# High-Temperature Nano-Indentation Creep of Reduced Activity High Entropy Alloys Based on 4-5-6 Elemental Palette

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## Abstract

**:**

^{3}, indicating dislocation dominated mechanism. The stress exponent increased with increasing indentation depth due to a higher density of dislocations and their entanglement at larger depth and the exponent decreased with increasing temperature due to thermally activated dislocations. Smaller creep displacement and higher activation energy for the two high entropy alloys indicate superior creep resistance compared to refractory pure metals like tungsten.

## 1. Introduction

## 2. Experimental

_{2}gas environment to avoid oxidation. A Berkovich sapphire tip was used for all the creep tests. A standard fused quartz reference sample was used for the initial tip calibration. For each material, two different types of tests were performed: (i) static constant load hold (CLH) and (ii) dynamic load hold in DMA mode. The static creep tests were done by ramping the load to 1 N and 5 N at temperatures of 298 K, 423 K, and 573 K, and then held at maximum load for 120 s to determine creep response before unloading. High loads were used to avoid surface effects. In dynamic load tests, 100 mN, 500 mN, and 1000 mN loads were used to study the creep behavior. The frequency and amplitude were set to 100 Hz and 10% of the peak load, respectively. In all tests, a high loading rate of 20 mN/s was chosen to minimize plastic deformation during the loading segment. The samples were held at a prescribed temperature for at least 20 min to reduce the temperature gradient between the tip and the sample and to allow the indenter tip to reach a steady state. In addition, thermal drift was automatically corrected by the Triboindenter software and was between 0.05 and 0.1 nm/s during testing. At least 12 indents were made for each condition to get statistical variation. The distance between two indents was kept larger than 100 μm to avoid overlapping of their plastic zones.

## 3. Results

_{2}gas environment and high loads used for the creep tests.

## 4. Discussion

^{2}> 0.95 with the experimental data as shown in Figure 2c,d with dashed lines. For the self-similar Berkovich indentation tip, the following were used to obtain indentation strain rate (Equation (2)) and hardness (Equation (3)) [28]:

_{c}is contact depth, given by h

_{c}= h

_{max}−0.75 P/S for Berkovich indenter, and h

_{max}and S are maximum penetration depth and material stiffness, respectively.

^{3}(~13b

^{3}), 0.5 ± 0.11 nm

^{3}(~20b

^{3}) and 0.4 ± 0.09 nm

^{3}(~16b

^{3}) for W, Ta-Hf, and Ta-W, respectively. Lattice parameter (a

_{0}) is ~0.34 nm for current HEAs [9] and ~0.31 nm for W, and b = 1/2 a

_{0}[111] is Burgers vector of BCC alloys/metals. The activation volumes for all three systems were in the range for kink-pair nucleation and movement of screw dislocations in BCC alloys/metals [35]. V* value is in the range of 10b

^{3}–1000b

^{3}for dislocation creep while diffusion-mediated creep is typically associated with lower values of V*. Tungsten showed a slightly smaller activation volume compared to the two HEAs. Activation volume describes the degree of dislocation nucleation, the smaller activation volume indicating easier nucleation of dislocations [35]. Activation volume for BCC CoCrFeNiCuAl

_{2.5}thin film HEA measured using a Berkovich nano-indenter was reported to be ~0.5 nm

^{3}[15], while FCC CoCrFeCuNi thin film and coarse-grained CoCrFeMnNi showed one order of magnitude lower activation volume of 0.08 nm

^{3}and 0.05 nm

^{3}, respectively [15,27].

^{n}) versus 1/T yields a slope of −Q/R [46,47] as plotted in Figure 5 for all the studied alloys. The average strain rate and hardness over holding time at each temperature were selected for analysis. Linear regression indicated creep activation energy of 352 ± 10 kJ/mol, 925 ± 100 kJ/mol, and 1000 ± 50 kJ/mol for W, Ta-Hf, and Ta-W, respectively. The calculated higher activation energy of 900–1000 kJ/mol for HEAs compared to pure W may be associated with severe lattice distortion and sluggish diffusion in HEAs resulting in a greater degree of dislocation interaction and supporting their higher creep resistance [48]. Activation energy for CoCrFeNiMn [12] and precipitation-hardened (FeCoNiCr)

_{94}Ti

_{2}Al

_{4}[49] HEAs were reported to be ~300–400 kJ/mol and ~300–800 kJ/mol, respectively, from tensile tests. However, to the best of the authors’ knowledge, there are no reports on activation energy of HEAs by the nano-indentation creep test. In summary, the high activation energy for Ta-Hf and Ta-W compared to pure refractory metals like tungsten support their excellent creep resistance. This suggests the potential use of these alloys in next-generation nuclear reactors as well as fossil fuel power plants where refractory metals are currently used.

## 5. Conclusions

- (1)
- The creep exponent was in the range of 20–140 and activation volume was in the range of 13–20b
^{3}, indicating that the time-dependent deformations for all alloys were dislocation dominated. - (2)
- The stress exponent decreased with increasing temperature owing to thermally activated dislocations and the reduction was sharper for HEAs compared to pure W.
- (3)
- The creep exponent increased with increasing load (depth) leading to an apparent size effect due to a higher generation rate of dislocation and their entanglement at larger penetration depth. A higher diffusion/annihilation rate of dislocations near the free surface at a smaller depth may be another possible explanation.
- (4)
- HEAs showed smaller creep displacement and higher activation energy compared to pure tungsten, which may be attributed to sluggish diffusion and severe lattice strains.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**a**) Refractory elements belonging to the 4-5-6 group/period; (

**b**) time in years required for group 4-5-6 refractory elements to reach “hands-on” level after exposure [34]. X-ray diffraction analysis of (

**c**) HfTaTiVZr (Ta-Hf) and (

**d**) TaTiVWZr (Ta-W) refractory high entropy alloys in as-cast and annealed conditions showing single-phase body-centered cubic (BCC) crystal structure for Ta-Hf and a BCC1 major phase and BCC2 minor phase for Ta-W; backscattered scanning electron microscopy image of (

**e**) Ta-Hf and (

**f**) Ta-W alloys showing equiaxed grains with an average grain size of ~250 μm for Ta-Hf and formation of two phases in Ta-W; insets showing selected area diffraction pattern of the alloys. Energy-dispersive X-ray spectroscopy of (

**g**) Ta-Hf and (

**h**) Ta-W alloys confirming a homogeneous distribution of elements in Ta-Hf alloy and partitioning of Ta and W into dendrite phase and Ti, V, and Zr into the matrix in Ta-W alloy.

**Figure 2.**Nano-indentation load–displacement curves of W, HfTaTiVZr (Ta-Hf), and TaTiVWZr (Ta-W) alloys determined during creep experiments at (

**a**) 1 N, 298 K and (

**b**) 1 N, 573 K. Creep displacement versus holding time for all alloys at (

**c**) 1 N, 298 K and (

**d**) 1 N, 573. Creep displacement as a function of temperature for W, Ta-Hf and Ta-W alloys at (

**e**) 1 N and (

**f**) 5 N showing the increase of displacement with increasing temperature and load. Creep displacement was smaller for high entropy alloys compared to pure tungsten.

**Figure 3.**Creep displacement versus holding time for TaTiVWZr (Ta-W) alloy as a function of load at (

**a**) 298 K and (

**b**) 423 K. Maximum creep displacement dependence on applied load for W, Ta-Hf, and Ta-W at (

**c**) 298 K and (

**d**) 423 K showing larger creep displacement with increasing load and temperature.

**Figure 4.**Stress exponent versus temperature for W, HfTaTiVZr (Ta-Hf), and TaTiVWZr (Ta-W) alloys at (

**a**) 1 N and (

**b**) 5 N showing the decrease of stress exponent with increasing temperature. Stress exponent versus load for all three systems at (

**c**) 298 K and (

**d**) 423 K showing indentation size effect of stress exponent.

**Figure 5.**ln($\dot{\epsilon}$/H

^{n}) versus 1000/T with slope giving the activation energy (Q) for W, HfTaTiVZr, and TaTiVWZr high entropy alloys. The activation energies for the current refractory high entropy alloys were higher than tungsten by almost a factor of three.

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**MDPI and ACS Style**

Sadeghilaridjani, M.; Muskeri, S.; Pole, M.; Mukherjee, S.
High-Temperature Nano-Indentation Creep of Reduced Activity High Entropy Alloys Based on 4-5-6 Elemental Palette. *Entropy* **2020**, *22*, 230.
https://doi.org/10.3390/e22020230

**AMA Style**

Sadeghilaridjani M, Muskeri S, Pole M, Mukherjee S.
High-Temperature Nano-Indentation Creep of Reduced Activity High Entropy Alloys Based on 4-5-6 Elemental Palette. *Entropy*. 2020; 22(2):230.
https://doi.org/10.3390/e22020230

**Chicago/Turabian Style**

Sadeghilaridjani, Maryam, Saideep Muskeri, Mayur Pole, and Sundeep Mukherjee.
2020. "High-Temperature Nano-Indentation Creep of Reduced Activity High Entropy Alloys Based on 4-5-6 Elemental Palette" *Entropy* 22, no. 2: 230.
https://doi.org/10.3390/e22020230