Skip to main content
SpringerLink
Log in

Grain boundary and volume diffusion experiments in yttrium aluminium garnet bicrystals at 1,723 K: a miniaturized study

  • Original Paper
  • Published:
Contributions to Mineralogy and Petrology Aims and scope Submit manuscript

Abstract

Yb-Y inter-diffusion along a single grain boundary of a synthetic yttrium aluminium garnet (YAG) bicrystal has been studied using analytical transmission electron microscopy (ATEM). To investigate the diffusion, a thin-film containing Yb as the diffusant was deposited perpendicular to the bicrystal grain boundary by pulsed laser deposition (PLD). Structural properties and their change with time in both the diffusant source and the grain boundary are reported. The diffusion profiles are incorporated in a numerical diffusion model, which is applied to determine the grain boundary diffusion coefficient, D gb , at 1.723 K it is equal to 3 × 10−15 m2/s. We find that grain boundary diffusion is 4.85 orders of magnitude faster than volume diffusion, which was determined from the same diffusion experiment. This result is discussed in the context of special versus general grain boundaries. Finally, we successfully tested the capability of synchrotron-based nano-X-ray fluorescence analysis to map micro-chemical patterns in two dimensions with sub-micrometre resolution.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  • Boye P (2009) Nanofocusing Refractive X-Ray Lenses. Institut für Strukturphysik, Doktor, Technische Universität Dresden, Dresden, p 145

  • Brandon DG (1966) The structure of high-angle grain boundaries. Acta Metall 14:1479–1484

    Article  Google Scholar 

  • Chadwick GA, Smith DA (1976) Grain boundary structure and properties. Academic Press, London

    Google Scholar 

  • Chrisey DB, Hubler GK (2003) Pulsed laser deposition of thin films. Wiley, VCH, London, p 648

    Google Scholar 

  • Clarke DR, Wolf D (1986) Chapter 3 grain boundaries in ceramics and at ceramic-metal interfaces. Mater Sci Eng 83(2):197–204

    Article  Google Scholar 

  • Cliff G, Lorimer GW (1975) The quantitative analysis of thin specimens. J Microsc 103:203–207

    Article  Google Scholar 

  • Crank J (1975) The mathematics of diffusion. Oxford University Press, New York

    Google Scholar 

  • Dobrzycki L, Bulska E, Pawlak DA, Frukacz Z, Wozniak K (2004) Structure of YAG crystals doped/substituted with erbium and ytterbium. Inorg Chem 43:7656–7664

    Article  Google Scholar 

  • Dohmen R, Becker H-W, Meißner E, Etzel T, Chakraborty S (2002) Production of silicate thin films using pulsed laser deposition (PLD) and applications to studies in mineral kinetics. Eur J Miner 14:1155–1168

    Article  Google Scholar 

  • Evans AG, Charles EA (1977) Strength recovery by diffusive crack healing. Acta Metall 25(8):919–927

    Article  Google Scholar 

  • Farver JR, Yund RA (1991) Measurement of oxygen grain boundary diffusion in natural, fine-grained, quartz aggregates. Geochim Cosmochim Acta 55(6):1597–1607

    Article  Google Scholar 

  • Fisher JC (1951) Calculations of diffusion penetration curves for surface and grain boundary diffusion. J Appl Phys 22(1):74–77

    Article  Google Scholar 

  • Gleiter H, Chalmers B (1972) High-angle grain boundaries. Pergamon Press, Oxford

    Google Scholar 

  • Gösele U, Tong QY, Schumacher A, Kräuter G, Reiche M, Plößl A, Kopperschmidt P, Lee TH, Kim WJ (1999) Wafer bonding for microsystems technologies. Sens Actuators A Phys 74(1–3):161–168

    Article  Google Scholar 

  • Guan Z (2003) Korngrenzstrukturen, Fremdatomdiffusion und Homogenität in nanokristallinen Metallen und Legierungen. Naturwissenschaftlich-Technische Fakultät II—Physik und Elektrotechnik -, Doctor, Universität des Saarlandes, Saarbrücken, p 140

  • Gupta TK (1975) Crack healing in thermally shocked MgO. J Am Ceram Soc 58(3–4):143

    Article  Google Scholar 

  • Hailong Z, Jun S (2002) Morphological evolution during diffusive healing of internal cracks within grains of α-iron. Acta Mech Sin 18(5):516–527

    Article  Google Scholar 

  • Hanke M, Dubslaff M, Schmidbauer M, Boeck T, Schoder S, Burghammer M, Riekel C, Patommel J, Schroer CG (2008) Scanning x-ray diffraction with 200 nm spatial resolution. Appl Phys Lett 92(19):193109-3

    Article  Google Scholar 

  • Harris KE, Singh VV, King AH (1998) Grain rotation in thin films of gold. Acta Mater 46(8):2623–2633

    Article  Google Scholar 

  • Hartmann K, Wirth R, Heinrich W (2010) Synthetic near Σ5 (210)/[100] grain boundary in YAG fabricated by direct bonding: structure and stability. Phys Chem Miner 37(5):291–300

    Article  Google Scholar 

  • Heinemann S, Wirth R, Dresen G (2001) Synthesis of feldspar bicrystals by direct bonding. Phys Chem Miner 28(10):685–692

    Article  Google Scholar 

  • Heinemann S, Wirth R, Gottschalk M, Dresen G (2005) Synthetic [100] tilt grain boundaries in forsterite: 9.9 to 21.5°. Phys Chem Miner 32(4):229

    Article  Google Scholar 

  • Herbeuval I, Biscondi M, Goux C (1973) Influence of Intercrystalline Structure on the Diffusion of Zinc in Symmetrical Bending Boundaries of Aluminum Mem. Sci Rev Met 70(1):39–46

    Google Scholar 

  • Humphreys FJ, Hatherly M (1996) Recrystallization and related annealing phenomena. Pergamon, Oxford

    Google Scholar 

  • Jiménez-Melendo M, Haneda H, Nozawa H (2001) Ytterbium cation diffusion in Yttrium Aluminum Garnet (YAG)—implications for creep mechanisms. J Am Ceram Soc 84(10):2356–2360

    Article  Google Scholar 

  • Joesten R (1991) Grain-boundary diffusion kinetics in silicate and oxide minerals. Diffusion, atomic ordering, and mass transport; selected topics in geochemistry, vol 8. Springer, New York, pp 345–395

    Google Scholar 

  • Kaur I, Mishin Y, Gust W (1995) Fundamentals of grain and interphase boundary diffusion. Wiley, Chichester

    Google Scholar 

  • Kingery WD (1974) Plausible Concepts Necessary and Sufficient for Interpretation of Ceramic Grain-Boundary Phenomena: II, Solute Segregation, Grain-Boundary Diffusion, and General Discussion*. J Am Ceram Soc 57(2):74–83

    Article  Google Scholar 

  • Kliewer KL, Koehler JS (1965) Space charge in ionic crystals. I. General approach with application to NaCl. Phys Rev 140(4A):A1226

    Article  Google Scholar 

  • Klugkist P, Aleshin AN, Lojkowski W, Shvindlerman LS, Gust W, Mittemeijer EJ (2001) Diffusion of Zn along tilt grain boundaries in Al: pressure and orientation dependence. Acta Mater 49(15):2941–2949

    Article  Google Scholar 

  • Le Claire AD (1963) The analysis of grain boundary diffusion measurements. British J Appl Phys 14(6):351–356

    Article  Google Scholar 

  • Lee MR, Bland PA, Graham G (2003) Preparation of TEM samples by focused ion beam (FIB) techniques; applications to the study of clays and phyllosilicates in meteorites. Miner Mag 67(3):581–592

    Article  Google Scholar 

  • Lee MR, Brown DJ, Smith CL, Hodson ME, MacKenzie M, Hellmann R (2007) Characterization of mineral surfaces using FIB and TEM: a case study of naturally weathered alkali feldspars. Am Miner 92:1383–1394

    Article  Google Scholar 

  • Lehovec K (1953) Space-Charge Layer and Distribution of Lattice Defects at the Surface of Ionic Crystals. J Chem Phys 21(7):1123–1128

    Article  Google Scholar 

  • Lupei V, Lupei A, Pavel N, Taira T, Ikesue A (2001) Comparative investigation of spectroscopic and laser emission characteristics under direct 885-nm pump of concentrated Nd:YAG ceramics and crystals. Appl Phys B Lasers Opt 73(7):757–762

    Article  Google Scholar 

  • Marquardt H, Ganschow S, Schilling F (2009) Thermal diffusivity of natural and synthetic garnet solid solution series. Phys Chem Miner 36(2):107–118

    Article  Google Scholar 

  • Marquardt K, Petrishcheva E, Abart R, Gardés E, Wirth R, Dohmen R, Becker H-W, Heinrich W (2010) Volume diffusion of Ytterbium in YAG: thin-film experiments and combined TEM–RBS analysis. Phys Chem Miner 37(10):751–760

    Article  Google Scholar 

  • Milke R, Dohmen R, Becker H-W, Wirth R (2007) Growth kinetics of enstatite reaction rims studied on nano-scale, Part I: methodology, microscopic observations and the role of water. Contrib Miner Petrol 154(5):519–533

    Article  Google Scholar 

  • Mishin Y, Herzig C (1999) Grain boundary diffusion: recent progress and future research. Mater Sci Eng A 260(1–2):55–71

    Google Scholar 

  • Nicholls AW, Jones IP (1983) Determination of low temperature volume diffusion coefficients in an Al-Zn alloy. J Phys Chem Solids 44(7):671–676

    Article  Google Scholar 

  • Overwijk MHF, van den Heuvel FC, Bulle-Lieuwma CWT (1993) Novel scheme for the preparation of transmission electron microscopy specimens with a focused ion beam. J Vac Sci Technol B 11(6):2021–2024

    Article  Google Scholar 

  • Phaneuf MW (1999) Applications of focused ion beam microscopy to materials science specimens. Micron 30(3):277–288

    Article  Google Scholar 

  • Pößl A, Kräuter G (1999) Wafer direct bonding: tailoring adhesion between brittle materials. Materials Science and Engineering. Reports(25): 1–88

  • Reiche M (2006) Semiconductor wafer bonding. Phys Status Solidi a 203(4):747–759

    Article  Google Scholar 

  • Schroer CG, Kurapova O, Patommel J, Boye P, Feldkamp J, Lengeler B, Burghammer M, Riekel C, Vincze L, van der Hart A, Kuchler M (2005) Hard x-ray nanoprobe based on refractive x-ray lenses. Appl Phys Lett 87(12):124103-3

    Article  Google Scholar 

  • Schropp A, Boye P, Feldkamp JM, Hoppe R, Patommel J, Samberg D, Stephan S, Giewekemeyer K, Wilke RN, Salditt T, Gulden J, Mancuso AP, Vartanyants IA, Weckert E, Schoder S, Burghammer M, Schroer CG (2010) Hard x-ray nanobeam characterization by coherent diffraction microscopy. Appl Phys Lett 96(9):091102-3

    Article  Google Scholar 

  • Schwarz SM, Kempshall BW, Giannuzzi LA, Stevie FA (2002) Utilizing the SIMS technique in the study of grain boundary diffusion along twist grain boundaries in the Cu(Ni) system. Acta Mater 50(20):5079–5084

    Article  Google Scholar 

  • Smith CS (1948) Introduction to grains, phases, and interfaces-an interpretation of microstructure. Trans AIME 175:15–51

    Google Scholar 

  • Smoluchowski R (1952) Theory of grain boundary diffusion. Phys Rev 87(3):482

    Article  Google Scholar 

  • Suzuoka T (1961) Lattice and grain boundary diffusion in polycrystals. Trans Jpn Inst Met 2:25–33

    Google Scholar 

  • Suzuoka T (1964) Exact Solutions of Two Ideal Cases in Grain Boundary Diffusion Problem and the Application to Sectioning Method. J Phys Soc Jpn 19:839

    Article  Google Scholar 

  • Tong QY, Gösele U (1999) Semiconductor wafer bonding : science and technology. Wiley, New York

    Google Scholar 

  • Tong QY, Gösele U, Martini T, Reiche M (1995) Ultrathin single-crystalline silicon on quartz (SOQ) by 150°C wafer bonding. Sens Actuators A 48(2):117–123

    Article  Google Scholar 

  • Turnbull D, Hoffman RE (1954) The effect of relative crystal and boundary orientations on grain boundary diffusion rates. Acta Metall 2(3):419–426

    Article  Google Scholar 

  • Wanamaker BJ, Evans B (1985) Experimental diffusional crack healing in olivine. In: Schock RN (ed) Point defects in minerals, vol 31. American Geophysical Union, Washington, pp 194–210

    Google Scholar 

  • Weber R, Abadie J (2001) Processing and optical properties of YAG- and Rare-Earth-Aluminum Oxide-Composition Glass Fibers. Mater Res Soc 702:193–204

    Article  Google Scholar 

  • Whipple RTP (1954) Concentration contours in grain boundary diffusion. Philos Mag 45(371):1225–1236

    Google Scholar 

  • White S (1973) Syntectonic recrystallization and texture development in quartz. Nature 244(5414):276–278

    Article  Google Scholar 

  • Williams DB, Carter BC (1996) Transmission electron microscopy. Springer, New York

    Google Scholar 

  • Wirth R (2004) Focused ion beam (FIB): a novel technology for advanced application of micro- and nanoanalysis in geosciences and applied mineralogy. Eur J Miner 16(6):863–876

    Article  Google Scholar 

  • Yin H, Deng P, Gan F (1998) Defects in YAG:Yb crystals. J Appl Phys 83(7):3825–3828

    Article  Google Scholar 

Download references

Acknowledgments

We would like to express our appreciation to the group of Christian Schroer from the Universität Dresden for measuring the Yb distribution in our sample using nano-XRF at the European Synchrotron Radiation Facility and we would like to thank Manfred Burghammer and Sebastian Schoeder for assistance in using beam line ID13. Furthermore, the financial support from the German GeoForschungsZentrum Potsdam, GFZ. Finally, we thank Ralf Dohmen for his support during PLD thin-film production. K. M. thanks the CNV foundation for financial support and Hauke Marquardt fort the manifold discussions. Finally, we thank the reviewers Daniele Cherniak and Bruce Watson for their thorough reading that improved the manuscript and reduced sources of misunderstanding.

Author information

Authors and Affiliations

  1. German Research Centre for Geosciences GFZ, Section 3.3, 14473, Potsdam, Germany

    Katharina Marquardt (née Hartmann), Emmanuel Gardés, Richard Wirth & Wilhelm Heinrich

  2. Institute for Geological Sciences, Freie Universität Berlin, 12249, Berlin, Germany

    Elena Petrishcheva & Rainer Abart

  3. Department for Lithosphere Research, University of Vienna, Vienna, Austria

    Rainer Abart

Authors
  1. Katharina Marquardt (née Hartmann)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Elena Petrishcheva
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Emmanuel Gardés
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Richard Wirth
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Rainer Abart
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Wilhelm Heinrich
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Katharina Marquardt (née Hartmann).

Additional information

Communicated by J. Hoefs.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Marquardt (née Hartmann), K., Petrishcheva, E., Gardés, E. et al. Grain boundary and volume diffusion experiments in yttrium aluminium garnet bicrystals at 1,723 K: a miniaturized study. Contrib Mineral Petrol 162, 739–749 (2011). https://doi.org/10.1007/s00410-011-0622-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00410-011-0622-7

Keywords

Search

Navigation