# In-Situ XRD Study of Phase Transformation Kinetics in a Co-Cr-W-Alloy Manufactured by Laser Powder-Bed Fusion

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Sample Preparation

#### 2.2. Heat Treatment and Hot Stage

#### 2.3. XRD

#### 2.4. QXRD

#### 2.5. SEM

## 3. Results

#### 3.1. Phase Identification and Morphology

#### 3.2. Phase Transformation Kinetics

#### 3.3. Secondary In-Situ Fit Variables

## 4. Discussion

## 5. Conclusions

- The AB condition was mainly composed of an fcc $\gamma $-phase;
- HTs at temperatures below a certain threshold (probably close to ${T}_{\mathrm{S}}\approx 828{\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$) induced a $\gamma $-to-$\u03f5$ matrix transformation, which was slightly below the surface likely assisted by the formation of an oxide imposing stresses and strains onto the matrix and thus, evoking a partially strain-induced transformation there;
- Increasing amounts of Laves-phase and of another phase, likely $\sigma $-phase, precipitated with increasing HT temperatures;
- Inter- and intragranular stresses seemed to be reduced within 30 to $60\phantom{\rule{0.166667em}{0ex}}\mathrm{min}$ during HTs;
- The existence of a high-temperature phase, not present at room temperature and not distinctively assignable, was observed at the highest applied HT temperature (${T}_{\mathrm{S}}\approx 908{\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$).

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Abbreviated | Unabbreviated | ||

fcc | Face-centered cubic | ||

hcp | Hexagonal close-packed | ||

AB | As built | ||

AlN | Aluminiumnitride | ||

BSE | Backscattered electron | ||

CNC | Computerized numerical control | ||

DHS | Domed hot stage | ||

EDS | Energy-dispersive X-ray spectroscopy | ||

FWHM | Full width at half maximum | ||

HT | Heat treatment | ||

L-PBF | Laser powder-bed fusion | ||

PFM | Porcelain fused to metal | ||

QXRD | Quantitative X-ray diffraction | ||

RPD | Removable partial denture | ||

SE | Secondary electron | ||

SEM | Scanning electron microscopy | ||

SiC | Silicon carbide | ||

TiAl | Titaniumaluminide | ||

XRD | X-ray diffraction | ||

Symbol | Meaning | First | Unit |

Use | |||

${a}^{\mathrm{L}}$ | First lattice parameter | Section 2.4 | $\stackrel{\u02da}{\mathrm{A}}$ |

${c}^{\mathrm{L}}$ | Third lattice parameter | Section 2.4 | $\stackrel{\u02da}{\mathrm{A}}$ |

c | Weight fraction | Section 2.4 | w.-% |

$\overline{c}$ | Model based weight fraction | Section 2.4 | w.-% |

$\chi $ | Azimuthal angle of the diffraction cone | Section 2.3 | ${\phantom{\rule{0.166667em}{0ex}}}^{\circ}$ |

$\widehat{d}$ | Measured lattice-spacing | Section 3.3 | $\stackrel{\u02da}{\mathrm{A}}$ |

E | Young’s modulus | Section 1 | $\mathrm{GPa}$ |

${\widehat{FWHM}}_{\mathrm{G}}$ | Measured FWHM of Gaussian component | Section 2.4 | ${\phantom{\rule{0.166667em}{0ex}}}^{\circ}$ |

${\widehat{FWHM}}_{\mathrm{L}}$ | Measured FWHM of Lorentzian component | Section 2.4 | ${\phantom{\rule{0.166667em}{0ex}}}^{\circ}$ |

${h}_{\mathrm{O}}$ | Oxide layer thickness | Section 2.4 | $\mathsf{\mu}\mathrm{m}$ |

${\overline{h}}_{\mathrm{O}}$ | Model based oxide layer thickness | Section 2.4 | $\mathsf{\mu}\mathrm{m}$ |

i | Counting variable referring to observed phases | Section 2.4 | - |

I | Peak intensity | Section 2.4 | $\mathrm{a}.\mathrm{u}.$ |

$\widehat{I}$ | Measured peak intensity | Section 2.4 | $\mathrm{a}.\mathrm{u}.$ |

$\overline{I}$ | Model based peak intensity | Section 2.4 | $\mathrm{a}.\mathrm{u}.$ |

j | Counting variable referring to certain peaks | Section 2.4 | - |

k | Point in time throughout the treatment | Section 2.4 | - |

$\mathrm{K}$ | Calibration constant | Section 2.4 | $\frac{\mathrm{a}.\mathrm{u}.}{\mathrm{cm}}$ |

l | Counting variable referring to a temperature | Section 2.4 | - |

${\mu}^{\u2605}$ | Average mass absorption coefficient of matrix phases | Section 2.4 | $\frac{{\mathrm{cm}}^{2}}{\mathrm{g}}$ |

${\mu}_{\mathrm{O}}^{\u2605}$ | Mass absorption coefficient of ${\mathrm{Cr}}_{2}{\mathrm{O}}_{3}$ | Section 2.4 | $\frac{{\mathrm{cm}}^{2}}{\mathrm{g}}$ |

n | Number of all phases | Section 2.4 | - |

p | Counting variable referring a setup | Section 2.4 | - |

$\rho $ | Average density of matrix phases | Section 2.4 | $\frac{\mathrm{g}}{{\mathrm{cm}}^{3}}$ |

${\rho}_{\mathrm{O}}$ | Density of the oxide | Section 2.4 | $\frac{\mathrm{g}}{{\mathrm{cm}}^{3}}$ |

$\varsigma $ | Weight fraction relative to matrix phases | Section 2.4 | w.-% |

$\overline{\varsigma}$ | Model based weight fraction relative to matrix phases | Section 2.4 | w.-% |

t | Time throughout the treatment | Section 2.4 | $\mathrm{min}$ |

${T}_{\mathrm{DHS}}$ | Controller temperature of DHS | Section 2.2 | ${\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$ |

${T}_{\mathrm{S}}$ | Sample surface temperature | Section 2.2 | ${\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$ |

$\Theta $ | Glancing angle or Bragg angle | Section 2.3 | ${\phantom{\rule{0.166667em}{0ex}}}^{\circ}$ |

$\widehat{\Theta}$ | Measured glancing angle | Section 2.3 | ${\phantom{\rule{0.166667em}{0ex}}}^{\circ}$ |

## Appendix A. Additional In-Situ XRD-Data

**Figure A1.**Estimated FWHM of the Gaussian component ${\widehat{FWHM}}_{\mathrm{G}}$ of the used Voigt peak shape function fitted to the $\left(002\right)$-$\gamma $-peak over the time spent in the HT measured with in-situ XRD.

**Figure A2.**Estimated FWHM of the Lorentzian component ${\widehat{FWHM}}_{\mathrm{L}}$ of the used Voigt peak shape function fitted to the $\left(002\right)$-$\gamma $-peak over the time spent in the HT measured with in-situ XRD.

**Figure A3.**Estimated FWHM of the Gaussian component ${\widehat{FWHM}}_{\mathrm{G}}$ of the used Voigt peak shape function fitted to the $\left(111\right)$-$\gamma $-peak over the time spent in the HT measured with in-situ XRD. Values for samples 1 and 2 could not be given due to peak overlap with $\left(002\right)$-$\u03f5$-peak.

**Figure A4.**Estimated FWHM of the Lorentzian component ${\widehat{FWHM}}_{\mathrm{L}}$ of the used Voigt peak shape function fitted to the $\left(111\right)$-$\gamma $-peak over the time spent in the HT measured with in-situ XRD. Values for samples 1 and 2 could not be given due to peak overlap with $\left(002\right)$-$\u03f5$-peak.

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**Figure 2.**Image of the Domed Hot Stage: (1) AlN base plate; (2) sample; (3) TiAl holders; (4) graphite dome; (5) ring with cooling air exhausts; (6) heat sink; (7) feed pipes.

**Figure 3.**Diffractogram of the last frame of the in-situ dataset from sample 4 at ${T}_{\mathrm{TH}4}$ with graphs of the various models fitted to the raw data. Diamond markers: Possible peaks of a high temperature phase not present in ambient conditions.

**Figure 4.**Flow chart for the calculation of calibration constants for all phases present in samples 1 and 2.

**Figure 5.**In color: Ex-situ XRD diffractograms, with intensities normalized to the highest peak in the respective pattern, of samples composed of a Co-Cr-W alloy in states AB by L-PBF and after HTs measured on the samples’ surface. Additionally in grey: Stick reference pattern calculated with VESTA [32] of a solution of W in Co fcc $\gamma $-phase (COD:1524796 [33]), a solution of W in Co hcp $\u03f5$-phase (COD:1524797 [33]), a ${\mathrm{Cr}}_{2}{\mathrm{O}}_{3}$ oxide (COD:2104122 [34]), and a $\mathrm{Cr}{\mathrm{Mn}}_{1.5}{\mathrm{O}}_{4}$ spinel (COD:7222202 [35]).

**Figure 6.**In color: Ex-situ XRD diffractograms, with intensities normalized to the highest peak in the respective pattern, of samples composed of a Co-Cr-W alloy in states AB by L-PBF and after HTs measured on the samples’ bulk. Additionally in grey: Stick reference pattern calculated with VESTA [32] of a solution of W in Co fcc $\gamma $-phase (COD:1524796 [33]), a solution of W in Co hcp $\u03f5$-phase (COD:1524797 [33]), and a ${\mathrm{W}}_{2}{\mathrm{Co}}_{3}\mathrm{Si}$ Laves-phase [37].

**Figure 7.**SEM images, measured with secondary electron (SE) and backscattered electron (BSE) detectors, as well as quantitative maps acquired with EDS of the bulk in sample 4 after HT with ${T}_{\mathrm{HT}4}$ (${T}_{\mathrm{S}}\approx 908{\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$). Spotty dots: Laves-phase; Light gray patches: $\sigma $-phase.

**Figure 8.**Estimated peak intensities ${\widehat{I}}_{i,j,\mathrm{in},l}$ as acquired by fitting Voigt-functions to the in-situ datasets recorded during HT with XRD of (

**a**) sample 1 at ${T}_{\mathrm{HT}1}$(${T}_{S}\approx 644{\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$) and (

**b**) sample 2 at ${T}_{\mathrm{HT}2}$(${T}_{S}\approx 732{\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$). Additionally given: Graph of the linear model fitted to the estimated peak intensities with smaller marks indicating datapoints excluded from the fit.

**Figure 9.**Calculated weight fractions ${c}_{i,\mathrm{in}}$ and weight fractions relative to the matrix phases ${\varsigma}_{i,\mathrm{in}}$ over the time spent in the HT based on the in-situ XRD measurements for (

**a**) sample 1 and (

**b**) sample 2.

**Figure 10.**Calculated oxide layer thickness ${h}_{\mathrm{O},\mathrm{in}}$ over the time spent in the HT for sample 2 based on in-situ XRD measurements.

**Figure 11.**XRD based estimation of peak positions $2\widehat{\Theta}$ of the $\left(002\right)$-$\gamma $-peak over the time spent in the HT measured in situ. The estimated lattice spacing was calculated using the Bragg equation. Error bars are related to the $2\widehat{\Theta}$-scale.

**Table 1.**Recordings of the steady state temperatures measured in the reference set-up at the controller and the sample’s surface.

Controller Temperature | Sample Surface Temperature | HT Conditions | |
---|---|---|---|

${\mathit{T}}_{\mathbf{DHS}}$ in ${}^{\circ}$C | ${\mathit{T}}_{\mathbf{S}}$ in ${}^{\circ}$C | Applied to | |

${T}_{\infty}$ | 25 | 25 | |

${T}_{\mathrm{HT}1}$ | 800 | 644 | sample 1 |

${T}_{\mathrm{HT}2}$ | 900 | 732 | sample 2 |

${T}_{\mathrm{HT}3}$ | 1000 | 828 | sample 3 |

${T}_{\mathrm{HT}4}$ | 1100 | 908 | sample 4 |

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**MDPI and ACS Style**

Hegele, P.; von Kobylinski, J.; Hitzler, L.; Krempaszky, C.; Werner, E.
In-Situ XRD Study of Phase Transformation Kinetics in a Co-Cr-W-Alloy Manufactured by Laser Powder-Bed Fusion. *Crystals* **2021**, *11*, 176.
https://doi.org/10.3390/cryst11020176

**AMA Style**

Hegele P, von Kobylinski J, Hitzler L, Krempaszky C, Werner E.
In-Situ XRD Study of Phase Transformation Kinetics in a Co-Cr-W-Alloy Manufactured by Laser Powder-Bed Fusion. *Crystals*. 2021; 11(2):176.
https://doi.org/10.3390/cryst11020176

**Chicago/Turabian Style**

Hegele, Patrick, Jonas von Kobylinski, Leonhard Hitzler, Christian Krempaszky, and Ewald Werner.
2021. "In-Situ XRD Study of Phase Transformation Kinetics in a Co-Cr-W-Alloy Manufactured by Laser Powder-Bed Fusion" *Crystals* 11, no. 2: 176.
https://doi.org/10.3390/cryst11020176