Methods for Gibbs triple junction excess determination: Ti segregation in \(\hbox {CoSi}_2\) thin film


Methods are presented determining the Gibbs triple junction excess (\({\varGamma }^{\text{TJ}}\)) of solute segregation in polycrystalline materials from single atom counting in 3D volumes. One method bases on cumulative profile analysis, while two further methods use radial integration of solute atoms. The methods are demonstrated and compared on simulated model volumes which include three grain boundaries joining together at a triple junction with set values for Gibbs grain boundary and triple junction excess. An experimental technique that provides 3D volumes with single atom detection and spatial resolution close to atomic scale is atom probe tomography. An atom probe tomography volume of a \(\hbox {CoSi}_2\) thin film that contains three grain boundaries and a triple junction has been acquired. Ti segregation is found qualitatively at the grain boundaries and triple junction. The quantification of the Ti excess at the investigated \(\hbox {CoSi}_2\) triple junction reveals for the three introduced methods positive Gibbs triple junction excess values. It demonstrates that there is an excess of Ti at \(\hbox {CoSi}_2\) triple junctions and provides opportunities for its quantification.

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  1. 1

    King AH (1999) The geometric and thermodynamic properties of grain boundary junctions. Interface Sci 7:251–271

    CAS  Google Scholar 

  2. 2

    Taylor JE (1999) Mathematical models of triple junctions. Interface Sci 7:243–249

    CAS  Google Scholar 

  3. 3

    Caro A, Van Swygenhoven H (2001) Grain boundary and triple junction enthalpies in nanocrystalline metals. Phys Rev B 63(13):134101

    Google Scholar 

  4. 4

    Gottstein G, Shvindlerman LS, Zhao B (2010) Thermodynamics and kinetics of grain boundary triple junctions in metals: recent developments. Scr Mater 62(12):914–917

    CAS  Google Scholar 

  5. 5

    Fortier P, Palumbo G, Bruce GD, Miller WA, Aust KT (1991) Triple line energy determination by scanning tunneling microscopy. Scr Metall Mater 25(1):177–182

    CAS  Google Scholar 

  6. 6

    Zhao B, Ch Verhasselt J, Shvindlerman LS, Gottstein G (2010) Measurement of grain boundary triple line energy in copper. Acta Mater 58(17):5646–5653

    CAS  Google Scholar 

  7. 7

    Srinivasan SG, Cahn JW, Jónsson H, Kalonji G (1999) Excess energy of grain-boundary trijunctions: an atomistic simulation study. Acta Mater 47(9):2821–2829

    CAS  Google Scholar 

  8. 8

    Eich SM, Schmitz G (2016) Embedded-atom study of low-energy equilibrium triple junction structures and energies. Acta Mater 109:364–374

    CAS  Google Scholar 

  9. 9

    King AH (2007) Triple junction energy and prospects for measuring it. Mater Sci Technol 23(5):505–508

    CAS  Google Scholar 

  10. 10

    Yin KM, King AH, Hsieh TE (1997) Segregation of bismuth to triple junctions in copper. Microsc Microanal 3(5):417–422

    CAS  Google Scholar 

  11. 11

    Tian J, Chiu YL (2019) Study the grain boundary triple junction segregation of phosphorus in a nickel-base alloy using energy dispersive X-ray spectroscopy on a transmission electron microscope. Mater Charact 148(December 2018):156–161

    CAS  Google Scholar 

  12. 12

    Kim H, Xuan Y, Ye PD, Narayanan R, King AH (2009) Anomalous triple junction surface pits in nanocrystalline zirconia thin films and their relationship to triple junction energy. Acta Mater 57(12):3662–3670

    CAS  Google Scholar 

  13. 13

    Gault B, Moody MP, Cairney JM, Ringer SP (2012) Atom probe microscopy. Springer, Berlin

    Google Scholar 

  14. 14

    Lefebvre W, Vurpillot F, Sauvage X (2016) Atom probe tomography: put theory into practice. Elsevier, Amsterdam

    Google Scholar 

  15. 15

    Chellali MR, Balogh Z, Zheng L, Schmitz G (2011) Triple junction and grain boundary diffusion in the Ni/Cu system. Scr Mater 65(4):343–346

    CAS  Google Scholar 

  16. 16

    Chellali MR, Balogh Z, Bouchikhaoui H, Schlesiger R, Stender P, Zheng L, Schmitz G (2012) Triple junction transport and the impact of grain boundary width in nanocrystalline Cu. Nano Lett 12(7):3448–3454

    CAS  Google Scholar 

  17. 17

    Chellali MR, Balogh Z, Schmitz G (2013) Nano-analysis of grain boundary and triple junction transport in nanocrystalline Ni/Cu. Ultramicroscopy 132:164–170

    Google Scholar 

  18. 18

    Stender P, Balogh Z, Schmitz G (2011) Triple junction segregation in nanocrystalline multilayers. Phys Rev B Condens Matter Mater Phys 83(12):1–4

    Google Scholar 

  19. 19

    Stender P, Balogh Z, Schmitz G (2011) Triple line diffusion in nanocrystalline Fe/Cr and its impact on thermal stability. Ultramicroscopy 111(6):524–529

    CAS  Google Scholar 

  20. 20

    Eich SM, Schmitz G (2018) Embedded-atom study of grain boundary segregation and grain boundary free energy in nanosized iron-chromium tricrystals. Acta Mater 147:350–364

    CAS  Google Scholar 

  21. 21

    Josiah Willard Gibbs (1928) The collected works of J. W. Gibbs: thermodynamics. Longmans, Green, & Co., London, p 463

    Google Scholar 

  22. 22

    Krakauer BW, Seidman DN (1993) Absolute atomic-scale measurements of the Gibbsian interfacial excess of solute at internal interfaces. Phys Rev B 48(9):6724–6727

    CAS  Google Scholar 

  23. 23

    Murarka SP (1995) Silicide thin films and their applications in microelectronics. Intermetallics 3(3):173–186

    CAS  Google Scholar 

  24. 24

    Lau SS, Mayer JW, Tu KN (1978) Interactions in the Co/Si thin film system. I. Kinetics. J Appl Phys 49(7):4005–4010

    CAS  Google Scholar 

  25. 25

    D’Heurle FM, Petersson CS (1985) Formation of thin films of CoSi2: nucleation and diffusion mechanisms. Thin Solid Films 128(3–4):283–297

    Google Scholar 

  26. 26

    Dass MLA, Fraser DB, Wei C-S (1991) Growth of epitaxial CoSi2 on (100)Si. Appl Phys Lett 58(12):1308–1311

    CAS  Google Scholar 

  27. 27

    Hsia SL, Tan TY, Smith P, McGuire GE (1991) Formation of epitaxial CoSi2 films on (001) silicon using Ti–Co alloy and bimetal source materials. J Appl Phys 70(12):7579–7587

    CAS  Google Scholar 

  28. 28

    Liu P, Li B-Z, Sun Z, Zhi-Guang G, Huang W-N, Zhou Z-Y, Ni R-S, Lin C-L, Zou S-C, Hong F, Rozgonyi GA (1993) Epitaxial growth of CoSi2 on both (111) and (100) Si substrates by multistep annealing of a ternary Co/Ti/Si system. J Appl Phys 74(3):1700–1706

    CAS  Google Scholar 

  29. 29

    Hong F, Rozgonyi GA, Patnaik BK (1994) Mechanisms of epitaxial CoSi2 formation in the multilayer Co/Ti–Si(100) system. Appl Phys Lett 64(17):2241–2243

    CAS  Google Scholar 

  30. 30

    Selinder TI, Roberts TA, Miller DJ, Beno MA, Knapp GS, Gray KE, Ogawa S, Fair JA, Fraser DB (1995) In situ x-ray diffraction study of CoSi2 formation during annealing of a Co/Ti bilayer on Si(100). J Appl Phys 77(12):6730–6732

    CAS  Google Scholar 

  31. 31

    Detavernier C, Van Meirhaeghe RL, Cardon F, Maex K, Vandervorst W, Brijs B (2000) Influence of Ti on CoSi2 nucleation. Appl Phys Lett 77(20):3170–3172

    CAS  Google Scholar 

  32. 32

    Detavernier C, Van Meirhaeghe RL, Cardon F, Donaton RA, Maex K (2000) Influence of Ti capping layers on CoSi2 formation. Microelectron Eng 50:125–132

    CAS  Google Scholar 

  33. 33

    Detavernier C, Van Meirhaeghe RL, Vandervorst W, Maex K (2004) Influence of processing conditions on CoSi2 formation in the presence of a Ti capping layer. Microelectron Eng 71:252–261

    CAS  Google Scholar 

  34. 34

    Zschiesche H, Charaï A, Mangelinck D, Alfonso C (2019) Ti segregation at CoSi2 grain boundaries. Microelectron Eng 203–204:1–5

    Google Scholar 

  35. 35

    Miller MK, Russell KF, Thompson K, Alvis R, Larson DJ (2007) Review of atom probe FIB-based specimen preparation methods. Microsc Microanal 13:428–436

    CAS  Google Scholar 

  36. 36

    Felfer PJ, Alam T, Ringer SP, Cairney JM (2012) A reproducible method for damage-free site-specific preparation of atom probe tips from interfaces. Microsc Res Tech 75(4):484–491

    CAS  Google Scholar 

  37. 37

    Bas P, Bostel A, Deconihout B, Blavette D (1995) A general protocol for the reconstruction of 3D atom probe data. Appl Surf Science 87–88(1–4):298–304

    Google Scholar 

  38. 38

    Vurpillot F, Gault B, Geiser BP, Larson DJ (2013) Reconstructing atom probe data: a review. Ultramicroscopy 132:19–30

    CAS  Google Scholar 

  39. 39

    Warren PJ, Cerezo A, Smith GDW (1998) Observation of atomic planes in 3DAP analysis. Ultramicroscopy 73(1–4):261–266

    CAS  Google Scholar 

  40. 40

    Jenkins BM, Danoix F, Gouné M, Bagot PAJ, Peng Z, Moody MP, Gault B (2018) Reflections on the analysis of interfaces and grain boundaries by atom probe tomography. arXiv:1806.03851

  41. 41

    Sneddon GC, Trimby PW, Cairney JM (2016) Transmission Kikuchi diffraction in a scanning electron microscope: a review. Mater Sci Eng R Rep 110:1–12

    Google Scholar 

  42. 42

    Schwarz T, Stechmann G, Gault B, Cojocaru-Mirédin O, Wuerz R, Raabe D (2017) Correlative transmission Kikuchi diffraction and atom probe tomography study of Cu(In, Ga)Se2 grain boundaries. Prog Photovolt Res Appl 26:196–204

    Google Scholar 

  43. 43

    Rauch EF, Portillo J, Nicolopoulos S, Bultreys D, Rouvimov S, Moeck P (2010) Automated nanocrystal orientation and phase mapping in the transmission electron microscope on the basis of precession electron diffraction. Z fur Kristallographie 225:103–109

    CAS  Google Scholar 

  44. 44

    Zaefferer S (2011) A critical review of orientation microscopy in SEM and TEM. Cryst Res Technol 46(6):607–628

    CAS  Google Scholar 

  45. 45

    Moody MP, Tang F, Gault B, Ringer SP, Cairney JM (2011) Atom probe crystallography: characterization of grain boundary orientation relationships in nanocrystalline aluminium. Ultramicroscopy 111(6):493–499

    CAS  Google Scholar 

  46. 46

    Breen AJ, Babinsky K, Day AC, Eder K, Oakman CJ, Trimby PW, Primig S, Cairney JM, Ringer SP (2017) Correlating atom probe crystallographic measurements with transmission Kikuchi diffraction data. Microsc Microanal 23(2):279–290

    CAS  Google Scholar 

  47. 47

    Hellman OC, Vandenbroucke JA, Rüsing J, Isheim D, Seidman DN (2000) Analysis of three-dimensional atom-probe data by the proximity histogram. Microsc Microanal 6(05):437–444

    CAS  Google Scholar 

  48. 48

    Hellman OC, Seidman DN (2002) Measurement of the Gibbsian interfacial excess of solute at an interface of arbitrary geometry using three-dimensional atom probe microscopy. Mater Sci Eng A 327(1):24–28

    Google Scholar 

  49. 49

    Felfer P, Scherrer B, Demeulemeester J, Vandervorst W, Cairney JM (2015) Mapping interfacial excess in atom probe data. Ultramicroscopy 159:438–444

    CAS  Google Scholar 

  50. 50

    Peng Z, Yifeng L, Hatzoglou C, Silva AKD, Vurpillot F, Ponge D, Raabe D, Gault B (2019) An automated computational approach for complete in-plane compositional interface analysis by atom probe tomography. Microsc Microanal 25(2):389–400

    Google Scholar 

  51. 51

    Zhao B, Gottstein G, Shvindlerman LS (2011) Triple junction effects in solids. Acta Mater 59(9):3510–3518

    CAS  Google Scholar 

  52. 52

    Mattissen D, Molodov DA, Shvindlerman LS, Gottstein G (2005) Drag effect of triple junctions on grain boundary and grain growth kinetics in aluminium. Acta Mater 53(7):2049–2057

    CAS  Google Scholar 

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This work was supported by the French government through the program “Investissements d’Avenir A*MIDEX” (Project APODISE, No. ANR-11-IDEX-0001-02) managed by the National Agency for Research (ANR). The authors would like to thank Maxime Bertoglio for assistance with sample preparation and Marion Descoins for assistance with APT tip preparation and APT measurements.

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Appendix: Geometrical considerations

Appendix: Geometrical considerations

TJ radius (\(r_{\text{TJ}}\)) and GB overlap determination

Figure 7 is an visualization of the TJ geometry similar to Fig. 1 with only two GBs that have identical GB width (\(d_{\text{GB,1}}=d_{\text{GB,2}}=d_{\text{GB}}\)) for simplicity. The projected GB1 appears in a green frame, while GB2 is framed in orange. The center of their junction represents the TJ. The frame of the TJ cylinder projection is drawn as a blue circle. The radius of the TJ cylinder (\(r_{\text{TJ}}\)) was defined as the radius of the circle that includes all occurring GB overlap at the TJ. The overlapping area is a tetragon and marked in yellow. The illustration shows that \(r_{\text{TJ}}\) is thereby defined as the diagonal of the overlapping area of the adjacent GBs in the considered case. The angle of the diagonal of the GB overlap area can be calculated to

$$\begin{aligned} \epsilon &= \frac{\pi -\gamma }{2} \end{aligned}$$

and with the knowledge of the GB width, the radius of the TJ is

$$\begin{aligned} r_{\text{TJ}} &= \frac{d_{\text{GB}}}{2}\cdot \frac{1}{\cos (\epsilon )}. \end{aligned}$$
Figure 7

Schema of GB overlap in TJ region for visualization of TJ radius and its calculation as well as calculating the overlap area

Furthermore, the overlapping area of the adjacent GBs is

$$\begin{aligned} S_{12} &= \frac{d_{\text{GB}}}{2}\cdot {\overline{CB}}\nonumber \\ {\overline{CB}} &= \frac{d_{\text{GB}}}{2}\cdot \tan (\epsilon )\nonumber \\ S_{12} &= \left( \frac{d_{\text{GB}}}{2}\right) \cdot \tan (\epsilon ) \end{aligned}$$
Figure 8

Visualization of single GB fraction in TJ cylinder (no GB overlap). The area of a single GB in the TJ projected along the TJ axis is the sum of the horizontally stripped rectangular area \(A_{\text{rect}}\) and the vertically stripped arc area \(A_{\text{arc}}\)

GB fraction in TJ

The volume fraction of a single GB in the TJ is related to the area of the GB slice in the TJ cylinder projected along the TJ axis (Fig. 8). It is composed of the horizontally dashed rectangular area \(A_{\text{rect}}\) and the vertically dashed arc area \(A_{\text{arc}}\).

$$\begin{aligned} A_{\text{rect}} &= \sqrt{r_{\text{TJ}}^2-\frac{d_{\text{GB}}^2}{4}}\cdot d_{\text{GB}}\nonumber \\ A_{\text{arc}} &= \pi r_{\text{TJ}}^2\cdot \frac{2 \arcsin \left( \frac{d_{\text{GB}}/2}{r_{\text{TJ}}}\right) }{360^{\circ}}- \frac{A_{\text{rect}}}{2}. \end{aligned}$$

The so calculated projected GB area requires additional correction when all three GBs are considered in the TJ because of GB overlap (Figs. 1, 7): The half of each of the GB overlap rectangles to the adjacent GBs needs to be subtracted

$$\begin{aligned} A_{\text{GB},i}^{\text{TJ}} &= A_{\text{rect},i}+A_{\text{arc},i}-{\varSigma }_{j\ne i}S_{\text{ij}}/2. \end{aligned}$$

Knowing this projected GB area in the TJ, the volume fraction is calculated by the ratio to the base area of the TJ cylinder

$$\begin{aligned} f_{\text{GB},i}^{\text{TJ}} &= \frac{A_{\text{GB},i}^{\text{TJ}}}{\pi r_{\text{TJ}}^2}. \end{aligned}$$

In general, \(d_{\text{GB}}\) is not necessarily the same for all three GBs and \(r_{\text{TJ}}\) depends on both the GB widths and the dihedral angles of the adjacent GBs. The overlapping areas are than more complex and three cases can be distinguished. In the case that the widths of the GBs are different and \(d_{\text{GB},i}>d_{\text{GB,j}}\) and \(d_{\text{GB},i}\le |{d_{\text{GB,j}}/\cos (\gamma )}|\) is fulfilled, the equations for \(S_{\text{ij}}\) and \(r_{\text{TJ}}\) become:

$$\begin{aligned} S_{\text{ij}} &= \frac{d_{\text{GB},i}\cdot d_{\text{GB,j}}}{4}\sin (\gamma )+\frac{d_{\text{GB,j}}^2}{8}\sin (\gamma )\cos (\gamma )\nonumber \\&\quad +\frac{1}{2}\left( \frac{d_{\text{GB},i}}{2}+ \frac{d_{\text{GB,j}}}{2}\cos (\gamma )\right) ^2\arctan (\gamma ) \end{aligned}$$
$$\begin{aligned} r_{\text{TJ}} &= \sqrt{(d_{\text{GB},i}/2)^2+ (d_{\text{GB},i}/(2\cdot \tan (\gamma ))+d_{\text{GB,j}}/(2\cdot \sin (\gamma )))^2}. \end{aligned}$$

When \(d_{\text{GB},i}<|{d_{\text{GB,j}}/\cos (\gamma )}|\) and \(\gamma >\pi /2\), Eqs. 14 and 15 reduce to

$$\begin{aligned} S_{\text{ij}} &= \quad \frac{1}{2}\left( \frac{d_{\text{GB,j}}}{2}\right) ^2\left| \tan (\gamma )\right| \end{aligned}$$
$$\begin{aligned} r_{\text{TJ}} &= \left| \frac{d_{\text{GB,j}}}{2\cdot \cos (\gamma )}\right| . \end{aligned}$$

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Zschiesche, H., Charai, A., Alfonso, C. et al. Methods for Gibbs triple junction excess determination: Ti segregation in \(\hbox {CoSi}_2\) thin film. J Mater Sci 55, 13177–13192 (2020).

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