Structure and tensile properties of Mx(MnFeCoNi)100-x solid solution strengthened high entropy alloys

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Structure and Tensile Properties of Mx (MnFeCoNi)100-x Solid Solution Strengthened High Entropy Alloys Dongsheng Wen , Chia-Hsiu Chang , Sae Matsunaga , Gyuchul Park , Lynne Ecker , Simerjeet K. Gill , Mehmet Topsakal , Maria A. Okuniewski , Stoichko Antonov , David R. Johnson , Michael S. Titus PII: DOI: Reference:

S2589-1529(19)30335-7 https://doi.org/10.1016/j.mtla.2019.100539 MTLA 100539

To appear in:

Materialia

Received date: Accepted date:

6 November 2019 17 November 2019

Please cite this article as: Dongsheng Wen , Chia-Hsiu Chang , Sae Matsunaga , Gyuchul Park , Lynne Ecker , Simerjeet K. Gill , Mehmet Topsakal , Maria A. Okuniewski , Stoichko Antonov , David R. Johnson , Michael S. Titus , Structure and Tensile Properties of Mx (MnFeCoNi)100-x Solid Solution Strengthened High Entropy Alloys, Materialia (2019), doi: https://doi.org/10.1016/j.mtla.2019.100539

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Structure and Tensile Properties of Mx(MnFeCoNi)100-x Solid Solution Strengthened High Entropy Alloys Dongsheng Wena, Chia-Hsiu Changa, Sae Matsunagaa, Gyuchul Parka, Lynne Eckerb, Simerjeet K. Gillb, Mehmet Topsakalb, Maria A. Okuniewskib, Stoichko Antonovc, David R. Johnsona, Michael S. Titusa a

School of Materials Engineering, Purdue University, West Lafayette, IN, 47907, USA

b

Brookhaven National Laboratory, Nuclear Science and Technology Department, Upton, NY

11973-5000, USA c

Beijing Advanced Innovation Center for Material Genome Engineering, State Key

Laboratory for Advanced Metals and Materials, University of Science and Technology Beijing, Beijing 100083, China

Abstract Complex concentrated alloys represent the idea that alloys and materials need not be based on one or two principal elements. Instead, there exists an enormous and unexplored composition space, which enables the development of new materials. However, this vast composition space is difficult to efficiently investigate due to the high degree of compositional freedom and high experimental cost required to measure material properties, such as the yield strength. Integrating computational models with selected experiments is thus essential for the rapid exploration of this enormous compositional space. To validate a recently-developed solid solution strengthening model, we have investigated a family of facecentered-cubic (FCC) quaternary-based Mx(MnFeCoNi)100-x alloys (M = Al, Cu, Cr, Mo, Ti, and V). By employing the Voce hardening law and stress relaxation experiments, the solidsolution strengthening for various alloys was quantified. To accelerate the discovery process of CCAs, an approach combining strength predictions, phase stability predictions, and experiments is proposed.

Keywords: High entropy alloys; Mechanical properties; Solute strengthening; Face-centered cubic crystals; Thermodynamic stability

1. Introduction 1

Traditional alloys, although containing multiple elements, are typically based on one or two principal elements with others added to improve their mechanical properties, corrosion resistance, and processability, among other properties. Complex concentrated alloys (CCAs), on the other hand, are not composed of a single principal element, and the number of principal elements is usually greater than four. Since the introduction of the high entropy alloy concept and multi-principal element alloys [1,2], metallurgists have begun exploring multicomponent alloys. The rich range of composition and microstructures offers a wide variety of promising mechanical properties in numerous alloy classes [1–7]. For example, it has been found that refractory CCAs (e.g. NbMoTaW) exhibit a high compression strength at 1600 ˚C [4] and 3d transition metal CCAs (e.g. CoCrFeMnNi [2,5,8]) exhibit good ductility and toughness via targeted modification of microstructures, all of which suggest their applicability as a new generation of structural materials. These promising discoveries with limited trials imply that in the vast composition space of CCAs, it is possible to discover materials with improved mechanical properties over traditional alloys and to tailor material properties to specific applications. The process of discovery, however, is complicated by the multi-dimensional nature of the alloy compositions: the alloys can (1) comprise of many alloy families with (2) numerous compositions within a family. Therefore, to accelerate the search for potential alloys with enhanced mechanical properties, an integrated computational and experimental approach is required. Laplanche et al. [8] proposed that, in solid solution alloys, the enhanced strength of a material is the cumulative results of different strengthening mechanisms: (Eq.1) in which

,

, and

represent the Hall-Petch effect, solid solution strengthening, and

forest strengthening, respectively, and

is the average grain size of the alloy. This is similar

to the flow stress superposition principle by Kocks [9], who decomposed the flow stress into yield stress and strain hardening. In the post-yielding region, forest hardening (or strain hardening) is mainly due to dislocation-dislocation interactions during multiplication of dislocations. The superposition of strengths in Eq.1 is the framework of constructing the strength of an alloy family based on its composition and microstructure. To predict the yield strengths of a single-phase, well-annealed, solid solution alloy, only and

are considered. Since the Hall-Petch relation is well established and widely

used to account for grain size hardening, successful yield strength predictions rely on a good

2

understanding of the solid solution strengthening. Based on the underlying idea of solute fluctuations proposed by Labusch [10,11], and a quantitative binary alloy model developed by Leyson et al [12], Varvenne et al. [8,13–15] proposed a solid solution strengthening theory of random alloys based on interactions between dislocations and solute atoms. By incorporating the concept of misfit volume to describe lattice distortion, it envisions that all solute in the average media contribute to the misfit volume according to their concentration in the average medium, which further interacts with the pressure field of curved dislocation lines [13,14]. One advantage of the model is that the misfit volume is a function of the alloy composition, which enables researchers to study different alloy classes [8,15,16]. Several reported CCAs/HEAs have validated the reliability of the abovementioned solid solution strengthening model, including Cantor’s alloy family and its Al-containing variations and some noble element HEAs such as PdPtRhIrCuNi [13–17]. Therefore, to extend the predictive power of the simplified Labusch-type strengthening model proposed by Varvenne et al. [13], we focus on the energy barriers and the activation volumes of solid solution strengthened alloys based on a family of 3d transition CCAs – Mx(MnFeCoNi)100-x alloys with M = Al, Cu, Cr, Mo, Ti, and V. In this paper, with an aim to accelerate the discovery and development process, a method to integrate a strength prediction model with thermodynamic databases is presented. This study systematically employs the strengthening frameworks to investigate the Mx(MnFeCoNi)100-x (M = Al, Cu, Cr, Mo, Ti, and V). The alloys studied here are variations of Cantor’s alloy family, solid solution strengthening effect of each alloying element can be applied to similar alloys. In addition, studying the solid solution strengthening in this MnFeCoNi family with alloying perturbations will help us fulfill the theoretical framework within the solid solution strengthening of CCAs. Below, we first describe the general strength prediction framework. We next present the experiments regarding activation volume determination and elastic constants of the alloys. We compare our results of experiments and predictions with respect to the solid solution strengthening and provide further analysis. Finally, we present our method to accelerate the discovery of new single-phase solid-solution CCAs by combining thermodynamic predictions of phase stability and solid solution strengthening diagrams. The method will provide a guideline to discovering new single-phase solid solution CCAs.

2. Framework of Strengthening of CCAs

3

The contributions to the strength of CCAs can be expressed as additive effects of intrinsic strength hardening

, solid solution strengthening

, grain-size effect

, and forest

, which is given by [8]: Δ

Δ

𝑔𝑏

d

Δ

(Eq.2) Each contribution is outlined below. 2.1. Intrinsic strength The intrinsic strength accounts for the Peierls barrier of the average alloy and leads to the intrinsic critical resolved shear stress of the CCAs. It has been known that Peierls stresses of FCC materials are usually 10-3 to 10-4 of their shear modulus [18,19] and that the values are estimated to be magnitude of one to several MPa [13,15]. 2.2. Grain size effect The grain size effect of the alloy can be described with the Hall-Petch equation that the increase of strength is related to the average grain size, : 𝑘

𝑔𝑏

√𝑑

0

(Eq.3) where 𝑘 is the grain size coefficient [20,21]. Note that the constant of the

Δ

0

is implicitly comprised

terms from Eq. 2.

2.3.Forest hardening Forest hardening,

, is the micromechanics of work hardening that only contributes

after yielding. It is believed that once a gliding dislocation cuts through the forest formed by a dislocation network (Frank network), jogs will be created and thermal activation is required to overcome the barriers [22]. The strengthening model of forest hardening can be expressed as: 𝑀𝛼𝜇𝑏√𝜌 (Eq.4) where M is the Taylor factor (3.06 for polycrystalline materials) [23], the parameter 𝛼 is the interaction coefficient that represents the dislocation-junction strength in the dislocation network, and 𝜌 is the dislocation density [24].

4

2.4. Solid Solution Strengthening The formulation of the solid solution strength is based on the Labusch model further developed by Leyson, and then generalized by Varvenne [10–13]. The LLV model envisions the weak-pinning events of random solutes to the dislocations and regards a random alloy with n components as an average matrix in which every element contributes to the distortion of the matrix. This contribution of misfit volume is computed using the concept of atomic misfit volume: ∑ in which

*

̅

̅

+

(Eq.5)

represents the mismatch between the solute n and the average matrix, ̅ is the is the concentration of the mth species. For simplicity, we

volume of the average alloy, and

̅ , in which

apply Vegard’s Law to the averaged volume, and Eq.5 becomes: is the atomic volume of pure element n.

To estimate the elastic solute-dislocation interaction, dislocations are considered to be in a quasi-sinusoidal configuration to minimize its total self-energy [13]. Thus, the elastic interaction energy of a single solute atom and a sinusoidal dislocation can be expressed as the product of the stress field of the dislocation at the site

,

and the misfit

volume created by the solutes: (Eq.5) This elastic picture is robust for a variety of systems and allows researchers to compute the pressure field arising from the dislocation by first-principles calculations with lower computational costs [13,14]. A full discussion of the theory can be found in the reference [13,14], and its application to some random FCC high entropy alloys has been reported in later works [8,15,16]. Important approximations of the theory were made by Varvenne et al. [13,14] to the study of FCC alloys with low intrinsic friction. To predict the yield strength contributed by solid solution strengthening, we apply the rewritten expressions of zero-temperature yield stress and thermal activation energy barrier [15] to the materials of interest: 0

𝛼

𝜇̅

𝛼

𝜇̅ 𝑏

̅

∑

̅

𝑏

(Eq.6) 𝑏

̅ ̅

∑ 𝑏

(Eq.7)

5

in which 𝜇̅ , ̅ and 𝑏̅ are the averaged shear modulus, Poisson ratio, and Burgers vector, calculated with the rules-of-mixtures: 𝜇̅ = ∑ respectively, where 𝜇

𝜇 , ̅ =∑

, and 𝑏̅ = ∑

𝑏 [13],

and 𝑏 are the respective pure element properties. The factors

0.01785 and 1.5618 arise from the dimensionless pressure field of core structure of the edge dislocation separated into two Shockley partials. Stacking faults with separation distances larger than 10 𝑏 were observed in Cantor’s alloy [25]. Varvenne et al. have shown that these two coefficients are suitable for a wide range of separation distance [13]. The dislocation line tension parameter, α, is set to 0.123 obtained from the atomistic simulation of FeNiCr alloy [13]. It should be noted that accurate determination of α is challenging and 0.123 is applicable to a wide range of CCAs related to Cantor’s family [13]. At a given temperature T and strain rate ̇ , the thermal activation of dislocation glide influences the yield stress according to: ̇

𝑘

0

̇ ̇

(Eq.8) in which ̇ is the experimental strain rate, 0̇ is reference strain rate, and 𝑘 is the Boltzmann constant. Eq.8 is the historical solid solution strengthening that applies to medium to high [14,26,27]. Multiplying Eq.8 by the Taylor factor, 𝑀, yields the

yield strengths (

solid-solution strength for polycrystalline materials: 𝑀

̇

To calculate the yield stress for an alloy with the model above, the misfit volume

(Eq.9) and the

elastic constants of alloying elements are required at the temperature of interest.

3. Experimental and Analysis Methods

3.1. Materials and Characterization Mx(MnFeCoNi)100-x (M=Al, Cu, Cr, Mo, Ti, and V) CCAs ingots (400g) were vacuum induction melted and cast in Cu molds from >99.9% pure elements. Small ingots (10g) used for preliminary analysis were also prepared by arc melting in flowing Ar. The ingots were then homogenized, cold rolled, and annealed to prepare metallographic and tensile test specimens. The heat treatment parameters are listed in Table 1. Differential thermal analysis (DTA) was conducted on cylindrical specimens with 3 mm in diameter and 5 mm in height

6

cut from the arc-melted buttons using wire electrical discharge machining (EDM). A scanning rate of 5 K/min under ultra-high purity Ar atmosphere with an empty reference crucible was used to determine onset melting and freezing temperatures of all alloys. Oxide layers and the EDM heat affected zone were removed via mechanical grinding before DTA experiments. The onset melting temperatures of the Mx(MnFeCoNi)100-x alloys are provided in Section 1 of the supplementary document, according to which the homogenization temperature and annealing temperature were determined. X-ray diffraction (XRD) and scanning electron microscopy (SEM) were employed to analyze the fully annealed samples regarding their structural information and microstructures. Lattice parameters were obtained from XRD patterns using Bruker D8 Focus X-ray diffractometer. Regression analyses were used for unit cell refinement to obtain lattice constants. At least four reflections were input to UnitCell [28] to determine the lattice constants from diffraction data. Detailed material fabrication and characterizations can be found in ref. [29].

Table 1. Homogenization and annealing parameters of CCAs M6(MnFeCoNi)94 Alloy MnFeCoNi Al6 (MnFeCoNi)94 Cr6 (MnFeCoNi)94 Cu6 (MnFeCoNi)94 Mo6 (MnFeCoNi)94 Ti6 (MnFeCoNi)94 V6 (MnFeCoNi)94

Homogenization Temperature (oC) 1150 1150 1150 1150 1150 1050 1150

Annealing Temperature (oC) 1150 1150 1150 1050 1150 1000 1150

Annealing Time (min) 3,6 and 9 3,6 and 9 3,6 and 15 3,6 and 9 3,6 and 9 3,6 and 20 3,6 and 15

3.2. Determination of Tensile Properties To prepare samples for tensile tests, a 30 mm x 20 mm x 5 mm slab was first cut from the center of the as-cast ingot for each alloy. The slab was homogenized at the designed temperature (Table 1) for more than 48 hours followed by water quenching. The slab was then cold-rolled to 90% reduction in thickness. Dog-bone shaped tensile samples with a 10 mm gauge length were fabricated by wire EDM with their loading direction parallel to the rolling direction. The tensile samples were then annealed to recrystallize the microstructure at desired temperatures and times (annealing parameters in Table 1) to achieve various grain sizes. The specimens were ground with 800 grit SiC paper, and the final thickness and width were approximately 0.5mm and 2.5mm, respectively. Tensile tests were carried out under a constant strain rate of 10-3 s-1. The elongations of the specimens were measured by the cross-

7

head displacement. The yield strengths of the alloys were obtained from the 0.2% offset strain extrapolation. For each engineering stress-strain curve, the true stress-strain curve was calculated from the relation: engineering quantities,

and

( ), in which

is the real-time elongation of the sample gauge, and

and 0

are the

is the initial

gauge length. To determine the Hall-Petch coefficients in Eq.3, the averaged grain size of each alloy were determined from the micrographs obtained from the SEM or optical microscope. Three micrographs were taken for each alloy, and three random straight lines were drawn on each micrograph to determine the number of grains intercepted. The averaged grain size was calculated through the length of the straight line over the number of grains intercepted. To determine the activation volumes, repeated stress relaxation tests were performed [30] by holding the applied load for 30 s five consecutive times at a variety of strains. The activation volumes of the alloys were determined with the stress-relaxation data. Guiu and Pratt [31] observed and derived the logarithmic relationship between time, apparent activation volume, and the stress drop of the stress relaxation. The stress drop relation is given by: ̇

0 𝑘 𝑘

(Eq.10) is the change of true stress, t is relaxation time, S is the stiffness of the machine-sample assembly, and ̇ is the strain rate used in the tensile test. The apparent activation volumes,

,

were calculated using the above relationship to fit the first set of stress relaxation data. Apparent activation volumes have been shown to be related to the physical activation volume, , with the relationship [32]: (

)

(Eq.11) is the correction of activation volume, and Θ is the work-hardening rate, dσ/dε,

in which

in the stress-plastic strain curve. The stress-strain response can be fitted with the Voce Hardening Law from the stress-plastic strain data [33,34]: ( )

0

(

)*

(

)+

(Eq.12) where σ0, σ1, θ1 and θ0 are four key fitting parameters. The work hardening rate, Θ, is then determined by the derivative of the stress curve with respect to plastic strain

. More details 8

of the fitting and the application of the Voce Law are provided in Section 4 of the supplementary material, where the fitting parameters are tabulated in Table S5. In addition to Voce Law, the determination of the physical activation volume can be carried out with the repeated stress-relaxation experiments [30,35], which requires the correction of activation volume, 0 𝑘 ̅̅̅̅

(

, through successive stress-relaxation experiments:

(

)

(

)

)

(Eq.13) represents the nth stress relaxation. In this

where n is the number of repetitions and

method, the repeated relaxation data was used to determine the activation volume by determining the average drop of stress through ̅̅̅̅

∑

, in which

is the total

number of stress relaxation steps. By plotting the right hand side of Eq.13 against n,

was

calculated from the slope of the linear relationship and V was determined by Eq. 12. The physical activation volume is generally expressed as

with G being the

total activation free enthalpy and σ the applied stress. With more than one type of dislocation obstacle, such as solute atoms and dislocation forests, materials exhibit a linear relationship between

and the flow stress [36]. In other words, the additive effect of solid solution

strengthening and forest hardening in the plastic region leads to the physical activation volume, which is given by [36]:

(Eq.14) where

and

are the activation volumes of solid solution strengthening and forest

hardening, respectively. From the LLV model,

can be estimated via the activation energy

of a dislocation that only interacts with solute atoms during activation process [13]. The energy barrier,

𝑏,

of solid solution strengthening represent the energy required to activate

the dislocation to cross the barrier. Then 0

can be evaluated via [8,13]:

(when

(Eq.15) in which theoretical The variable

𝑏

and

have been determined through Eq.6 and Eq.7, respectively.

is associated with the area swept by the dislocations that cut through

dislocation networks [22]. Thus,

scales with 𝑏

√𝜌 , where 𝑏 is the Burgers vector

9

magnitude,

represents the length scale overcome in the activation process, and

√𝜌 is the

length of the dislocation. Combining it with Eq.4, we can write: 0

𝑏

0

Δ 𝜌

Δ 𝜌

(Eq.16) 𝛼𝜇𝑏 . We combine the Eq.14, Eq.15 and Eq.16 to obtain:

with

𝜌

0

0

(Eq.17) which yields the well-known Haasen plot by plotting post-elastic region

vs. the increase of stress in the

. The linear relationship between

and

shows that

its slope is associated with forest hardening while its intercept with the y-axis relates to solid solution hardening. 3.3. Atom Probe Tomography The absence of precipitates and/or short-range ordering in the annealed materials was confirmed via atom probe tomography (APT). APT samples were prepared from several alloys using a Zeiss Auriga® focused ion beam. The microtips were polished with Ga+ ions down to a ~80 nm radius using a final energy of 5 kV and a current of 16 pA. APT was conducted using a CAMECA LEAP® 5000 XR local electrode tomograph (with a reported detection efficiency of 52%) equipped with a picosecond ultraviolet (wavelength of 355 nm) laser. The tips were analyzed in laser pulse mode with a pulse repetition rate of 200 kHz and 30-40 pJ laser pulse energy. The base temperature was set to -243°C (30 K), and evaporation rate of up to 1.0% was used. The data was analyzed using IVAS 3.8.2 software from CAMECA Instruments Inc. 3.4. Synchrotron X-ray Diffraction Higher-resolution synchrotron X-ray diffraction measurements were performed at the Xray Powder Diffraction (XPD) beamline (28-ID-2) at the National Synchrotron Light SourceII (NSLS-II). Two-dimensional (2D) diffraction patterns were collected by a large-area, twodimensional detector (Perkin-Elmer). The Perkin-Elmer detector, installed perpendicularly to the direction of the incident x-ray beam, had 2048 x 2048 pixels, with pixel sizes of 200 µm in both the x and y dimensions. The energy of the incident X-rays was 66.1 keV with a beam size of 0.5 mm wide by 0.5 mm high. Lanthanum hexaboride (LaB6) was used as a calibrant

10

to refine the sample-to-detector distance and tilts of the detector with respect to the X-ray beam. The calibrated sample-to-detector distance was 1564 mm. The integration process was conducted using the xpdtools package [37]. The samples were spun during the measurements in order to minimize the detector saturation due to the presence of large grains. Nine to fourteen measurements which have higher diffraction intensity compared to other scans were taken in twenty-one uniquely different areas of the sample and then subsequently averaged and fit. A dark current image was subtracted from the specimen image. Also, the undesirable areas of the 2D image, which included the beam stop and dead pixels, were masked, therefore removing them from the analysis. Additionally, a measurement of the empty sample holder with a Kapton tape was obtained separately and utilized for background subtraction. Pawley refinement was performed to calculate lattice parameters by using the software package GSAS-II [38,39]. Synchrotron XRD was performed on all the fully-recrystallized M6(MnFeCoNi)94

alloy

alloys

and

three

processing/testing

conditions

of

the

Ti6(MnFeCoNi)94 alloy: (1) fully annealed, (2) cold-rolled at 90% thickness reduction, (3) cold-rolled, annealed, and post tensile deformed at around 50% true strain. 3.5. Elastic Constants Determination The elastic constants of the M6(MnFeCoNi)94 were determined through resonant ultrasound spectroscopy (RUS) with a pulse-echo transducer configuration. A small piece of metal was cut from the homogenized slab and cold-rolled to a thickness thinner than 3 mm, which was then annealed to fully recrystallize the microstructure. An effective area of 12mm by 12mm was guaranteed for the RUS measurements. The first three echoed peaks were used to calculate the velocities of the longitudinal and transverse pulses. More details of the method and calculations can be found in the reference [40].

3.6. Phase Diagram Calculation Phase diagrams of the alloys were calculated with Thermo-Calc software using the CALPHAD method and the TCFE8, TCHEA1, and TCNI8 databases [41,42]. By comparing the predicted solidus and liquidus temperatures of the alloys with the experimentally measured values by DTA (see supplementary Figure S1 for details), it was found that the TCFE8 database provided the most reliable and accurate phase equilibria predictions for Al-, Ti- and Mo-containing alloys, and TCNI8 provided reliable predictions for Cr-, Cu-, and Vadded alloys. For alloying elements ranging from 0 to 10 at.%, the predicted solidus and liquidus temperatures from TCFE8 exhibited reasonable agreements with the experimental 11

results (Figure S1). The pseudo-ternary diagrams were built for all the alloys at the annealing temperature given in Table 1 under ambient pressure. To group the elements into pseudoternary diagrams, three schemes were used: (1) FeCo-NiMn-M, (2) FeMn-CoNi-M, and (3) FeNi-CoMn-M, in which grouped elements were always kept with a 1:1 ratio and M represents the quinary alloying elements.

3.7. First-Principles Calculations Density Functional Theory (DFT) calculations were carried out to estimate the lattice constant and bulk modulus of the base alloy MnFeCoNi. The random alloy distribution was modeled by a special quasi-random structure (SQS) [43] supercell using the Alloy Theoretic Automated Toolkit (ATAT) [44]. The ideal random distribution of elements was achieved by minimizing the correlation functions up to 2nd neighbors of quadruplets. The SQS supercell is provided in the supplementary Figure S3 and Table S1, and the correlation functions are tabulated in Table S2. DFT calculations were performed using the Vienna Ab-initio Simulation Package (VASP) [45,46]. Projector augmented-wave (PAW) method was used to approximate the core electron-ion interaction [47,48], and the exchange-correlation was described by the generalized gradient approximation (GGA) parameterized by Perdew et al. [49]. Spin polarization was considered for Mn, Fe, Co, and Ni, and the initial magnetic moments were initialized to 2, 2, 2, and 1, respectively. The kinetic energy cutoff was set to 500eV, sufficient to achieve good convergence. A high degree of freedom (cell shape, cell volume, and ionic positions) was first allowed in the geometric relaxation, followed by an additional static run to achieve high accuracy. The k-point mesh was generated using the Monkhorst–Pack method with four nodes along each basis vector in the Brillouin zone [50]. The partial occupancies of electron orbitals were set using the second order MethfesselPaxton scheme with a smearing width of 0.2 eV [51]. Calculations were considered converged when energy difference between two subsequent steps in the self-consistent loops fell within 0.001 eV per cell. Equilibrium lattice constants and bulk modulus were obtained by fitting the Murnaghan equation of states to a series of energy-volume data ranging from 30% to + 30% of the converged cell volume and calculated with static settings [52,53]. 4. Results and Discussion

4.1. Physical Properties and Microstructure

12

The lattice parameters of all alloys ranged from 3.595 – 3.615 nm, as shown from the example spectrum in Figure 1 (a) and lattice constant vs. alloy concentration plot in Figure 1(b). The lattice constants obtained from both table-top (filled markers) and synchrotron XRD patterns (open markers) were comparable (Figure. 1(b)). Vegard’s law was invoked using elemental lattice constants from the ab-initio calculations to predict the alloy lattice constants. The theoretical lattice constants of pure elements were acquired from the Materials Project [54] according to which the first-principles calculations [55] were performed with the starting structural information from the inorganic crystal-structure data-base (ICSD) [56]. The Vegard’s law agreed well with the XRD measurements that most predictions fall within 0.5% of the measured values, as shown in Figure 1(b). All lattice constants were observed to increase with increasing alloying concentration except for Cr additions.

Figure 1. (a) XRD pattern of a fully annealed Al6(MnFeCoNi)94 sample; (b) Lattice constants of Mx(MnFeCoNi)100-x measured by Table-top (closed markers) and synchrotron (open markers) XRD. Error bars are of magnitude of 1e-3 and are not visible with the length scale of the plot. The solution-annealed M6(MnFeCoNi)94 alloys exhibited a single FCC microstructure with no second phase detected after annealing. For example, the XRD pattern of the Al6(MnFeCoNi)94 alloy in Figure 1(a) shows that all peaks belong to an FCC solid solution. The SEM back scattered image of Al6(MnFeCoNi)94 (Figure 2(a)) also indicates no observable chemical inhomogeneity nor secondary phases. Similar results were seen in other alloys, whose microstructures are shown in Figure 3. Equiaxed grains with some twins were observed in the materials after annealing. Three to five oxide/carbide inclusions with

13

diameters of about 1 μm were observed per image with the same scale of Figure 2(a), which was considered trivial in the alloy. By comparing the synchrotron diffraction data and the lattice parameters of Ti6(MnFeCoNi)94 samples after three different treatments (cold rolled, annealed, annealed + tensile deformed), the alloy maintained an FCC structure under different experimental conditions, showing no signs of phase transformation and precipitate formation (Figure S4 and Table S4).

Figure 2. (a) Back-scattered SEM image of the Al6(MnFeCoNi)94 alloy after annealing 15mins at 1150˚C; (b) APT elemental frequency distribution analysis along with a 3D reconstruction showing all elements in a Al6(MnFeCoNi)94 needle.

14

Figure 3. Back-scattered SEM images of (a) MnFeCoNi, (b) Ti6(MnFeCoNi)94, (c) V6(MnFeCoNi)94, (d) Cr6(MnFeCoNi)94, (e) Cu6(MnFeCoNi)94, and (f) Mo6(MnFeCoNi)94. The absence of nm-scale precipitates and clustering was confirmed by frequency distribution analysis [57] using the reconstructed APT data, as shown in Figure 2(b). The binomial curves (solid lines in Figure 2(b)) represent a random distribution accounting for random chemical fluctuations, while the bar plots represent the actual elemental frequency distribution of the APT data binned in 100 ion sized bins (10 and 200 ion bins were also evaluated). The absence of any tails in the frequency distribution, as compared to the random curves, signifies that no lean or rich region can be detected within the detection limits of the 15

APT reconstruction, and thus the elemental distribution can be deemed as a random single phase solid solution. The means of the random normal distributions of each element are comparable to the nominal targeted values, as shown in Figure 2(b). The lack of clustering can also be visually observed within the example inset image of the 3D reconstruction of the atom probe tip in Figure 2(b). The single FCC phase in the MnFeCoNi and Al6(MnFeCoNi)94 alloy at the annealing temperature was also predicted by thermodynamic modeling using the TCFE8 database, as shown in Figure 4 (a) to (c). The single-phase regions of FCC solid solution were observed in the lower, MnFeCoNi-rich portions of the pseudo-ternary phase diagrams. Similar thermodynamic predictions were obtained for the other investigated alloys (See Section 6 in the supplementary document).

Figure 4. Phase diagrams of Alx(MnFeCoNi)100-x at the annealing temperature (1150˚C): (a) FeCo-NiMn-Al, (b) FeMn-CoNi-Al, and (c) FeNi-CoMn-Al pseudo ternary alloys, unit of axis: at. %. In (a)-(c) red circles represent MnFeCoNi and black diamonds represent Al6(MnFeCoNi)94. 4.2. Tensile Properties

16

The

post-yielding

tensile

true

stress-strain

responses

of

MnFeCoNi

and

M6(MnFeCoNi)94 (M=Al, Cu, Cr, Mo, V and Ti) alloys exhibited typical behaviors of annealed solid solution alloys, as shown in Figure 5(a). The materials exhibited significant strain upon straining from 0 to ~25 % plastic strain. Repeated stress-relaxation experiments at a variety of strains were performed to determine the activation volumes as a function of strain in each of the M6 alloys. An example of the stress-relaxation procedure was shown in Figure 5(b), in which the stress was recorded as a function of time during the consecutive relaxations with constant applied loads. The noises in the stress-strain curves above approximately 500 MPa were due to the load frame and were not associated with the material response. The stress-strain responses in Figure 5(a) were smoothened with a Savitzky–Golay filter [58] to avoid confusion with the dynamic strain aging, which has been observed in some HEAs upon straining [59–65]. Unlike dynamic strain aging that occurs with a wide range of plastic strain and identifiable patterns, the serration-like noises cannot be reproduced in the low-strain region or in the samples with coarser grains (yield stresses are lowered). The data without smoothening is provided in Figure S5 (a). All the data acquisitions stopped before 25% of strain and below the ultimate strengths, which were observed near 60% strain. The work hardening rate for each alloy was fit with the plastic stress-plastic strain response (Figure S5) using Eq.12, and the values of the work-hardening rate, Θ = dσ/dε, were determined at the strains where the stress-relaxations were performed.

Figure 5. (a) The stress-strain response of MnFeCoNi and M6(MnFeCoNi)94 high entropy alloys (M = V, Ti, Mo, Cu, Cr). (b) Repeated stress-relaxation experiments at desired strains is plot as a function of time.

17

Before interpreting the magnitude of the solid solution strengthening, the grain size hardening effects were subtracted from the yield strength. Grain size hardening was determined from individual tensile tests for each alloy with three different grain sizes resulting from various annealing times defined in Table 1. Hall-Petch hardening coefficients were determined by fitting the yield strength vs. linearly proportional to

plots in Figure 6. The yield stress is

, and the size-independent term at

to the solid solution strengthening, Δ

mainly correspond

(as intrinsic friction is only a magnitude of 1 to

several MPa). With the 6 at.% addition, all the alloying elements except Cr increased the yield strength over the MnFeCoNi alloy at

.

The slopes of the curves show that Ti- and Cr-containing alloys exhibited a strong dependence on grain size, with Hall-Petch coefficients (k) of 700 MPa μm-1/2 and 370 MPa μm-1/2, respectively, while other additions slightly increased the Hall-Petch coefficient (150MPa μm-1/2) of the base alloy. The considerable increase of Hall-Petch coefficient, was also reported in Cu-Ti solid solution alloys compared with Cu-Zn and Cu-Ni alloys [66]. This could be due to the increased strength of dislocation obstacles (grain boundary) or shear modulus with increasing Ti content [66]. From the elastic constants determined by RUS, 6 at.% addition of Ti slightly increased the shear modulus of the base alloy from 75 GPa to 78 GPa, and Cr slightly decrease the modulus to 74 GPa. Therefore, it is more likely that Ti and Cr strengthened the grain boundary. Such an increase of grain boundary strength can be related to the composition enhancement at the interface. However, we do not have direct evidence from the SEM or APT results nor does the literature. If composition enhancement occurred at the grain boundaries, the extent of enhancement was not strong because APT results showed that compositions of alloying elements were close to nominal compositions.

18

Figure 6. Grain size effect with different alloying elements Al, Cu, Co, Cr, Mo, V, and Ti.

The physical activation volumes for different alloys are shown in Figure 7 at various strains. The results show good agreement between the Voce Law and the repeated stressrelaxation corrections (see Figure S7). Error bars were added to the data by propagating the initial uncertainties in the measurements (stresses, strains, temperatures) to the calculated quantities (fitting parameters, apparent activation volume, and physical activation volume) using Eq.10 to Eq. 14. The alloys exhibited a decreasing activation volume with increasing plastic strain, corresponding to an increase of dislocation density at larger strains. This is consistent with the formulation of forest hardening, Eq.4 and Eq.16, where the length of pinned dislocation segments decreases with increasing dislocation density [8,22]. This also indicates that at the beginning of plastic deformation, the dislocation density is low, and solute-dislocation interactions dominate at low strains [8,67]. With the theoretical framework of Eq.17, the solid solution contribution to the activation volume remains unchanged during the plastic straining while the forest hardening

scales with √𝜌 according to Eq.4.

Therefore, it is expected that the activation volume decrease with increasing strains following a Hollomon-type relation 𝐴

𝐵𝜖

[68], where A, B, and n are fitting parameters. As shown in

Figure 7, the activation volumes were higher than 500 𝑏 at the beginning of the plastic deformation for most alloys. Employing Eq.16, if we consider that the activation process occurs at a length scale (

of the order of 𝑏, a rough estimation of the dislocation density

at the beginning leads to some value between 1012 to 1013 m-2, comparable to that of the Cantor alloy at room temperature [67]. And at around 20% strain, the activation volumes dropped to around 150 to 300 𝑏 for the alloys, leading to densities higher than 1014 m-2. As 19

shown in Figure 5(a), such 20% strain contributed more than 200MPa to the flow stresses of all the alloys.

Figure 7. Physical activation volume for different alloys as a function of true plastic strain. Error bars are added by comparing the results determined by propagation of the uncertainties in the experiments and the symbols encompass error bars for some data points. 4.3. Solid Solution Strengthening The effect of each alloy addition on the solid solution hardening can be understood through the construction of a Haasen plot, as shown in Figure 8. By plotting the evolving against the flow stress that the energy barrier,

, the linear relationship follows Eq.17. It should be noted 𝑏,

refers to the solute obstacles, and that the term 0

relates to the solid solution hardening and does not depend on the flow stress

solely .

Therefore, changes to the y-intercept of in the Haasen plot for each alloy compared to the base MnFeCoNi alloy directly corresponds to changes in the solid solution strengthening of additional elements in the alloy. The energy barrier can then be quantitatively determined for each alloy using the solid solution hardening, Δ Eq.7, because Δ 𝑏,

, determined from earlier. From Eq.6 and

̇ increases with both the 0K yield stress,

0,

and the energy barrier,

quantitative comparisons can be made between different alloys with respect to their

energy barrier values. The experimentally-determined energy barriers are tabulated in Table 2. Δ Δ

, and

represent experimentally determined solid solution stress contribution and energy

barrier. Since FCC metals usually exhibit low Peierls stress, with a magnitude of

20

approximately 1MPa and a yield stress to shear modulus ratio of 10-4~10-3 [11,17] due to low stacking fault energy, solid solution strengthening dominates, and the Peierls stress is therefore neglected here in the analysis. The solid solution strength and energy barrier of the base MnFeCoNi alloy were 138 MPa and 1.63 – 1.87 eV, respectively. The experimentallydetermined solid-solution strength was lower in the base alloy compared to all of the M6(MnFeCoNi)94 alloys, while the experimentally-determined energy barrier of the base alloy was determined to be near the average barrier values of all M6(MnFeCoNi)94 alloys. The solid solution strength increased for all M6(MnFeCoNi)94 alloys and increased the most (by 61 MPa) for the Mo6(MnFeCoNi)94 alloy. The solid-solution strength for the alloys followed the trend, from highest to lowest increase of solid solution strengthening of: Mo > Ti = Cu ~ Al > V > Cr. The solid solution strength has been proposed to depend on the Δ (Mo > Ti > Al > Cr > Cu > V from Figure 1(b)) and 𝜇 (Cu > Ti > Cr > Base > Al from Table 3). While the trend of increasing solid solution strength qualitatively follows the trend of increasing the misfit volume, it is clear that multiple factors influence the final solid solution strength. According to Eq.6 and Eq.7, increasing the shear modulus, Poisson’s ratio or misfit volume will increase both the zero-temperature yield stress and the thermal barrier. Table 3 tabulates the shear modulus and Poisson’s ratio determined by RUS. Mo and Ti increase the strength because they increase both the misfit volumes and elastic constants in the alloy. The contributions to strengths from Cr and V become less effective because their lattice constants and Poisson’s ratios are more or less equivalent to the base alloy. For the Al-containing alloy, although the misfit volume created by Al atoms is large, it does not contribute to the shear modulus of the MnFeCoNi so that its strengthening effects become moderate. As an opposite, Cu increases the shear modulus of the base alloy but the contribution to the strength is limited by the misfit volume.

21

Figure 8. The Haasen plot of MkT/V versus flow stress σ-σy indicates the solid solution strengthening at the y-intercept and a slope corresponding to forest hardening.

4.4. Comparisons to the LLV Solid Solution Strengthening Model To compare and contrast the experiment and theory, the theoretical solid solution strengths, energy barriers, and activation volumes of the new alloys were determined with different inputs. The input properties include atomic volume ( ) and elastic constants (

,

) of element n in the alloy. With a purpose to inform future researchers that care should be taken to treat these inputs, we present the influences of different inputs on the predicted results and possible improvements by employing three input schemes. (1) Both atomic volume and elastic moduli were determined by first-principles calculations (DFT), the predicted results are denoted by the subscript ―DFT‖ (i.e. Δ

, and Δ

in Table 2).

These inputs listed in Table 6 were obtained from the Materials Project [54], according to which the elastic constants were determined using DFT stiffness matrix and Voigt averaging scheme. (2) Using the same elastic constants as the first scheme, the inputs of atomic volumes were determined in this study with XRD results. The predicted properties in Table 2 are denoted as Δ

, and Δ

, respectively. (3) Both the atomic volume and

elastic constants were determined from experiments in this study (XRD and RUS). And the results are Δ

, and Δ

In general, both theoretical

. and experimental

𝑏

values reflect the solid

𝑏

solution strengthening effects of different elements as seen in Table 2. Both the theory and experiments show that Ti, Mo, and Al increase the energy barriers compared to the base alloy and the solid solution strength while Cu, Cr, and V are less likely to strengthen the base alloy. A decrease of

𝑏

and

𝑏

is observed in Cr-containing alloy compared to that of

base alloys, both in measured and predicted values. For Ti-, Mo-, and Al-added alloys, a good agreement is observed between Δ containing alloys where predicted

and Δ 𝑏

. Discrepancies are observed in V-

values indicate an increase of solid solution

strengthening while the experimental data shows a slight decrease of

𝑏

compared to the

base alloys. Although both the theoretical and experimental values qualitatively reflect the trends of strengthening for the Ti-, Mo-, and Al-containing alloys, the predicted Δ values are not consistent with the experimentally measured Δ

.

22

In addition, we perform analysis on the activation volumes for the alloys that the theoretical results along with the experimental values at ~300K are shown in Figure 9 in a log-log plot. The activation volumes were normalized by 𝑏 of the alloys and determined from the isotropic yield stress by

values were

𝑀, where M is known as the Taylor factor.

The experimental activation volumes were obtained from the fitted curves in Figure 7 at zero plastic strain and the error bars were added from the fitting results. For the experimental values, a universal 1 MPa was subtracted from the experimental values due to low intrinsic friction [13]. The theoretical values followed a power-law relationship

indicated by

the black curve in Figure 9. For experimental values, the activation volumes decreased as the yield stress increase while the power-law relationship is unclear with these results. The predicted activation volumes are generally about 100 𝑏 to 200 𝑏 smaller than the experiments except Al6 and Mo6. This agrees with Laplanche et al’s study on Cantor alloy that the experimental activation volumes were larger than the predicted values when the same theory was applied [8].

Figure 9. Normalized activation volumes versus yield stress

at ~300K for experimental

MnFeCoNi-M alloys (symbols with dark edges error bars) and theoretical predictions (symbols without edges and error bars). The reasons to the discrepancies between theoretical and experimental results could be many-fold. From Eq.5 there are significant approximations in the our calculations. First, the misfit volume was simplified through Vegard’s Law because the misfit volume utilized in Eq.5 would otherwise require a full knowledge of the atomic volume as a function of each alloy component near the average alloy composition. Second, the elastic moduli of the alloys were also determined through a simplified compositionally-weighted method similar to the

23

first point. Third, in Eq.6 and Eq.7 only the core effect of edge dislocation with a large partial separation was considered and the line tension parameter of FeNiCr was adopted [13]. The influences on the solid-solution strength and energy predictions of these three approximations are discussed below. On the discrepancies between LLV model envisions a high

0

and

, one possible reason is that the

by emphasizing the effect of misfit volumes created by each

component. As Vegard’s Law was used to simplify calculation of misfit volume, it might imply that Vegard’s Law failed to capture the actual misfit volume when solutes with large volume misfit were added to the alloy. This can be seen in Ti-, Al- and Mo-added alloys in which Ti, Al, Mo atoms are larger and have different electronic structures from 3d transition metals. According to previous studies, the actual misfit volume deviates from its linear relationship due to intrinsic residual strains [69,70]. First-principles calculations [71] and experiments [72] have shown that the atomic radii of the elements tended to approach the averaged radii of the alloy. Local fluctuations of the first-nearest neighbor bonds could potentially change the picture of mean misfit volume employed in the LLV theory [72]. Although in our experiments, lattice constants agreed very well with the Vegard’s law (Figure 1(b) and Table 4), the calculations of misfit volume might not. The misfit volume of each element was calculated by

̅ , where

was the ideal atomic volume of a

pure element and ̅ was from Vegard’s law. However, elements could adapt its atomic volume when allowed. To correct for this change of misfit volume, alloys with different compositions were examined via XRD and the lattice constants of alloying elements (Al, Cu, Cr, Mo, Ti, and V) were determined. By plotting the lattice parameters against the concentrations of alloying elements (Figure 1(b)), the corrected lattice parameters were obtained by finding the value of the fitted line at

equals 1. These corrected atomic volumes

for alloying elements were tabulated in Table 6, as atomic volumes,

, together with the ideal FCC

. Theoretical predictions of solid solution strengthening become more

reasonable with the corrected atomic volumes. The new results are tabulated in Table 2 in the columns of Δ volumes, the values of Δ

and Δ

. With the experimentally determined atomic for Al-, Ti-, and Mo-alloys seem to be closer to the

measured values than the results using Vegard’s law. The second source of errors is similar to the first one discussed above. Our use of compositionally-weighted averages of elastic properties may be insufficient, especially for non-FCC elements. An example is that the shear modulus, 𝜇, and Poisson ratio, , are not

24

available for Fe in the FCC structure at room temperature. The input quantities were instead given by 𝜇 and

from stable structures such as BCC Fe. However, the actual 𝜇̅ and ̅ of the

alloys may not follow the linear relationship which could possibly lead to inaccurate predictions. This can be seen in Table 4 where the bulk modulus of MnFeCoNi is tabulated. By fitting the calculated energy-volume data to the Murnaghan equation of states (Figure S3), the DFT-determined bulk modulus is 133 GPa which agrees with the experimentallydetermined value of 126 GPa. The bulk modulus predicted by Vegard’s law is 177 GPa, using the elemental data tabulated in Table 6. This could justify the application of SQS supercell and DFT calculations in determining the elastic moduli of the CCAs, instead of computing the compositionally-weighted moduli with inputs of moduli of pure elements. In the elastic picture of the LLV theory, the dislocation pressure field scales with which plays an important role in Eq.6 and Eq.7 [14]. For the MnFeCoNi alloy, Vegard’s law overestimated the shear modulus from 75 GPa (RUS) to 79 GPa and overestimated the Poisson ratio from 0.252 (RUS) to 0.305. Such overestimation further posed a factor of 1.18 in the elastic dislocation pressure field which further went into the yield stress and energy barrier predictions. In addition, Wilson et al. found that misfit volume is not the only primary contributor to the solid solution strength that fluctuations arising from elastic moduli misfit could also be significant [73]. While it is beyond the scope of this study, addressing the contributions from elastic moduli misfit could be the focus of future studies. Finally, the third source of inaccuracy comes from the simplified Eqs.6 and 7, which blur the picture of the compositional dependence of core configurations. The change of core interactions and line tension is due to the solute atoms present in the average matrix that give rise to a compositional dependence of stacking fault energies [27]. The factors 0.01785 and 1.5618 in Eqs. 6 and 7 were related to the core structure of the dislocations and they were estimated through a dissociated edge dislocation [13]. Varvenne et al have shown that the core effect remain constant for a wide range of separation distance (>10 b) between the partials [13]. In a recent study of a Cantor-like alloy, the equiatomic CrFeCoNiPd alloy exhibited smaller stacking fault widths and a higher stacking fault energy than the Cantor alloy [74]. This might jeopardize the application of the simplified Eq.6 and Eq.7 because the pressure fields of two partials would complicate the picture when their separation distance is smaller than 5b [13]. Ding et al found that the pair correlations in the CrFeCoNiPd alloy were stronger than the Cantor alloy, leading to a higher stacking fault energy [74]. The theory of the interactions between stacking faults and correlated solutes was proposed by Suzuki that

25

chemical fluctuations in the vicinity of the stacking faults may change the stacking fault energy [75]. The influence of the solute-pair in Ni-Al FCC alloys was recently studied by Antillon et al [76] that the a wide range of characteristic distances was possible when Al-Al bond formation and breaking were considered. Such information, however, remains unknown to the HEAs and would be of great importance to study within the multicomponent systems. In addition to the solute-edge dislocation interaction, which is expected to govern FCC solid solutions, other microscopic features such as twinning can complicate the picture. Ma et al. [77] have shown that, in Al-Mg and Al-Li binary alloys, screw dislocations might play an important role in the strengthening process while the interplay between edge and screw components have not been understood. The LLV theory does not reflect clearly the contributions from edge and screw dislocations [13], which is also important but difficult to investigate experimentally. Furthermore, although the influence of line tension is small (𝛼

),

it would be difficult to estimate without fitting to experimental data [8]. Therefore, it is suggested that further efforts should emphasize the dislocation configurations and identify the stacking fault energies in the random medium.

Table 2. Predicted and measured solid solution strengthening and energy barrier of M6(MnFeCoNi)94 alloys. Values in the parentheses are errors propagated from the measurements. (subscripts ―exp‖: experimental measurements, ―DFT‖: LLV model with theoretical inputs, and ―DFT+XRD‖: LLV model with theoretical (DFT) elastic constants and experimentally (XRD) corrected atomic volumes) (MPa)

(eV)

(MPa)

(eV)

V6(MnFeCoNi)94 Ti6(MnFeCoNi)94 Mo6(MnFeCoNi)94 Cu6(MnFeCoNi)94 Cr6(MnFeCoNi)94

158(27) 164(27) 199(36) 164(34) 141(17)

130 486 310 130 143

Al6(MnFeCoNi)94 MnFeCoNi

163(12) 138(39)

1.68(0.41) 1.93(0.35) 1.80(0.25) 1.58(0.36) 1.28(0.17) 1.30(0.23) 1.77(0.25) 1.63(0.38) 1.87(0.44)

393 150

1.30 1.90 1.61 1.11 1.19

(MPa) 131 224 265 147 143

(eV) 1.11 1.37 1.50 1.16 1.17

1.73 1.16

161 142

1.20 1.16

Table 3. Elastic constants of Mx(MnFeCoNi)100-x. Values in the parentheses are errors propagated from the measurements. (GPa) 26

(GPa) V6(MnFeCoNi)94 Ti6(MnFeCoNi)94 Mo6(MnFeCoNi)94 Cu6(MnFeCoNi)94 Cr6(MnFeCoNi)94 Al6(MnFeCoNi)94 MnFeCoNi

0.3089 0.3041 0.3049 0.3049 0.3017 0.3026 0.3052

0.282(0.039) 0.236(0.012) 0.263(0.013) 0.297(0.017) 0.260(0.013)

76.4 76.3 82.0 77.4 82.2 76.0 79.3

78.1(9.8) 80.1(4.1) 75.2(3.9) 74.3(2.5) 75.0(3.3)

Table 4. Predicted and measured lattice constants and bulk modulus of MnFeCoNi. Values in the parentheses are errors propagated from the measurements. (Å) 3.597(0.004)

MnFeCoNi

(Å) 3.547

(Å) 3.602

(GPa) 126(6)

(GPa) 133

(GPa) 177

4.5. Comparison to Similar 3d Transition Metal CCAs Yield strengths of some reported 3d transition metal FCC solid solution CCAs are summarized in Table 5. In Wu et al.’s study, the yield strength of MnFeCoNi was 175MPa with an average grain size of 48μm [78], close to our Hall-Petch fitting in Figure 6, where MnFeCoNi’s yield strength is 169 MPa when the same grain size is applied. CoCrMnNi [78], CoCrFeNi [79], CoCrFeMnNi [5], and Al(CoCrCuFeNi2) [80] show higher yield strengths than V-, Mo-, Cu-, Cr-, and Al- added alloys except Ti-added alloys with comparable grain sizes. The Hall-Petch effect of Ti-added alloys can be seen in Figure 6 in which the grain size coefficient, k, is 700MPa μm-1/2. By applying the grain size values reported in Table 5 to the Hall-Petch relation of Ti6(MnFeCoNi)94, a yield strength of 864MPa is predicted with average grain size of 1μm, higher than the Al(CoCrCuFeNi2) with the same grain size [80]. Therefore, Ti can be considered as a component to strengthen in this alloy family through grain size reduction.

Table 5. Reported yield strengths and average grain size (with uncertainties) of FCC 3d transition metal CCAs from experiments at room temperature. Alloy MnFeCoNi V6(MnFeCoNi)94

Microstructure FCC FCC FCC FCC

Grain Size (μm) 20(1) 60(14) 88(12) 20(3)

Temperature (˚C) 25 25 25 25

Ref. (MPa) 181 170 162 211

this study this study this study this study

27

Ti6(MnFeCoNi)94 Mo6(MnFeCoNi)94 Cu6(MnFeCoNi)94 Cr6(MnFeCoNi)94 Al6(MnFeCoNi)94 Al(CoCrCuFeNi2), Al = 9.1at.% CoCrFeMnNi

FCC FCC FCC FCC FCC FCC FCC FCC FCC FCC FCC FCC FCC FCC FCC FCC FCC FCC

38(7) 53(5) 20(2) 29(1) 44(4) 24(3) 36(3) 62(10) 18(1) 58(7) 88(11) 20(2) 36(2) 54(5) 24(2) 39(1) 61(7) 1.0

25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25

198 190 321 293 270 240 237 224 202 181 184 224 202 192 207 197 191 655

this study this study this study this study this study this study this study this study this study this study this study this study this study this study this study this study this study [80]

FCC

4.4 50 11 24 36 48

23 23 23 23 23 23

362 197 300 273 280 175

[5] [5] [79] [78] [78] [78]

CoCrFeNi

FCC

CoCrMnNi MnFeCoNi

FCC FCC

5. Coupling Phase Diagram with Strength Prediction of Solid Solution CCAs

The advantage of the LLV model is that it can theoretically predict the solid solution contribution to the yield stress for an arbitrary single phase solid solution FCC alloy. Another objective of this paper is to integrate the strength prediction model with thermodynamic modeling to accelerate the discovery and development of CCAs. High-throughput discovery of multicomponent solid solutions proposed by Coury et al. was used to investigate the CrNiCo family in the solid solution limit [71]. First, the solid solution strength diagram with respect to the ternary compositions of the alloy were generated based on Eq.6, Eq.7 and Eq.8 in Section 2.4, as shown in Figure 10. Then the pseudo-ternary phase diagrams were superimposed onto the strength diagram to evaluate the strengths within the solid solution phase field. The relationship between strength, composition and phase becomes straightforward and researchers will be guided in the right direction when searching for alloys with high solid solution strengthening.

28

The pseudo-ternary stress diagrams were based on the theory provided by Varvenne et al. [13] and were generated by a Python-based tool [81]. Eq.5 to Eq.8 are the key formulations. We applied the abovementioned theories to predict Δ

for alloys of interest:

Mx(MnFeCoNi)100-x, in which X = Al, Cu, Cr, Mo, Ti, and V. The data of individual elements was listed in Table 6, where we used Reuss-Voigt-Hill representation of the isotropic elastic constants.

Table 6. Atomic volumes and elastic constants for pure elements in Mx(MnFeCoNi)100-x.

Elements

(Å),

(Å),

(MPa),

𝜇 (MPa),

(MPa),

𝜇 (MPa),

stable

stable

structure

structure

FCC

FCC

FCC

FCC

Ni

10.94 [82]

-

199.1 [54]

76.0

Co

11.12 [82]

-

262.9 [54]

101.6 [54] 269.1 [54] 104.4 [54]

Fe

12.09 [83]

-

26.4 [54]

8.9

[54] 194.3 [54] 73.4

[54]

Mn

12.60 [78]

-

130.5 [54] 197.7 [54] 76.5

[54]

Al

16.47 [54]

13.30 [TS]

338.8 [54] 65.5 [54]

23.9

[54] -

Ti

17.35 [54]

14.39 [TS]

82.8 [54]

30.2

[54] 154.6 [54] 60.8

Cu

11.81 [54]

12.79 [TS]

128.6 [54]

48.0

[54] -

Mo

15.18 [54]

14.63 [TS]

-

-

321.7 [54] 124.1 [54]

V

13.93 [54]

12.23 [TS]

-

-

87.7

Cr

12.29 [84]

11.47 [TS]

-

-

330.3 [54] 128.3 [54]

[54] -

-

[54]

-

[54] 30.9

[54]

Table 7. Predicted solid solution strengths and energy barriers for M6(MnFeCoNi)94 using experimentally determined elastic constants and lattice parameters.

V6(MnFeCoNi)94 Ti6(MnFeCoNi)94 Mo6(MnFeCoNi)94 Cu6(MnFeCoNi)94 Cr6(MnFeCoNi)94 Al6(MnFeCoNi)94 MnFeCoNi

(MPa)

(eV)

210

1.347

105 109 139 104

1.039 1.032 1.136 1.015

As seen in Table 3, although Vegard’s Law predicts reasonable results for shear modulus, it significantly overestimate the Poisson ratio for MnFeCoNi, Cu6(MnFeCoNi)94,

29

and Cr6(MnFeCoNi)94. This is a result of using questionable elastic constant data for nonFCC metals. For example, the Young’s modulus and shear modulus of Fe in FCC are 26.4 GPa and 8.9 GPa, much lower than the elastic constants of other elements in the MnFeCoNi. This is because Fe is elastically unstable in FCC form at lower temperatures. Even though the predicted results seem reasonable compared to experimental data, the predictive power of the theory could be hampered. By using experimentally determined elastic constants and lattice parameters as inputs to Eq.5 to Eq.8, new predicted results are tabulated in Table 7, given by Δ 𝑏

and

. Again, 6 at.% Cu and Cr exhibit limited contribution to strengthening to the

base alloy MnFeCoNi, as seen in both by Δ

and

𝑏

. Despite the

differences of results between different inputs discussed above and in Section 4, consistency is maintained between different kinds of input in the prediction that V, Cr, and Cu are less likely to strengthen the alloy while Ti, Al, and Mo increase the strengths. It can be seen that the LLV theory is very sensitive to the elastic constants and misfit volume that precise composition-dependent elastic constants and atomic volumes are necessary to accurately evaluate the strengths. To employ the standard thermal activation theory of Eq.8, the finite temperature was set to 300K and finite strain rate ̇ to 10-3 /s, consistent with our tensile experiment conditions. Figure 10 shows the Δ

predictions of Alx(MnFeCoNi)100-x alloys in the form of pseudo-

ternary plots. The contour plots provide straightforward interpretation of the yield stress of these alloys with respect to their compositions. The more saturated regions correspond to the accessible single FCC phase predicted by ThermoCalc at 1150˚C. The variation of solid solution strength with respect to the composition predicts high strengths at regions rich in Ni and Co, as seen in Figure 10(b), which is yet to be validated by experiments.

30

Figure 10. Contour plots of predicted

for Alx(MnFeCoNi)100-x at T=300K and ̇ = 10-3 /s:

(a) FeCo-NiMn-Al, (b) FeMn-CoNi-Al, and (c) FeNi-CoMn-Al pseudo ternary alloys. High color saturations regions represent FCC solid solution phase predicted at 1150˚C.

With the same technique described above, the combined strength-phase diagrams for MnFe-CoNi-X (X = Ti, V, Cr, Cu, and Mo) were produced in Figure 11. Similar diagrams were also calculated for FeCo-MnNi-X and FeNi-MnCo-X in Figure S8. For each alloy, its phase diagram was produced with the database that predicted reasonable solidus/liquidus temperatures compared to DTA analysis. Specifically, we used TCNI8 for Cr-, Cu-, and Vadded alloys and TCFE8 for Ti- and Mo-added alloys. The temperatures were set according to the annealing temperatures provided in Table 1 that we selected 1150˚C for Cr-, V-, and Mo-added alloys, 1050˚C for MnFe-CoNi-Cu, and 1000˚C for MnFe-CoNi-Ti. The high color saturation regions represents FCC single solution phase fields where the strengthening model may remain valid. In general, the strength increases with higher Co-Ni concentration

31

and alloying concentration, except MnFe-CoNi-Cu which shows increasing strengths in the MnFeCoNi-rich portions. As suggested in both experiments and predictions, Al, Ti, and Mo strongly contribute to the solid solution strengthening that the highest strengths within the accessible regions exceed 700 MPa (Figure 10(b), Figure 11(a) and (e)). As discussed in the previous section, this is due to the high lattice mismatch between the alloying elements and the base alloy, which should be interpreted with care. However, the solubilities of Al, Ti, and Mo in the base alloy are relatively low that in the predicted diagrams second phases would be expected when alloying concentration is above 10 – 20 at.%. On the other hand, V, Cr, and Cu provide a larger area of single phase field. The FCC phase regions are available for higher alloying concentrations (>30 at.%). The predicted solid solution strength for V-, Cr-, and Cucontaining alloys are relatively low, in the range of 0 to 350 MPa. Therefore, it would be interesting to further validate the model by selecting unexamined compositions with such diagrams, especially those compositions linked to high strengths.

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Figure 11. Combined strength-phase diagrams for (a) MnFe-CoNi-Ti, (b) MnFe-CoNi-V, (c) MnFe-CoNi-Cr, (d) MnFe-CoNi-Cu, and (e) MnFe-CoNi-Mo. Diagrams share the same color bar next to (e). The solid solution strengths were predicted at 300 K with a strain rate of 0.001 s-1, and the phase diagrams were produced at annealing temperatures in Table 1.

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Summary and Conclusion

The tensile properties and microstructures of FCC Mx(MnFeCoNi)100-x (M=Al, Cu, Cr, Mo, V and Ti) quaternary-based CCAs were investigated at room temperature to understand their solid solution strengthening. 1. With alloying up to at least 6 at.% M, quenched alloys exhibit only the FCC solid solution phase at room temperature. SEM and XRD characterization, together with thermodynamic

predictions,

confirm

the

stability

of

FCC

phase

at

annealing/homogenization temperature from 1000˚C to 1150˚C. APT results also prove the random distribution of all the elements and no clustering/segregation were observed. DFT calculations and Vegard’s law show good agreements with the experimentally measured lattice parameters for this alloy family.

2. The solid solution strengthening effects of the alloying elements have been evaluated that predictions from a recently developed elasticity-based model qualitatively agree with the experimental results. From experiments, 6 at.% Al, Ti, and Mo strengthen the base alloy, MnFeCoNi, by increasing the yield stress (and energy barrier) of the base alloy from 138MPa (1.75eV) to 163MPa (1.77eV), 164MPa (1.93eV), and 199MPa (1.80eV), respectively. Cu, Cr, and V are less likely to contribute to the energy barriers of the base alloy, with 1.58eV, 1.30eV, and 1.68eV at 6 at.% while slight increases of yield stress are observed. Predictions generally indicate the same trends of strengthening effects of alloying elements. The model successfully predicts the strengths of MnFeCoNi, Cr6(MnFeCoNi)94, Cu6(MnFeCoNi)94, and V6(MnFeCoNi)94 but fails to predict the strengths of Ti-, Al-, and Mo-added alloys. 3. The grain size effect was examined for the MnFeCoNi and M6(MnFeCoNi)94 alloys. The 6 at.% Ti-added alloys exhibit a large grain size reduction effect, with its k = 700MPa μm-1/2. Other elements mildly increase the coefficient of MnFeCoNi, whose k is 150MPa μm-1/2.

4. The major contribution to the increase of strength is the misfit volume when an element is added to the alloy: a greater difference of atomic volume between M and MnFeCoNi leads to higher yield stress and energy barrier. Precise misfit volumes and elastic constants (ν and μ) are essential to increase the predictive power of the

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discussed model. Although the rule of mixtures yields reasonable lattice constants of the alloy, the picture of the mean misfit volume could be subject to local fluctuations of atomic bonds. And the linear relation is not sufficient to provide accurate elastic constants because some elements, such as Fe and Ti, are not elastically stable with FCC phase at room temperature.

5. A method coupling the solid solution strengthening model and thermodynamic predictions was employed to explore the strengths in the complex composition space of CCAs. The predictive power of the method can be enriched with a better understanding of misfit volume and elastic constants as a function of composition and temperature.

Acknowledgement:

D.W., C-H.C., S.M., and M.S.T. would like to acknowledge Purdue University for supporting this work through start-up funds. This research was supported in part through computational resources provided by Information Technology at Purdue, West Lafayette, Indiana. S.A. would like to acknowledge the funding from the National Natural Science Foundation of China [grant No. 51850410518]. The synchrotron work was supported by the U.S. Department of Energy, Office of Nuclear Energy under DOE Idaho Operations Office Contract DE-AC07-051D14517, as part of Nuclear Science User Facilities. This research used the x-ray powder diffraction beamline at the National Synchrotron Light Source-II, a DOE Office of Science User Facility operated for the DOE Office of Science by Brookhaven National Laboratory under Contract No. DE-SC0012704. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Reference [1] J.-W. Yeh, S.-K. Chen, S.-J. Lin, J.-Y. Gan, T.-S. Chin, T.-T. Shun, C.-H. Tsau, S.-Y. Chang, Nanostructured high‐ entropy alloys with multiple principal elements: novel alloy design concepts and outcomes, Advanced Engineering Materials. 6 (2004) 299– 303. [2] B. Cantor, I.T.H. Chang, P. Knight, A.J.B. Vincent, Microstructural development in equiatomic multicomponent alloys, Materials Science and Engineering: A. 375 (2004) 213–218. [3] Y. Zhang, T.T. Zuo, Z. Tang, M.C. Gao, K.A. Dahmen, P.K. Liaw, Z.P. Lu, Microstructures and properties of high-entropy alloys, Progress in Materials Science. 61 (2014) 1–93. [4] O. Senkov, G. Wilks, J. Scott, D. Miracle, Mechanical properties of Nb25Mo25Ta25W25 and V20Nb20Mo20Ta20W20 refractory high entropy alloys, Intermetallics. 19 (2011) 698–706. [5] F. Otto, A. Dlouhý, C. Somsen, H. Bei, G. Eggeler, E.P. George, The influences of temperature and microstructure on the tensile properties of a CoCrFeMnNi high-entropy alloy, Acta Materialia. 61 (2013) 5743–5755. [6] D.B. Miracle, O.N. Senkov, A critical review of high entropy alloys and related concepts, Acta Materialia. 122 (2017) 448–511. [7] B. Gwalani, S. Gorsse, D. Choudhuri, M. Styles, Y. Zheng, R.S. Mishra, R. Banerjee, Modifying transformation pathways in high entropy alloys or complex concentrated alloys via thermo-mechanical processing, Acta Materialia. 153 (2018) 169–185. [8] G. Laplanche, J. Bonneville, C. Varvenne, W. Curtin, E.P. George, Thermal activation parameters of plastic flow reveal deformation mechanisms in the CrMnFeCoNi highentropy alloy, Acta Materialia. 143 (2018) 257–264. [9] U. Kocks, Superposition of alloy hardening, strain hardening, and dynamic recovery, in: Strength of Metals and Alloys, Elsevier, 1980: pp. 1661–1680. [10] R. Labusch, A Statistical Theory of Solid Solution Hardening, phys. stat. sol. (b). 41 (1970) 659–669. https://doi.org/10.1002/pssb.19700410221. [11] R. Labusch, Statistische theorien der mischkristallhärtung, Acta Metallurgica. 20 (1972) 917–927. https://doi.org/10.1016/0001-6160(72)90085-5. [12] G.P.M. Leyson, L. Hector Jr, W.A. Curtin, Solute strengthening from first principles and application to aluminum alloys, Acta Materialia. 60 (2012) 3873–3884. [13] C. Varvenne, G.P.M. Leyson, M. Ghazisaeidi, W.A. Curtin, Solute strengthening in random alloys, Acta Materialia. 124 (2017) 660–683. [14] C. Varvenne, A. Luque, W.A. Curtin, Theory of strengthening in fcc high entropy alloys, Acta Materialia. 118 (2016) 164–176. [15] C. Varvenne, W.A. Curtin, Predicting yield strengths of noble metal high entropy alloys, Scripta Materialia. 142 (2018) 92–95. [16] C. Varvenne, W.A. Curtin, Strengthening of high entropy alloys by dilute solute additions: CoCrFeNiAlx and CoCrFeNiMnAlx alloys, Scripta Materialia. 138 (2017) 92–95. [17] G. Bracq, M. Laurent-Brocq, C. Varvenne, L. Perrière, W. Curtin, J.-M. Joubert, I. Guillot, Combining experiments and modeling to explore the solid solution strengthening of high and medium entropy alloys, Acta Materialia. 177 (2019) 266–279. [18] F. Nabarro, Theoretical and experimental estimates of the Peierls stress, Philosophical Magazine A. 75 (1997) 703–711. [19] F. Nabarro, Fifty-year study of the Peierls-Nabarro stress, Materials Science and Engineering: A. 234 (1997) 67–76.

36

[20] E. Hall, The deformation and ageing of mild steel: III discussion of results, Proceedings of the Physical Society. Section B. 64 (1951) 747. [21] Petch, N. J., The Cleavage Strength of Polycrystals, The Journal of the Iron and Steel Institute. 173 (1953) 25–28. [22] J. Friedel, Dislocations, 1st Edition, Pergamon Press, Oxford, 1964. [23] G.I. Taylor, Plastic strain in metals, J. Inst. Metals. 62 (1938) 307–324. [24] G. Saada, P. Veyssière, Work hardening of face centred cubic crystals. Dislocations intersection and cross slip, in: Dislocations in Solids, Elsevier, 2002: pp. 413–458. [25] T.M. Smith, M.S. Hooshmand, B.D. Esser, F. Otto, D.W. McComb, E.P. George, M. Ghazisaeidi, M.J. Mills, Atomic-scale characterization and modeling of 60 dislocations in a high-entropy alloy, Acta Materialia. 110 (2016) 352–363. [26] D. Hull, D.J. Bacon, Introduction to dislocations, Butterworth-Heinemann, 2001. [27] A. Argon, Strengthening mechanisms in crystal plasticity, Oxford University Press on Demand, 2008. [28] T. Holland, S. Redfern, Unit cell refinement from powder diffraction data: the use of regression diagnostics, Mineralogical Magazine. 61 (1997) 65–77. [29] C.-H. Chang, Solid-solution Strengthening of FCC Complex, Concentrated Alloys, Thesis, Purdue University, 2018. [30] P. Spätig, J. Bonneville, J.-L. Martin, A new method for activation volume measurements: application to Ni3 (Al, Hf), Materials Science and Engineering: A. 167 (1993) 73–79. [31] F. Guiu, P. Pratt, Stress relaxation and the plastic deformation of solids, Physica Status Solidi (b). 6 (1964) 111–120. [32] P. Groh, R. Conte, Stress relaxation and creep in α-iron filamentary single crystals at low temperature, Acta Metallurgica. 19 (1971) 895–902. [33] E. Voce, The relationship between stress and strain for homogeneous deformation, Journal of the Institute of Metals. 74 (1948) 537–562. [34] C. Tome, G. Canova, U. Kocks, N. Christodoulou, J. Jonas, The relation between macroscopic and microscopic strain hardening in FCC polycrystals, Acta Metallurgica. 32 (1984) 1637–1653. [35] P.L. Kubin, Description de la préplasticité par la théorie des phénomènes thermiquement activés, Philosophical Magazine. 30 (1974) 705–718. [36] R. Mulford, Analysis of strengthening mechanisms in alloys by means of thermalactivation theory, Acta Metallurgica. 27 (1979) 1115–1124. [37] Christopher Wright, xpdtools, 2016. https://github.com/xpdAcq/xpdtools. [38] G. Pawley, Unit-cell refinement from powder diffraction scans, Journal of Applied Crystallography. 14 (1981) 357–361. [39] B.H. Toby, R.B. Von Dreele, GSAS-II: the genesis of a modern open-source all purpose crystallography software package, Journal of Applied Crystallography. 46 (2013) 544– 549. [40] M. Markham, Measurement of elastic constants by the ultrasonic pulse method, British Journal of Applied Physics. 8 (1957) S56. [41] J.-O. Andersson, T. Helander, L. Höglund, P. Shi, B. Sundman, Thermo-Calc & DICTRA, computational tools for materials science, Calphad. 26 (2002) 273–312. [42] Thermo-Calc Software TCFE8 Steels/Fe-alloys database (accessed 11 November 2018), n.d. [43] A. Zunger, S.-H. Wei, L. Ferreira, J.E. Bernard, Special quasirandom structures, Physical Review Letters. 65 (1990) 353.

37

[44] A. Van de Walle, P. Tiwary, M. De Jong, D. Olmsted, M. Asta, A. Dick, D. Shin, Y. Wang, L.-Q. Chen, Z.-K. Liu, Efficient stochastic generation of special quasirandom structures, Calphad. 42 (2013) 13–18. [45] G. Kresse, J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Physical Review B. 54 (1996) 11169. [46] J. Hafner, Materials simulations using VASP—a quantum perspective to materials science, Computer Physics Communications. 177 (2007) 6–13. [47] P.E. Blöchl, Projector augmented-wave method, Physical Review B. 50 (1994) 17953. [48] G. Kresse, D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Physical Review B. 59 (1999) 1758. [49] J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple, Physical Review Letters. 77 (1996) 3865. [50] H.J. Monkhorst, J.D. Pack, Special points for Brillouin-zone integrations, Physical Review B. 13 (1976) 5188. [51] M. Methfessel, A. Paxton, High-precision sampling for Brillouin-zone integration in metals, Physical Review B. 40 (1989) 3616. [52] F. Murnaghan, The compressibility of media under extreme pressures, Proceedings of the National Academy of Sciences. 30 (1944) 244–247. [53] C.-L. Fu, K.-M. Ho, First-principles calculation of the equilibrium ground-state properties of transition metals: Applications to Nb and Mo, Physical Review B. 28 (1983) 5480. [54] A. Jain, S.P. Ong, G. Hautier, W. Chen, W.D. Richards, S. Dacek, S. Cholia, D. Gunter, D. Skinner, G. Ceder, Commentary: The Materials Project: A materials genome approach to accelerating materials innovation, Apl Materials. 1 (2013) 011002. [55] A. Jain, G. Hautier, C.J. Moore, S.P. Ong, C.C. Fischer, T. Mueller, K.A. Persson, G. Ceder, A high-throughput infrastructure for density functional theory calculations, Computational Materials Science. 50 (2011) 2295–2310. [56] G. Bergerhoff, R. Hundt, R. Sievers, I. Brown, The inorganic crystal structure data base, Journal of Chemical Information and Computer Sciences. 23 (1983) 66–69. [57] M.P. Moody, L.T. Stephenson, A.V. Ceguerra, S.P. Ringer, Quantitative binomial distribution analyses of nanoscale like‐ solute atom clustering and segregation in atom probe tomography data, Microscopy Research and Technique. 71 (2008) 542–550. [58] A. Savitzky, M.J. Golay, Smoothing and differentiation of data by simplified least squares procedures., Analytical Chemistry. 36 (1964) 1627–1639. [59] J. Antonaglia, X. Xie, Z. Tang, C.-W. Tsai, J. Qiao, Y. Zhang, M. Laktionova, E. Tabachnikova, J. Yeh, O. Senkov, Temperature effects on deformation and serration behavior of high-entropy alloys (HEAs), Jom. 66 (2014) 2002–2008. [60] H.Y. Yasuda, K. Shigeno, T. Nagase, Dynamic strain aging of Al0. 3CoCrFeNi high entropy alloy single crystals, Scripta Materialia. 108 (2015) 80–83. [61] R. Carroll, C. Lee, C.-W. Tsai, J.-W. Yeh, J. Antonaglia, B.A. Brinkman, M. LeBlanc, X. Xie, S. Chen, P.K. Liaw, Experiments and model for serration statistics in lowentropy, medium-entropy, and high-entropy alloys, Scientific Reports. 5 (2015) 16997. [62] S. Chen, X. Xie, B. Chen, J. Qiao, Y. Zhang, Y. Ren, K.A. Dahmen, P.K. Liaw, Effects of temperature on serrated flows of Al 0.5 CoCrCuFeNi high-entropy alloy, Jom. 67 (2015) 2314–2320. [63] S. Niu, H. Kou, Y. Zhang, J. Wang, J. Li, The characteristics of serration in Al0. 5CoCrFeNi high entropy alloy, Materials Science and Engineering: A. 702 (2017) 96– 103.

38

[64] J. Fu, C. Cao, W. Tong, Y. Hao, L. Peng, The tensile properties and serrated flow behavior of a thermomechanically treated CoCrFeNiMn high-entropy alloy, Materials Science and Engineering: A. 690 (2017) 418–426. [65] S. Chen, X. Xie, W. Li, R. Feng, B. Chen, J. Qiao, Y. Ren, Y. Zhang, K.A. Dahmen, P.K. Liaw, Temperature effects on the serrated behavior of an Al0. 5CoCrCuFeNi highentropy alloy, Materials Chemistry and Physics. 210 (2018) 20–28. [66] S. Nagarjuna, M. Srinivas, K. Balasubramanian, D. Sarma, The alloy content and grain –2293. [67] G. Laplanche, A. Kostka, O. Horst, G. Eggeler, E. George, Microstructure evolution and critical stress for twinning in the CrMnFeCoNi high-entropy alloy, Acta Materialia. 118 (2016) 152–163. [68] J.H. Hollomon, Tensile deformation, Aime Trans. 12 (1945) 1–22. [69] Y. Ye, C. Liu, Y. Yang, A geometric model for intrinsic residual strain and phase stability in high entropy alloys, Acta Materialia. 94 (2015) 152–161. [70] Y. Ye, Y. Zhang, Q. He, Y. Zhuang, S. Wang, S. Shi, A. Hu, J. Fan, Y. Yang, Atomicscale distorted lattice in chemically disordered equimolar complex alloys, Acta Materialia. 150 (2018) 182–194. [71] F.G. Coury, K.D. Clarke, C.S. Kiminami, M.J. Kaufman, A.J. Clarke, High Throughput Discovery and Design of Strong Multicomponent Metallic Solid Solutions, Sci Rep. 8 (2018) 8600. https://doi.org/10.1038/s41598-018-26830-6. [72] H. Oh, D. Ma, G. Leyson, B. Grabowski, E. Park, F. Körmann, D. Raabe, Lattice Distortions in the FeCoNiCrMn High Entropy Alloy Studied by Theory and Experiment, Entropy. 18 (2016) 321. https://doi.org/10.3390/e18090321. [73] P. Wilson, R. Field, M. Kaufman, The use of diffusion multiples to examine the compositional dependence of phase stability and hardness of the Co-Cr-Fe-Mn-Ni high entropy alloy system, Intermetallics. 75 (2016) 15–24. [74] Q. Ding, Y. Zhang, X. Chen, X. Fu, D. Chen, S. Chen, L. Gu, F. Wei, H. Bei, Y. Gao, M. Wen, J. Li, Z. Zhang, T. Zhu, R.O. Ritchie, Q. Yu, Tuning element distribution, structure and properties by composition in high-entropy alloys, Nature. 574 (2019) 223– 227. https://doi.org/10.1038/s41586-019-1617-1. [75] H. Suzuki, Chemical interaction of solute atoms with dislocations, Science Reports of the Research Institutes, Tohoku University. Ser. A, Physics, Chemistry and Metallurgy. 4 (1952) 455–463. [76] E. Antillon, C. Woodward, S.I. Rao, B. Akdim, T.A. Parthasarathy, A molecular dynamics technique for determining energy landscapes as a dislocation percolates through a field of solutes, Acta Materialia. 166 (2019) 658–676. https://doi.org/10.1016/j.actamat.2018.12.037. [77] D. Ma, M. Friák, J. von Pezold, D. Raabe, J. Neugebauer, Computationally efficient and quantitatively accurate multiscale simulation of solid-solution strengthening by ab initio calculation, Acta Materialia. 85 (2015) 53–66. [78] Z. Wu, H. Bei, G.M. Pharr, E.P. George, Temperature dependence of the mechanical properties of equiatomic solid solution alloys with face-centered cubic crystal structures, Acta Materialia. 81 (2014) 428–441. [79] A. Gali, E.P. George, Tensile properties of high-and medium-entropy alloys, Intermetallics. 39 (2013) 74–78. [80] C.-W. Tsai, M.-H. Tsai, J.-W. Yeh, C.-C. Yang, Effect of temperature on mechanical properties of Al0. 5CoCrCuFeNi wrought alloy, Journal of Alloys and Compounds. 490 (2010) 160–165. [81] D.-S. Wen, M.S. Titus, SSPredict: A Solid Solution Strengthening Prediction and Visualization Tool, (2019). https://doi.org/10.5281/zenodo.2631415.

39

[82] J. Bandyopadhyay, K.P. Gupta, Low temperature lattice parameter of nickel and some nickel-cobalt alloys and Grüneisen parameter of nickel, Cryogenics. 17 (1977) 345–347. [83] R.W. Smith, G.S. Was, Application of molecular dynamics to the study of hydrogen embrittlement in Ni-Cr-Fe alloys, Physical Review B. 40 (1989) 10322. [84] F. Abe, T. Tanabe, Change in lattice spacing of nickel by dissolved chromium and tungsten, Zeitschrift Fuer Metallkunde. 76 (1985) 420–425.

Graphcial Abstract

Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

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