Physical Factors Controlling Large Shape Memory E ﬀ ect in FCC ↔ HCP Martensitic Transformation in CrMnFeCoNi High-Entropy-Alloy Single Crystals

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New non-equiatomic CrMnFeCoNi high-entropy alloys (HEAs) with a FCC lattice have the features that are presented below and can improve the reversible deformation, εrev, and SME governed by the FCC ↔ HCP MT.Firstly, the high concentration of substitution atoms in FCC HEAs leads to the solid solution strengthening of the FCC phase, heavy lattice distortion, and the high mobility of a/6<112> partial Shockley dislocations compared to that of a/2<110> perfect dislocations [13][14][15].This increases the tendency of the HEAs toward twinning deformation or the FCC-HCP transition [13,14,16].Secondly, HEAs are concentrated solid solutions in which the role of the short-range order (SRO) increases in the (i) localization of deformation in one system with the formation of dislocation pile-ups in the dislocation structure [17]; (ii) difficulty in the formation of large HCP martensite plates during growth in thickness due to the need to destroy the SRO via partial dislocations through one {111}FCC plane [14,17]; (iii) the delayed multiple development of a HCP martensite [18]; and (iv) a significant latent hardening of the secondary slip systems or HCP martensite at low strain levels, which manifests in the overshoot of the crystal axis through the [001]- [111] boundary of the stereographic triangle during tension [16,17].In CrMnFeCoNi HEA single crystals under these conditions, the FCC ↔ HCP MT can occur with the elastic accommodation of thin HCP martensitic crystals in the FCC phase and is not accompanied by the generation of dislocations during a stress-induced MT.To date, the SME of 1.91% was received in polycrystals of the Cr20Mn20Fe20Co35Ni5 HEA under bending deformation [13], 6.8 and 3.6%, respectively, in [111] -and [001]-single crystals of this alloy, oriented for multiple shear, at tension [19,20], and 12 and 15.6% under external tensile stress of 160 MPa in [144] -oriented crystals of Cr20Mn20Fe20Co37Ni3 and Cr20Mn20Fe20Co34.5Ni5.5 alloys, respectively, oriented for one system [18].The effect of a grain size from 3.0 to 82.2 µm on the SME was studied using polycrystals of the Cr20Mn20Fe20Co35Ni5 HEA [21].In this paper, it is shown that the maximum SME of 1.2% was obtained from a sample with a large grain size of 82.2 µm.In another hot-rolled Fe47.7Mn15.5Co9.8Cr10.8Ni5.1Si11.1 HEA with Si alloying, the maximum SME reached 5.7%, which is close to that of Fe-Mn-Si-based alloys [22].Nevertheless, the main factors ensuring the achievement of a large SME under the reversible FCC ↔ HCP MT in CrMnFeCoNi HEAs remain unclear in the literature.
In the present paper, the task was to investigate the SME governed by the FCC ↔ HCP MT in the Cr20Mn20Fe20Co34.5Ni5.5 (at.%)HEA single crystals along two different crystallographic orientations, i.e., [123] and [011], under tensile deformation in order to establish the general physical factors that determine a large SME, as well as the dependence of the SME on the crystal orientation for the case when the HCP martensite develops predominantly in one system.
The choice of crystal orientations was determined based on the following points.Firstly, for geometric reasons, [123] -and [011]-oriented crystals are oriented toward the development of the HCP martensite predominantly in one system compared to [001]and [111] -oriented crystals oriented toward the development of the HCP martensite in several systems.Therefore, in [123] and [011] orientations, the effect of the variantvariant interaction of the HCP martensite on the SME is excluded from the beginning of deformation.Secondly, these orientations are characterized by a large theoretical value of the transformation strain for the FCC-HCP transition under tension, which weakly depends on the crystal orientation [1,4].Thirdly, in the [011] orientation under tension, the Schmid factor for the FCC-HCP MT, mFCC-HCP, is greater than the Schmid factor for slip, msl, while in [123] -oriented crystals, mFCC-HCP = msl, and these orientations are favorable for the development of the FCC-HCP MT [23,24].

Preparation of Single Crystals and Samples for Testing
Single crystals of the Cr20Mn20Fe20Co34.5Ni5.5 (at.%)HEA were grown via the Bridgman method in alumina (Al2O3) crucibles and a helium atmosphere on a Redmet installation (Firm "Kristallooptika", Tomsk, Russia).The crucibles had a conical shape with a diameter of 38 mm and a length of 100 mm.To achieve a homogeneous distribution of the elements in the bulk of the ingots, they were remelted three times in a resistance furnace (InterSELT, St.-Petersburg, Russia).The crystals were homogenized in a helium atmosphere at 1473 K for 48 h.To determine the crystal orientation, the diffractometric method was used with a DRON-3M X-ray diffractometer (Bourevestnik, St.-Petersburg, Russia) and monochromatic Fe Kα radiation, the technique of which was presented in [25].Dog-bone-shaped tension samples with a gauge length of 12 mm and a cross section of 2 × 1.5 mm 2 were cut using wire electrical discharge machining via ARTA-5.9(DEL-TA-TEST, Fryazino, Moscow region, Russia).The damaged surface layer was ground off mechanically, and then electrically polished in 200 mL of a H3PO4 + 50 g CrO3 (phosphoric acid with chromium trioxide) electrolyte at room temperature.The samples were then quenched into water after heat treatment in a helium atmosphere at 1473 K for one hour.The chemical composition of the single crystals after quenching was determined using the X-ray fluorescence method, with a wavelength-dispersive X-ray fluorescence XRF-1800 spectrometer (SHIMADZU, Kyoto, Japan), giving the atomistic percentages Co = 34.31%,Cr = 20.57%,Fe = 19.75%,Ni = 5.56%, and Mn = 19.81(аt.%).

Optical and Microstructural Studies
The surfaces of deformed samples were examined using a KEYENCE VHX-2000 optical microscope (KEYENCE, Osaka, Japan).Transmission electron microscopy (TEM) studies were performed using a JEOL-2010 electron microscope (JEOL, Tokyo, Japan) at an accelerating voltage of 200 kV.Thin foils were prepared via double-jet electropolishing (TenuPol-5, "Struers", Ballerup, Denmark) with an electrolyte containing 20% sulfuric acid in methyl alcohol at room temperature, with a 12.5 V applied voltage.TEM tests showed that, at 296 K, the Cr20Mn20Fe20Co34.5Ni5.5 HEA single crystals had the expected FCC structure after quenching (Figure 1).

Thermal Transformation Studies
The MT was monitored via differential scanning calorimetry (DSC) (a NETZSCH DSC 404F1 machine, with a cooling capacity down to ~130 K) (NETZSCH Geratebau GmbH, Selb, Germany) at a cooling/heating rate of 10 K/min and on the basis of the temperature dependence of electrical resistance, ρ(Т), (a Russian-manufactured installation (Firm "Kristallooptika", Tomsk, Russia), with a heating/cooling rate of 10 K/min within a temperature range of 77 to 623 K).Starting, Ms, and finishing, Mf, temperatures of the forward FCC-HCP MT during cooling and starting, As, and finishing, Af, temperatures of the reverse HCP-FCC MT during heating were determined via the intersection of tangents on ρ(Т) and DSC curves.The viscoelastic properties of the material were analyzed using a testing machine for dynamic-mechanical analysis, with DMA/SDTA 861e (Mettler Toledo, Columbus, OH, USA), under tension with a maximum strain of 10 µm (a working length of 10 mm) at frequencies of 0.1Hz.

Mechanical Studies
Mechanical tests and the SME at different temperatures were determined using an Instron 5969 universal testing machine (Instron, Norwood, MA, USA), at a strain rate of 4 × 10 −4 s −1 .The SME under constant external stress in the "cooling-heating" cycle was studied using a dilatometer (Firm "Kristallooptika", Tomsk, Russia) with a heating/cooling rate of 10 K/min.Strains in SME studies under constant temperature in the "stress-strain" cycle and under constant external stress in the "cooling-heating" cycle were measured using a miniature extensometer attached directly to the gauge length of the sample.The MT temperatures under stress were determined via deviation from linear dependence in the "strain-temperature" (εtr-Т) curves.The yield stress, σ0.1, at the 0.1% offset strain yield point at different temperatures in the temperature range of 77 to 573 K was determined in two ways.The first way was to determine σ0.1 on one sample in a temperature range from 296 to 573 K and to determine that on the second sample from a temperature range from 296 to 77 K.At 296 K, two samples showed similar values with a difference of ±5 MPa.Then, at each temperature, σ0.1 was determined from fresh samples.The values obtained from different samples via the two ways are in good agreement with each other (±5 MPa).The critical resolved shear stresses were calculated using the equation  = σ0.1•mslfor slip and τ = σ0.1•mFCC-HCPfor HCP martensite (where σ0.1 is the uniaxial stress at the 0.1% offset strain yield point; msl is the Schmid factor for slip; mFCC-HCP is the Schmid factor for the HCP martensite) [23,24].The theoretical value, ε0 Theory , for the FCC-HCP transition is determined via the following relation [1,4]: ( Here, S = √2 /4 is the shift value at the FCC-HCP MT [1,2].The Schmid factor for the FCC-HCP transition, mFCC-HCP, the Schmid factor for slip, msl, and ε0 Theory are presented in Table 1.

Thermal Transformation Behavior
The studies of the temperature dependence of electrical resistance, ρ(T), DSC curves, and Tanδ (the characterization of internal friction obtained via the DMA method) for the Cr20Mn20Fe20Co34.5Ni5.5 HEA single crystals during cooling/heating are shown in Figure 2. In terms of the ρ(Т) dependence during cooling/heating, a closed loop is observed in the temperature range of 450 to 77 K (Figure 2a).It can be seen that the forward FCC-HCP MT upon cooling starts at a temperature of Ms = 200 K, and the reverse HCP-FCC MT finishes at a temperature of Af = 380 K when heated.The FCC ↔ HCP MT is characterized by wide thermal hysteresis, ΔТh = Аf-Ms = 180 К.
In terms of the DSC curves during cooling/heating, one peak of exothermic and endothermic heat associated with the FCC-HCP and HCP-FCC MT, respectively, is detected (Figure 2b).During heating, the peak with a thermal effect of 4.87 J/g is more diffuse than that during cooling.Upon cooling, the FCC-HCP transition begins at Ms = 200 K, and, upon heating, the reverse HCP-FCC transition starts at As = 350 K and finishes at Af = 390 K.The thermal hysteresis is as follows: ΔТh = Аf-Ms = 190К.
Peaks of internal friction appear in the temperature range of 145-195 K upon cooling and 310-395 К upon heating, and they are associated with the FCC-HCP and HCP-FCC MT, respectively (Figure 2c).The ΔTh obtained via this method is 200 K. Three methods show good agreement in the Ms and Af temperatures for the FCC ↔ HCP MT.A minor difference in the determination of the MT temperatures via the three methods can be caused by different cooling/heating rates during the experiment.With all the used methods, the Ms temperature is 195-200 K, and the Af temperature is 380-395 K.An analysis of the presented data shows that the FCC ↔ HCP MT is characterized by a low temperature range of overcooling, ΔM = Ms-Mf, and overheating, ΔA = Af-As.
According to the ρ(T) dependence, ΔM = 25 K and ΔA = 40 K; according to DSC data, ΔM = 20 K and ΔA = 40 K; and according to the DMA results, ΔM = 50 K and ΔA = 85 K.The ΔM and ΔA temperature ranges for the FCC ↔ HCP MT, obtained from the DMA results, turned out to be larger than those when studying the MT temperatures from the ρ(T) and DSC curves; ΔM was 2-2.5 times greater, and ΔA was 2 times greater.This may have been due to different cooling/heating rates during the experiment and different sample sizes.All methods used to characterize the thermal transformation behavior of FCC ↔ HCP MT in Cr20Mn20Fe20Co34.5Ni5.5 HEA single crystals show that the Ms temperature for the start of the forward MT upon cooling is lower than the As temperature for the start of the reverse MT upon heating (Figure 2).According to the Tong-Wayman classification, the FCC ↔ HCP MT in Cr20Mn20Fe20Co34.5Ni5.5 HEA single crystals belongs to MTs of the first type, for which the condition ΔGdis > ΔGel/2 is fulfilled (ΔGel and Gdis are, respectively, the elastic and dissipated energy during the MT) [4,8].In this case, the reverse HCP-FCC MT starts under the condition that the chemical driving force and the elastic energy accumulated during the forward FCC-HCP MT make work against the friction forces, ΔGdis, for the reverse motion of the interface boundary.

Temperature Dependence of Yield Stress
The temperature dependence of yield stress, σ0.1(Т), for two orientations and the stress-strain curves of the Cr20Mn20Fe20Co34.5Ni5.5 HEA single crystals under tension within a wide temperature range are shown in Figure 3.The stress-strain curves showing the determination of the 0.1% offset yield stress are presented for crystals with a [011] orientation (Figure 3b).Three stages are observed in the σ0.1(T) dependence which differ in the magnitude and sign of dσ0.1/dT (Figure 3a).Such a σ0.1(T) dependence is characteristic of alloys undergoing a MT under stress [4,8,10].For the studied orientations, the minimum stresses, σ0.1, are observed at the Ms temperature, which coincides with the Ms temperature determined from the ρ(T) dependence and DSC curves (Figure 2a,b).The values of σ0.1(Ms) for the studied crystals are close and vary within 115 ± 5-120 ± 5 MPa.At T < Ms, the first low-temperature stage is observed, which is associated with the thermally activated motion of the interphase boundaries and the introduction of thermally induced HCP martensite [4,8,10].At 300 K, the maximum stress level of 185 ± 5-205 ± 5 MPa is reached in terms of the σ0.1(T) dependence in the studied orientations (Figure 3a).This temperature is the Md temperature, at which the stresses for the onset of stress-induced martensite (SIM) transformation are equal to the stresses of the onset of the plastic deformation of the FCC phase.The σ0.1(T) dependence in the temperature range Ms<T>Md shows a close-to-linear increase in stresses with increasing temperature.This is the second stage, which is associated with the stress-induced FCC-HCP MT and is described via the Clausius-Clapeyron relation [4,8,10]: Here, ΔS and ΔH are the change in entropy and enthalpy, respectively, at the FCC-HCP MT per unit volume, Т0 is the phase equilibrium temperature, and ε0 is the lattice deformation.The temperature range for the SIM transformation, ΔTSIM, is 105 K for the studied orientations.The value of α = dσ0.1(Т)/dT in this temperature range is close to α = 0.7 MPa/K in the [123] -oriented crystals and α = 0.8 MPa/K in the [011]-oriented crystals.These values turned out to be close for α = 0.85 MPa/K in [144] -oriented crystals of this alloy, which were previously studied in [18].Therefore, according to relation (2), in the studied orientations, the stress-induced FCC-HCP MT should be characterized by close values of ε0.As a matter of fact, the values of ε0 Theory estimated via relation (1) for the studied orientations have similar values (Table 1).It follows from relation (2) that the value of α is proportional to that of 1/ε0.Using relation (2), we compared the experimental values of α with the theoretical values of ε0 Theory for crystals of two orientations, taking into account that Т0, ΔS, and ΔH do not depend on the crystal orientation.The ratio of the experimental α values has the value of α([011]))/α([123] ) = 1.14, and the corresponding ratio of the theoretical ε0 Theory value is ε0 Theory ([011]))/ε0 Theory ([123] ) = 1.04.A comparison of these ratios shows that for the studied orientations, the theoretically expected ratio of the ε0 Theory values are close to the ratio of the experimentally observed α values.Consequently, the orientation dependence of the stress-induced FCC-HCP MT in the Cr20Mn20Fe20Co34.5Ni5.5 HEA single crystals is described via the Clausius-Clapeyron relation (2), as is the orientation dependence of the FCC-BCC MT, B2-L10 MT, and B2-B19 MT under stress in single crystals of FeNICoAlTa, FeNiGa(Co), and TiNi alloys, respectively [4,10].
At Т > Md, the third stage is observed, which is associated with the plastic deformation of the FCC phase.In the third stage, σ0.1 decreases with increasing temperature, as is the case in single crystals and polycrystals of the Co20Cr20Fe20Mn20Ni20 HEA under slip deformation [17,26].In the third stage, the α = −0.4MPa/K and does not depend on the crystal orientation.

Shape Memory Effect under External Tensile Stress
The transformation strain, εtr, recorded during "cooling-heating" cycles under different external tensile stresses, σex, from 100 to 180 MPa, and the "strain-temperature" (εtr-T) curves under σex = 150 and 170 MPa for [011]-and [123] -oriented Cr20Mn20Fe20Co34.5Ni5.5 HEA crystals are shown in Figure 4.In these experiments, the transformation strain, εtr, is the full strain that occurred in the "cooling-heating" cycle under tensile stress, σex, during cooling.The reversible deformation, εrev, or SME, εSME, is determined in the "cooling-heating" cycle without σex after heating.If after heating in the "cooling-heating" cycle, there is no irreversible deformation; when εir = 0, εtr = εSME, and when εir ≠ 0, then εSME = εtr − εir and εtr > εSME.In order to exclude the plastic deformation of the FCC phase during cooling, σex is applied to the sample at a temperature at which σex is lower than σ0.1 at the Md temperature, and when heated, σex is removed.In "cooling-heating" cycles, the σex values are limited by the narrow temperature range of SIM and the stress level at the Md temperature.The temperatures at which σex is applied or removed are shown on the εtr-T curves via filled circles.
For two studied orientations, common patterns were established for the SME dependence, εSME, on the σex level in the "cooling-heating" cycle.Firstly, in each new "cooling-heating" cycle, the SME increased with an increase in σex.Secondly, at σex = 130-150 MPa, an irreversible strain, εir, appeared, the value of which increased with increasing σex. .The full strain is the strain in the "strain-temperature" curve under tensile stress, σex, during cooling.The SME is defined as the difference between the full during cooling and irreversible during heating strains in the "strain-temperature" curve; the blue line represents cooling and the red line represents heating.
When irreversible strain, εir, remained during heating, TEM studies of the microstructure revealed stacking faults (SFs) at 296 K (Figure 5).In the case of a closed εtr-Т curve (εir = 0), for instance, in [011]-oriented crystals at σex = 100 MPa, SFs and HCP martensite were not observed after heating in the study of the microstructure.Consequently, HCP martensite is unstable and completely disappears upon heating without stress.Thirdly, under external stress, the temperature hysteresis, ΔТh, is as wide as that in a free state.Under external stresses of 150 and 170 MPa, ΔТh is 150 K and 185 K, respectively, for [011]-and [123] -oriented crystals.Fourthly, at σex, the Ms temperature is lower than the As temperature.Therefore, the stress-induced FCC-HCP MT, as well as that during cooling/heating in a free state, according to the Tong-Wayman classification, belongs to MTs of the first type, for which the condition ΔGdis > ΔGel/2 is satisfied [4,8].7a,c).The HCP martensite crystals are thin with a thickness of 5-10 nm, like twins in FCC HEAs [16,17,26,27].At ε > 10%, a sharp increase in Θ = dσ/dε to 2400 and 3600 MPa, respectively, at Ms and 77 K is observed in the σ−ε curves, which is associated with an increase in the number of active HCP martensite systems.At this stage, TEM studies revealed HCP martensite in one system and SFs in the other system (Figure 7b).Then, at a strain of 14-16%, when the stage with a high Θ = dσ/dε is completed, the deformation develops again with a low Θ = dσ/dε.Figure 8 displays the reversible strain obtained with a successive increase in εtr according to the σ−ε curves and after heating in a furnace in a free state after each case for the [011]-and [123] -oriented Cr20Mn20Fe20Co34.5Ni5.5 HEA crystals under tension at a temperature of Ms = 200 K and 77 K.In this case, the specimens were first deformed to given strain ,εtr, at a temperature of Ms = 200 K or 77 K, and then heated in a furnace in a free state at a temperature of 523 K > Af for 15 min.After heating, the specimen sizes were measured.If the specimen sizes were restored after annealing, then the SME was realized.Every time, the given strain level increased by 1.5-2%.These experiments show that the maximum SME has close values (Figure 8).In fact, at the Ms temperature with a given strain of 16%, in the [123] -and [011]-oriented crystals, the maximum SME of 14 ± 0.2% and 13.2 ± 0.2% is observed, respectively.With a further increase in strain, the SME decreases in both orientations.At 77 K, in the [011]-oriented crystals, the maximum SME is 13 ± 0.2% and is equal to the SME at the Ms temperature.It is important to note that when HCP martensite develops in one system at the stage of Lüders band deformation, it completely disappears upon heating above the Af temperature.Previously, this was discovered in a study of the SME in [144] -oriented crystals of this alloy at the Ms temperature [18].This was confirmed experimentally in a metallographic study of the specimen surface.After strain from the Lüders band at the Ms temperature, HCP martensite was observed on the sample surface in one system, and after heating at a temperature above Af, it disappeared (Figure 9).Irreversible strain, εir, appeared when the tensile strain exceeded the strain from the Lüders band.Therefore, in crystals oriented for a single shear, the reversible strain or SME is determined via the extension of the first stage with a low Θ = dσ/dε, at which the FCC-HCP MT develops in one <211>{111} system.In the case of [001]-and [111] -oriented Cr20Mn20Fe20Co35Ni5 HEA crystals [19,20], in which the FCC-HCP MT develops from the very beginning simultaneously in several systems, the SME of 3.6 and 6.8%, respectively, is significantly lower than that in [011]-and [123] -oriented Cr20Mn20Fe20Co34.5Ni5.5 crystals, where the FCC-HCP MT develops mainly in one system.In [001]-and [111] -oriented Cr20Mn20Fe20Co35Ni5 HEA crystals at a direct MT, shear transfer through HCP martensite plates by a/6<112> partial Shockley dislocations is difficult, and when the load is removed, their reverse movement is blocked by the HCP martensite formed on different (111) planes [5,19,20,28].Therefore, the variant-variant interaction of the HCP martensite limits the reversible deformation.

Shape Memory Effect under Tensile Strain at Different Temperatures
The SME for the [011]-oriented crystals at Ms and 77 K temperatures and for [123] -oriented crystals at the Ms temperature was additionally explored in the second way, which is depicted in Figure 10.For this way, for each "stress-strain" cycle, a fresh sample was taken.The tensile strain varied from 2.5% to 19% (Figure 10).After unloading, the specimens were placed in a dilatometer at room temperature and heated without stress until the reverse HCP-FCC transition was completed.An analysis of the data presented in Figures 8 and 10 shows that the SMEs obtained from one sample (the first way, Figure 8) and from fresh samples (the second way, Figure 10) agree well with each other.
In addition, heating in a dilatometer in a free state makes it possible to obtain additional information about the As and Af temperatures and the reversible deformation of the reverse HCP-FCC transition.Once the strain increases in the "stress-strain" cycle, the As and Af temperatures for the reverse HCP-FCC transition increase.When perfect reversibility is observed (when the strain in the cycle is equal to or less than the Lüders band deformation) and when the difference between As and Af temperatures of the first and subsequent cycles, ΔAs(ε) ≈ ΔAf(ε) is observed, then the reverse HCP-FCC transition occurs under conditions closer to those of ideal reversible transitions in terms of the kinetics characteristic of a transformation with one interface [29].In this case, the HCP-FCC transition occurs similarly to the Lüders band, which was formed in the studied orientations during the direct FCC-HCP transition under load at 77 K and Ms temperatures.At ε > 10%, when the forward MT develops in several systems, the reverse HCP-FCC transition requires significant chemical energy, ΔGch, which is necessary to overcome resistance to reverse transformation due to the variant-variant interaction of the HCP martensite.This manifests itself in an increase in the As temperature and ΔAf(ε) on the "strain-temperature" curve upon heating (Figure 10).

The Main Parameters for the Implementation of a Reversible FCC-HCP MT
The studies presented above show that in Cr20Mn20Fe20Co34.5Ni5.5 HEA single crystals, the FCC ↔ HCP MT develops upon cooling/heating in a free state and under stress.The SME was found; it depends on the crystal orientation and the external stress level in the "cooling-heating" cycle under constant σex, and has similar values in the case of the "stress-strain" cycle at a constant test temperature.As was mentioned above, at σex = 150 and 170 MPa, the maximum SME of 13.6 ± 0.2% and 8.4 ± 0.2% was obtained in [011]-and [123] -oriented crystals, respectively.As for the "stress-strain" cycle, in [123] -oriented crystals at the Ms temperature, the maximum SME reached 14 ± 0.2% and was greater than that in the "cooling-heating" cycle at σex = 170 MPa.In the [011]-oriented crystals, the maximum SME had similar values of 13-13.6% in both cases.The SME for FCC ↔ HCP MT for [011]-and [123] -oriented crystals under tension has been obtained for the first time.The SME value in the [011] orientation turned out to be close to the SME in the [144] orientation of this alloy, as presented in [18], and notably exceeded the SME for this transformation in single crystals and polycrystals of the Fe-Mn-Si alloy [1][2][3][4][5][6][7].
Table 2 presents the main parameters, at which a large SME is realized under tension in single crystals of Fe-Mn-Si alloys and Cr20Mn20Fe20Co34.5Ni5.5 HEA, experiencing a FCC ↔ HCP MT [3,13,30].An analysis of the data presented in Table 2 shows that the magnetic transition in single crystals of Cr20Mn20Fe20Co34.5Ni5.5 HEA does not play an important role in achieving a large SME, since the Néel point, TNe = 23 K, in FCC HEAs is much lower than the Ms temperature, in contrast to the case of the Fe-Mn-Si alloys, where TNe ≈ Ms [13].The main factors, which provide large reversibility in Cr20Mn20Fe20Co34.5Ni5.5 HEA single crystals experiencing the FCC ↔ HCP MT, as compared to that in Fe-Mn-Si alloys, are a higher yield stress, σ0.1, of the FCC phase at the Md temperature, a large difference between the critical shear stresses for slip,  , in the <110>(111) system, and for HCP martensite,  , in the <112>(111) system, Δτcr = ( −  ), at the Ms temperature and SRO.The stress level of σ0.1 of the FCC phase is a fundamental parameter for improving the SME [4,8].On the one hand, when the FCC phase is characterized by a high level of σ0.1, the stress-induced FCC-HCP MT is not accompanied by local plastic deformations of the FCC phase [4,8,9].On the other hand, under the reverse HCP-FCC MT, when the stress is removed, the reverse motion of partial Shockley dislocations is facilitated.Solid solution hardening by substitution atoms in equal or close-to-equal atomic concentrations in the Cr20Mn20Fe20Co34.5Ni5.5 HEA single crystals leads to a notable increase in σ0.1 at the Md temperature compared to that in Fe-Mn-Si crystals (Table 2).In addition to this, as was shown earlier in [13], the volume change between the FCC and HCP phases in the Cr20Mn20Fe20Co35Ni5 HEA was lower than that in Fe-Mn-Si.Therefore, the combination of a higher stress level of σ0.1(Md) at the Md temperature with a low volume change between the FCC and HCP phases [13] improves the SME in Cr20Mn20Fe20Co34.5Ni5.5 HEA single crystals at the FCC ↔ HCP MT compared to that in Fe-Mn-Si single crystals.This is indirectly confirmed via studies of the SME in [001]-oriented Cr20Mn20Fe20Co35Ni5 HEA crystals, in which the SME is 2.5-3 times higher than that in crystals Fe-Mn-Si alloys of this orientation (Table 2) [1,20,30].

The Role of Difference between the Critical Shear Stresses for Slip and HCP Martensite at the Ms Temperature
An important role in improving the SME of Cr20Mn20Fe20Co34.5Ni5.5 HEA single crystals can be filled by the difference between the critical shear stresses for slip,  , in the <110>(111) system and for HCP martensite,  , in the <112>(111) system, Δτcr = ( −  ), at the Ms temperature.Previously, as seen in Refs.[1][2][3], it was shown that the greater this difference is, the higher the probability of developing a HCP martensitic shear in the primary system and the larger the SME value.The role of Δτcr = ( −  ) in improving the SME was also shown in the study of the SME at the FCC-HCP MT in the [144] -oriented CrMnFeCoNi HEAs crystals by varying the Co/Ni concentration [18].It was shown in [18] that in [144] -oriented crystals of Cr20Mn20Fe20Co37Ni3 HEAs with Δτcr = 30 MPa, the maximum SME was 12% at σex = 160 MPa.In [144] -oriented crystals of Cr20Mn20Fe20Co34.5Ni5.5,Δτcr = ( −  ) was 65 MPa and the maximum SME was 15.7% at σex = 160 MPa [18].In the present paper, we compared the Δτcr = ( −  ) of the HEA and Fe-Mn-Si alloy single crystals (Table 2).The values of  were obtained from the temperature dependence of σ0.1(T), presented in [1,18,30] for [144] -oriented crystals of the Cantor HEA and Fe-Mn alloy.The  values were received from σ0.1(T) dependences in Figure 3 for crystals of the Cr20Mn20Fe20Co34.5Ni5.5 HEA and in [1] for the Fe-Mn-Si alloy.As was mentioned above in Section 2 of the present paper, the  for slip and  for HCP martensite were calculated using the equations  = σ0.1•msland τ = σ0.1•mFCC-HCP,respectively.In the Cr20Mn20Fe20Co34.5Ni5.5 HEA single crystals, Δτcr = ( −  ) was two times greater than that in the Fe-Mn-Si single crystals (Table 2).The factor contributing to the increase in Δτcr = ( - ) in Cr20Mn20Fe20Co34.5Ni5.5 HEA single crystals compared to that in Fe-Mn-Si alloys is the different mobilities of the a/2<110> perfect and a/6<112> partial dislocations in a the heavy distorted crystal lattice of the FCC phase due to the high concentration of substitution atoms in equal or close-to-equal atomic concentrations [14,15].On the polycrystalline Cantor HEA, it was shown that heavy lattice distortions in the HEAs reduced the resistance to movement of the a/6<112> partial Shockley dislocations, which turned out to be very mobile compared to the a/2<110> perfect dislocations [15].

The Role of Short-Range Order
The SRO inCr20Mn20Fe20Co34.5Ni5.5 HEA single crystals is confirmed by the following factors.Firstly, at 77 K and Ms temperatures, the FCC-HCP MT develops due to the Lüders band from the beginning of deformation (Figure 6).Usually, during slip deformation in crystals of FCC pure metals and their substitutional alloys, oriented for the development of slip in one system, the first stage of "easy glide" with low Θ = dσ/dε is always observed on the σ−ε curve [31,32].The decrease in the SF energy, γ0 < 0.050 J/m 2 , and the formation of a SRO in FCC substitutional alloys, including FCC HEAs, leads to the appearance of a "yield point" (i.e., the instability of plastic deformation) from the beginning of plastic deformation to the development of deformation by the Lüders band with Θ = dσ/dε = 0 [17,18].With the development of a FCC-HCP MT in [011]-and [123] -oriented crystals of the Cr20Mn20Fe20Co34.5Ni5.5 HEA, deformation by the Lüders band was 10%.In the ideal case, when the full FCC-HCP transition in the primary system is completed, the extent of the deformation due to the Lüders band should correspond to the theoretical value of the transformation strain of 15.7 and 16.4% for [123] -and [011]-oriented crystals, respectively, under tension.
The position of the crystal axis after the completion of deformation by the Lüders band, under the assumption that the FCC-HCP MT develops in the primary system, [211] (111), was calculated via the following relation [32]: Here, λ0 and λ1 are the angles between the [211] shear direction in the (111) plane and the crystal axis before and after deformation from the Lüders band, respectively.Figure 11   In [011]-and [123] -oriented crystals of the Cr20Mn20Fe20Co34.5Ni5.5 HEA, the calculated position of the crystal axis for a ε0 Theory value of a full FCC-HCP transition in the primary system, [211] (111), was not achieved.Consequently, in these orientations, the inclusion of secondary systems of HCP martensite occurs before the FCC-HCP transition in the primary system is completed due to the precession of the crystal axis [32].In [144] -oriented crystals of Fe-Mn-Si alloys, where the SRO is less pronounced than that in HEAs, the transition to the development of HCP martensite in several systems occurs at a lower deformation and the position of the crystal axis after deformation by the Lüders band is closer to the initial position (Figure 11).Consequently, the SRO in Cr20Mn20Fe20Co34.5Ni5.5 HEA single crystals hinders the activation of secondary systems of HCP martensite.This is qualitatively confirmed via SME studies on [111] -oriented Cr20Mn20Fe20Co35Ni5 HEA single crystals oriented for multiple shear [19].In the [111] -oriented Cr20Mn20Fe20Co35Ni5 HEA crystals, due to SRO, the localization of deformation was observed in one system.This made it possible to obtain the SME of 6.8% in this orientation under tensile deformation at the Ms temperature, which was 63% of the theoretical value of the transformation strain of 10.8% for the FCC-HCP MT in the [111] orientation under tension [4,19].
Secondly, SRO affects the dislocation structure in the FCC phase and the fine structure of HCP martensite.In the dislocation structure, a change in the a/2<110> dislocation splitting into a/6<112> partial Shockley dislocations in a head of pile-up, which is characteristic of the SRO, was found.The second dislocation is split much less than the first or third is, since its leading partial dislocation is blocked by the SRO, while the trailing one moves with ease (Figure 7d) [18,33].HCP martensite is thin and has a thickness of 5-10 nm (Figure 7c).Therefore, SRO hinders the formation of large HCP martensite plats due to the need to destroy SRO via partial Shockley dislocations when they move through one {111}FCC plane.Thin HCP martensite under a direct stress-induced MT does not create high stress concentrations in the head of the martensite plate.In this case, when the stress is removed, thin martensite can easily move "exactly backward" according to the kinetics characteristic of an MT with one interface and improve the SME [29,34].This was observed in the SME study under external stresses, σex, when the forward and reverse transitions occurred according to explosive kinetics.In addition, the reverse HCP-FCC transition in the SME experiments always occurred without external stresses.Therefore, it can be assumed that the SRO recovery during the reverse motion of partial Shockley dislocations, provided that there is no diffusion of atoms in the temperature range of the reverse HCP-FCC MT, together with the reverse long-range stress fields that arise during the direct FCC-HCP transformation, contribute to the reverse "exactly backward" transformation, and there is a full reversibility of the FCC ↔ HCP MT [4,[18][19][20]  The low SF energy, γ0, is an important parameter for the development of the FCC-HCP MT, since it determines the equilibrium splitting, d0, of the a/2<110> perfect dislocations into a/6<112> partial Shockley dislocations [23].The theoretical values of γ0 for FCC HEAs were obtained in [35].In this paper [35], it was shown that in FCC HEAs γ0 decreases with decreasing temperature, and the FCC-HCP MT in a free state and under stress can develop if the γ0 value is less than 0.014 J/m 2 .It is important to note that the theoretically estimated γ0 values of the FCC HEA in [23] are in good agreement with the experimentally determined values of γ0 = 0.018-0.022J/m 2 for poly-and single crystals of the Cantor alloy at a temperature of 300 K [36,37].
An additional factor contributing to the splitting, d0, of the a/2<110> perfect dislocations into a/6<112> partial Shockley dislocations is the increase in splitting, d, which is additional to the stress-free equilibrium state caused by external stress, σ, and, accordingly, a decrease in the value of the effective SF energy, γef [23,38,39].This is due to the well-known result of the dislocation theory [38,39], when, under tension of [011]-and [123] -oriented crystals, the external stresses acting on the leading Shockley dislocation, b1, are greater than that on the trailing Shockley dislocation, b2.The change in the splitting value of dislocations and γef in the external stress field is determined via the following relation [38]: Here, γef is the effective SF energy, which is determined not only via γ0, but also via external stresses, σ, and temperatures, m1 and m2 are the Schmid factors for the leading and trailing Shockley dislocations, respectively, b1 is the Burgers vector modulus of a partial Shockley dislocation, the orientation factor  = , and ± takes the sign of the applied stress, i.e., tension or compression, into account [23,38,39].In Cr20Mn20Fe20Co34.5Ni5.5 HEA single crystals, γ0 = 0.012 J/m 2 at a temperature of Ms = 200 K [35].Using relation (4), γ0 = 0.012 J/m 2 [35] and the shear modulus G = 81 GPa [40], d0, d, and γef were estimated at σ0.1(Ms), and are presented in Table 3. Data analysis shows that at σ0.1(Ms) = 115 MPa, the value of d increases and γef decreases with respect to d0 and γ0, respectively.Due to this difference between d0 and d, γ0 and γef will increase with increasing strain at Ms and 77 K temperatures.This, in turn, leads to the suppression of cross-slip, to the development of a planar structure, which enhances the localization of deformation in one system, and, like the SRO, hinders the development of HCP martensite in other systems [17,18].This manifests itself in the SME study under tension, when the SME was studied for one sample with a successive increase in deformation, for example, at a temperature of Ms or 77 K (Figure 8).In the studied crystals, the reversible strain increased even at a strain exceeding the Lüders band deformation.For instance, in the case of [123] -oriented crystals, the SME in the "stress-strain" cycle exceeded the maximum SME under σex = 170 MPa (Figures 4b and 8).In this case, the reversible motion of splitting dislocations is associated with an additional surface energy of SFs, due to an increase in stresses at the yield point and with an increase in the strain level, as well as with a heavy lattice distortion of the FCC phase due to the high concentration of substitution atoms in equal or close-to-equal atomic concentrations [4].As a result of all these factors (the stress level of the FCC phase, Δτcr = ( −  ), the SRO, and the change in the value of splitting dislocation in the external stress field), the reversible FCC ↔ HCP MT is realized in Cr20Mn20Fe20Co34.5Ni5.5 HEA single crystals.This is confirmed via studies of surface relief under tension at the Ms temperature, when HCP martensite appears in one system at the stage of the Lüders band deformation and then disappears when heated above the Af temperature (Figure 9).In the case of external stresses, σex, it is confirmed via the absence of HCP martensite in the study of the microstructure after the completion of the reverse HCP-FCC transition under heating without stress (Figure 5).

Orientation Dependence of SME in Cr20Mn20Fe20Co34.5Ni5.5 HEA Single Crystals
The orientation dependence of the SME in the studied single crystals of the Cr20Mn20Fe20Co34.5Ni5.5 HEA under tensile deformation is due to the Schmid factor for the a/6<112>(111) system (Table 1) and the factor Q (Table 3), which depend on the crystal orientation.The Schmid factor determines the dependence on the crystal orientation of the theoretical value of ε0 Theory for the FCC-HCP transition according to relation (1).The Q factor determines the value of splitting of a/2<110> perfect dislocations into a/6<112> partial Shockley dislocations in the external stress field according to relation (4) [17,23,38,39].The SRO does not depend on the crystal orientation, but hinders the development of HCP martensite in other systems [17,18].Hence, the SRO competes with shear multiplicity for the FCC-HCP transformation.The more pronounced the SRO, the later the second systems are included in plastic deformation.An additional factor hindering the development of HCP martensite in secondary systems is the distance between the position of the crystal axis and the [001]-[111] boundary of the stereographic triangle.In [011]-oriented crystals, mFCC-HCP and the Q factors have maximum values compared to those of [123] -oriented crystals.In addition, in [011]-oriented crystals, the position of the crystal axis is much further from the [001]-[111] boundary of the stereographic triangle than that in [123] -oriented crystals (Figure 11).As a result, in [011]-oriented crys-tals, the activation of secondary systems of HCP martensite during deformation occurs later than that in [123] -oriented crystals.This contributes to an increase in the shear during the FCC-HCP transition in the primary system and an increase in the SME, and also determines the dependence of the SME on crystal orientation under σex, when HCP martensite develops predominantly in one system.Under tension at the Ms temperature, the orientation dependence of the SME is degenerated due to an increase in the splitting of dislocations in the external stress field with an increase in the strain level.The splitting of dislocations in the external stress field simultaneously with the SRO enhances the localization of the deformation of HCP martensite in the primary system and hinders its development in secondary systems with increasing deformation.

Conclusions
The SME studies conducted under the tensile deformation of [011]-and [123] -oriented Cr20Mn20Fe20Co34.5Ni5.5 HEA single crystals, oriented for the development of HCP martensite predominantly in one system, lead to the following conclusions: Funding: Financial support by the Russian Science Foundation (RSF) grant no.22-19-00016.Work was conducted using equipment from the Tomsk Regional Core Shared Research Facilities Centre of National Research Tomsk State University.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.

Figure 2 .
Figure 2. Temperature dependence of resistivity (a), DSC curves (b) and Tanδ (c) in Cr20Mn20Fe20Co34.5Ni5.5 high-entropy alloy single crystals; blue line represents cooling and red line represents heating.

Figure 3 .
Figure 3. Temperature dependence of 0.1% offset yield stress (a) and stress-strain curves at different temperatures showing the determination of the 0.1% offset yield stress of the Cr20Mn20Fe20Co34.5Ni5.5 HEA single crystals under tension (b).

Figure 4 .
Figure 4. "Strain-temperature" curves at external tensile stresses of 150 and 170 MPa and "Strain-external stress" dependence in the Cr20Mn20Fe20Co34.5Ni5.5 HEA single crystals under tension.(a) [011] orientation; (b) [123].The full strain is the strain in the "strain-temperature" curve under tensile stress, σex, during cooling.The SME is defined as the difference between the full during cooling and irreversible during heating strains in the "strain-temperature" curve; the blue line represents cooling and the red line represents heating.

Figure 5 .
Figure 5. Bright-field image of stacking faults at 296 K, which were observed when irreversible strain remained during heating after tensile deformation at an external stress of 150 MPa in the [011]-oriented Cr20Mn20Fe20Co34.5Ni5.5 HEA crystals.Thus, it has been experimentally established that the maximum SME of 13.6 ± 0.2% and 8.4 ± 0.2% is achieved in [011]-and [123] -oriented single crystals at tensile stresses of σex = 150 and 170 MPa, respectively, and depends on the crystal orientation.

Figure 6
Figure 6 shows the "stress-strain" (σ−ε) curves under tension for [011]-oriented crystals at Ms = 200 K and 77 K temperatures and [123] -oriented crystals at the Ms temperature.It can be seen that the [011]-and [123] -oriented crystals demonstrate remarkable plasticity.The σ−ε curves are characterized by a low "yield point" (i.e., the instability of plastic deformation), after which the FCC-HCP MT develops as a Lüders band with strain-hardening coefficients, Θ = dσ/dε = 0.At the Ms temperature, the extent of deformation by the Lüders band is ~10% in the [123] -and [011]-oriented crystals.TEM studies have shown that at the stage of deformation by the Lüders band, extended SFs and HCP martensite in one system are observed in these crystals (Figure7a,c).The HCP martensite crystals are thin with a thickness of 5-10 nm, like twins in FCC HEAs[16,17,26,27].At ε > 10%, a sharp increase in Θ = dσ/dε to 2400 and 3600 MPa, respectively, at Ms and 77 K is observed in the σ−ε curves, which is associated with an increase in the number of active HCP martensite systems.At this stage, TEM studies revealed HCP martensite in one system and SFs in the other system (Figure7b).Then, at a strain of 14-16%, when the stage with a high Θ = dσ/dε is completed, the deformation develops again with a low Θ = dσ/dε.

Figure 7 .
Figure 7. Microstructure of the Cr20Mn20Fe20Co34.5Ni5.5 high-entropy alloy single crystals undergoing FCC ↔ HCP martensitic transformation under tensile strain.(a,b) [123] orientation; (c,d) [011] orientation; (a) 5% of strain at temperature Ms = 200 K; (b) 12% at Ms temperature; (c) bright-field image of thin HCP martensite in one system under a strain of 10% at the Ms temperature with the corresponding microdiffraction pattern; (d) splitting dislocations and stacking faults after a strain of 13% at the Ms temperature.

Figure 8 .
Figure8.Reversible strain after heating in a furnace in a free state at 573 K for 15 min of the deformed Cr20Mn20Fe20Co34.5Ni5.5 HEA single crystals.Given strain is strain in "stress-strain" curve before heating.

Figure 9 .
Figure 9. Optical microscopy images of the specimen surface after a Lüders band deformation of 6% at the Ms temperature (a) and after heating in a furnace in a free state at a temperature of 523 K > Af for 15 min (b) of the [011]-oriented Cr20Mn20Fe20Co34.5Ni5.5 high-entropy alloy single crystals undergoing FCC ↔ HCP martensitic transformation under tension.The particle is a reference point, showing that the images before and after heating were taken from one place.

Figure 10 .
Figure 10.Reversible strain after tension and subsequent heating in dilatometer without stress until the completion of the reverse HCP-FCC transition in the Cr20Mn20Fe20Co34.5Ni5.5 high-entropy alloy single crystals.(a) [011]-oriented single crystals at 77 K; (b) [011]-oriented single crystals at the Ms temperature; (c) [123]-oriented single crystals at the Ms temperature.
displays the initial position of the crystal axis and that after deformation by the Lüders band (for a theoretical value of ε0 Theory and experimentally observed εSME), estimated via relation (3) for the [123] -and [011]-oriented crystals.The position of the crystal axis of the [144] -oriented crystals of the Fe-Mn-Si alloy, in which the deformation by the Lüders band varied from 3 to 7%, is also shown in Figure 11 [1].

1 .
In [011]-and [123] -oriented Cr20Mn20Fe20Co34.5Ni5.5 HEA single crystals, FCC-HCP transformation develops upon cooling and heating in a free state and under stress.The start temperature of the forward FCC-HCP transformation upon a cooling Ms temperature is 195-200 K.The FCC-HCP transformation during cooling/heating in a free state and under stress is characterized by wide temperature hysteresis: ΔTh= Аf − Ms = 180-195 K in a free state and ΔTh = 150-185 K at σex = 150-170 MPa. 2. The temperature dependence of the yield stress, σ0.1(Т), has the form characteristic of alloys experiencing a martensitic transformation under stress and consists of three stages.The first stage at T < Ms is associated with the thermally activated motion of the interphase boundaries and introduction of thermally induced HCP martensite.The second one in the temperature range Ms < T < Md, on which a linear increase in stresses with increasing temperature is observed, is associated with the development of stress-induced HCP martensite and is described via the Clapeyron-Clausius relation.This stage in [011]-and [123] -oriented crystals develops in a narrow temperature range, ΔTSIM = 105 K, and α = dσcr/dT at this stage weakly depends on the crystal orientation.The orientation dependence, α = dσcr/dT, is described via the orientation dependence of the theoretical value of the transformation strain, ε0 Theory , for the FCC-HCP transition under tension in accordance with the Clausius-Clapeyron relation.The third stage, associated with the deformation of the FCC phase, takes place at a temperature above the Md temperature.3.For the first time, in [011]-and [123] -oriented Cr20Mn20Fe20Co34.5Ni5.5 HEA crystals oriented for the development of HCP martensite in one system, the SME is realized under tension, which depends on the crystal orientation and external stresses, σex, in the "cooling-heating" cycle.The maximum SME is 13.6 ± 0.2% in [011]-oriented crystals at an external stress of 150 MPa, and 8.4 ± 0.2% in [123]-oriented crystals at an external stress of 170 MPa.In the "stress-strain" cycle under tension, the maximum SME has the value of 14 ± 0.2% in [123] -oriented crystals at the Ms temperature and of 13 ± 0.2% in [011]-oriented crystals at Ms and 77 K.The following physical factors are identified that contribute to the reversible movement of a/6<211> partial Shockley dislocations that are "exactly backward" when the stress is removed and lead to large SME: the stress level of the FCC phase, short-range order, and an increase in the splitting of a/2<110> perfect dislocations into a/6<211> partial Shockley dislocations in the external stress field.Author Contributions: Conceptualization, I.V.K. and Y.I.C.; methodology, I.V.K. and Y.I.C..; validation, I.V.K.; formal analysis, I.V.K. and Y.I.C.; investigation, I.V.K., A.A.S. and A.V.V.; writing-original draft preparation, I.V.K. and Y.I.C.; writing-review and editing, I.V.K. and Y.I.C.; supervision, I.V.K.; project administration, I.V.K.; funding acquisition, I.V.K.All authors have read and agreed to the published version of the manuscript.

Table 1 .
Theoretical values of deformation transformation of FCC-HCP martensitic transformation under tension, ε0 Theory ; Schmid factor for FCC-HCP transition, mFCC-HCP; Schmid factor for slip, msl.

Table 2 .
The main parameters determining the large shape memory effect under tension in single  ); the short-range order, SRO; the maximum shape memory effect in different orientations,  .
crystals of Fe-Mn-Si alloys and Cr20Mn20Fe20Co34.5Ni5.5 HEAs, experiencing the FCC ↔ HCP martensitic transformation; the volume change between the FCC and HCP phases ΔV; the Néel point TNe; the yield stress at the Md temperature, σ0.1(Md); the yield stress at the Ms temperature, σ0.1(Ms); the stress difference between slip and HCP martensite at the Ms temperature, Δτcr = ( − 4.1.1.The Role of the Yield Stress σ0.1 of the Initial FCC Phase

Table 3 .
Change in the splitting value of a a/2<110> perfect dislocation into a/6<211> partial Shockley dislocations and the effective value of the stacking fault energy in an external stress field of 115 MPa under tension at the Ms temperature of Cr20Mn20Fe20Co34.5Ni5.5 HEA single crystals experiencing a FCC ↔ HCP martensitic transformation.The Schmid factors for the leading dislocation, m1; the Schmid factors for the trailing Shockley dislocation, m2; the orientation factor  = ; the equilibrium stacking fault energy, γ0; the effective stacking fault energy, γef; equilibrium dislocation splitting, d0; dislocation splitting in an external stress field, d. [