# 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.

## References

- Helsen, J.A.; Missirlis, Y. Biomaterials; Springer: Berlin/Heidelberg, Germany, 2010. [Google Scholar]
- Roberts, H.W.; Berzins, D.W.; Moore, B.K.; Charlton, D.G. Metal-Ceramic Alloys in Dentistry: A Review. J. Prosthodont.
**2009**, 18, 188–194. [Google Scholar] [CrossRef] - Kassapidou, M.; Franke Stenport, V.; Hjalmarsson, L.; Johansson, C.B. Cobalt-Chromium Alloys in Fixed Prosthodontics in Sweden. Acta Biomater. Odontol. Scand.
**2017**, 3, 53–62. [Google Scholar] [CrossRef] [PubMed] - Al Jabbari, Y.S. Physico-mechanical Properties and Prosthodontic Applications of Co-Cr Dental Alloys: A Review of the Literature. J. Adv. Prosthodont.
**2014**, 6, 138–145. [Google Scholar] [CrossRef][Green Version] - Wataha, J.C. Biocompatibility of Dental Casting Alloys: A Review. J. Prosthet. Dent.
**2000**, 83, 223–234. [Google Scholar] [CrossRef] - Bürgel, R.; Jürgen Maier, H.; Niendorf, T. Handbuch Hochtemperatur-Werkstofftechnik: Grundlagen, Werkstoffbeanspruchungen, Hochtemperaturlegierungen und-Beschichtungen, 4th ed.; Vieweg+Teubner Verlag: Wiesbaden, Germany, 2011. [Google Scholar]
- Karaali, A.; Mirouh, K.; Hamamda, S.; Guiraldenq, P. Microstructural Study of Tungsten Influence on Co–Cr Alloys. Mater. Sci. Eng. A-Struct.
**2005**, 390, 255–259. [Google Scholar] [CrossRef] - Yamanaka, K.; Mori, M.; Kuramoto, K.; Chiba, A. Development of New Co–Cr–W-based Biomedical Alloys: Effects of Microalloying and Thermomechanical Processing on Microstructures and Mechanical Properties. Mater. Des.
**2014**, 55, 987–998. [Google Scholar] [CrossRef] - Asgar, K. Casting Metals in Dentistry: Past-Present-Future. Adv. Dent. Res.
**1988**, 2, 33–43. [Google Scholar] [CrossRef] [PubMed] - Hitzler, L.; Alifui-Segbaya, F.; Williams, P.; Heine, B.; Heitzmann, M.; Hall, W.; Merkel, M.; Öchsner, A. Additive Manufacturing of Cobalt-based Dental Alloys: Analysis of Microstructure and Physicomechanical Properties. Adv. Mater. Sci. Eng.
**2018**, 2018, 1–12. [Google Scholar] [CrossRef][Green Version] - Koutsoukis, T.; Zinelis, S.; Eliades, G.; Al-Wazzan, K.; Rifaiy, M.A.; Al Jabbari, Y.S. Selective Laser Melting Technique of Co-Cr Dental Alloys: A Review of Structure and Properties and Comparative Analysis with Other Available Techniques. J. Prosthodont.
**2015**, 24, 303–312. [Google Scholar] [CrossRef] - Hitzler, L.; Merkel, M.; Hall, W.; Öchsner, A. A Review of Metal Fabricated with Laser- and Powder-Bed Based Additive Manufacturing Techniques: Process, Nomenclature, Materials, Achievable Properties, and its Utilization in the Medical Sector. Adv. Eng. Mater.
**2018**, 20, 1700658. [Google Scholar] [CrossRef][Green Version] - Hitzler, L. The Anisotropic and Inhomogeneous Nature of Additively Manufactured Metals, and the Application of Selective Laser Melting in Dentistry. Ph.D. Thesis, Griffith University, Gold Coast, Australia, 2018. [Google Scholar] [CrossRef]
- Takaichi, A.; Nakamoto, T.; Joko, N.; Nomura, N.; Tsutsumi, Y.; Migita, S.; Doi, H.; Kurosu, S.; Chiba, A.; Wakabayashi, N.; et al. Microstructures and Mechanical Properties of Co–29Cr–6Mo Alloy Fabricated by Selective Laser Melting Process for Dental Applications. J. Mech. Behav. Biomed. Mater.
**2013**, 21, 67–76. [Google Scholar] [CrossRef] - Verein Deutscher Ingenieure. VDI 3405: Additive Fertigungsverfahren - Grundlagen, Begriffe, Verfahrensbeschreibungen; Beuth Verlag: Berlin, Germany, 2014. [Google Scholar]
- Alifui-Segbaya, F.; Evans, J.; Eggbeer, D.; George, R. Clinical Relevance of Laser-Sintered Co-Cr Alloys for Prosthodontic Treatments: A Review. In Proceedings of the 1st International Conference on Progress in Additive Manufacturing, Singapore, 26–28 May 2014; Research Publishing Services: Singapore, 2014; pp. 115–120. [Google Scholar] [CrossRef]
- Kim, H.R.; Jang, S.H.; Kim, Y.K.; Son, J.S.; Min, B.K.; Kim, K.H.; Kwon, T.Y. Microstructures and Mechanical Properties of Co-Cr Dental Alloys Fabricated by Three CAD/CAM-Based Processing Techniques. Materials
**2016**, 9, 596. [Google Scholar] [CrossRef] - von Kobylinski, J.; Hitzler, L.; Lawitzki, R.; Krempaszky, C.; Öchsner, A.; Werner, E. Relationship between Phase Fractions and Mechanical Properties in Heat–Treated Laser Powder–Bed Fused Co–based Dental Alloys. ISR J. Chem.
**2020**. [Google Scholar] [CrossRef][Green Version] - Kajima, Y.; Takaichi, A.; Kittikundecha, N.; Nakamoto, T.; Kimura, T.; Nomura, N.; Kawasaki, A.; Hanawa, T.; Takahashi, H.; Wakabayashi, N. Effect of Heat-treatment Temperature on Microstructures and Mechanical Properties of Co–Cr–Mo Alloys Fabricated by Selective Laser Melting. Mater. Sci. Eng. A-Struct.
**2018**, 726, 21–31. [Google Scholar] [CrossRef] - Hitzler, L.; von Kobylinski, J.; Lawitzki, R.; Krempaszky, C.; Werner, E. Microstructural Development and Mechanical Properties of Selective Laser Melted Co–Cr–W Dental Alloy. In TMS 2020 149th Annual Meeting & Exhibition Supplemental Proceedings; The Minerals, Metals & Materials Series; Springer International Publishing: Cham, Switzerland, 2020; pp. 195–202. [Google Scholar] [CrossRef]
- Dentaurum: Remanium Star CL Powered by Dentaurum. Available online: https://www.dentaurum.de/files/1105_remaniumstarCL_Materialdatenblatt-10.pdf (accessed on 13 January 2021).
- Instruction Manual DHS 1100: Domed Hot Stage: Version PANalytical. Available online: https://pf18b.neocities.org/docu/Anton%20Paar%20DHS%201100.pdf (accessed on 15 January 2021).
- Resel, R.; Tamas, E.; Sonderegger, B.; Hofbauer, P.; Keckes, J. A Heating Stage up to 1173 K for X-Ray Diffraction Studies in the Whole Orientation Space. J. Appl. Crystallogr.
**2003**, 36, 80–85. [Google Scholar] [CrossRef] - Samarati, J.; Iengo, P.; Longo, L.; Sekhniaidze, G.; Sidiropoulou, O.; Wotschack, J. Characterisation of the Charging Up Effect in Resistive Micromegas Detectors. J. Phys. Conf. Ser.
**2020**, 1498, 012030. [Google Scholar] [CrossRef] - Mittemeijer, E.J.; Welzel, U. The “State of the Art” of the Diffraction Analysis of Crystallite Size and Lattice Strain. Z. Kristallogr.
**2008**, 223, 134. [Google Scholar] [CrossRef] - Schreier, F. Optimized Implementations of Rational Approximations for the Voigt and Complex Error Function. J. Quant. Spectrosc. Radiat.
**2011**, 112, 1010–1025. [Google Scholar] [CrossRef] - James, F. Minuit: Function Minimization and Error Analysis Reference Manual. Available online: https://cds.cern.ch/record/2296388/files/minuit.pdf (accessed on 13 January 2021).
- Alexander, L.; Klug, H.P. Basic Aspects of X-Ray Absorption in Quantitative Diffraction Analysis of Powder Mixtures. Anal. Chem.
**1948**, 20, 886–889. [Google Scholar] [CrossRef] - Zevin, L.S.; Kimmel, G.; Mureinik, I. Quantitative X-ray Diffractometry; Springer US: New York, NY, USA, 1995. [Google Scholar]
- He, B.B. Two-Dimensional X-ray Diffraction; Wiley: Hoboken, NJ, USA, 2009. [Google Scholar]
- Persson, K. Materials Data on Cr
_{2}O_{3}by Materials Project. Available online: https://materialsproject.org/materials/mp-19399/ (accessed on 13 January 2021). - Momma, K.; Izumi, F. VESTA 3 for Three-dimensional Visualization of Crystal, Volumetric and Morphology Data. J. Appl. Crystallogr.
**2011**, 44, 1272–1276. [Google Scholar] [CrossRef] - Larikov, L.N.; Shmatko, O.A. Solubility of Tungsten in Cobalt in Solid Phase. Dopov. Akad. Nauk A
**1967**, 29, 540–541. [Google Scholar] - Yang, J. Structural Analysis of Perovskite LaCr1-xNixO3 by Rietveld Refinement of X-Ray Powder Diffraction Data. Acta Crystallogr. B
**2008**, 64, 281–286. [Google Scholar] [CrossRef] - Priebe, R.; Sabrowsky, H. Über einen Chrom-Mangan-Spinell mit Kationenmangelstruktur, CrMn
_{1,5}O_{4}: About a Chromium Manganese Spinel with Cation Deficient Structure, CrMn_{1,5}O_{4}. Z. Naturforschung B**1979**, 34, 1663–1665. [Google Scholar] [CrossRef] - Magneli, A.; Westgren, A. Röntgenuntersuchung von Kobalt-Wolframlegierungen. Zeitschrift für Anorganische und Allgemeine Chemie
**1938**, 238, 268–272. [Google Scholar] [CrossRef] - Villars, P.; Cenzual, K. W2Co3Si (WCo1.5Si0.5) Crystal Structure: Datasheet from “PAULING FILE Multinaries Edition-2012” in SpringerMaterials. Available online: https://materials.springer.com/isp/crystallographic/docs/sd_0539453 (accessed on 9 September 2020).
- Fanfoni, M.; Tomellini, M. The Johnson-Mehl- Avrami-Kohnogorov Model: A Brief Review. Il Nuovo Cimento D
**1998**, 20, 1171–1182. [Google Scholar] [CrossRef] - Hanawa, T.; Hiromoto, S.; Asami, K. Characterization of the Surface Oxide Film of a Co–Cr–Mo Alloy after Being Located in Quasi-biological Environments Using XPS. Appl. Surf. Sci.
**2001**, 183, 68–75. [Google Scholar] [CrossRef] - Alifui-Segbaya, F.; Lewis, J.; Eggbeer, D.; Williams, R.J. In Vitro Corrosion Analyses of Heat Treated Cobalt-Chromium Alloys Manufactured by Direct Metal Laser Sintering. Rapid Prototyp. J.
**2015**, 21, 111–116. [Google Scholar] [CrossRef] - Peng, Y.; Du, Y.; Materials Science International Team (MSIT). Co-Cr-W Ternary Phase Diagram Evaluation: Phase Diagrams, Crystallographic and Thermodynamic Data: MSI Eureka in SpringerMaterials. Available online: https://materials.springer.com/msi/docs/sm_msi_r_10_017469_01 (accessed on 3 November 2019).
- Yang, S.Y.; Jiang, M.; Li, H.X.; Wang, L. Thermodynamic Assessment of Co-Cr-W Ternary System. Trans. Nonferr. Met. Soc.
**2011**, 21, 2270–2275. [Google Scholar] [CrossRef] - Turrubiates-Estrada, R.; Salinas-Rodriguez, A.; Lopez, H.F. FCC to HCP Transformation Kinetics in a Co–27Cr–5Mo–0.23C Alloy. J. Mater. Sci.
**2011**, 46, 254–262. [Google Scholar] [CrossRef] - Bauer, R.; Jägle, E.A.; Baumann, W.; Mittemeijer, E.J. Kinetics of the Allotropic hcp–fcc Phase Transformation in Cobalt. Philos. Mag.
**2011**, 91, 437–457. [Google Scholar] [CrossRef][Green Version] - Trömel, M.; Hübner, S. Metallradien und Ionenradien. Z. Krist. Cryst. Mater.
**2000**, 215. [Google Scholar] [CrossRef] - Pjetursson, B.E.; Sailer, I.; Zwahlen, M.; Hämmerle, C.H.F. A Systematic Review of the Survival and Complication Rates of All-Ceramic and Metal-Ceramic Reconstructions after an Observation Period of at Least 3 Years. Part I: Single Crowns. Clin. Oral Implants Res.
**2007**, 18 (Suppl. 3), 73–85. [Google Scholar] [CrossRef] [PubMed] - Sailer, I.; Pjetursson, B.E.; Zwahlen, M.; Hämmerle, C.H.F. A Systematic Review of the Survival and Complication Rates of All-ceramic and Metal-ceramic Reconstructions after an Observation Period of at Least 3 Years. Part II: Fixed Dental Prostheses. Clin. Oral Implants Res.
**2007**, 18 (Suppl. 3), 86–96. [Google Scholar] [CrossRef] [PubMed]

**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 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**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