1 LX 2 Grain Boundary Properties Mobility 27

1 LX 2 Grain Boundary Properties: Mobility 27 -750, Spring 2008 A. D. Rollett

2 References • Interfaces in Crystalline Materials, Sutton & Balluffi, Oxford U. P. , 1998. Very complete compendium on interfaces. • Interfaces in Materials, J. Howe, Wiley, 1999. Useful general text at the upper undergraduate/graduate level. • Grain Boundary Migration in Metals, G. Gottstein and L. Shvindlerman, CRC Press, 1999. The most complete review on grain boundary migration and mobility. • Materials Interfaces: Atomic-Level Structure & Properties, D. Wolf & S. Yip, Chapman & Hall, 1992.

3 Outline • Motivation, examples of anisotropic grain boundary properties • Grain boundary mobility – Basic theory – Experimental evidence

4 Grain Boundary Mobility • The mobility of grain boundaries is dominated by solute. Solutes tend to segregate to any interface and lower the free energy of the system (because of size misfit, for example). Therefore for a boundary to move away from the segregated solute requires energy to be supplied. • Mobility is also strongly sensitive to boundary type (i. e. atomic structure). High mobilities tend to be associated with a few CSL boundary types, e. g. 7 in fcc metals. • Mechanistic explanation is still lacking (and controversial!). Even a detailed understanding of mobility in pure systems is not available.

5 Mobility, contd. • Highest mobility observed for <111> tilt boundaries. At low temperatures, the peaks occur at a few CSL types 7, especially. • This behavior is inverse to that deduced from classical theory (Turnbull, Gleiter). • For stored energy driving force, strong tilt-twist anisotropy observed. • No simple theory available. • Atomistic simulation (MD) is in good agreement with experimental data. <111> Tilts general boundaries

6 G. B. Properties Overview: Mobility • • • If mobility depends on easy atomic transfer, does mobility scale with energy MGB (g. GB )n? NO! Consider the energies of boundaries in fcc metals based on the {111}-plane model for various low index axes. Note how the <100> twists have the highest energy, whereas experimentally, <111> tilts exhibit the highest mobility under all conditions. Similar picture in bcc metals.

7 Mobility: LAGB characteristics • Low angle boundaries with dislocation structures are, in general, much less mobile than high boundaries. In broad terms, the diffusion distances are much larger in the case of LAGBs (diffusion between dislocations). • With only a few high mobility boundary types, the general picture is of very low mobility for LAGBs, moderate mobility for general boundaries, and the occasional peak for high angle boundaries. • Mobility of low angle boundaries dominated by climb of the dislocations making up the boundary. • Even in a symmetrical tilt boundary the dislocations must move non-conservatively in order to maintain the correct spacing as the boundary moves.

8 LAGB to HAGB Transitions • Read-Shockley for energy of low angle boundaries • Exponential function for transition in mobility from lowto highangle boundaries

9 LAGB to HAGB Mobility Transitions Transfer of atoms from the shrinking grain to the growing grain by atomic bulk diffusion mechanism Low Angle Boundaries Diffusion of vacancies (generally through the bulk) permits non-conservative motion (climb) of the dislocations in the grain boundary

10 Tilt Boundary Motion Burgers vectors inclined with respect to the boundary plane in proportion to the misorientation glide angle. - Bauer and Lanxner, Proc. JIMIS-4 (1986) 411 - Read, W. T. (1953). Dislocations in Crystals. New York, Mc. Graw-Hill. boundary displacement h dx climb

11 HAGB mobility: theory • The standard theory for HAGB mobility is due to Burke & Turnbull, based on thermally activated atomic transfer across the interface. • For the low driving forces typical in grain growth, recrystallization etc. , it gives a linear relation between force and velocity (as typically assumed). Burke, J. E. and D. Turnbull (1952). Progress in Metal Physics 3: 220.

12 Burke-Turnbull • Given a difference in free energy for an atom attached to one side of the boundary versus the other, ∆P, the rate at which the boundary moves is: Given similar attack frequencies and activation energies in both directions,

13 Velocity Linear in Driving Force • Then, for small driving forces compared to the activation energy for migration, ∆Pb 3 «k. T, which allows us to linearize the exponential term. Mobility

14 Linearity of migration rate against driving force • At what point is the linear relation no longer reasonable? • The criterion is the ratio of the driving force to thermal activation energy, k. T. • For a radius of curvature of 10 nm, for example, and a g. b. energy of 1 J. m-2, ∆P=108 Pa. In terms of energy per atom in, say, Al, we multiply the volumetric pressure by the volume per atom, ~ 16 Å3, to obtain ∆P= 1. 6. 10 -21 J. Compare with k. T ~ 1. 2 10 -20 at 600°C. Clearly for very small scale microstructures (and low temperatures) we may expect the linearity to break down.

15 HAGB Mobility • The basic Burke-Turnbull theory ignores details of g. b. structure: – The terrace-ledge-kink model may be useful; the density of sites for detachment and attachment of atoms can modify the pre-factor. – Atomistic modeling is starting to play a role: see work by Srolovitz group: [M. Upmanyu, D. Srolovitz and R. Smith, Int. Sci. , 6, (1998) 41. – – – 1. Zhang H, Mendelev MI, Srolovitz DJ. 2004. Computer simulation of the elastically driven migration of a flat grain boundary. Acta mater. 52: 2569 -76. 2. Zhang H, Mendelev MI, Srolovitz DJ. 2005. Mobility of Sigma 5 tilt grain boundaries: Inclination dependence. Scripta mater. 52: 1193 -8. 3. Zhang H, Srolovitz DJ. 2006. Simulation and analysis of the migration mechanism of Sigma 5 tilt grain boundaries in an fcc metal. Acta mater. 54: 623 -33. 4. Zhang H, Srolovitz DJ, Douglas JF, Warren JA. 2006. Characterization of atomic motion governing grain boundary migration. Phys. Rev. B 74. 5. Zhang H, Srolovitz DJ, Douglas JF, Warren JA. 2007. Atomic motion during the migration of general [001] tilt grain boundaries in Ni. Acta mater. 55: 4527 -33. 6. Zhang H, Upmanyu N, Srolovitz DJ. 2005. Curvature driven grain boundary migration in aluminum: molecular dynamics simulations. Acta mater. 53: 79 -86. ]. • Much room for research!

16 HAGB Mobility: experiments • Following slides are taken from thesis research by Mitra Taheri. • Single crystals of aluminum (with alloy additions) are rolled to moderate reductions, a scratch is applied to induce nucleation of new grains along a line, and annealed to allow new grains to grow. • The growth rate of the recrystallizing grains, and the crystallography of their boundaries with the deformed matrix are studied.

17 Grain Morphology: HPAl+Zr at 350ºC • IPF images above show the annealing sequence from 187 to 237 minutes at 350°C • The most mobile grains (with ~38°<111>) exhibit faceting and are elongated • <111> pole figure suggests that the side facets of the highly mobile 38°<111> grain are sessile pure twist boundaries (111 planes) Thesis research by M. Taheri

18 Grain Morphology: HPAl+Zr at 485ºC • IPF images at 8 and 20 minutes, respectively • Faceting not exhibited in the high temperature anneal of HPAl+Zr

19 Grain Boundary Mobility: HPAl+Zr • Minimum Mobility: 2. 10 -14 m 4 J-1 s-1 • Minimum Mobility: 5. 10 -13 m 4 J-1 s-1 • Change from low to high annealing temperature yields peak shift: maximum at 38º shifts to minimum with 2 maxima at 35º and 48º

21 Mobility in Rodrigues space: 350 vs. 485ºC 485 C 350 C 7 7 • At 485ºC, other boundary types become mobile: <100>, others, and the peak near 38°<111> splits.

22 Commercial Purity Al + Zr R 2 485 C 525 C R 1 7 Broad range of mobile boundary types, with peaks near <111>. 7 Some near-<100> mobility appears, with minor 38°<111> peak.

23 Compensation Effect Both curvature and stored energy driving forces appear to yield similar results. The apparent activation enthalpy varies significantly, leading to a “compensation effect. ” Huang, Humphreys et al. Gottstein, Shvindlerman et al. 40° or 36° <111> 38°<111>

24 Compensation Effect The compensation effect can be understood in terms of a proportionality between the enthalpy (∆H) and entropy (∆S) associated with a process, in this case, grain boundary migration.

25 Activation Energy for GB Migration in Al • A minimum in activation energy near 38º<111> is apparent for both the present work and from the literature. • Note: Gottstein et al. and Molodov et al. studied Al bicrystals under curvature driving force. “This work” refers to experiments by Taheri with stored energy as the driving force. “Simulation” refers to molecular dynamics simulations by Zhang with an interatomic potential to represent Al. curvature Stored E simulation

26 Solute effect on HAGB Mobility • Solutes play a major role in g. b. mobility by reducing absolute mobilities, even at very low levels • Simulations typically have no impurities included: therefore they model ultra-pure material • Simulations of mobility typically show (much) lower activation energies than those measure experimentally

27 HAGB: Impurity effects • Impurities known to affect g. b. mobility strongly, depending on segregation and mobility. • CSL structures with good atomic fit less affected by solutes • Example: Pb bicrystals [Aust] special general

28 increasing Cu content HAGB Mobility: impurity effect on recrystallization kinetics R. Vandermeer and P. Gordon, Proc. Symposium on the Recovery and Recrystallization of Metals, New York, TMS AIME, (1962) p. 211.

29 HAGB Mobility: impurity effect on recrystallization kinetics decreasing Fe content = increasing mobility V (cm. s-1) 1/T F. R. Boutin, J. Physique, C 4, (1975) C 4. 355.

30 Impurity (solute) effect on mobility, contd. • Example of Ga additions to Al (LHS) show that at low levels, certain solutes can increase mobility. Adding 10 ppm Ga to 99. 999% Al increases the mobility whereas adding 410 ppm Ga to Al decreases the mobility (as expected). • Note the low levels of solute that have measurable effects on mobility. Example (RHS) of adding Cu to Al shows an effect at 0. 0002 a/o, i. e. at the ppm level. Gottstein & Shvindlerman: grain boundary mobility in Al. Gordon & Vandermeer: impurities in aluminum

31 Impact of Mobility on Evolution • What impact does the anisotropy of mobility have on microstructural evolution? • None on interface texture (GBCD), to 1 st order, if the texture is random (based on moving finite element simulations, Ph. D thesis by Jason Gruber) • Strong effect on texture development (grain texture) is there is a non-random texture present to begin with. – Strongest effect known for grain growth – Appreciable but less important effect in recrystallization (Ph. D thesis by Abhijit Brahme)

32 3 D Grain Growth Simulation (MC) Strong fcc rolling texture (FC, e = 2) with ~6% cube added Copper component: {112}<111> ND 3 cub 13; E&M; T=0. 5; Emin=0. 55 RD TD

33 Grain Boundary Energy, Mobility • • Energy: only the Read-Shockley equation for grain boundary energy at small misorientations was used. Mobility: only the peak mobility at 40°<111> was used. m=0. 01 also a peak w. r. t. axis

34 Texture Components 2° spread; 6% initial cube fraction. Copper: monotonic decrease S: initial increase before decrease Goss: marked increase before cube dominates Brass: first to decrease Cube: monotonic increase copper {112}<111> S {412}<634> cube {001}<100> Dillamore brass {110}<112> Goss {011}<100> plot '3 cub 32. comps' using 1: 2 w l lw 3, '3 cub 32. comps' using 1: 3 w l lw 3, '3 cub 32. comps' using 1: 4 w l lw 3, '3 cub 32. comps' using 1: 5 w l lw 3, '3 cub 32. comps' using 1: 6 w l lw 3, '3 cub 32. comps' using 1: 7 w l lw 3

35 Peak: Plateau Ratio The probability of the cube component becoming dominant increases with increasing peak: plateau ratio (smaller number). This corresponds roughly to either increasing temperature or to increasing solute levels. Average growth rate decreases because the average mobility in the system decreases with increasing ratio.

36 Mechanical Stress as Driving Force on Grain Boundaries • The work of Dr. Myrjam Winning at the RWTH Aachen has shown, remarkably enough, that mechanical stresses can cause grain boundaries to migrate even for high angle grain boundaries, for which no dislocation structure has been observed. • The following slides were provided by Dr. Winning to illustrate the effect.

37 Mechanical stresses and grain boundaries Systematic investigations of interactions between grain boundaries and mechanical stress fields. individual and planar grain boundaries no interactions of other grain boundaries no other driving forces constant grain boundary structure bicrystals (high purity Al) with planar grain boundaries + constant shear stress in-situ observation of grain boundary motion

38 Determination of gb position by X-ray diffraction Grain I in Bragg-position Area of X-ray spot (350µm x 800µm) Grain II not in Bragg-position Grain boundary

39 Determination of gb position by X-ray diffraction I 0 Im Iu x

40 Determination of gb position by X-ray diffraction I 0 Im Iu x

41 Determination of gb position by X-ray diffraction I 0 Im Iu x

42 Determination of gb position by X-ray diffraction I 0 Im Iu x

43 Determination of gb position by X-ray diffraction I 0 Im Iu x

44 Determination of gb position by X-ray diffraction I 0 Im Iu x

45 Determination of gb position by X-ray diffraction I 0 Im Iu x

46 Determination of gb position by X-ray diffraction I 0 Im Iu x

47 Determination of gb position by X-ray diffraction I 0 Im Iu x

48 Determination of gb position by X-ray diffraction I 0 Im Iu x

49 Determination of gb position by X-ray diffraction I 0 Im Iu x

50 Determination of gb position by X-ray diffraction I 0 Im Iu x

51 Determination of gb position by X-ray diffraction I 0 Im Iu x

52 Determination of gb position by X-ray diffraction I 0 Im Iu x

53 Determination of gb position by X-ray diffraction I 0 Im Iu x

54 Determination of gb position by X-ray diffraction I 0 Im Iu x

55 Determination of gb position by X-ray diffraction I 0 Im Migration of grain boundary requires movement of the sample => speed of sample is the same as velocity of grain boundary Iu x

56 XICTD* detector sample *X-ray interface continuous tracking device X-ray source

57 XICTD spring sample thermo couple grain boundary

58 grain boundary position [µm] Stress-induced grain boundary motion <112>-tilt axis q=12. 9° time [s] M. Winning, G. Gottstein, L. S. Shvindlerman Acta Materialia 49 -2001, 211 -219

Macroscopic evidence for grain boundary motion 300µm 400µm 390µm 150µm <111>-tilt grain boundary with q=16. 0° Swept distance: 390µm Measured distance (in-situ): 365µm M. Winning, G. Gottstein, L. S. Shvindlerman Acta Materialia 49 -2001, 211 -219 <100>-tilt grain boundary with q=10. 6° Swept distance: 300µm Measured distance (in-situ): 293µm M. Winning, Acta Materialia 51 -2003, 6465 -6475

60 Arrhenius diagram LAGBs Temperature [K] temperature [K] 900 825 725 625 <111> DH = 1. 29 e. V lnm 0 = 23. 99 <112> DH = 1. 28 e. V lnm 0 = 23. 07 <100> DH = 1. 19 e. V lnm 0 = 19. 32 reciprocal temperature [1/K]

61 Arrhenius diagram HAGBs Temperature[K] temperature 850 800 750 <112> DH = 0. 81 e. V lnm 0 = 16. 47 <100> DH = 0. 74 e. V lnm 0 = 13. 63 <111> DH = 0. 74 e. V lnm 0 = 14. 26 reciprocal temperature [1/K] 700

62 Activation parameters 1. 5 activation enthalpy [e. V] 1. 3 129 119 1. 2 13. 6° 1. 1 109 99 1 8. 6° 0. 9 89 0. 8 79 0. 7 69 0. 6 59 0. 5 49 0 5 10 15 20 25 30 35 activation enthalpy [k. J/mol] 139 <112> <111> <100> 1. 4 misorientation angle [°] M. Winning, Acta Materialia 51 -2003, 6465 -6475 M. Winning, G. Gottstein, L. S. Shvindlerman Acta Materialia 50 -2002, 353 -363

63 Results of bicrystal experiments Review of Bicrystal Experiments Mechanical stress activates motion of planar grain boundaries. Activation enthalpy for tilt grain boundaries ~1. 2 -1. 3 e. V (LAGB) and ~0. 7 -0. 85 e. V (HAGB). Migration mechanism of planar grain boundaries can be explained by motion of dislocations in the grain boundaries. Sharp transition from LAGB to HAGB: qtrans=13. 6° for <112>/<111> tilt grain boundaries qtrans=8. 6° for <100> tilt grain boundaries. M. Winning, G. Gottstein, L. S. Shvindlerman Acta Materialia 49 -2001, 211 -219 M. Winning, G. Gottstein, L. S. Shvindlerman Acta Materialia 50 -2002, 353 -363 M. Winning, Acta Materialia 51 -2003, 6465 -6475 M. Winning, A. D. Rollett Acta Materialia 53 -2005, 2901 -2907

64 GB Mobility: Summary • The properties of low angle grain boundaries are dictated by their discrete dislocation structure: energy logarithmic with angle; mobility exponential with angle. • The kinetic properties of high angle boundaries are (approx. ) plateau dictated by local atomic transfer. Special boundary types have low energy and high/low mobility. • In fcc metals, the most mobile boundaries (at low temperatures) are near to 38°<111>. No theory explaining this maximum (or its variations) exists - a challenge for research! • Inversions of ranking in mobility can occur with changes in temperature.

65 Summary, contd. • Anisotropy of mobility is similar regardless of driving force. • Mobilities vary over orders of magnitude, in contrast to energies that only vary by about a factor of 2. • Solutes strongly decrease boundary mobilities, even at low concentrations. • Mobility is much more complex than energy and little exists beyond the basic activated rate theory of Burke & Turnbull. Computer simulation shows similar trends to experimental observations. • Mechanical driving force also causes high angle boundaries to migrate, despite the lack of an observable dislocation structure. This behavior also seen in MD simulations by Cahn, Mishin.