattice misfit is negative (i.e.,

<

, where a is the lattice

parameter) across the γ/γ' interfaces and is typical of the order of ~ 0.5% at room temperature [10,11]. Due to the difference in thermal expansion behavior of the γ and γ' phases, the misfit becomes more negative at higher temperatures [12]. The lattice misfit and the associated elastic

stresses influence the phenomenon of γ' coarsening that occurs at high temperatures during

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annealing and hence, the creep behavior of these alloys [13–18]. Recently, a class of Co-based ternary and quaternary alloys ( Co-Al-W and Co-Al-Mo-Ta/Nb) with γ/γ' microstructure has been introduced [19,20]. Addition of transition metals such as W, Mo/Nb, Mo/Ta and their combinations led to stabilization of the phase field containing γ and γ' similar to that observed in

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Ni-based superalloys [21–24]. The γ matrix is a disordered solid solution phase where solutes distribute randomly in the lattice. The γ' phase is an intermetallic ordered phase that form an L12

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lattice of A3B stoichiometry, with A-sites occupying the {1/2,1/2,0} face-centered positions and B-sites the {0,0,0} corner positions. Solute alloying and partitioning alters this strict intermetallic sublattice occupancy of the stoichiometric phase. Optimization of the γ' precipitate volume fraction, stability and shape, as well as the solute content in the γ channels through further alloying with Ni, Ti, Nb, Ru, Ta, Cr, and B, has led to significant improvement in their hightemperature properties and room temperature ductility which is important for manufacturing, maintenance and handling [25–34]. These solutes are accommodated either in the γ matrix and the γ' cuboidal precipitates with their respective preferential partitioning across the γ/γ' interface which altogether allow for tuning the bulk properties of these alloys. 2

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Density functional theory (DFT) calculations and pseudopotential approximation were recently used to predict the site preference of solute atoms in Ni-based superalloys, which assisted the design of improved alloys [35–38]. Atomic-scale compositional measurements by atom probe tomography (APT) supported these alloy design studies [39–41]. For example, in the model Ni-

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Al-Cr alloy, DFT simulations suggested preference of Cr to occupy the B-sites of the L12 ordered γ' phase [35–37]. This preference has been further confirmed experimentally by resolving the solute site occupancy across the γ' {100} lattice planes using spatial distribution maps (SDM) obtained from APT measurements [42,43]. Similar studies showed that even in the

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more complex multicomponent engineering alloy variants, such as in Rene 88, Cr indeed prefers to occupy B-sites in the γ' lattice [44]. Strong γ' stabilizers, such as Ta and W, have been shown

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to replace Cr atoms from the B-sites in the γ' lattice in the case of a Ni-Al-Cr model alloy [45– 50]. These changes in the site occupancy also influence the γ/γ' lattice misfit and thus the transitions in γ' morphology, i.e., either from a more cuboidal to a spherical shape or vice versa [51–53].

Here, we explore the consequences of the systematic addition of Cr to a low-density Co-based superalloy containing cuboidal γ' precipitates (L12 A3B) [24]. APT was used to observe the

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solute site preference by resolving the {100} lattice planes. Actual γ and γ' lattice parameters and the misfit across the γ/γ' phases at room temperature were evaluated by high-resolution X-ray diffraction (XRD) for the heat-treated alloys. The experimentally observed trend in the evolution of the γ and γ' lattice parameters with increasing Cr content were compared with lattice

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parameters estimated for both the γ and γ' phase by first-principles calculations at 0K. Also, the effect of the Cr site occupancy on the stability of the γ' phase was examined by estimating the

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Gibbs free energy for the γ' L12 compounds having stoichiometries near to the experimentally determined γ' compositions at 900°C (aging temperature). Finally, attempts are made to correlate the thermophysical properties of the alloys with the partitioning behavior of the solutes. 2. Experimental

2.1 Alloy preparation and heat treatment Alloys with nominal compositions of Co-30Ni-10Al-5Mo-2Ta-2Ti-XCr (X=0, 2, 5, and 8, all in at. % referred as Cr-0, Cr-2, Cr-5, and Cr-8 respectively), i.e., with systematically varied Cr content, were prepared through vacuum arc-melting in 50 grams batch portions using 99.99% 3

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purity ingredient elements. The ingots were re-melted 8-10 times to form homogeneous compositions. Subsequently, 3 mm (diameter) x 80 mm (height) rods (for TEM studies and microstructural stability analysis) and 3 mm (thick) x 10 mm (width) x 80 mm (height) slabs (for X-ray characterization) were cast from the arc-melted ingot buttons using a water-cooled split Cu

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mold in a vacuum suction casting unit. A field emission electron probe microanalyzer (EPMA, JEOL, JXA-8530F) using both energy and wavelength dispersive spectroscopy (EDS and WDS) detectors was used to measure the compositions of the melted alloys. Table 1 shows the measured compositions.

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The cast rods/slabs were solutionized by isothermally holding at 1250 °C for 25 hours in vacuum (10-5 mbar) followed by immediate water quenching. The solutionized samples were further aged

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under vacuum at 900 °C for 50 hours. For evaluating the microstructural stability at high temperature, the aged samples were vacuum sealed in quartz tubes and annealed in a box furnace at 900 °C for 100, 200, 500, 750, and 1000 hours respectively, followed by water quenching. The samples for metallographic examination were prepared using Si grid papers followed by final polishing in a Vibratory polisher (Buehler's VibroMet 2) using colloidal silica (250 nm)

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solution.

Table 1: Nominal and measured compositions (in at.%) of the prepared alloys along with their

Alloys Designation Cr-0

Nominal Composition (at.%)

Measured Composition (at.%)

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designations.

Co-30Ni-10Al-5Mo-2Ta2Ti

Co-30.5±0.4Ni-9.7±0.3Al-4.8±0.2Mo2.1±0.1Ta-1.9±0.2Ti

Co-30Ni-10Al-5Mo-2Ta2Ti-2Cr

Co-30.2±0.2Ni-9.8±0.2Al-4.6±0.1Mo1.9±0.1Ta-2.0±0.1Ti-2.0±0.1Cr

Cr-5

Co-30Ni-10Al-5Mo-2Ta2Ti-5Cr

Co-30.1±0.2Ni-9.8±0.3Al-4.9±0.1Mo2.0±0.1Ta-2.0±0.1Ti-4.9±0.1Cr

Cr-8

Co-30Ni-10Al-5Mo-2Ta2Ti-8Cr

Co-29.5±0.4Ni-10.4±0.3Al-4.9±0.2Mo2.0±0.2Ta-2.0±0.1Ti-8.0±0.2Cr

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Cr-2

2.2 Scanning and Transmission Electron Microscopy

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Microstructural characterization of the heat-treated samples was carried out in a field-emission scanning electron microscope (SEM, FEI SIRION XL 30) operated at 30 kV in secondary electron mode. Diffraction studies and high-annular-dark-field (HAADF) imaging for the samples were conducted using a 300kV transmission electron microscope equipped with a field

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emission gun (F30, FEI). Specimens for TEM examination were prepared by electropolishing (Fischione, twin jet electro polisher) using an electrolyte of 5 vol.% perchloric acid and 95 vol.% methanol at temperature of -35 °C and at 14 V [54]. 2.3 X-ray Diffraction (XRD)

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The X-ray diffraction measurements for the determination of the lattice misfit between γ and γ' were performed at room temperature using a Rigaku Smart lab high-resolution X-ray

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diffractometer with Cu Kα1 radiation and equipped with Johansson optics to eliminate the Kα2 and Kβ contributions from the anode. Asymmetric theta-2theta scans using a four-circle goniometer in a Eulerian cradle was performed to determine the asymmetric {200} Bragg reflections from the γ and γ' phases at room temperature. Before conducting the theta-2theta scan, the alignment conditions for the in-plane rotation and the lattice inclination (out-of-plane) were determined by performing phi (Φ) and chi (χ) scans, respectively. The diffraction data were

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collected for 0°-360° at a step width of 3° phi (Φ) and a tilting range of 52.5°-57.5° at a step width of 0.1° in the chi (χ) range. The theta-2theta scans were collected for an angular range of 50°- 53° with a scan step of 0.001°and integration time per step of 1°/minute. The peak positions corresponding to γ and γ' were determined by the de-convolution of the measured profile using a

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Fityk peak analysis program.

2.4 Atom Probe Tomography

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Atomic-scale compositional analysis on the phases was carried out using APT. First, electron backscattered diffraction (EBSD) orientation mapping was performed on the aged samples to locate grains with an orientation near to the [100] zone axis. Specimens for APT analysis were then extracted and fabricated from those sites using a dual beam SEM / focused-ion-beam instrument (FEI Helios Nanolab 600) via an in-situ lift-out protocol described in ref. [55,56]. A final cleaning procedure was carried out at 2 kV and 16 pA beam current to remove the regions severely damaged by the high-energy (30 kV) Ga ion beam. The APT measurements were conducted using a LEAP™ 5000XS instrument (Cameca Instruments). Laser pulsing mode operation was applied at a pulse repetition rate of 250 kHz and a pulse energy of 40 pJ. The 5

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specimen’s base temperature was kept at 25 K, and the target detection rate was set to five ions detected every 1000 pulses. Data analysis was performed using the software package IVASTM

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3.8.0.

2.5 Thermal and mechanical properties

Differential scanning calorimetry (DSC, STA449F3 NETSCH) was used to evaluate the γ' dissolution temperature (γ' solvus temperature) of the aged samples during the heating cycle. A

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50 mg sample was heated under argon atmosphere at a rate of 10 K/min till 1300 °C to allow dissolution of the γ' precipitates. After completion of the heating cycle, the sample was cooled to 50 °C at a cooling rate of 10 K/min. The onset of a first endothermic peak in the heating cycle

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corresponds to the γ' solvus temperature. Mass density measurements at room temperature were carried out using Archimedes’ principle following ASTM 311-17 [57]. Vickers hardness values of aged and long-term heat-treated alloys were obtained using a Vickers micro-hardness tester (Future Tech make, FM-800) operated with a load of 0.5 Kg. The volume fraction of the γ' precipitates was evaluated using a manual point count method following ASTM standard E56211 [58]. Low magnification SEM micrographs from at least five different regions were used to

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calculate the γ' volume fractions.

3. Density Functional simulations of γ fcc and γ' L12 structures The simulations of γ fcc and γ' L12 structures close to the experimentally determined

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compositions were performed using ab-initio spin-polarized density functional theory (DFT) based on a plane wave basis set approach as implemented in Vienna ab initio Simulation

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Package (VASP) [59,60]. The interaction between electrons and ions was represented by a pseudo potential using the projected argument wave (PAW) method [61]. In this method, the ion is represented by a frozen core approximation. The exchange-correlation potential of the electron is expressed using a Perdew, Burke, and Ernzerhof (PBE) function in conjunction with a generalized gradient approximation (GGA) [62,63]. A kinetic energy cutoff of 350 eV was used for the electronic wavefunction, and supercells of 3x3x2 (γ' phase-L12 Co3Al lattice) and 3x3x3 (γ phase-Co-fcc lattice) were considered for the present study. The Brillouin Zone was sampled with a 3x3x5 and 3x3x3 Monkhorst-Pack [64] k-mesh for the 3x3x2 and 3x3x3 supercells, respectively. The occupied Kohn–Sham states were smeared according to a Methfessel and 6

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Paxton [65] distribution method using a smearing parameter of 0.2 eV. The structures were relaxed until the force on each atom and the total energy change were < 0.005 eV/Å2 and <104

eV, respectively. The alloys are theoretically modeled by considering quasi-random structure

(SQS) of the constituting elements. SQSs combined with the first principles DFT is a promising

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method for predicting thermodynamic and elastic properties of alloys [66–68]. In this method, the correlation function of an infinite random alloy is mimicked within a finite supercell in such way that the distribution of atoms in the finite supercell is as close as possible to the alloy [69]. The SQSs are generated using the ATAT code [70,71] considering pairs, triplets and quadruplet

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clusters. The chemical potential of Cr is considered as the total energy per atom of its bulk bodycentered cubic (bcc) phase. The enthalpy of formation of a structure is calculated as

(1)

−∑

=

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Δ

where EXtotal, ni, and µi are the total energy of the structure, number of atoms and chemical potential of ith type element, respectively. Here, µi is considered as the total energy per atom of the most stable bulk phase of the ith element.

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The equilibrium volume (V0) of a structure is calculated by fitting a third-order Birch– Murnaghan isothermal equation of state [72–74] ( )=

+

' &

+

' &

"#$ % − 1( ) + #$ % − 1( × #6 − 4 $ % (/ *

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(2)

!

& '

where E and E0 and V are the total energy, constant and instantaneous volumes, respectively.

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The equilibrium lattice parameter of a structure is calculated as = $

1 × '× &

1 &

% , where l1, l2, and

l3 are supercell dimension along x, y, and z-direction, respectively. The total energy at different

volume is calculated by constraining atomic positions at the lattice sites. These calculations were carried out at 0K for the individual γ and γ' phases with their respective stoichiometric compositions, near to the experimentally determined values. The Gibbs free energy for the γ' phase in the different alloys at 900°C (aging temperature) is calculated as:

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γ′

− 3 4 γ′

where

γ′

is the enthalpy of formation which is evaluated from the DFT calculations conducted

(3)

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for the γ' phase. 4 γ′ is the entropy of γ' and for simplification, only the configurational entropy term has been considered here, neglecting the vibrational term. The configuration entropy for the γ'-A3B ordered compounds can be written as 8 9:

(4)



=

∑9@ [ ( > 7 ? = < <

-R

=

= <

> 7 ) + = ( > ? =

=

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∆4γ′67&



> )]

where > 7 , the mole fraction of the ith element in the A sub-lattice sites and > is the mole 4. Results 4.1 Microstructural analysis

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fraction of the ith element in the B sub-lattice sites.

Figs. 1(a-d) show a comparison of secondary electron (SE) micrographs for the alloys with different Cr content (Cr-0, Cr-2, Cr-5, and Cr-8) aged at 900 °C for 50 h. All of the alloys

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consists of a typical duplex γ/γ' microstructure with different morphological transition features of the γ' precipitates as a function of the Cr content. The initial cubic shape of γ' in the Cr-0 alloy gradually evolves into a globular shape for the Cr-8 alloy. The measured γ' volume fraction for the Cr-0 alloy was found to be ~ 62% while for the Cr-2 alloy the value increased to ~ 67% and

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remained similar for the Cr-5 and Cr-8 alloy variants. 4.2 Determination of solute partitioning across the γ/γ' interface and the γ' volume fraction

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The compositions of γ and γ' for the four alloys were determined by APT. Figs. 2(a) and 2(b) show, for comparison, the APT reconstruction of the Cr-0 and Cr-8 alloys. The γ/γ' interfaces are highlighted by iso-composition surfaces encompassing regions in the atomic point cloud containing more than 48 at.% Co. The Ti + Ta atoms (green color) partition to γ'. The γ/γ' interfaces for the Cr-0 alloy are relatively straight but appear curved for the Cr-8 alloy. The partitioning of the solutes across the γ/γ' interfaces were calculated by the equation: =

B

*

C B

(5)

8

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Where,

is the partitioning coefficient of element i, B

i in the γ' and γ phases, respectively.

*

and B are the compositions of element

Table 2 shows the composition values of the γ and γ' phases, respectively, with their respective . In all the four alloys, Ni/Al/Ta/Ti partition into the γ' precipitates (

> 1). In contrast, Cr partitions mainly to the γ phase, with

DE ~

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partitioning coefficients

0.25 for all the three Cr-

containing alloys. Increase in the Cr content of the alloys is reflected in an increase in the Cr composition in both, the γ' and γ phases. The partitioning behavior of Mo is not linear but ~1.25 > 1),

changes with the Cr content. In the Cr-free Cr-0 alloy, it partitions into γ' (

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becomes ~ 1.07 for the Cr-2 alloy and drops to a value even below 1 for the Cr-5/Cr-

while

8 alloys, indicating Mo partitioning into the γ matrix. Fig. 3(a) shows the effects on all solute values as a function of the Cr content in the alloys. Only the

value decreases

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partitioning

from 1.25 for Cr-0 to 0.82 and 0.78 for the Cr-5 and Cr-8 alloys, respectively. Figs. 2(c) and 2(d) show the Mo atoms (red color) across the γ/γ' interface for the Cr-0 and Cr-8 alloys obtained from APT. It is evident that the number density of the Mo atoms in the γ phase is higher with respect to γ' for the Cr-8 alloy compared to the Cr-0 alloy.

Elements

γ'

61.90 25.70 6.17 4.47 0.56 1.20 -

42.32 33.98 11.99 5.54 3.19 2.98 -

K

i

0.68 1.32 1.94 1.24 5.70 2.48 -

γ

γ'

62.38 43.55 23.16 33.75 5.65 12.14 4.00 4.26 0.51 2.84 1.10 2.66 3.2 0.8

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γ

(Cr-2)

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Co Ni Al Mo Ta Ti Cr

(Cr-0)

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Table 2: The average composition of the γ' and γ phases in the investigated alloys after aging at 900 °C for 50 hours, as obtained by APT. (Cr-5) K

i

γ

γ'

(Cr-8) K

i

γ

0.70 55.55 40.54 0.73 51.90 1.46 23.01 34.49 1.50 20.73 2.15 5.90 12.20 2.07 6.01 1.07 6.35 5.23 0.82 4.80 5.57 0.50 2.81 5.62 0.58 2.42 1.29 3.03 2.35 1.26 0.25 7.40 1.7 0.23 14.72

γ'

K

37.50 34.86 13.28 3.74 3.31 3.27 4.04

0.72 1.68 2.21 0.78 5.71 2.60 0.27

i

The composition of the solutes determined from APT was used to estimate the volume fraction of the γ′ and γ phases in each alloy by using the lever rule based on mass balance. The expression can be written as

B J1 − K * L + B K * = BM9 *

N9

(6)

9

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*

are the compositions of solute i in γ and γ' , respectively, and K * is the volume

fraction of γ'. Since the mass density values for γ and γ' are almost identical, there is a negligible

difference between volume fraction and weight fraction, and hence the weight fractions of the

written as: K * = (B 9

N9

− B )/ $B

′

−B %

Fig. 3(b) shows a plot for the values of (B 9

N9

− B ) vs. $B

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elements in the alloy are here taken as volume fractions. After rearranging equation (7), it can be

′

(7)

− B % as well as its linear

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regression analysis (to minimize the errors in composition measurement) that gives the linear gradient which corresponds to K * . The linear gradient values obtained for all the alloys are

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compared with the measured γ' volume fractions obtained from the SEM image analysis in the

Fig. 3(c). The γ' volume fractions from APT and image analysis for all the alloys are in good agreement. The plot shows an initial increase in the γ' volume fraction for Cr-2, while, upon further Cr addition, no significant changes are observed.

4.3 Evaluation of the γ/γ' lattice misfit

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The γ/γ' lattice parameters and their misfit for the aged samples were evaluated using highresolution XRD at room temperature. The diffraction peaks for the asymmetric {200} planes are plotted and compared in Figs. 4(a-d) for Cr-0, Cr-2, Cr-5 and Cr-8, respectively. All the

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asymmetric peaks consist of two overlapping peaks that pertain to the γ' precipitate and the γ matrix phase. The asymmetric shape of the peak is due to the difference in lattice parameters of γ and γ', and the tetragonal distortion of the γ matrix is due to coherency stresses [75,76]. With the

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increase in Cr content of the alloy, the two discernible overlapping peaks for Cr-0 merge almost into a single peak for Cr-8. We note that the angular resolution value (2θ) of the high resolution X-ray diffractometer used in this investigation is 0.008°, which is much lower than the smallest angular split value of 0.1° between the two peaks for Cr-8 alloy. However, the intensities of the peak cannot be compared quantitatively due to the possible presence of textures and the change in structure factors due to change in order parameters. A Pseudo-Voigt function was used to fit the experimental peaks. For the peak fitting, we have taken all the combination of peak fits that could give similarly good fits and have chosen the ones which have the best R2 values. 10

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Figs. 4(a-d) also show insets representing respective HAADF images taken in scanning TEM mode along the [100] cubic zone axis for all the alloys depicting γ' morphological transition with the Cr content. The deconvoluted high-intensity red peak corresponds to γ' precipitate appearing at a lower angle compared to γ matrix peak (blue color) indicating larger unit lattice size for γ'. constrained lattice misfit (δ) between the γ' and γ is defined as [75]

where

*

*

−

and

L/J

*

L

+

are the lattice parameters for γ' and γ matrix.

(8)

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P = 2J

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This results in the positive lattice misfit across the γ/γ' interfaces for all the alloys. The

The measured lattice parameter values for γ' and γ for all the alloys were compared in Fig. 5(a).

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Addition of 2at.% Cr to the alloy (Cr-2) results in the contraction of γ' lattice without significantly affecting the γ lattice parameter. Further addition of Cr leads to the expansion of both the γ' and the γ lattice. It is important to notice that the rate of lattice expansion for the γ matrix is higher than for the γ' precipitates and hence there is a reduction in the overall γ/γ' lattice misfit. The measured constrained lattice misfit evolution with the Cr content was also plotted as shown in the Fig. 5(b). The misfit reduces from + 0.48% for the Cr-0 to + 0.19% for the Cr-8.

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4.4 Thermal Properties and mass densities of the alloys The heating curves for the Cr-containing alloys obtained from DSC are shown in Fig. 6(a). The onset of the first endothermic peak (marked as arrows) corresponds to the start of the dissolution

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of the γ' precipitates and is hence identified as γ' solvus temperature. Fig. 6(b) shows the comparison of the different γ' solvus temperatures for the different Cr containing alloys together with Cr-0, Co-Al-W-based and Ni-based Waspaloy alloys [19,77]. The solvus temperature

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increases first with the Cr content with a peak of 1105°C for the Cr-5 alloy representing an increase of 39°C and decreases with further Cr addition. Fig. 6(c) shows the comparison of the measured mass densities of Cr-0 [24], Cr-2, Cr-5 and Cr-8 with other density values reported for the Co-based and Ni-based superalloys [19,77]. All the Cr containing alloys show lower mass density values in the range of 8.4 – 8.6 gm.cm-3. 4.5 Microstructural Stability The temporal evolution of the microstructures for all the Cr containing alloys after aging at 900 °C is shown as scanning electron micrographs in the Figs. 7(a1-a5), (b1-b5) and (c1-c5) 11

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corresponding to the Cr-2, Cr-5 and Cr-8 alloys, respectively. All the alloys show microstructural stability without any phase decomposition or nucleation of new phases like topologically closed packed (TCP) phases, even after 1000 hours of heat treatment. The change in γ' volume fraction in these alloys with heat treatment time is plotted in Fig. 8(a). The γ′ volume fraction initially

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decreases by ~ 10% until 200 hours of heat treatment for all the alloys and remains similar upon further annealing time.

Fig. 8(b) shows the variation of Vickers hardness (HV) with aging time at 900°C measured at room temperature for the Cr containing alloys. After 50 hours of aging, the Cr-8 alloy shows

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higher hardness (HV ~ 340) than alloys Cr-5 (~325) and Cr-2 (~320). The hardness remains similar for the three alloys even after 1000 hours of heat treatment. This observation shows that

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the present alloys have both considerable microstructural and mechanical stability at 900°C.

5. Discussion

5.1 Effect of Cr and its site preference in the γ' A3B L12 unit cell

The results presented in the preceding sections can be further analyzed to provide insights on the alloying behavior of Co-based superalloys at a fundamental level, in particular on the role of Cr.

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A key result from the current experiments is the change in the partitioning coefficient of Mo (KMo) from 1.24 observed for the Cr-0 alloy to 0.78 for the Cr-8 alloy. However, there was no significant effect of the Cr content on the partitioning coefficients of the other constituents. The

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Cr site preference in the γ' phase can be discussed in terms of the following considerations:

5.1.1 Spatial Distribution Maps (SDM) obtained by APT

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The Cr site preference is identified experimentally in the L12-ordered γ' phase by resolving the {100} lattice planes measured by APT. Figs. 9(a-b) show successive {100} planes occupied by Co + Ni (golden color), Al + Ta + Ti (green color), Cr (violet) and Mo (red) atoms across the γ/γ' interface for the Cr-2 and Cr-8 alloys, respectively. In both the alloys, it is evident that the solutes Co and Cr partition to the γ phase while the solutes Ni, Al, Ta, and Ti partition to γ' phase. The Mo atoms are higher in number density in the γ' phase for the Cr-2 alloy while they are more abundant in the γ phase for alloy variant Cr-8. Fig. 9(c) shows a schematic presentation of the A3B L12 unit cell. Spatial distribution maps (SDM) [78–80] were plotted for the Cr atoms

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in the γ' precipitate perpendicular to the {100} lattice planes for the Cr-2, Cr-5, and Cr-8 alloys as shown in Figs. 10(a-c), respectively. For the Cr-2 and Cr-5 alloys, the average distance between the Cr atoms (from successive peak spacing) is found to be ∼ 0.36 nm, Figs. 10(a-b). This also corresponds to the distance between

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two successive {100} planes in the L12 unit cell shown in Fig. 9(c). In contrast, for the Cr-8 alloy, the SDM shows additional peaks at ~ 0.18 nm. This result provides evidence of Cr site occupancy also in the {200} planes along with the {100} planes. From the L12 unit cell, the {100} planes are the mixed ones (both A and B-sites) while the {200} planes contain only A-

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sites. Thus, from the Cr peak positions in the SD maps, it is clear that the Cr atoms preferentially occupy the B-sites in alloys Cr-2 and Cr-5 while they additionally occupy A-sites in the Cr-8

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alloy along with the B-sites in the L12 A3B unit cell. 5.1.2 The sum of Co and Ni composition in the γ' phase

We next consider the total composition Co + Ni in the γ' phase. Fig. 10(d) shows that the total Co + Ni composition changes from ~ 77.3 at.% for the alloy Cr-2 to ~ 75.03 at. % for Cr-5 and ~ 72.36 at. % for Cr-8. In the Cr-0 alloy, the Co + Ni composition was found to be ~ 76.3 which is

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higher than the expected stoichiometric composition (75at.%) where the Co/Ni atoms occupy only the A-sites of the L12 unit cell. Additionally, in all the alloys, the Ni content in the γ' precipitates remains similar while only the Co content varies. Hence the excess composition of ~ 1.3at.% and 2.3at.% in the Cr-0 and Cr-2 alloys pertains to Co in the γ' phase. This excess Co

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composition is known to enhance the phase stability of the γ' phase in Co-based γ/γ' alloys by shifting the Fermi level towards the pseudogap [24,81,82]. In the Cr-8 alloy, the Co + Ni

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composition drops to a value < 75at.% from 76.3at.% (in Cr-0 alloy). Hence, we can deduce that in the Cr-2 and Cr-5 alloy variants, as also suggested by the SDMs calculated perpendicular to the {100} planes, the Cr atoms occupy the B-sites while in the Cr-8 alloy, Cr atoms additionally occupy the A-sites, thereby maintaining the 3 :1 stoichiometric ratio (A3B). 5.1.3 Estimation of Gibbs free energy values for the γ' at different Cr site occupancy The effect of the Cr site occupancy on the phase stability of the γ' L12 (Co,Ni)3(Al,Mo,Ta) compound was also examined by estimating the Gibbs free energy values (see section 3 for formulation) for the L12 stoichiometries having compositions close to the experimentally 13

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determined values. An excess of 2at.% Co on the B-sites of the L12 unit cell was also included. Fig. 11(a) shows the change in the free energy values with the systematic addition of Cr atoms at different sites (B or A) of the A3B unit cell. In our calculations, three different Cr site preferences have been considered. These are cases where Cr replaces: 1) Mo atoms from the B-

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sites, 2) excess anti-site Co atoms from the B-sites and 3) Co atoms from the A-sites. The stoichiometric compositions were summarized in the Supplementary Tables S1 and S2. The free energy value reduces when a Cr atom substitutes for a Mo atom on a B-site. This results shows that the stoichiometric composition assumes higher stability. With higher Cr composition, an

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additional preference of the Cr atoms to replace the anti-site Co atoms from the B-sites shows lower free energy value compared to the other site occupancies. Upon further increase in Cr

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content, the free energy values indicate that some of the Cr atoms preferentially replace Co atoms from the A-sites in the L12 A3B unit cell. The stability of the γ' stoichiometry hence depends on the Cr site preference behavior and hence its composition in the γ' phase, which increases with the Cr content in the alloy as reported in Table 2.

5.1.4 Evolution of the γ' lattice parameter with the Cr site occupancy behavior

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Fig. 11(b) shows the change in the lattice parameter (estimated by DFT) of the γ' stoichiometry (Co,Ni)3(Al,Mo,Ta) taking into account the Cr site occupancy in either B (Mo and Co anti-sites) or/and A (Co sites) lattice position. The lattice parameter tends to decrease when the Cr atom occupies the B-sites either replacing Mo or the anti-site excess Co atoms, while the lattice

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parameter increases when the Cr atoms tend to replace Co atoms present in the A-sites. The calculated lattice parameters of the hypothetical L12-Co3Al1-xCrx structure (Cr occupying B-sites,

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see supplementary Fig. S1(a)) also shows that the lattice parameter decreases with the increase in the Cr composition. The lattice parameter of the L12-Co3Cr is 3.478 Å, which is lower by ~ 0.1 Å compared to the L12-Co3Al (a= 3.575 Å). This observation indicates that the lattice parameter of γ' will decrease if the Cr atoms occupy the B-sites (Mo or/and excess Co anti-sites). The calculated projected density of state (PDOS) confirms that the hybridization among the Cr-d orbitals and the Co-d orbitals is stronger compared to the Co-d orbitals and the Al-p orbitals (as shown in the supplementary Figs. S2(a-b)). The additional contribution to the reduction of the γ' lattice parameter when the Cr atoms replace the Mo atoms can be attributed to the smaller atomic radius of Cr (140 pm) compared to Mo (145 pm) [83]. 14

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The γ' lattice parameter increases when the Cr atoms replace the Co atoms from the A-sites as the atomic size of Cr is larger than that of Co (135 pm) [83]. It has also been known that the hybridization of nearly free electron sp-orbitals and the transition metal d-orbitals causes the free sp-electrons to move towards the d-orbital [84]. Bader charge analysis of the Co3Al also shows

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that each Co atom gains 1.0 electron and Al loses all its valence electrons (as shown in the supplementary Fig. S3) indicating that the p-orbitals electrons of Al will move towards the Co-d orbitals. Since Cr is less electronegative compared to Co, the Cr atoms also lose ~0.4e irrespective of the lattice site they occupy, as shown in the supplementary Fig. S3. In the Co3Al

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structure, each Al atom has 12 first nearest neighbors of Co atoms while each Co atom has 4 Al atoms and 8 Co atoms as first nearest neighbors. This result indicates that if Cr occupies the A-

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site of the Co3Al, then the Cr will see a positive charge of the Al atoms around it that will create a strong repulsion between the Cr and Al atoms. To reduce the repulsive energy, the lattice parameter of the γ' phase increases with increasing the Cr composition in the A-site of the A3B lattice.

The trend in the evolution of the γ' lattice parameter observed by the X-ray measurements shows a similar contraction of the γ' unit cell for the Cr-2 alloy while it expands when the Cr

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composition in the alloys exceeds a certain limit. We also underline that the absolute values of the γ and γ' lattice parameters, as obtained from the XRD and DFT analysis, cannot be expected to give the same results owing to two reasons: 1) The lattice parameter values and the γ/γ' misfit determined by X-ray diffraction were taken in the real constrained state where the two phases are

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attached to each other. 2) The experimental measurements were taken at room temperature while the DFT simulations reflect the ground states of the two phases. However, when comparing the

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evolution trends of the γ' lattice parameter with increasing Cr site occupancy between the XRD and DFT results we can infer that at low Cr compositions, the γ' lattice parameter decreases when the Cr atoms occupy the B-sites. Above a critical Cr composition, the lattice parameter will increase when the Cr atoms additionally replace Co atoms from the A-sites. The insights on the effects of Cr site substitution obtained from the calculated free energy values of the γ' L12 compounds and the evolution trends of the DFT-calculated and XRD-measured γ' lattice parameters can be summarized as follows: Cr first replace only Mo atoms on B-sites (Cr-2 alloy) that are located on the {100} planes of the L12 unit cell. In the Cr-5 alloy, Cr atoms additionally replace the excess anti-site Co atoms from the B-sites. Beyond a critical Cr 15

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composition in the alloy (such as in the Cr-8 alloy), Cr atoms also replace Co atoms from the Asites along with excess anti-site Co and Mo atoms from the B-sites.

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5.2 γ' Morphological transition with the Cr content in the alloy In the present alloys, the morphological transition, observed with increase in the Cr content, is related to the variation in the lattice misfit across the γ/γ' interface. From the above discussion, this misfit depends on the preference of the Cr site occupancy in the γ' A3B lattice. The XRD measurements show that the γ lattice parameter increases with the Cr composition in the alloy.

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This can be attributed to the accommodation of the larger sized Mo (resulting from the Cr site occupancy in the B-sites containing Mo atoms in the γ' lattice) and additional Cr atoms (due to

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partitioning into the γ matrix relative to γ'). Supplementary Fig. S4 shows similar evolution trend of the γ lattice parameter measured and estimated by XRD (at room temperature) and DFT (0K, for the compositions shown in supplementary Table S3) respectively. Even in the case of the CoAl-W system, it was shown that the partitioning behavior of bigger atoms like Mo and W across the γ/γ' interface affects the lattice parameters of γ and γ' [19,30,85]. Hence, in the Cr-2 alloy, the γ' lattice parameter decreases due to the Cr preference to replace Mo atoms from the B-sites

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while the γ lattice parameter increases due to the accommodation of the replaced larger sized Mo atoms resulting in a reduced lattice misfit. Further Cr addition and its accommodation results in the expansion of the γ lattice at a higher rate than for the γ' that leads to further reduction in the overall lattice misfit across the γ/γ' interface. This effect is reflected as a change in the γ'

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morphology from cuboidal to spheroidal or ellipsoidal with increasing Cr content in the alloys as shown in Figs. 1(a-d). The γ/γ' lattice misfit reduction leads to lessen the strain energy

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contribution to the total free energy and hence, the interfacial energy contribution dominates and the system chooses spherical shaped γ' precipitates to lower its total free energy. Similar observations were well documented in the γ/γ' Ni-based superalloys [9,45,46,48–50,86,87]. 5.3 Thermophysical properties In the γ/γ' based alloys, the dissolution temperature, i.e., the solvus temperature, of the γ' precipitates dictates the high-temperature creep response of the alloy. For the present alloys, we observe that with increasing Cr content up to 5at.%, the solvus point increases from 1066°C to 1105°C followed by a decrease (1095°C) for the Cr-8 alloy. Addition of Cr is known to 16

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destabilize the γ' precipitates in Co-Al-W based alloys. It was shown recently that a correlation exists between the solute partitioning tendency across the γ/γ' interface and the formation enthalpy of the γ' compound [88]. The larger the negative value of the formation enthalpy is, the more stable is the γ' structure, and thus a higher temperature is required for the γ' dissolution.

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Additionally, the solute site preference also governs the γ' formation enthalpy and thus can be responsible for altering the solvus temperature of the alloy. In the Co-Al-W alloys exhibiting a γ/γ' morphology, addition of 2at.% Cr decreases the γ' solvus temperature, and it was shown that the solutes with positive or low negative formation enthalpy (such as Cr, Mn, Fe) values

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partitions to the γ phase and are responsible for lowering the γ' dissolution temperature. The effect of the Cr site occupancy on the stability of the γ' stoichiometric compounds was evaluated

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by estimating their Gibbs free energy values at a temperature of 900°C (The corresponding enthalpy formation values for the L12 compounds were plotted in supplementary Fig. S5). With the addition of 2 Cr atoms to the DFT supercell (~ Cr-5 alloy), the free energy value of the γ' phase is first reduced and then increases again with further Cr increase in the γ' unit cell. Hence, we conclude that the higher solvus temperature for the Cr-5 alloy is related to the increased

6. Conclusions

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stability of the γ' phase.

The following points summarize the outcome of the present work:

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1. All the present Cr containing alloys (Cr-2, Cr-5, and Cr-8) develop a characteristic γ/γ' microstructure upon aging at 900°C. Cr strongly partitions to the γ matrix phase with respect to the γ' phase and does not affect the partitioning of the other solutes except for Mo In the Cr-0 alloy, the Mo partitions to the γ' phase with a segregation ~1.25 > 1 while with increasing Cr content in the alloy

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significantly. coefficient

value of ~0.78 < 1 for the Cr-8 alloy.

reduces to a

2. High-resolution X-ray diffraction at room temperature reveals that the γ/γ' lattice misfit reduces with increasing Cr content, i.e., from + 0.48%, for the Cr-0 alloy, to + 0.19% for the Cr-8 alloy. This results in the change of the γ' morphology from cuboidal (for the Cr-0 alloy) to round-cornered (for the Cr-2 and Cr-5 alloys) to spheroidal shaped (for the Cr-8 alloy) precipitates.

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3. In the γ' phase with its L12 A3B stoichiometry, the Cr content increases with the overall Cr content in the alloy. Additionally, Cr prefers different site occupancies (A-sites and B-sites) as a function of its composition in the γ' phase. The evolution trend of the γ' lattice parameter

B-sites while it expands when the Cr atoms occupy the A-sites.

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(estimated by DFT at 0K) reveals a contraction of the γ' lattice when the Cr atoms occupy the

4. The spatial distribution maps (SDM, probed perpendicular to the {100} planes of the γ' phase by using APT), the variation in total sum of Co and Ni composition in the γ' phase, and the evolution trend of the γ' lattice parameter that was measured by XRD at room temperature

additionally occupy A-sites in the Cr-8 alloy.

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promote a trend of the Cr atoms to occupy the B-sites in Cr-2 and Cr-5 alloy while they

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5. From the estimated free energy values of the γ' L12 compounds, the Cr site substitution behavior with its increasing composition in the alloy can be summarized as follows: Cr first prefers to replace only Mo atoms on B-sites (Cr-2 alloy) that are located on the {100} planes of the L12 unit cell. In the Cr-5 alloy, the Cr atoms additionally prefer to replace the excess anti-site Co atoms from the B-sites. Beyond a critical Cr composition in the alloy (such as in Cr-8 alloy), Cr atoms also prefer to replace Co atoms from the A-sites along with excess anti-

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site Co and Mo atoms from the B-sites.

6. All the Cr containing alloys show γ/γ' microstructural stability at 900°C even after 1000 hours of aging. The alloy with a Cr content up to 5at. % (Cr-5) has a solvus temperature of 1105°C, increased from 1066°C relative to the Cr-free alloy variant.

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7. In summary, the present work shows various trends for microstructural tuning options of new

Co-based superalloys associated with adding Cr. This additional alloy ingredient thus offers

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to tune various microstructural parameters for improving its high temperature properties.

Acknowledgements

The authors would like to acknowledgement the microscopy facility available at the Advanced Facility for Microscopy and Microanalysis (AFMM) center, Indian Institute of Science, Bangalore. The authors are also thankful to the Supercomputer Education and Research center and Materials Research Center, IISc, Bangalore for providing the computation facility. KC is grateful for the financial support from Department of Science and Technology (DST) in the form of J.C. Bose national fellowship. KC also acknowledges the Gas Turbine Materials and

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Processes (GTMAP) programme of Aeronautics Research and Development Board, DRDO for the financial support.

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The authors are grateful to U. Tezins and A. Sturm for their technical support of the atom probe tomography and focused ion beam facilities at the Max-Planck-Institut für Eisenforschung. SKM acknowledges financial support from the Alexander von Humboldt Foundation.

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Figure 1: Scanning electron micrographs of the (a) Cr-0, (b) Cr-2, (c) Cr-5 and (d) Cr-8 alloys taken in secondary electron mode showing two-phase mixtures of γ' and γ with specific transition features in the γ' morphology from a cuboidal to rounded edges and further into spherical shapes. Figure 2: APT reconstructions for the (e) Cr-0 and (f) Cr-8 alloys show relative flat γ/γ′ interfaces for the Cr-0 alloys and more curved interfaces for the Cr-8 alloy. Distribution of the Mo atoms (red color) across the γ/γ′ interface for (g) Cr-0 and (d) Cr-8 alloys.

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Figure 3: (a) Partitioning coefficients (kxγ′/γ = Cxγ′ / Cxγ) of solute elements plotted in the bar graph for the Cr-0, Cr-2, Cr-5 and Cr-8 alloys. (b) Linear regression analysis plots between (Cxnominal - Cxγ) and (Cxγ′ - Cxγ) for Cr-0, Cr-2, Cr-5 and Cr-8 alloys for estimation of γ′ volume fraction. (c) A comparison plot for change in the γ′ fraction with Cr composition in the alloys, as calculated from the APT composition using a lever rule / mas balance and also an image analysis approach applied to experimentally obtained micrographs. Figure 4: Typical asymmetric X-ray diffraction peaks of (200) planes for (a) Cr-0, (b) Cr-2, (c) Cr-5 and (d) Cr-8 alloys, respectively. Peak fitting using pseudo-Voigt function shows two peaks corresponding to γ′ and γ phases. The insets show STEM-HAADF images of the corresponding alloys taken along [100] cubic direction. Figure 5: (a) Change in lattice parameter of the γ′ and γ phases with Cr content for the different alloys, as calculated from X-ray measurements at room temperature. (b) Comparison of lattice

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misfit between γ′ and γ for the different Cr containing alloys, as calculated by X-ray measurements.

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Figure 6: (a) Differential scanning calorimetry heating curves for the different Cr containing (Cr-2, Cr-5, and Cr-8) alloys. (b) Comparison of the γ′ solvus temperatures for the current Cr-0, Cr-2, Cr-5, Cr-8 alloy variants together with Co-9Al-9.8W [19] and Waspaloy [77] alloys. (c) Mass density comparison of the current alloys together with other commercially used Co-based and Ni-based superalloys [19,77].

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Figure 7: (a1) - (a5), (b1) – (b5) and (c1) - (c5) Scanning electron micrographs taken in secondary electron mode for alloys Cr-2, Cr-5 and Cr-8. The images reveal the temporal evolution of the microstructure during heat treatment at 900 °C.

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Figure 8: (a) Change in γ′ volume fraction with aging time at 900°C for the different Cr containing alloys (Cr-2, Cr-5, and Cr-8) calculated from SEM image analysis. (b) Vickers hardness (HV) vs. aging time for the Cr containing alloys (Cr-2, Cr-5, and Cr-8) at 900°C. Figure 9: Planar APT reconstructions showing the atomic planes along the [100] crystallographic direction for the (a) Cr-2 and (b) Cr-8 alloys. (c) A schematic of the A3B type L12 ordered lattice showing a mixed type of atoms (face centered A atoms in golden color and corner B atoms in green) on the {100} planes which are 0.36nm spaced and only face centered A atoms on the {200} planes.

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Figure 10: Spatial distribution maps obtained from the successive {100} planes of the (a) Cr-2 (b) Cr-5, and (c) Cr-8 alloys along the [100] direction. (d) Variation in the composition of Co + Ni in the γ' phase.

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Figure 11: (a) Plot of variation in Gibbs free energy values for the γ′ phase with different Cr site occupancies as shown in the table. (b) The change in lattice parameter of the γ′ precipitate as estimated by first-principles calculations with different Cr site occupancies.

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Figure 1: Scanning electron micrographs of the (a) Cr-0, (b) Cr-2, (c) Cr-5 and (d) Cr-8 alloys taken in secondary electron mode showing two-phase mixtures of γ' and γ with specific transition features in the γ' morphology from a cuboidal to rounded edges and further into spherical shapes.

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Figure 10: Spatial distribution maps obtained from the successive {100} planes of the (a) Cr-2 (b) Cr-5, and (c) Cr8 alloys along the [100] direction. Variation in the composition of (d) Co + Ni in the γ' phase

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Figure 11: (a) Plot of variation in Gibbs free energy values for the γ′ phase with different Cr site occupancies as shown in the table S1 (see supplementary file) . (b) The change in lattice parameter of the γ′ precipitate as estimated by first-principles calculations with different Cr site occupancies.

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Figure 2: APT reconstructions for the (a) Cr-0 and (b) Cr-8 alloys show relative flat γ/γ′ interfaces for the Cr-0 alloy and more curved interfaces for the Cr-8 alloy. Distribution of the Mo atoms (red color) across the γ/γ′ interface for the (c) Cr-0 and (d) Cr-8 alloys.

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Figure 3: (a) Partitioning coefficients (kxγ′/γ = Cxγ′ / Cxγ) of solute elements plotted in the bar graph for the Cr-0, Cr-2, Cr-5 and Cr-8 alloys. (b) Linear regression analysis plots between (Cxnominal - Cxγ) and (Cxγ′ - Cxγ) for Cr-0, Cr-2, Cr-5 and Cr-8 alloys for estimation of γ′ volume fraction. (c) A comparison plot for change in the γ′ fraction with Cr composition in the alloys, as calculated from the APT composition using a lever rule / mas balance and also an image analysis approach applied to experimentally obtained micrographs.

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Figure 4: Typical asymmetric X-ray diffraction peaks of (200) planes for (a) Cr-0, (b) Cr-2, (c) Cr-5 and (d) Cr-8 alloys, respectively. Peak fitting using pseudo-Voigt function shows two peaks corresponding to γ′ and γ phases. The insets show STEM-HAADF images of the corresponding alloys taken along [100] cubic direction.

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Figure 5: (a) Change in lattice parameter of the γ′ and γ phases with Cr content for the different alloys, as calculated from X-ray measurements at room temperature. (b) Comparison of lattice misfit between γ′ and γ for the different Cr containing alloys, as calculated by X-ray measurements.

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Figure 6: (a) Differential scanning calorimetry heating curves for the different Cr containing (Cr-2, Cr-5, and Cr-8) alloys. (b) Comparison of the γ′ solvus temperatures for the current Cr-0, Cr-2, Cr-5, Cr-8 alloy variants together with Co-9Al-9.8W [19] and Waspaloy [76] alloys. (c) Mass density comparison of the current alloys together with other commercially used Co-based and Ni-based superalloys [19,76].

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Figure 7: (a1) - (a5), (b1) – (b5) and (c1) - (c5) Scanning electron micrographs taken in secondary electron mode for alloys Cr-2, Cr-5 and Cr-8. The images reveal the temporal evolution of the microstructure during heat treatment at 900 °C.

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Figure 8: (a) Change in γ′ volume fraction with aging time at 900°C for the different Cr containing alloys (Cr-2, Cr-5, and Cr-8) calculated from SEM image analysis. (b) Vickers hardness (HV) vs. aging time for the Cr containing alloys (Cr-2, Cr-5, and Cr-8) at 900°C.

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Figure 9: Planar APT reconstructions showing the atomic planes along the [100] crystallographic direction for the (a) Cr-2 and (b) Cr-8 alloys. (c) A schematic of the A3B type L12 ordered lattice showing a mixed type of atoms (face centered A atoms in golden color and corner B atoms in green) on the {100} planes which are 0.36nm spaced and only face centered A atoms on the {200} planes.