# Microstructural Evolution and Phase Formation in 2nd-Generation Refractory-Based High Entropy Alloys

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{25}Nb

_{25}Ta

_{25}W

_{25}and Mo

_{20}Nb

_{20}Ta

_{20}V

_{20}W

_{20}, both are BCC and possess a single solid solution [4,5]. Owing to the resilience of HEAs at high temperatures, researchers most aspire to apply them in the aerospace industry (such as turbine engine blades). The one significant drawback to such an application is the high density and low corrosion resistance exhibited by the refractory elements, separately or alloyed [5].

_{x}HEAs on the magnetic properties and found a good coincidence between the experimental results and the results of a Monte Carlo simulation of the nearest neighbor distribution, as well as between the elastic modulus and magnetic moment.

_{20}Nb

_{20}Ti

_{20}V

_{20}Zr

_{20}

_{20}Mo

_{10}Nb

_{20}Ti

_{20}Ta

_{10}Zr

_{20}

## 2. Results

#### 2.1. Cr_{20}Nb_{20}Ti_{20}V_{20}Zr_{20} Alloy

_{2}O

_{3}powder used in the experiment setting, resulting in a thick pure ZrO

_{2}layer and incorporation of some Al in the Zr-depleted matrix. However, it may indicate that the Zr segregation process was finalized and the free Zr was able to react with Al

_{2}O

_{3}as thermodynamics would otherwise dictate. Furthermore, no trace of the Zr rich phase was found.

#### 2.2. Cr_{20}Mo_{10}Nb_{20}Ta_{10}Ti_{20}Zr_{20} Alloy

_{20}Mo

_{10}Nb

_{20}Ta

_{10}Ti

_{20}Zr

_{20}alloy.

## 3. Discussion

## 4. Thermodynamic Modelling

_{20}Nb

_{20}Ti

_{20}V

_{20}Zr

_{20}alloy at 800, 1000, 1300, and 1600 °C have been performed based on the CALPHAD-method using the algorithm determined in [11]. This algorithm was tested previously in thermodynamic calculations for a number of multicomponent systems (see for example [12,13,14,15,16]), and appropriate results were obtained. In this method, the calculation is performed by finding an alloy phase composition corresponding to the global minimum of its Gibbs free energy. Mathematically, the Gibbs free energy (G) of a system is a function of many variables, such as component concentrations in phases and mole fractions of phases. Thus, the search for the G function’s minimum was performed in the presence of non-linear limitations in the form of equalities and inequalities, i.e., a general problem of nonlinear programming was solved. To find phase compositions corresponding to the global minimum of the Gibbs free energy a special procedure of choosing starting points described in [11] was used.

_{s}is a number of sites in sublattice s per one mole of formula units of a phase, ${Y}_{i}^{s}$ is a mole fraction of component i in sublattice s of phase f. Parameter ${}^{0}G_{I0}^{f}$ denotes Gibbs free energy of one mole of formula units of a compound with the same crystal structure as phase f, corresponding to an element of array I0 determining one element for every sublattice; $\prod}_{I0}(Y){}^{0}G_{I0}^{hf$ denotes the product of the corresponding elements of matrix $\Vert Y\Vert $; I1 denotes the array determining such variants of atoms distribution in sublattices where one sublattice contains atoms of two elements, whereas the rest contains atoms of only one element; and ${\prod}_{I1}(Y)$ corresponds to the product of the appropriate elements of matrix $\Vert Y\Vert $. Array I1 is referred to as the first order array contrary to the array of 0th order. Arrays of higher orders IZ correspond to various combinations of higher numbers of elements from different sublattices. Parameters L

_{IZ}characterize the interaction energy of components of the corresponding element of array IZ.

_{2}with negligible V amounts, which is not the actual case (it consists mostly of ZrCr

_{2}and ZrV

_{2}).

## 5. Materials and Methods

## 6. Conclusions

- In high-entropy alloys based on Zr and BCC elements, such as Cr, Ti, and Nb (the first two falling under the wider definition of refractory elements and Nb being a refractory element), a unique phenomenon of gradual Zr segregation as the temperature rises can be observed. This phenomenon is apparently related to the contrasting crystal structures of the HCP Zr solid solution and the BCC Cr-Nb based solid solution. It is more than likely that this phenomenon is not in equilibrium since Zr is expected to have a BCC structure at high temperatures as well.Some Ti is also incorporated in the secluded Zr solid solution regions and, to a small degree, it behaves in the same manner, being an HCP element itself.
- The Zr segregation is initiated by the onset of Laves phase decomposition at around 1000 °C, which leaves behind a Zr-rich phase. The other elements are then incorporated in the increasingly Zr-depleted BCC solid solution phase, which gradually grows in volume as the temperature rises further.
- The thermodynamic simulation successfully predicts the general trend of increasing volume percentage of the Cr-inclusive solid solution phase, as well as the increasing Cr incorporation in it, as a function of temperature (around 1000 °C and higher), however, Zr segregation is not accounted for, due to the fact that it may not be an equilibrium phenomenon. The Nb-Ti-Zr based solid solution phase appearing at low to moderate temperatures in both alloys forms as a result of the relatively rapid cooling associated with arc melting and is not likely to be the equilibrium solid solution phase predicted at those temperatures by the model.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**SEM micrographs of Cr

_{20}Nb

_{20}Ti

_{20}V

_{20}Zr

_{20}at (

**a**) 25 °C, (

**b**) 800 °C, (

**c**) 1000 °C, and (

**d**) 1300 °C at 1000× magnification in BSE mode.

**Figure 2.**XRD traces of the Cr

_{20}Nb

_{20}Ti

_{20}V

_{20}Zr

_{20}alloy at 25 °C, 1000 °C, and 1300 °C; the shifts in 2θ values of certain peaks as a result of the rising temperature are marked in arrows.

**Figure 3.**SEM micrograph of Cr

_{20}Mo

_{10}Nb

_{20}Ta

_{10}Ti

_{20}Zr

_{20}at 25 °C at (

**a**) 1000× and (

**b**) 4000× magnifications in BSE mode.

**Figure 4.**SEM micrograph of Cr

_{20}Mo

_{10}Nb

_{20}Ta

_{10}Ti

_{20}Zr

_{20}at 800 °C at (

**a**) 1000× and (

**b**) 8000× magnifications in BSE mode.

**Figure 5.**SEM micrograph of Cr

_{20}Mo

_{10}Nb

_{20}Ta

_{10}Ti

_{20}Zr

_{20}at 1000 °C at (

**a**) 1000× and (

**b**) 2000× magnifications in BSE mode.

**Figure 6.**SEM micrograph of Cr

_{20}Mo

_{10}Nb

_{20}Ta

_{10}Ti

_{20}Zr

_{20}at 1300 °C at (

**a**) 1000× and (

**b**) 4000× magnifications in BSE mode.

**Figure 7.**SEM micrograph of Cr

_{20}Mo

_{10}Nb

_{20}Ta

_{10}Ti

_{20}Zr

_{20}at 1600 °C at (

**a**) 1000× and (

**b**) 4000× magnifications in BSE mode.

**Figure 8.**XRD traces of the Cr

_{20}Mo

_{10}Nb

_{20}Ta

_{10}Ti

_{20}Zr

_{20}alloy at 25 °C, 1000 °C, 1300 °C, and 1600 °C; the shifts in 2θ values of certain peaks as a result of the rising temperature are marked in arrows.

**Figure 9.**Flowchart depicting the evolution of phases as the temperature rises in the Cr

_{20}Nb

_{20}Ti

_{20}V

_{20}Zr

_{20}alloy. Diffusion processes occurring at 1600 °C are tentative.

**Figure 10.**Flowchart depicting the evolution of phases as the temperature rises in the Cr

_{20}Mo

_{10}Nb

_{20}Ta

_{10}Ti

_{20}Zr

_{20}alloy.

**Table 1.**Model prediction of chemical composition of every phase in equilibrium at the designated temperatures.

Temperature (°C) | Phase | Weight Fraction (%) | Chemical Composition (at%) | ||||
---|---|---|---|---|---|---|---|

Ti | V | Cr | Zr | Nb | |||

800 °C | BCC_A2 | 72.68 | 23.86 | 28.29 | 2.04 | 26.52 | 19.29 |

Laves_C15 | 27.32 | 10.74 | 0.14 | 63.02 | 4.39 | 21.71 | |

1000 °C | BCC_A2 | 74.88 | 23.24 | 27.30 | 4.73 | 24.90 | 19.83 |

Laves_C15 | 25.12 | 11.21 | 0.19 | 61.46 | 6.68 | 20.46 | |

1300 °C | BCC_A2 | 86.14 | 21.34 | 23.42 | 13.23 | 21.69 | 20.32 |

Laves_C15 | 13.86 | 12.25 | 0.26 | 59.13 | 10.22 | 18.14 | |

1600 °C | BCC_A2 | 100.00 | 20.00 | 20.00 | 20.00 | 20.00 | 20.00 |

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**MDPI and ACS Style**

Eshed, E.; Larianovsky, N.; Kovalevsky, A.; Popov Jr., V.; Gorbachev, I.; Popov, V.; Katz-Demyanetz, A.
Microstructural Evolution and Phase Formation in 2nd-Generation Refractory-Based High Entropy Alloys. *Materials* **2018**, *11*, 175.
https://doi.org/10.3390/ma11020175

**AMA Style**

Eshed E, Larianovsky N, Kovalevsky A, Popov Jr. V, Gorbachev I, Popov V, Katz-Demyanetz A.
Microstructural Evolution and Phase Formation in 2nd-Generation Refractory-Based High Entropy Alloys. *Materials*. 2018; 11(2):175.
https://doi.org/10.3390/ma11020175

**Chicago/Turabian Style**

Eshed, Eyal, Natalya Larianovsky, Alexey Kovalevsky, Vladimir Popov Jr., Igor Gorbachev, Vladimir Popov, and Alexander Katz-Demyanetz.
2018. "Microstructural Evolution and Phase Formation in 2nd-Generation Refractory-Based High Entropy Alloys" *Materials* 11, no. 2: 175.
https://doi.org/10.3390/ma11020175