# Temperature Dependent Solid Solution Strengthening in the High Entropy Alloy CrMnFeCoNi in Single Crystalline State

^{1}

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## Abstract

**:**

## 1. Introduction

_{conf}[6]. The latter is directly linked to the solid solution strengthening behavior in HEA and CCA [7,8]. Such alloys have higher strength than pure elements due to the solute atoms dissolved in the solvent matrix which provide resistance to dislocation motion. Solid solution strengthening (often referred in context with lattice distortion and subsequently sluggish diffusion) is a way to increase the strength of a metal by alloying elements [9,10,11,12,13].

_{m}. The predominant deformation mechanism is non-conservative dislocation movement by climbing even at very low stress levels. In addition, the effect of solid solution strengthening (in the context with sluggish diffusion kinetics) of two alloys can also be investigated by creep testing, as Fleischmann et al. showed [28] by comparing two Ni-based superalloys by adding Re to one of the two alloys.

_{conf}= 1.61 × R (R = universal gas constant 8.314 J mol

^{−1}K

^{−1}) and pure Ni with ΔS

_{conf}= 0 × R, which exhibits no solid solution [29].

## 2. Materials and Methods

#### 2.1. Alloy Fabrication

^{4}Pa) was used as atmosphere. Thereby manganese loss does not occur during the single crystal casting process (see Figure 1). In addition, single crystalline pure nickel was cast as in the same way but under vacuum.

_{2}O, 200 mL HCl, 60 g FeCl

_{3}·6 H

_{2}O and 12 g (NH

_{4}) 2 [CuCl

_{4}]·2 H

_{2}O (Adler etch) to remove adhering mold shell residues. The quality check of both single crystals by electron backscatter diffraction (EBSD, AMETEK, Berwyn PA, USA) shows no further grains and a crystallographic orientation of [001] ± 3° for CrMnFeCoNi and 8° for pure Ni.

#### 2.2. Sample Preparation

_{2}O, 10 mL HNO

_{3}and 1 mL pickling solution, to remove the remaining layer of wire EDM and with the side effect of bringing out the dendritic structure. Before testing, the samples were ground with SiC paper 2400. The samples had a rectangular cross-section of 1.0 × 2.9 mm, a measuring length of 5 mm, and a total length of 30 mm and were similar to the geometry reported in [32].

#### 2.3. Mechanical Testing

^{−4}Pa) using a vacuum creep testing device (Metals and Alloys, University of Bayreuth, Bayreuth, Germany) as described in [33]. The tests were performed at high temperatures of 700, 980, 1100, and 1200 °C, controlled by a type-S thermocouple close to the sample. The specimens were griped by Al

_{2}O

_{3}rods and heated up to the test temperature with a rate of 20 K/min in a resistance-heated furnace. The strain was measured by non-contacting video extensometer [34]. The load was chosen in the range of 2–125 MPa in order to achieve stationary creep rates in a wide range of 10

^{−8}–10

^{−3}s

^{−1}. As a starting point for determination of the creep loads, the yield strength of tensile tests according to [35] were determined with an strain rate of 10

^{−3}s

^{−1}at 700 and 1000 °C using the same sample geometry. This test resulted in a yield strength of 46 MPa at 700 °C and 7 MPa at 1000 °C for pure nickel and 62 MPa at 700 °C and 42 MPa at 1000 °C for CrMnFeCoNi.

## 3. Results and Discussion

^{−5}1/s is achieved at 26% strain, whereas for 0° deviation it is already achieved after 11% at a similar creep rate of 1.0 × 10

^{−5}1/s (Figure 3a). This shows that primary creep behavior (Figure 3b) is sensitive to orientation, but without any influence on the minimum creep rate.

_{0-new}was calculated (equation in Figure 5). A

_{0}is the initial cross section of the specimen, A

_{0-new}is the difference between A

_{0}and A

_{new}and ε

_{load before}is the achieved strain until load increase. Thus, the strain up to the load increase was considered.

^{−4}1/s is already in the range as tensile tests and the time to failure was less than 0.1 h. The plotted line of pure Ni was extrapolated to a value of 50 MPa to compare it with CrMnFeCoNi. The minimum creep rate of pure nickel is more than three orders of magnitude higher than that of CrMnFeCoNi at 50 MPa: The necessary stress for achieving a minimum creep rate ${\dot{\mathsf{\epsilon}}}_{\mathrm{min}}$ of 1 × 10

^{−6}s

^{−1}is 80 MPa higher for CrMnFeCoNi than for pure Ni.

_{2%}in h) for the different temperatures 700, 980, 1100 and 1200 °C and stress levels. The time to reach 2% strain is more relevant in the field of application and better reproducible than the time to failure. Equation (2) is used to calculate the Larson-Miller parameter P

_{2%}, where T is the temperature in K:

_{2%}are listed in Table 2. For the tests using stress increase only the values up to a total strain of 5% were determined. At low loads of 2 MPa, the load increases were carried out before the 2% limit was reached, because the minimum creep rate was achieved. Therefore, the time to reach 2% were extrapolated. Both pure nickel and CrMnFeCoNi show a linear behavior at different slopes. For pure nickel the slope is −0.09 and for CrMnFeCoNi it is −0.15. The results of the Ni samples with the deviation from [001] ± 0° lie in the same range as the results of the samples with 8° deviation. The straight lines diverge at lower temperature (or increasing stress level). This is due to the increasing solid solution strengthening effect with decreasing temperature. At higher temperatures above 980 °C and a low load of 2 MPa the point of intersection of both materials can be identified. The value for the Larson–Miller parameter P

_{2%}at this point is 31.7.

_{H}can be determined by ${\mathrm{T}}_{\mathrm{H}}=\frac{\mathrm{T}}{{\mathrm{T}}_{\mathrm{m}}}$ using the melting points T

_{m}for both materials, with 1607 K for CrMnFeCoNi and 1728 K for pure Ni. By changing T to T/T

_{m}in Equation (2), the Larson–Miller parameter for homologous temperature can be calculated.

_{H}is shown in Figure 8b. As already shown in Figure 8a, there exists also a difference in the slope of materials, –0.16 for pure nickel and −0.24 for CrMnFeCoNi. The characteristic feature between Figure 8a,b is a shift to the left of pure Ni, which increases the difference between the two materials from 80 MPa (Figure 8a) to 105 MPa (Figure 8b).

_{2%}of 10 h, the temperature difference between the two materials can be determined from Figure 8b. At 50 MPa, the CrMnFeCoNi alloy requires 198 K more than pure Ni to achieve a strain of 2% in the same time. This difference decreases to higher temperatures, therefore, at 3 MPa there is only a difference of 37 K.

## 4. Conclusions

- Creep testing of single crystals under vacuum allows a comparison of pure solid solution strengthening, excluding oxidation effects, grain size effects, grain boundary sliding, diffusion, and no precipitate effects.
- The 8° deviation from the [001] orientation for SX-Ni leads to an orientation sensitive primary creep behavior compared to [001] ± 0°, but there is no detected effect on the minimum creep rate.
- The SX CrMnFeCoNi alloy has a strong solid solution strengthening effect at 700 °C compared to SX pure nickel. The stress necessary to reach the same creep rate is 80 MPa higher in CrMnFeCoNi than in Ni.
- The solid solution strengthening effect due to high configurational entropy depends on the temperature and is strongly reduced at 980 °C and no longer present at 1100 °C.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Elemental concentration of the SX-CrMnFeCoNi alloy measured with µ-XRF cast in argon atmosphere.

**Figure 2.**Creep rate over strain diagram for vacuum creep tests at 700 °C of the single crystalline (

**a**) CrMnFeCoNi alloy, and (

**b**) pure nickel with a detail of the 50 MPa curve of the CrMnFeCoNi alloy in the inset.

**Figure 3.**Influence of deviation from exact orientation [001] of pure Ni at 700 °C, (

**a**) creep rate over strain (extracted from Figure 2b), and (

**b**) strain over time.

**Figure 4.**Creep rate over strain diagram for the creep tests of the single crystalline (

**a**) CrMnFeCoNi alloy, and (

**b**) pure nickel at 980 °C and at different loads under vacuum.

**Figure 5.**Creep rate over strain diagrams for the creep tests of the single crystalline (

**a**) CrMnFeCoNi alloy, and (

**b**) pure nickel at 1100 °C and with different stress levels by stress increase under vacuum.

**Figure 6.**Creep rate over strain diagram for the creep tests of the single crystalline pure nickel at 1200 °C with different stress levels by using stress increase under vacuum.

**Figure 7.**Double logarithmic scaling of minimum creep rate over stress of the single crystalline CrMnFeCoNi alloy in comparison to the single crystalline pure nickel (with 0° and 8° deviation from [001]) at 700, 980, 1100, and 1200 °C under vacuum.

**Figure 8.**Larson–Miller plot of the CrMnFeCoNi alloy compared with pure nickel under vacuum: (

**a**) using absolute temperature, and (

**b**) using homologous temperature. The time to reach 2% strain was used to calculate the Larson–Miller parameter P

_{2% and}P

_{2%_homologous.}

**Table 1.**Minimum creep rates and stress exponents for the creep tests of pure nickel and CrMnFeCoNi at different loads and temperatures under vacuum.

${\mathbf{log}}_{10}{\dot{\mathcal{E}}}_{\mathbf{min}}\mathbf{in}\mathbf{s}{-}^{1}$ | |||||||
---|---|---|---|---|---|---|---|

Material | SX-Ni | SX-CrMnFeCoNi | |||||

Temperature in °C | 700 | 980 | 1100 | 1200 | 700 | 980 | 1100 |

Load in MPa | |||||||

2 | −8.2 | −7.4 | −8.1 | ||||

3 | −7.5 | −6.4 | −7.9 | ||||

4 | −6.7 | −6.0 | −7.1 | ||||

5 | −7.7 | −6.4 | −5.5 | −6.5 | |||

6 | −6.0 | −5.8 | |||||

8 | −7.1 | −5.5 | −4.5 | −7.2 | −5.1 | ||

9 | −6.8 | −4.2 | |||||

13 | −5.5 | −6.0 | |||||

20 | −6.5 | −5.2 | |||||

25 | −5.3 ^{1} | −4.6 | |||||

35 | −4.8/–5.0 ^{1} | ||||||

45 | −4.0 | ||||||

50 | −8.3 | ||||||

65 | −7.6 | ||||||

80 | −6.8 | ||||||

100 | −6.3 | ||||||

125 | −5.6 | ||||||

Norton exp. n | 7.3 | 5.3 | 4.5 | 4.8 | 6.8 | 5.0 | 5.3 |

^{1 }Creep samples with deviation from [001] ± 0°.

**Table 2.**Time to reach 2% strain for the creep tests in pure nickel and CrMnFeCoNi at different loads and temperatures under vacuum.

t_{2%} in h | |||||||
---|---|---|---|---|---|---|---|

Material | SX-Ni | SX-CrMnFeCoNi | |||||

Temperature in °C | 700 | 980 | 1100 | 1200 | 700 | 980 | 1100 |

Load in MPa | |||||||

2 | 740.7 | 28.4 ^{2} | 564.4 ^{2} | ||||

3 | 70.8 | 6.7 | 289.5 ^{2} | ||||

4 | 9.5 | 1.5 | 72.0 ^{2} | ||||

5 | 32.0 | 15.2 | |||||

8 | 1.5 | 72.0 | |||||

9 | 0.7 | ||||||

13 | 0.1 | 5.0 | |||||

20 | 3.1 | 1.0 | |||||

25 | 0.8 ^{1} | 0.2 | |||||

35 | 0.1/0.2 ^{1} | ||||||

45 | <0.1 | ||||||

50 | 830.0 ^{2} | ||||||

65 | 130.0 | ||||||

80 | 35.0 | ||||||

100 | 3.5 | ||||||

125 | 0.3 |

^{1 }Creep samples with deviation from [001] ± 0°.

^{2}Extrapolated after reaching the minimum creep rate.

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**MDPI and ACS Style**

Gadelmeier, C.; Haas, S.; Lienig, T.; Manzoni, A.; Feuerbacher, M.; Glatzel, U.
Temperature Dependent Solid Solution Strengthening in the High Entropy Alloy CrMnFeCoNi in Single Crystalline State. *Metals* **2020**, *10*, 1412.
https://doi.org/10.3390/met10111412

**AMA Style**

Gadelmeier C, Haas S, Lienig T, Manzoni A, Feuerbacher M, Glatzel U.
Temperature Dependent Solid Solution Strengthening in the High Entropy Alloy CrMnFeCoNi in Single Crystalline State. *Metals*. 2020; 10(11):1412.
https://doi.org/10.3390/met10111412

**Chicago/Turabian Style**

Gadelmeier, Christian, Sebastian Haas, Tim Lienig, Anna Manzoni, Michael Feuerbacher, and Uwe Glatzel.
2020. "Temperature Dependent Solid Solution Strengthening in the High Entropy Alloy CrMnFeCoNi in Single Crystalline State" *Metals* 10, no. 11: 1412.
https://doi.org/10.3390/met10111412