Microstructural investigation of plastically deformed Ti20Zr20Hf20Nb20Ta20 high entropy alloy by X-ray diffraction and transmission electron microscopy

    Microstructural investigation of plastically deformed Ti 20 Zr20 Hf20 Nb20 Ta20 high entropy alloy by X-ray diffraction and transmission electron microscopy G. Dirras, J. Gubicza, A. Heczel, L. Lilensten, J.-P. Couzini´e, L. Perri`ere, I. Guillot, A. Hocini PII: DOI: Reference:

S1044-5803(15)00302-2 doi: 10.1016/j.matchar.2015.08.007 MTL 8003

To appear in:

Materials Characterization

Received date: Revised date: Accepted date:

31 July 2015 10 August 2015 11 August 2015

Please cite this article as: Dirras G, Gubicza J, Heczel A, Lilensten L, Couzini´e J-P, Perri`ere L, Guillot I, Hocini A, Microstructural investigation of plastically deformed Ti20 Zr20 Hf20 Nb20 Ta20 high entropy alloy by X-ray diffraction and transmission electron microscopy, Materials Characterization (2015), doi: 10.1016/j.matchar.2015.08.007

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ACCEPTED MANUSCRIPT Microstructural investigation of plastically deformed Ti20Zr20Hf20Nb20Ta20 high entropy

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alloy by X-ray diffraction and transmission electron microscopy

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G. Dirras1,*, J. Gubicza2, A. Heczel2, L. Lilensten3, J.-P. Couzinié3, L. Perrière3, I. Guillot3, A. Hocini1

Université Paris 13, Sorbonne Paris Cité, LSPM (UPR 3407) CNRS, 99 avenue JB

Clément, 93430 Villetaneuse, France 2

Department of Materials Physics, Eötvös Loránd University, Budapest, P.O.B. 32, H-

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1518, Hungary

Université Paris Est, ICMPE (UMR 7182), CNRS, UPEC, 94320 Thiais, France

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* Corresponding author: [email protected] - Tel: +33 1 49 40 34 88 – Fax: +33 1

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Abstract

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The microstructure evolution in body-centered cubic (bcc) Ti20Zr20Hf20Nb20Ta20 high entropy alloy during quasi-static compression test was studied by X-ray line profile analysis (XLPA) and transmission electron microscopy (TEM). The average lattice constant and other important parameters of the microstructure such as the mean crystallite size, the dislocation density and the edge/screw character of dislocations were determined by XLPA. The elastic anisotropy factor required for XLPA procedure was determined by nanoindentation. XLPA shows that the crystallite size decreased while the dislocation density increased with strain during compression, and their values reached about 39 nm and 15 × 1014 m-2, respectively, at a plastic strain of 20%. It was

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ACCEPTED MANUSCRIPT revealed that with increasing strain the dislocation character became more screw. This can be explained by the reduced mobility of screw dislocations compared to edge

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dislocations in bcc structures. These observations are in line with TEM investigations.

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The development of dislocation density during compression was related to the yield strength evolution.

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Keywords: High entropy alloy; X-ray diffraction; dislocations; TEM; yield strength

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ACCEPTED MANUSCRIPT 1. Introduction Since the pioneering works by Yeh et al. [1] and Cantor et al. [2] high-entropy alloys

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(HEA) have triggered a lot of expectation as potential new family of structural

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component materials [3,4]. Actually, HEAs refer to multi-elementary (disordered) solid solutions with at least 5 elements whose concentration is close to equimolarity. One of the proposed empirical parameters involved in HEA concept – and also in the formation

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of the multicomponent solid solutions – is the contribution of the mixing entropy term to the Gibbs free energy of mixing for the alloy system [5]. For HEAs the value of the

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mixing entropy is high and therefore sufficient to overcome the enthalpies of compound formation and phase separation. In such a case, solid solution is expected to be

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stabilized [6]. However, a recent work [7] has revealed that although the above concept can explain the single-phase state of some multi-element alloys [2], it cannot be used as

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a general rule for all HEAs. Indeed, many alloys meeting the proposed criteria,

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including HEAs, possess complex microstructures with multiple phases [8,9], since other quntities, such as mixing enthalpy or valence electron concentration, also

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influence the phase stability [10]. HEAs with simple solid solution structures, whatever face-centered cubic (fcc) or bodycentered cubic centered (bcc) are reported to exhibit excellent properties such as high hardness and strength [1,11-13], good resistance to softening at high temperatures [11,14-16], outstanding wear and fatigue properties [17], good corrosion resistance [18] and biocompatibility [19], making them promising materials for industrial and structural applications [13]. Among all the attractive new compositions, refractory HEAs have been intensively studied by many groups, particularly by Senkov and collaborators [1416,20-23]. In particular, the equimolar bcc TiZrHfNbTa is a promising HEA for the

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ACCEPTED MANUSCRIPT applications performed in a wide temperature range from room temperature (RT) to approximately 600°C [21]. The effect of the crystal structure, the chemical composition

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and the testing temperature on the mechanical behavior has been studied in different

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HEAs [13]. However, the effect of the lattice defects, such as dislocations, formed during plastic straining on the mechanical performance (e.g. the strength) has been not investigated in details. Recently and for the first time, detailed transmission electron

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microscopy (TEM) investigations have been carried out in order to comprehend the dislocation controlled mechanisms of plastic deformation in equimolar TiZrHfNbTa

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HEA alloy during compression at RT [24]. The operation of thermally activated deformation processes has been evidenced by the joint observation of low apparent

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activation volumes compatible with a Peierls mechanism and the glide of screw dislocation with the Burgers vector b = a/2<111> in the first stage of plastic

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deformation.

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In the present work, the density, the arrangement and the edge/screw character of dislocations in an equimolar bcc TiZrHfNbTa HEA are monitored during compression

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at RT. According to the knowledge of the authors, this is the first study which gives a detailed characterization of the dislocation structure in a HEA material applying the combination of X-ray line profile analysis and post mortem TEM investigations. For a correct evaluation of X-ray diffraction peak broadening, the elastic anisotropy factor of the crystal is necessary. This paper also gives a method for the determination of this quantity in polycrystalline HEAs. The investigation of the relationship between the dislocation density and the yield strength yields the dislocation strengthening parameter in the present HEA material.

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ACCEPTED MANUSCRIPT 2. Experimental procedure 2.1 Materials and Processing

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A refractory HEA with equi-atomic composition (Ti20Zr20Hf20Nb20Ta20) was processed

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by arc melting and induction processes under argon atmosphere. Two master alloys, Nb–Ta and Ti–Zr–Hf, were first melted on a water-cooled copper plate from high purity metals (exceeding 99.9% purity) in the form of slugs and wires. Both alloys were re-

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melted twice in order to improve homogeneity and then mixed together. A titanium getter was used prior each arc-melting fusion in order to capture the residual oxygen in

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the chamber. Homogenization of the alloy was then assessed by high frequency induction melting in sectorised cooled copper crucible under helium atmosphere.

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Finally, the homogenized refractory alloy was obtained by arc melting in the form of an

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ingot with 60 mm in length and approximately 10 mm in diameter.

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2.2 Compression tests

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Compression tests were carried out at room temperature at a strain rate of 1.5  10-3 s-1 on a cylindrical specimen with 5 mm in diameter and 7 mm in length using a 100 kN MTS testing machine (20/MH). In order to study the microstructure evolution during compression, samples were deformed up to different plastic strain values between 2 and 20%.

2.3 EBSD and TEM investigations The grain structure of the intial sample was studied by electron backscatter diffraction (EBSD) investigations. The investigated surface was prepared by mechanical grinding using 1200 to 4000 grit SiC papers followed by a final polishing step using a 20 nm

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ACCEPTED MANUSCRIPT alumina oxide particle suspension (OPS) from Struers™. EBSD investigations were carried out using a Zeiss Supra 40VP FEG scanning electron microscope (SEM). After

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mechanical testing, transmission electron microscopy (TEM) analyses were conducted

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on samples cut perpendicular to the load axis. Thin foils with 3 mm in diameter were prepared by mechanical polishing to 100 μm and finally thinned by the classical twin-jet electropolishing apparatus using a HF/H2SO4 solution at -35°C. The TEM observations

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were carried out by a JEOL 2000EX operating at 200 kV.

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2.4 Lattice parameter and microstructure from X-ray diffraction The average lattice parameter for the initial and the deformed HEA samples was

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investigated by X-ray diffraction (XRD) using a Philips Xpert Θ–2Θ powder

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diffractometer with CuKα radiation (wavelength:  = 0.15418 nm). XRD patterns revealed that all the studied samples have body-centered cubic (bcc) structure. The

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average lattice parameter was determined by extrapolating the lattice parameters

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obtained from the different reflections to the diffraction angle of 2Θ = 180° using the Nelson–Riley method [25]. The microstructure in the specimens was studied by X-ray line profile analysis (XLPA). The X-ray line profiles were measured by a highresolution rotating anode diffractometer (type: RA-MultiMax9, manufacturer: Rigaku) using CuK1 (wavelength, =0.15406 nm) radiation. Two-dimensional imaging plates detected the Debye-Scherrer diffraction rings. The line profiles were determined as the intensity distribution perpendicular to the rings obtained by integrating the two dimensional intensity distribution along the rings. The diffraction patterns were evaluated by the Convolutional Multiple Whole Profile (CMWP) analysis [26,27]. In this method, the diffraction pattern is fitted by the sum of a background spline and the

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ACCEPTED MANUSCRIPT convolution of the instrumental pattern and the theoretical line profiles related to crystallite size and dislocations. The instrumental diffraction peaks were measured on a

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LaB6 standard material (SRM 660). The CMWP evaluation procedure yields the area-

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weighted mean crystallite size (area), the dislocation density (ρ) and parameter q which describes the edge/screw character of dislocations.

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3. Results and discussion 3.1. As-cast microstructure

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A detailed characterization for the as-cast microstructure of this refractory alloy has been given elsewhere [28]. Figure 1 is a typical inverse pole figure of the initial

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microstructure. There is no preferential crystallographic orientation of the grains (see the inset showing of the standard stereographic triangle). The grain shape is irregular

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and the grain size distribution is broad, ranging between 10 and 350 m. As it was

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revealed in a previous study [28], the size and morphology of grains as well as the chemical composition depend on the cooling rate during HEA processing. Indeed, it

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was shown that in the upper part of the ingot (lower cooling rate) the grains have a dendritic structure and the dendrite arms are mostly of Ta and Nb enriched while microsegregations consisting of Ti, Zr and Hf rich zones are found in the interdendritic zones

3.2. Mechanical behavior Typical engineering stress versus engineering strain and deduced true stress versus true strain compression curves for the as-processed HEA are shown in Fig. 2. In accordance with the work by Senkov et al. [21], the engineering stress versus engineering strain plot display strong linear hardening behavior. The yield strength is about 890 MPa. It should

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ACCEPTED MANUSCRIPT be noticed that when the true stress is plotted against true strain, the observed hardening

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is reduced.

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3.3. Microstructure of the compressed samples from X-ray line profile analysis The average lattice constants determined for the initial and the deformed samples are listed in Table 1. All lattice constants are in the range between 0.3397-0.3414 nm. For

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the compressed samples the lattice parameter remains unchanged within the experimental error. The small difference between the lattice constants of the initial and

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compressed specimens can be explained by the slight variation of the chemical composition in the as-cast specimen, as revealed by coupled energy and wavelength

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dispersive spectrometry (EDS/WDS) in a previous paper [28].

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The average crystallite size and dislocation density were determined by XLPA in samples compressed up to true plastic strains of 3, 10 and 20 %. As an example, Fig. 3

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shows the X-ray diffraction pattern for the sample compressed up to 20%. Reflection

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222 was omitted from the pattern due to its weak intensity. The dependence of the peak breadths on the diffraction order (i.e. on the indices hkl) can be visualised by plotting the full width at half maximum (FWHM) as a function of the modulus of the diffraction vector, g (classical Williamson-Hall plot) [29]. FWHM and g can be calculated as: FWHM 

2  cos 2 sin  and g  ,  

(1)

where Θ is the Bragg angle of the peak, Δ(2Θ) is the breadth of the line profiles in radians and λ is the wavelength of X-rays. The classical Williamson-Hall plot for the sample compressed up to 20% is shown in Fig. 4a. The non-monotonous variation of FWHM as a function of g for plastically deformed metallic materials is usually caused

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ACCEPTED MANUSCRIPT by the anisotropic strain field of dislocations, and this phenomenon is referred to as strain anisotropy [29]. The contrast effect of dislocations on line broadening can be

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taken into account by the average contrast (or orientation) factor of dislocations [29].

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For a polycrystalline material containing dislocations the FWHM values fit to a smooth curve, when they are plotted as a function of g 2Chkl , where C hkl is the average contrast

 h 2 k 2  k 2 l 2  h 2 l 2  . Chkl  Ch 00 1  q 2 2 2 2   h  k  l  

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

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factor given as:

(2)

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In eq. (2) hkl are the indices of reflections and Ch 00 is the contrast factor for reflection h00. Figure 4b shows the modified Williamson-Hall plot for the sample compressed up

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to 20%. The datum points follow a smooth curve if q = 2.4 is selected. It is noted that

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the fitting of the measured diffraction pattern by the CMWP procedure also gives the value of q which was the same within the experimental error as the value obtained by

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the modified Williamson-Hall plot. The values of q for all deformed samples determined by CMWP fitting are listed in Table 1.

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The comparison of the experimentally obtained q with the theoretical values calculated for pure edge and screw dislocations enables the determination of the edge/screw character of the dislocation structure. The theoretical values of q for pure edge and screw dislocations depend on the anisotropic elastic constants of the studied material. The dependence of parameter q on the elastic constants of bcc polycrystals can be given using the ratio of the elastic constant c12/c44 and the elastic anisotropy factor ( A

2c44 ) [4]. Figure 5 shows parameter q for edge and screw dislocations in bcc c11  c12

crystals as a function of A for three different usual values of c12/c44 (0.5, 1 and 2). The

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ACCEPTED MANUSCRIPT data were taken from Ref. [29]. As the single crystal anisotropic elastic constants are not known for the present HEA composition, therefore the exact value of parameter q

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for pure edge and screw dislocations cannot be determined. In addition, in the CMWP

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evaluation of the diffraction patterns, one fitting parameter is C h 00b 2  , where b is the modulus of the Burgers vector of dislocations. Assuming the usual Burgers vector in bcc structure (a/2<111>{110}), b equals 0.2944 nm in the present HEA material. Since

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C h 00 depends on the anisotropic elastic constants, without the knowledge of their values the dislocation density cannot be determined.

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For a polycrystalline material the single crystal elastic anisotropy factor can be determined by depth-sensing indentation technique, as shown by Vlassak and Nix [30].

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Then, this factor may be used for the estimation of the edge/screw character of

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dislocations from the experimental value of parameter q and for the determination of the dislocation density from CMWP fitting. The analysis of a load-penetration depth curve

E , 1  2

(3)

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M

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obtained by depth-sensing indentation provides the indentation modulus defined as:

where E and ν are the average Young’s modulus and Poisson’s ratio. If the size of the indentation is much smaller than the grain size, the value of M depends on the orientation of the indented grain due to the elastic anisotropy of the crystal. Vlassak and Nix [30] have shown that the indentation modulus Mhkl measured on the (hkl) surface by a Berkovich indenter can be expressed as the product of the isotropic indentation modulus, Miso, a correction factor βhkl due to the elastic anisotropy, and another factor

hkl owing to the anisotropic (triangular) shape of the Berkovich punch: M hkl   hkl  hkl M iso ,

(4)

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ACCEPTED MANUSCRIPT where Miso is the indentation modulus measured on a randomly oriented, polycrystalline aggregate consisting of crystals which are much smaller than the indent (i.e. this is the

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average indentation modulus). The dependence of factor hkl on the orientation of the

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triangular indent on the surfaces (001), (101) and (111) is plotted in Fig. 8 of Ref. [30]. For the surface (001) this factor equals 1.058 independently of the indent orientation. For surfaces (101) and (111) the value of factor hkl varies with the angle between one

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of the sides of the indenter and directions 10 1  and 112  , respectively. In the present experiments 101 and 111 are 1.057 and 1.051, respectively.

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For grains with cubic crystal structure the correction factor βhkl is a function of the Poisson’s ratio in the cube directions (ν100) and the anisotropy factor (A) [30]. βhkl can

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be given by the following formula [30]: (5)

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 hkl  a  c A  A0 B ,

where a, c, A0 and B depend on ν100. The parameters in eq. (5) for β001, β101 and β111 are

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listed in Table 1 of Ref. [30] for six different values of ν100, namely for 0.2, 0.25, 0.3,

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0.35, 0.4 and 0.45. Due to the very large average grain size of the present HEA material (several hundreds of microns as shown by the EBSD images in Figs. 1 and 6), Miso cannot be determined. However, Miso can be eliminated by expressing the ratios of M001, M101 and M111 using eq. (4): M 001  001 001 M   and 001  001 001 .  M 101 101101 M 111 111111

(6)

The left sides in the formulas of eq. (6) can be determined experimentally from the indentation moduli measured on surfaces (001), (101) and (111). The right sides can be calculated as a function of A and ν100 (see eq. (5)), therefore, if the ratio of the

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ACCEPTED MANUSCRIPT experimentally determined indentation moduli and the theoretically calculated ratio of the correction factors are made equal, the values of A and ν100 can be obtained.

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In the present experiment the indentation moduli were determined on the area shown in

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Fig. 6 using a UMIS nanoindentation device with a Berkovich indenter and applying a maximum load of 100 mN. The following values were obtained for the indentation moduli: M001=88 GPa, M101=97 and M111=99 GPa. Figures 7 and 8 show the calculated

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ratio of the correction factors (  hkl  hkl ) for the surface pairs 001-101 and 001-111 as a function of the anisotropy factor A, respectively, for six different values of ν100 between

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0.2 and 0.45. The intersection of each curve with the experimental ratio of the indentation moduli gives a possible value of A for a given value of ν100. Then, for 001-

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101 and 001-111 surface pairs the functions of the anisotropy factor A versus the Poisson ratio ν100 are plotted in Fig. 9. From the coincidence of the two curves for 001-

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101 and 001-111, the values of 2.3 ± 0.2 and 0.25 ± 0.05 are obtained for A and ν100,

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respectively. This anisotropy factor was used for the estimation of the theoretical values of parameter q for pure screw and edge dislocations. According to the vertical dashed

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line in Fig. 5 the values of q for pure screw and edge dislocations are 2.65  0.05 and 1.10  0.50, respectively. The comparison of the theoretically calculated and the experimentally obtained q values (see Table 1) suggests that with increasing strain the dislocation character became more screw. This can be explained by the reduced mobility of screw dislocations compared to edge dislocations in bcc structures. This difficulty in motion of screw dislocations is due to the core properties of screw dislocations, dissociated into a non-planar configuration while edge dislocations are splitted into partials only in their glide planes [31]. As a consequence, during plastic deformation edge dislocation segments can annihilate more

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ACCEPTED MANUSCRIPT easily than screw ones thereby the remaining dislocations have more screw character. It should be noted that the value of Ch 00 also depends on the anisotropy factor, as shown

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in [29]. For A = 2.3 ± 0.2 and 0.5 < c12/c44 < 2, the values of Ch 00 are 0.305 ± 0.015 and

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0.260 ± 0.045 in the cases of screw and edge dislocations, respectively [29]. Since Ch 00 only slightly depends on the edge/screw character of dislocations, the average of the

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values obtained for pure screw and edge cases (0.28) was used in the CMWP fitting procedure for the determination of the crystallite size and the dislocation density.

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The area-weigthed mean crystallite size and the dislocation density determined from the diffraction peak profile analysis for the compressed samples are listed in Table 1. For

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the initial material the diffraction peaks were as narrow as the instrumental profiles (Δ(2Θ)=0.02°), therefore these lines were not evaluated for the microstructure. It is

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noted that the peak breadths obtained for the initial (undeformed) sample reflect the

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diffraction line broadening caused by the distortion of the lattice due to different-sized atoms in the present HEA. Therefore, with the application of the instrumental correction

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this distortion effect was eliminated during the evaluation of line profiles. In the sample compressed plastically at 3%, the crystallite size and the dislocation density were 151 nm and 2.0 × 1014 m-2, respectively. It is noted that in plastically deformed metallic materials the crystallite size obtained by X-ray line profile analysis is usually smaller than the grain size determined by electron microscopy. This difference can be explained by the fact the crystallite is equivalent to the volume scattering X-rays coherently and dislocation patterns inside the grains may break the coherency of X-rays. The present investigation shows that the crystallite size decreased while the dislocation density increased with increasing strain during compression of the present HEA material, and their values reached about 123 nm and 10 × 1014 m-2, respectively, at the plastic strain 13

ACCEPTED MANUSCRIPT of 10%. After compression up to plastic strain of 20% the crystallite size was reduced to 39 nm, while the dislocation density increased to 15 × 1014 m-2. Similar high dislocation

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density in conventional alloys can be obtained only by severe plastic deformation at an

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equivalent strain of about 100% [32].

3.4. TEM investigation of the deformation substructure

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Figure 10 shows TEM micrographs for samples deformed at different plastic strains of 1 % (Fig. 10a), 3 % (Fig. 10b) and 10 % (Fig. 10c). It can be seen that for small strains

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the deformation localizes within bands that delineate defect free domains inside grains. Both the number of bands and the dislocation density inside the bands seem to increase

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with increasing plastic strain. The Burgers vector and the edge/screw character of dislocations within the bands have been studied in details by TEM [24]. Careful

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inspection of the TEM images using the extinction rule for dislocations showed that the

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Burgers vector is of a/2<111> type and the dislocations at higher strains are mainly of screw character, which is in line with XLPA results described above. Although TEM

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investigates much smaller volume than that in XLPA, the images reflects relatively well the order of magnitude of the average dislocation density determined by the latter method. For instance, the average dislocation spacing at a strain of 10% is 32 nm determined as the inverse square-root of the dislocation density obtained by XLPA. This value is in accordance with the visual observation of the dislocation spacing in Fig. 10c. The comparison of the TEM images obtained at different strains (see Fig. 10) reveals a high rate of the increase of dislocation density during plastic deformation which is also in accordance with the results of XLPA. This observation can be explained by the difficult annihilation of dislocations due to the high stress required for dislocation

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ACCEPTED MANUSCRIPT motion in HEA materials. The magnitude of attractive force between dislocations with opposite signs in HEAs is not very different from that in other bcc metals since the

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elastic constants and Burgers vector magnitude are similar. At the same time, the stress

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required for dislocation motion (i.e. the Peierls stress) is expected to reach much higher value in HEAs than in other bcc metals, therefore dislocations with opposite signs can exist closer to each other without annihilation. Due to the hindered annihilation, the

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dislocation density will be larger for a given strain.

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3.5. Correlation between the yield strength and the dislocation density The yield strength of the HEA samples compressed up to the strains of 3, 10 and 20%

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are 980, 1035 and 1050 MPa, respectively. The yield strength (σY) of plastically deformed metallic materials is usually related to the dislocation density using the Taylor

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equation [33]:

 Y   0  M T Gb  ,

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(7)

where  0 is the friction stress,  is a constant describing the dislocation hardening, G is

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the shear modulus, b is the modulus of the Burgers vector (0.2944 nm), MT is the Taylor factor. The value of MT in bcc crystals varies between 2.75 and 3.06, depending on the type of slip systems populated by dislocations [34]. If the microstructure is texture-free and the glide occurs only in the most common slip system (a/2<111>{110}), the Taylor factor is 3.06. In the present study this value was selected for MT. From the compression stress-strain curves 890 MPa was obtained for  0 . The average shear modulus, G, was determined from the average Young’s modulus (E = 87 GPa) obtained from the indentation measurements and the Poisson’s ratio (ν = 0.25) as G 

E  35 GPa . 21   

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ACCEPTED MANUSCRIPT Substituting these values into eq. (7), the dislocation hardening parameter  was found to be 0.16 ± 0.04 for the three compressed samples. This observation is in a reasonable

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agreement with the experimental results obtained previously for other, non-HEA bcc

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metallic materials such as different steels, Nb and Ta. For these materials  varies between 0.17 and 0.60 [35-38]. The relatively low value of  for the present HEA material is in line with the low strain hardening observed on the true stress – true strain

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curve. It seems that the main component in the compression flow stress is the Peierls

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stress and dislocation hardening has a lower contribution.

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ACCEPTED MANUSCRIPT 4. Conclusions Equimolar Ti20Zr20Hf20Nb20Ta20 high entropy alloy with bcc structure was deformed by

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XLPA and TEM. The following conlculsions were obtained:

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compression and the microstructure evolution as a function of strain was investigated by

1. In the intial sample the grain size distribution was broad, ranging between 10 and 350 m. A high density of dislocations was developed during compression

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even at moderate plastic strains. At the highest applied strain (20%) the dislocation density was 15 × 1014 m-2 as determined by XLPA. The dislocation

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density obtained by XLPA was in accordance with the dislocation spacing observed in the TEM images.

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2. TEM images revealed that for small strains deformation bands were formed with high dislocation density and between the bands defect free domains were

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observed. Both the number of bands and the dislocation density inside the bands

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seem to increase with increasing plastic strain. 3. The single crystal elastic anisotropy factor was determined as 2.3 ± 0.2 by

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indentation technique which was required for the determination of the edge/screw character and the density of dislocations by XLPA. Using the elastic anisotropy factor, the theoretical values of the parameter describing the dislocation character were determined for pure edge and screw dislocations. Comparing these values with the experimentally determined parameters, it was found that the screw character of dislocations became stronger with increasing strain. This observation was supported by TEM analysis. 4. The present HEA material has a high yield strength of about 890 MPa. The strain hardening during compression was caused by the increase of the

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dislocation density. The dislocation hardening parameter () has a relatively low value but it is still in the range determined for other bcc non-HEA metallic

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materials. The Peierls stress has the main component in the flow stress and

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dislocation hardening has a lower contribution even for high dislocation densities.

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Acknowledgements

This work was partly supported by the Hungarian Scientific Research Fund, OTKA,

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Grant No. K-109021. The study received additional funding from the project KMOP4.2.1/B-10-2011-0002. The authors are grateful to Mr. Peter Szommer and Mr. Gabor

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Varga for the nanoindentation and some EBSD investigations, respectively.

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the phase stability of equiatomic high-entropy alloys. Acta Mater 2013;61:2628–38. Tsai MH, Yeh JW. High-entropy alloys: a critical review. Mater Res Lett

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pressure-torsion processed Nb and Ta. Acta Mater 2013;61:632-642.

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Figure 1. EBSD inverse pole figures map showing the microstructure in the initial

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(undeformed) material.

Figure 2. Engineering stress vs engineering strain (red color) and true stress vs true

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strain (blue color) plots of the as-processed HEA during room temperature compression

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at a strain rate of 1.5  10-3s-1.

Figure 3. The CMWP fitting for the sample compressed up to 20% plastic strain. The

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open circles and the solid line represent the measured data and the fitted curve, respectively. The difference between the measured and the fitted patterns is shown at

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the bottom.

Figure 4. The classical (a) and the modified (b) Williamson-Hall plots for the sample

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compressed up to 20% plastic strain.

Figure 5. The variation of parameter q (defined in eq. (2)) for edge and screw dislocations in bcc crystals as a function of the anisotropy factor A 

2c44 for three c11  c12

different usual values of c12/c44. See the text for more details.

Figure 6. EBSD image showing the area investigated by nanoindentation. The numbers in some grains indicate the lattice planes parallel to the surface. The indentation moduli obtained for these grains were used to calculate the elastic anisotropy factor. 24

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Figure 7. The ratio of the correction factors for the indentation moduli measured on 2c44 . The curves c11  c12

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surfaces (001) and (101) as function of the anisotropy factor A 

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correspond to the Poisson ratio (ν100) values of 0.2, 0.25, 0.3, 0.35, 0.4 and 0.45. (M001/M101)exp is the experimental value of the ratio of the indentation moduli measured

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on surfaces (001) and (101). See the text for more details.

Figure 8. The ratio of the correction factors for the indentation moduli measured on

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surfaces (001) and (111) as function of the anisotropy factor A 

2c44 . The curves c11  c12

correspond to the Poisson ratio (ν100) values of 0.2, 0.25, 0.3, 0.35, 0.4 and 0.45.

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(M001/M111)exp is the experimental value of the ratio of the indentation moduli measured

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on surfaces (001) and (111). See the text for more details.

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Figure 9. The anisotropy factor A 

2c44 versus the Poisson ratio ν100 determined c11  c12

from the indentation moduli ratios for (001)-(101) and (001)-(111) surface pairs. The

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two curves coincide at the anisotropy factor of 2.3 ± 0.2.

Figure 10. TEM micrographs showing the dislocations patterning after compression test at room temperature for different plastic strains: (a) p  1%; (b) p  3%; (a) p  10%.

Table 1. The average lattice constant and the parameters of the microstructure obtained by X-ray line profile analysis. area is the area-weighted mean crystallite size, ρ is the

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dislocation density and q is a parameter describing the edge/screw character of

compressed, 3% compressed, 10%

ρ

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[10 m-2]

q

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-

2.0 ± 0.6

1.0 ± 0.1

123 ± 14

10 ± 2

2.1 ± 0.1

39 ± 5

15 ± 2

2.4 ± 0.1

-

151 ± 16

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compressed, 20%

area [nm]

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Initial

Lattice constant [nm] 0.3414 ± 0.0005 0.3401 ± 0.0002 0.3399 ± 0.0002 0.3397 ± 0.0003

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ACCEPTED MANUSCRIPT Highlights  Ti20Zr20Hf20Nb20Ta20 high entropy alloy was processed by arc-melting The mechanical was evaluated by RT compression test



The microstructure evolution was studied by XLPA and TEM

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With increasing strain the dislocation character became more screw.

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The yield strength was related to the development of the dislocation density

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