Materials Characterization 108 (2015) 1–7

Contents lists available at ScienceDirect

Materials Characterization

j ourna l homepage: www.e lsev ie r .com/ locate /matchar

Microstructural investigation of plastically deformedTi20Zr20Hf20Nb20Ta20 high entropy alloy by X-ray diffraction andtransmission electron microscopy

G. Dirras a,⁎, J. Gubicza b, A. Heczel b, L. Lilensten c, J.-P. Couzinié c, L. Perrière c, I. Guillot c, A. Hocini a

a Université Paris 13, Sorbonne Paris Cité, LSPM (UPR 3407) CNRS, 99 avenue JB Clément, 93430 Villetaneuse, Franceb Department of Materials Physics, Eötvös Loránd University, Budapest, P.O. Box 32, H-1518, Hungaryc Université Paris Est, ICMPE (UMR 7182), CNRS, UPEC, 94320 Thiais, France

⁎ Corresponding author.E-mail address: dirras@univ-paris13.fr (G. Dirras).

http://dx.doi.org/10.1016/j.matchar.2015.08.0071044-5803/© 2015 Elsevier Inc. All rights reserved.

a b s t r a c t

a r t i c l e i n f o

Article history:Received 31 July 2015Received in revised form 10 August 2015Accepted 11 August 2015Available online 14 August 2015

Keywords:High entropy alloyX-ray diffractionDislocationsTEMYield strength

Themicrostructure 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 meancrystallite 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 showsthat the crystallite size decreased while the dislocation density increased with strain during compression, andtheir values reached about 39 nm and 15 × 1014 m−2, respectively, at a plastic strain of ~20%. It was revealedthat with increasing strain the dislocation character became more screw. This can be explained by the reducedmobility of screw dislocations compared to edge dislocations in bcc structures. These observations are in linewith TEM investigations. The development of dislocation density during compression was related to the yieldstrength evolution.

© 2015 Elsevier Inc. All rights reserved.

1. Introduction

Since the pioneeringworks byYeh et al. [1] and Cantor et al. [2] high-entropy alloys (HEAs) have triggered a lot of expectation as potentialnew family of structural component materials [3,4]. Actually, HEAsrefer to multi-elementary (disordered) solid solutions with at least 5elements whose concentration is close to equimolarity. One of the pro-posed empirical parameters involved in HEA concept – and also in theformation of the multicomponent solid solutions – is the contributionof the mixing entropy term to the Gibbs free energy of mixing for thealloy system [5]. For HEAs the value of the mixing entropy is high andtherefore sufficient to overcome the enthalpies of compound formationand phase separation. In such a case, solid solution is expected to bestabilized [6]. However, a recent work [7] has revealed that althoughthe above concept can explain the single-phase state of some multi-element alloys [2], it cannot be used as a general rule for all HEAs.Indeed, many alloys meeting the proposed criteria, including HEAs,possess complex microstructures with multiple phases [8,9], sinceother quantities, such asmixing enthalpy or valence electron concentra-tion, also influence the phase stability [10].

HEAs with simple solid solution structures, whatever face-centeredcubic (fcc) or body-centered 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],outstandingwear and fatigue properties [17], good corrosion resistance[18] and biocompatibility [19], making them promisingmaterials for in-dustrial and structural applications [13]. Among all the attractive newcompositions, refractory HEAs have been intensively studied by manygroups, particularly by Senkov and collaborators [14–16,20–23]. In par-ticular, the equimolar bcc TiZrHfNbTa is a promising HEA for the appli-cations performed in awide temperature range from room temperature(RT) to approximately 600 °C [21]. The effect of the crystal structure, thechemical composition and the testing temperature on the mechanicalbehavior has been studied in different HEAs [13]. However, the effectof the lattice defects, such as dislocations, formed during plasticstraining on the mechanical performance (e.g. the strength) has beennot investigated in details. Recently and for thefirst time, detailed trans-mission electron microscopy (TEM) investigations have been carriedout in order to comprehend the dislocation controlled mechanisms ofplastic deformation in equimolar TiZrHfNbTa HEA alloy duringcompression at RT [24]. The operation of thermally activated deforma-tion processes has been evidenced by the joint observation of low ap-parent activation volumes compatible with a Peierls mechanism andthe glide of screw dislocation with the Burgers vector b = a/2b111N inthe first stage of plastic deformation.

In the present work, the density, the arrangement and theedge/screw character of dislocations in an equimolar bcc TiZrHfNbTa

Fig. 1. EBSD inverse pole figure map showing the microstructure in the initial (unde-formed) material.

2 G. Dirras et al. / Materials Characterization 108 (2015) 1–7

HEA are monitored during compression at RT. According to the knowl-edge of the authors, this is the first study which gives a detailed charac-terization of the dislocation structure in a HEA material applying thecombination of X-ray line profile analysis and post mortem TEMinvestigations. For a correct evaluation of X-ray diffraction peakbroadening, the elastic anisotropy factor of the crystal is necessary.This paper also gives a method for the determination of this quantityin polycrystalline HEAs. The investigation of the relationship betweenthe dislocation density and the yield strength yields the dislocationstrengthening parameter in the present HEA material.

2. Experimental procedure

2.1. Materials and processing

A refractoryHEAwith equiatomic composition (Ti20Zr20Hf20Nb20Ta20)was processed by arc melting and induction processes under argonatmosphere. Two master alloys, Nb–Ta and Ti–Zr–Hf, were first meltedon a water-cooled copper plate from high purity metals (exceeding99.9% purity) in the form of slugs and wires. Both alloys were re-melted twice in order to improve homogeneity and thenmixed togeth-er. A titanium getter was used prior each arc-melting fusion in order tocapture the residual oxygen in the chamber. Homogenization of thealloy was then assessed by high frequency induction melting insectorized cooled copper crucible under helium atmosphere. Finally,the homogenized refractory alloy was obtained by arc melting in theform of an ingot with 60 mm in length and approximately 10 mm indiameter.

2.2. Compression tests

Compression tests were carried out at room temperature at a strainrate of 1.5 × 10−3 s−1 on a cylindrical specimenwith 5mm in diameterand 7 mm in length using a 100 kN MTS testing machine (20/MH). Inorder to study the microstructure evolution during compression, sam-ples were deformed up to different plastic strain values between 2and 20%.

2.3. EBSD and TEM investigations

The grain structure of the initial sample was studied by electronbackscatter diffraction (EBSD) investigations. The investigated surfacewas prepared bymechanical grindingusing 1200 to 4000 grit SiC papersfollowed by a final polishing step using a 20 nm alumina oxide particlesuspension (OPS) from Struers™. EBSD investigations were carried outusing a Zeiss Supra 40VP FEG scanning electron microscope (SEM).After mechanical testing, transmission electron microscopy (TEM)analyses were conducted on samples cut perpendicular to the loadaxis. Thin foils with 3 mm in diameter were prepared by mechanicalpolishing to 100 μm and finally thinned by the classical twin-jetelectropolishing apparatus using a HF/H2SO4 solution at −35 °C. TheTEM observations were carried out by a JEOL 2000EX operating at200 kV.

2.4. Lattice parameter and microstructure from X-ray diffraction

The average lattice parameter for the initial and the deformed HEAsamples was investigated by X-ray diffraction (XRD) using a PhilipsX'Pert Θ–2Θ powder diffractometer with CuKα radiation (wavelength:λ = 0.15418 nm). XRD patterns revealed that all the studied sampleshave body-centered cubic (bcc) structure. The average lattice parameterwas determined by extrapolating the lattice parameters obtained fromthe different reflections to the diffraction angle of 2Θ = 180° usingthe Nelson–Riley method [25]. The microstructure in the specimenswas studied by X-ray line profile analysis (XLPA). The X-ray line profileswere measured by a high-resolution rotating anode diffractometer

(type: RA-MultiMax9, Manufacturer: Rigaku) using CuKα1 (wave-length, λ = 0.15406 nm) radiation. Two-dimensional imaging platesdetected the Debye–Scherrer diffraction rings. The line profiles weredetermined as the intensity distribution perpendicular to the ringsobtained by integrating the two dimensional intensity distributionalong the rings. The diffraction patterns were evaluated by theConvolutional Multiple Whole Profile (CMWP) analysis [26,27]. In thismethod, the diffraction pattern is fitted by the sum of a backgroundspline and the convolution of the instrumental pattern and the theoret-ical line profiles related to crystallite size and dislocations. The instru-mental diffraction peaks were measured on a LaB6 standard material(SRM 660). The CMWP evaluation procedure yields the area-weightedmean crystallite size (bxNarea), the dislocation density (ρ) and parame-ter q which describes the edge/screw character of dislocations.

3. Results and discussion

3.1. As-cast microstructure

A detailed characterization for the as-cast microstructure of thisrefractory alloy has been given elsewhere [28]. Fig. 1 is a typical inversepole figure of the initial microstructure. There is no preferential crystal-lographic orientation of the grains (see the inset showing of the stan-dard stereographic triangle). The grain shape is irregular and the grainsize distribution is broad, ranging between 10 and 350 μm. As it wasrevealed in a previous study [28], the size and morphology of grains aswell as the chemical composition depend on the cooling rate duringHEA processing. Indeed, it was shown that in the upper part of theingot (lower cooling rate) the grains have a dendritic structure andthe dendrite arms are mostly of Ta and Nb enriched while micro-segregations consisting of Ti, Zr and Hf rich zones are found in theinterdendritic zones

3.2. Mechanical behavior

Typical engineering stress versus engineering strain and deducedtrue stress versus true strain compression curves for the as-processedHEA are shown in Fig. 2. In accordance with the work by Senkov et al.[21], the engineering stress versus engineering strain plot display stronglinear hardening behavior. The yield strength is about 890 MPa. Itshould be noticed thatwhen the true stress is plotted against true strain,the observed hardening is reduced.

Fig. 2. Engineering stress vs engineering strain (red color) and true stress vs true strain(blue color) plots of the as-processed HEA during room temperature compression at astrain rate of 1.5 × 10−3 s−1. (For interpretation of the references to color in this figurelegend, the reader is referred to the web version of this article.)

Fig. 3. The CMWP fitting for the sample compressed up to 20% plastic strain. The open cir-cles and the solid line represent the measured data and the fitted curve, respectively. Thedifference between the measured and the fitted patterns is shown at the bottom.

3G. Dirras et al. / Materials Characterization 108 (2015) 1–7

3.3. Microstructure of the compressed samples from X-ray line profileanalysis

The average lattice constants determined for the initial and thedeformed samples are listed in Table 1. All lattice constants are in therange between 0.3397 and 0.3414 nm. For the compressed samplesthe lattice parameter remains unchanged within the experimentalerror. The small difference between the lattice constants of the initialand compressed specimens can be explained by the slight variation ofthe chemical composition in the as-cast specimen, as revealed bycoupled energy and wavelength dispersive spectrometry (EDS/WDS)in a previous paper [28].

The average crystallite size and dislocation density were determinedby XLPA in samples compressed up to true plastic strains of 3, 10 and20%. As an example, Fig. 3 shows the X-ray diffraction pattern for thesample compressed up to 20%. Reflection 222 was omitted from thepattern due to its weak intensity. The dependence of the peak breadthson the diffraction order (i.e. on the indices hkl) can be visualized byplotting the full width at half maximum (FWHM) as a function of themodulus of the diffraction vector, g (classical Williamson–Hall plot)[29]. FWHM and g can be calculated as:

FWHM ¼ Δ 2Θð Þ cosΘλ

andg2 sinΘ

λ; ð1Þ

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

Table 1The average lattice constant and the parameters of the microstructure obtained by X-rayline profile analysis. bxNarea is the area-weighted mean crystallite size, ρ is the dislocationdensity and q is a parameter describing the edge/screw character of dislocations.

Sample Lattice constant [nm] bxNarea [nm] ρ [1014 m−2] q

Initial 0.3414 ± 0.0005 – – –Compressed, 3% 0.3401 ± 0.0002 151 ± 16 2.0 ± 0.6 1.0 ± 0.1Compressed, 10% 0.3399 ± 0.0002 123 ± 14 10 ± 2 2.1 ± 0.1Compressed, 20% 0.3397 ± 0.0003 39 ± 5 15 ± 2 2.4 ± 0.1

anisotropic strain field of dislocations, and this phenomenon is referredto as strain anisotropy [29]. The contrast effect of dislocations online broadening can be taken into account by the average contrast(or orientation) factor of dislocations [29]. For a polycrystallinematerialcontaining dislocations the FWHM values fit to a smooth curve, whenthey are plotted as a function ofg2Chkl, whereChkl is the average contrastfactor given as:

Chkl ¼ Ch00 1−qh2k2 þ k2l2 þ h2l2

h2 þ k2 þ l2� �2

0B@

1CA: ð2Þ

In Eq. (2) hkl are the indices of reflections and Ch00 is the contrastfactor for reflection h00. Fig. 4b shows the modified Williamson–Hallplot for the sample compressed up to 20%. The datum points follow asmooth curve if q=2.4 is selected. It is noted that thefitting of themea-sured diffraction pattern by the CMWPprocedure also gives the value ofq which was the same within the experimental error as the valueobtained by the modified Williamson–Hall plot. The values of q for alldeformed samples determined by CMWP fitting are listed in Table 1.

The comparison of the experimentally obtained qwith the theoreti-cal values calculated for pure edge and screw dislocations enables thedetermination of the edge/screw character of the dislocation structure.The theoretical values of q for pure edge and screw dislocations dependon the anisotropic elastic constants of the studied material. The depen-dence of parameter q on the elastic constants of bcc polycrystals can begivenusing the ratio of the elastic constant c12/c44 and the elastic anisot-ropy factor (A ¼ 2c44

c11−c12) [4]. Fig. 5 shows parameter q for edge and screw

dislocations in bcc crystals as a function of A for three different usualvalues of c12/c44 (0.5, 1 and 2). The data were taken from Ref. [29]. Asthe single crystal anisotropic elastic constants are not known for thepresent HEA composition, therefore the exact value of parameter qfor pure edge and screw dislocations cannot be determined. In addition,in the CMWP evaluation of the diffraction patterns, one fitting

parameter is Ch00b2ρ, where b is the modulus of the Burgers vector

of dislocations. Assuming the usual Burgers vector in bcc structure(a/2b111N{110}), b equals 0.2944 nm in the present HEA material.Since Ch00 depends on the anisotropic elastic constants, without theknowledge of their values the dislocation density cannot be determined.

For a polycrystalline material the single crystal elastic anisotropyfactor can be determined by depth-sensing indentation technique, asshown by Vlassak and Nix [30]. Then, this factor may be used for theestimation of the edge/screw character of dislocations from the experi-mental value of parameter q and for thedetermination of the dislocation

Fig. 4. The classical (a) and the modified (b) Williamson–Hall plots for the sample compressed up to 20% plastic strain.

4 G. Dirras et al. / Materials Characterization 108 (2015) 1–7

density from CMWP fitting. The analysis of a load–penetration depthcurve obtained by depth-sensing indentation provides the indentationmodulus defined as:

M ¼ E1−ν2 ; ð3Þ

where E and ν are the average Young's modulus and Poisson's ratio. Ifthe size of the indentation is much smaller than the grain size, thevalue of M depends on the orientation of the indented grain due tothe elastic anisotropy of the crystal. Vlassak and Nix [30] have shownthat the indentation modulus Mhkl measured on the (hkl) surface by aBerkovich indenter can be expressed as the product of the isotropicindentation modulus, Miso, a correction factor βhkl due to the elasticanisotropy, and another factor αhkl owing to the anisotropic (triangular)shape of the Berkovich punch:

Mhkl ¼ αhklβhklMiso; ð4Þ

whereMiso is the indentation modulus measured on a randomly orient-ed, polycrystalline aggregate consisting of crystals which are muchsmaller than the indent (i.e. this is the average indentation modulus).The dependence of factor αhkl on the orientation of the triangular indenton the surfaces (001), (101) and (111) is plotted in Fig. 8 of Ref. [30]. Forthe surface (001) this factor equals 1.058 independently of the indentorientation. For surfaces (101) and (111) the value of factor αhkl

varies with the angle between one of the sides of the indenter anddirections ½101� and ½112�, respectively. In the present experimentsα101 and α111 are 1.057 and 1.051, respectively.

Fig. 5. The variation of parameter q (defined in Eq. (2)) for edge and screw dislocations in

bcc crystals as a function of the anisotropy factorA ¼ 2c44c11−c12

for three different usual values

of c12/c44. See the text for more details.

For grains with cubic crystal structure the correction factor βhkl isa function of the Poisson's ratio in the cube directions (ν100) andthe anisotropy factor (A) [30]. βhkl can be given by the followingformula [30]:

βhkl ¼ aþ c A−A0ð ÞB; ð5Þ

where a, c, A0 and B depend on ν100. The parameters in Eq. (5) for β001,β101 and β111 are listed in Table 1 of Ref. [30] for six different values ofν100, namely for 0.2, 0.25, 0.3, 0.35, 0.4 and 0.45. Due to the very largeaverage grain size of the present HEA material (several hundreds ofmicrons as shown by the EBSD images in Figs. 1 and 6), Miso cannot bedetermined. However, Miso can be eliminated by expressing the ratiosof M001, M101 and M111 using Eq. (4):

M001

M101¼ α001β001

α101β101and

M001

M111¼ α001β001

α111β111: ð6Þ

The left sides in the formulas of Eq. (6) can be determined experi-mentally from the indentation moduli measured on surfaces (001),(101) and (111). The right sides can be calculated as a function ofA and ν100 (see Eq. (5)), therefore, if the ratio of the experimentallydetermined indentation moduli and the theoretically calculated ratioof the correction factors are made equal, the values of A and ν100 canbe obtained.

In the present experiment the indentation moduli were determinedon the area shown in Fig. 6 using a UMIS nanoindentation device witha Berkovich indenter and applying a maximum load of 100 mN. The

Fig. 6. EBSD image showing the area investigated by nanoindentation. The numbers insome grains indicate the lattice planes parallel to the surface. The indentation moduliobtained for these grains were used to calculate the elastic anisotropy factor.

Fig. 7. The ratio of the correction factors for the indentation moduli measured on surfaces

(001) and (101) as function of the anisotropy factor A ¼ 2c44c11−c12

. The curves 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 theexperimental value of the ratio of the indentation moduli measured on surfaces (001)and (101). See the text for more details.

Fig. 9. The anisotropy factor A ¼ 2c44c11−c12

versus the Poisson ratio ν100 determined from the

indentation moduli ratios for (001)–(101) and (001)–(111) surface pairs. The two curvescoincide at the anisotropy factor of 2.3 ± 0.2.

5G. Dirras et al. / Materials Characterization 108 (2015) 1–7

following values were obtained for the indentation moduli: M001 =88GPa,M101= 97 andM111= 99GPa. Figs. 7 and 8 show the calculatedratio of the correction factors (αhkl, βhkl) for the surface pairs 001–101and 001–111 as a function of the anisotropy factor A, respectively, forsix different values of ν100 between 0.2 and 0.45. The intersection ofeach curve with the experimental ratio of the indentation moduligives a possible value of A for a given value of ν100. Then, for 001–101and 001–111 surface pairs the functions of the anisotropy factor Aversus the Poisson ratio ν100 are plotted in Fig. 9. From the coincidenceof the two curves for 001–101 and 001–111, the values of 2.3 ± 0.2 and0.25 ± 0.05 are obtained for A and ν100, respectively. This anisotropyfactorwas used for the estimation of the theoretical values of parameterq for pure screw and edge dislocations. According to the vertical dashedline in Fig. 5 the values of q for pure screw and edge dislocations are2.65 ± 0.05 and 1.10 ± 0.50, respectively.

The comparison of the theoretically calculated and the experimen-tally obtained q values (see Table 1) suggests thatwith increasing strainthe dislocation character became more screw. This can be explained bythe reduced mobility of screw dislocations compared to edge disloca-tions in bcc structures. This difficulty in motion of screw dislocations isdue to the core properties of screw dislocations, dissociated into anon-planar configuration while edge dislocations are split into partialsonly in their glide planes [31]. As a consequence, during plasticdeformation edge dislocation segments can annihilate more easily

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

(001) and (111) as function of the anisotropy factor A ¼ 2c44c11−c12

. The curves correspond to

the Poisson ratio (ν100) values of 0.2, 0.25, 0.3, 0.35, 0.4 and 0.45. (M001/M111)exp is the ex-perimental value of the ratio of the indentation moduli measured on surfaces (001) and(111). See the text for more details.

than screw ones thereby the remaining dislocations have more screwcharacter. It should be noted that the value of Ch00 also depends onthe anisotropy factor, as shown in [29]. For A = 2.3 ± 0.2 and0.5 b c12/c44 b 2, the values of Ch00 are 0.305 ± 0.015 and 0.260 ±0.045 in the cases of screw and edge dislocations, respectively [29].Since Ch00 only slightly depends on the edge/screw character ofdislocations, the average of the values obtained for pure screw andedge cases (0.28) was used in the CMWP fitting procedure for thedetermination of the crystallite size and the dislocation density.

The area-weighted mean crystallite size and the dislocation densitydetermined from the diffraction peak profile analysis for the com-pressed samples are listed in Table 1. For the initial material the diffrac-tion peakswere as narrowas the instrumental profiles (Δ(2Θ)=0.02°),therefore these lines were not evaluated for the microstructure. It isnoted that thepeak breadths obtained for the initial (undeformed) sam-ple reflect the diffraction line broadening caused by the distortion of thelattice due to different-sized atoms in the present HEA. Therefore, withthe application of the instrumental correction this distortion effect waseliminated during the evaluation of line profiles. In the samplecompressed plastically at 3%, the crystallite size and the dislocationdensity were 151 nm and 2.0 × 1014 m−2, respectively. It is noted thatin plastically deformed metallic materials the crystallite size obtainedby X-ray line profile analysis is usually smaller than the grain size deter-mined by electron microscopy. This difference can be explained by thefact the crystallite is equivalent to the volume scattering X-rays coher-ently and dislocation patterns inside the grains may break the coheren-cy of X-rays. The present investigation shows that the crystallite sizedecreasedwhile the dislocation density increasedwith increasing strainduring compression of the present HEA material, and their valuesreached about 123 nm and 10 × 1014 m−2, respectively, at the plasticstrain of 10%. After compression up to plastic strain of 20% the crystallitesize was reduced to 39 nm, while the dislocation density increased to15 × 1014 m−2. Similar high dislocation density in conventional alloyscan be obtained only by severe plastic deformation at an equivalentstrain of about 100% [32].

3.4. TEM investigation of the deformation substructure

Fig. 10 shows TEM micrographs for samples deformed at differentplastic strains of 1% (Fig. 10a), 3% (Fig. 10b) and 10% (Fig. 10c). It canbe seen that for small strains the deformation localizes within bandsthat delineate defect free domains inside grains. Both the number ofbands and the dislocation density inside the bands seem to increasewith increasing plastic strain. The Burgers vector and the edge/screwcharacter of dislocations within the bands have been studied in details

Fig. 10. TEM micrographs showing the dislocations patterning after compression test atroom temperature for different plastic strains: (a) εp ~ 1%; (b) εp ~ 3%; (c) εp ~ 10%.

6 G. Dirras et al. / Materials Characterization 108 (2015) 1–7

by TEM [24]. Careful inspection of the TEM images using the extinctionrule for dislocations showed that the Burgers vector is of a/2b111N typeand the dislocations at higher strains are mainly of screw character,which is in linewith XLPA results described above. Although TEM inves-tigates much smaller volume than that in XLPA, the images reflectsrelatively well the order ofmagnitude of the average dislocation densitydetermined by the latter method. For instance, the average dislocationspacing at a strain of 10% is 32 nm determined as the inverse square-root of the dislocation density obtained by XLPA. This value is inaccordance with the visual observation of the dislocation spacing inFig. 10c. The comparison of the TEM images obtained at different strains(see Fig. 10) reveals a high rate of the increase of dislocation densityduring plastic deformation which is also in accordance with the resultsof XLPA. This observation can be explained by the difficult annihilationof dislocations due to the high stress required for dislocation motionin HEA materials. The magnitude of attractive force between disloca-tions with opposite signs in HEAs is not very different from that in

other bcc metals since the elastic constants and Burgers vectormagnitude are similar. At the same time, the stress required for disloca-tion motion (i.e. the Peierls stress) is expected to reach much highervalue in HEAs than in other bcc metals, therefore dislocations withopposite signs can exist closer to each other without annihilation. Dueto the hindered annihilation, the dislocation density will be larger fora given strain.

3.5. Correlation between the yield strength and the dislocation density

The yield strength of the HEA samples compressed up to the strainsof 3, 10 and 20% are 980, 1035 and 1050 MPa, respectively. The yieldstrength (σY) of plastically deformed metallic materials is usuallyrelated to the dislocation density using the Taylor equation [33]:

σY ¼ σ0 þ αMTGbffiffiffiρ

p; ð7Þ

where σ0 is the friction stress,α is a constant describing the dislocationhardening, G is the shear modulus, b is the modulus of the Burgersvector (0.2944 nm), MT is the Taylor factor. The value of MT in bcccrystals varies between 2.75 and 3.06, depending on the type of slipsystems populated by dislocations [34]. If the microstructure istexture-free and the glide occurs only in the most common slip system(a/2b111N{110}), the Taylor factor is 3.06. In the present study thisvalue was selected for MT. From the compression stress–strain curves890MPawas obtained for σ0. The average shearmodulus, G, was deter-mined from the average Young's modulus (E = 87 GPa) obtained fromthe indentationmeasurements and the Poisson's ratio (ν=0.25) asG ¼

E2ð1þνÞ ¼ 35 GPa. Substituting these values into Eq. (7), the dislocation

hardening parameter α was found to be 0.16 ± 0.04 for the threecompressed samples. This observation is in a reasonable agreementwith the experimental results obtained previously for other, non-HEAbcc metallic materials such as different steels, Nb and Ta. For thesematerials α varies between 0.17 and 0.60 [35–38]. The relatively lowvalue of α for the present HEA material is in line with the low strainhardening observed on the true stress – true strain curve. It seemsthat the main component in the compression flow stress is the Peierlsstress and dislocation hardening has a lower contribution.

4. Conclusions

Equimolar Ti20Zr20Hf20Nb20Ta20 high entropy alloy with bccstructure was deformed by compression and the microstructureevolution as a function of strain was investigated by XLPA and TEM.The following conclusions were obtained:

1. In the initial sample the grain size distribution was broad, rangingbetween 10 and 350 μm. A high density of dislocations wasdeveloped during compression even at moderate plastic strains. Atthe highest applied strain (20%) the dislocation density was15 × 1014 m−2 as determined by XLPA. The dislocation densityobtained by XLPA was in accordance with the dislocation spacingobserved in the TEM images.

2. TEM images revealed that for small strains deformation bands wereformed with high dislocation density and between the bands defectfree domains were observed. Both the number of bands and thedislocation density inside the bands seem to increasewith increasingplastic strain.

3. The single crystal elastic anisotropy factor was determined as 2.3 ±0.2 by indentation technique which was required for the determina-tion of the edge/screw character and the density of dislocations byXLPA. Using the elastic anisotropy factor, the theoretical values ofthe parameter describing the dislocation character were determinedfor pure edge and screw dislocations. Comparing these values withthe experimentally determined parameters, it was found that the

7G. Dirras et al. / Materials Characterization 108 (2015) 1–7

screw character of dislocations became stronger with increasingstrain. This observation was supported by TEM analysis.

4. The present HEAmaterial has a high yield strength of about 890MPa.The strain hardening during compressionwas caused by the increaseof the dislocation density. The dislocation hardening parameter (α)has a relatively low value but it is still in the range determined forother bcc non-HEA metallic materials. The Peierls stress has themain component in the flow stress and dislocation hardening has alower contribution even for high dislocation densities.

Acknowledgments

Thisworkwas partly supported by theHungarian Scientific ResearchFund, OTKA, Grant No. K-109021. The study received additional fundingfrom the project KMOP-4.2.1/B-10-2011-0002. The authors are gratefultoMr. Peter Szommer andMr. Gabor Varga for the nanoindentation andsome EBSD investigations, respectively.

References

[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 alloydesign concepts and outcomes, Adv. Eng. Mater. 6 (2004) 299–303.

[2] B. Cantor, I.T.H. Chang, P. Knight, A.J.B. Vincent, Microstructural development inequiatomic multicomponent alloys, Mater. Sci. Eng. 375–377 (2004) 213–218.

[3] C.J. Tong, M.R. Chen, S.K. Chen, J.W. Yeh, S.J. Lin, S.K. Chen, T.T. Shun, S.Y. Chang,Mechanical performance of the AlxCoCrCuFeNi high-entropy alloy system withmultiprincipal elements, Metall. Mater. Trans. 36 (2005) 1263–1271.

[4] J.W. Yeh, Y.L. Chen, S.J. Lin, S.K. Chen, High-entropy alloys — a new era of exploita-tion, Mater. Sci. Forum 560 (2007) 1–9.

[5] S. Guo, C. Ng, J. Lu, C.T. Liu, Effect of valence electron concentration on stability of fccor bcc phase in high entropy alloys, J. Appl. Phys. 109 (2011) 103505, http://dx.doi.org/10.1063/1.3587228.

[6] C. Ng, S. Guo, J. Luan, S. Shi, C.T. Liu, Entropy-driven phase stability and slowdiffusion kinetics in an Al0.5CoCrCuFeNi high entropy alloy, Intermetallics 31(2012) 165–172.

[7] A. Gali, E.P. George, Tensile properties of high- and medium-entropy alloys,Intermetallics 39 (2013) 74–78.

[8] S. Singh, N. Wanderka, B.S. Murty, U. Glatzel, J. Banhart, Decomposition inmulticomponent AlCoCrCuFeNi high-entropy alloy, Acta Mater. 59 (2011) 182–190.

[9] J.M. Zhu, H.M. Fu, H.F. Zhang, A.M. Wang, H. Li, Z.Q. Hu, Synthesis and properties ofmultiprincipal component AlCoCrFeNiSix alloys, Mater. Sci. Eng. 527 (2010)7210–7214.

[10] F. Otto, Y. Yang, H. Bei, E.P. George, Relative effects of enthalpy and entropy onthe phase stability of equiatomic high-entropy alloys, Acta Mater. 61 (2013)2628–2638.

[11] M.H. Tsai, J.W. Yeh, High-entropy alloys: a critical review, Mater. Res. Lett. 2 (2014)107–123.

[12] Z. Tang, M.C. Gao, H. Diao, T. Yang, J. Liu, T. Zou, Y. Zhang, Z. Lu, Y. Cheng, Y. Zhang,Aluminum alloying effects on lattice types, microstructures, and mechanicalbehavior of high-entropy alloy systems, JOM 65 (2013) 1848–1858.

[13] Y. Zhang, T.T. Zuo, Z. Tang, M.C. Gao, K.A. Dahmen, P.K. Liaw, Z.P. Lu, Microstructuresand properties of high-entropy alloys, Prog. Mater. Sci. 61 (2014) 1–93.

[14] O.N. Senkov, G.B. Wilks, J.M. Scott, D.B. Miracle, Mechanical properties ofNb25Mo25Ta25W25 and V20Nb20Mo20Ta20W20 refractory high entropy alloys,Intermetallics 19 (2011) 698–706.

[15] O.N. Senkov, J.M. Scott, S.V. Senkova, D.B. Miracle, C.F. Woodward, Microstructureand room temperature properties of a high-entropy TaNbHfZrTi alloy, J. AlloysCompd. 509 (2011) 6043–6048.

[16] O.N. Senkov, S.V. Senkova, D.B.Miracle, C.Woodward,Mechanical properties of low-density, refractory multi-principal element alloys of the Cr–Nb–Ti–V–Zr system,Mater. Sci. Eng. 565 (2013) 51–62.

[17] M.A. Hemphill, T. Yuan, G.Y. Wang, J.W. Yeh, C.W. Tsai, A. Chuang, P.K. Liaw, Fatiguebehavior of Al0.5CoCrCuFeNi high entropy alloys, Acta Mater. 60 (2012) 5723–5734.

[18] C.P. Lee, C.C. Chang, Y.Y. Chen, J.W. Yeh, H.C. Shih, Effect of the aluminium content ofAlxCrFe1.5MnNi0.5 high-entropy alloys on the corrosion behavior in aqueousenvironments, Corros. Sci. 50 (2008) 2053–2060.

[19] V. Braic, M. Balaceanu, M. Braic, A. Vladescu, S. Panseri, A. Russo, Characterization ofmulti-principal-element (TiZrNbHfTa)N and (TiZrNbHfTa)C coatings for biomedicalapplications, J. Mech. Behav. Biomed. Mater. 10 (2012) 197–205.

[20] O.N. Senkov, G.B.Wilks, D.B. Miracle, C.P. Chuang, P.K. Liaw, Refractory high-entropyalloys, Intermetallics 18 (2010) 1758–1765.

[21] O.N. Senkov, J.M. Scott, S.V. Senkova, F. Meisenkothen, D.B. Miracle, C.F. Woodward,Microstructure and elevated temperature properties of a refractory TaNbHfZrTialloy, J. Mater. Sci. 47 (2012) 4062–4074.

[22] O.N. Senkov, C.F. Woodward, Microstructure and properties of a refractoryNbCrMo0.5Ta0.5TiZr alloy, Mater. Sci. Eng. 529 (2011) 311–320.

[23] O.N. Senkov, S.V. Senkova, C. Woodward, D.B. Miracle, Low-density, refractorymulti-principal element alloys of the Cr–Nb–Ti–V–Zr system: microstructure andphase analysis, Acta Mater. 61 (2013) 1545–1557.

[24] J.P. Couzinié, L. Lilensten, Y. Champion, G. Dirras, L. Perrière, I. Guillot, On the roomtemperature deformation mechanisms of a TiZrHfNbTa refractory high-entropyalloy, Mater. Sci. Eng. (2015) (in press).

[25] J. Nelson, D. Riley, An experimental investigation of extrapolation methods in thederivation of accurate until-cell dimensions of crystals, Proc. Phys. Soc. Lond. 57(1945) 160–177.

[26] G. Ribárik, J. Gubicza, T. Ungár, Correlation between strength and microstructure ofball-milled Al–Mg alloys determined by X-ray diffraction, Mater. Sci. Eng. 387–389(2004) 343–347.

[27] L. Balogh, G. Ribárik, T. Ungár, Stacking faults and twin boundaries in fcc crystalsdetermined by X-ray diffraction profile analysis, J. Appl. Phys. 100 (2006) 023512.

[28] J.P. Couzinié, G. Dirras, L. Perrière, T. Chauveau, E. Leroy, Y. Champion, I. Guillot,Microstructure of a near-equimolar refractory high-entropy alloy, Mater. Lett. 126(2014) 285–287.

[29] T. Ungár, I. Dragomir, Á. Révész, A. Borbély, The contrast factors of dislocations incubic crystals: the dislocation model of strain anisotropy in practice, J. Appl.Crystallogr. 32 (1999) 992–1002.

[30] J.J. Vlassak, W.D. Nix, Measuring the elastic properties of anisotropic materials bymeans of indentation experiments, J. Mech. Phys. Solids 42 (1994) 1223–1245.

[31] J. Gubicza, N.H. Nam, L. Balogh, R.J. Hellmig, V.V. Stolyarov, Ungár T. EstrinY,Microstructure of severely deformed metals determined by X-ray peak profileanalysis, J. Alloys Compd. 378 (2004) 248–252.

[32] J. Gubicza, N.Q. Chinh, Gy Krállics, I. Schiller, T. Ungár, Microstructure of ultrafine-grained fcc metals produced by severe plastic deformation, Curr. Appl. Phys. 6(2006) 194–199.

[33] G.I. Taylor, Plastic strain in metals, J. Inst. Met. 62 (1938) 307–324.[34] J.M. Rosenberg, H.R. Piehler, Calculation of the Taylor factor and lattice rotations for

bcc metals deforming by pencil glide, Metall. Trans. 2 (1971) 257–259.[35] Q. Li, Modeling the microstructure-mechanical property relationship for a 12Cr–

2W–V–Mo–Ni power plant steel, Mater. Sci. Eng. 361 (2003) 385–391.[36] R. Madec, L.P. Kubin, Second-order junctions and strain hardening in bcc and fcc

crystals, Scr. Mater. 58 (2008) 767–770.[37] P.L. Mosbrucker, D.W. Brown, O. Anderoglu, L. Balogh, S.A. Maloy, T.A. Sisneros, J.

Almer, E.F. Tulk, W. Morgenroth, A.C. Dippel, Neutron and X-ray diffraction analysisof the effect of irradiation dose and temperature onmicrostructure of irradiated HT-9 steel, J. Nucl. Mater. 443 (2013) 522–530.

[38] B. Jóni, E. Schafler, M. Zehetbauer, G. Tichy, T. Ungár, Correlation between themicrostructure studied by X-ray line profile analysis and the strength of high-pressure-torsion processed Nb and Ta, Acta Mater. 61 (2013) 632–642.