Effects of melt-pool geometry on crystal growth and microstructure development in laser surface-melted superalloy single crystals: Mathematical modeling of single-crystal growth in a melt pool (part I)
Abstract The effects of melt-pool geometrical parameters on crystal growth and microstructure development during laser surface melting of single-crystal alloys were studied by means of mathematical modeling and experiments. A mathematical model was developed for the three-dimensional (3-D) melt-pool geometry and single-crystalline melt-pool solidification in laser surface melting. The 3-D melt-pool geometry corresponding to the solidification interface is described by four geometrical parameters ( w , l , h , α ). The model was used to study the effects of variations in the geometrical parameters on crystal growth and microstructure development in the melt pool. Laser surface melting experiments with single-crystal nickel-base superalloys were conducted to verify the computational results of microstructure development in the melt pool. Results indicate that the melt-pool geometrical parameters have profound influences on the dendrite growth velocity and growth pattern in the melt pool. For the (0 0 1)/[1 0 0] substrate orientation, variations in l / w and α can influence both the number and the relative sizes of growth regions while the variation in h / w can only influence the relative sizes of the growth regions. Unidirectional dendrite growth along the [0 0 1] crystallographic direction can be achieved for an α value of 45° or below. The maximum ratio of dendrite-growth velocity to the beam velocity in the melt pool is related to α and l / w . Experimental microstructure observations agreed well with the computational results. These findings show that the desired dendrite growth velocity and microstructure can be obtained through proper control of the 3-D melt-pool geometry.
Effects of substrate crystallographic orientations on crystal growth and microstructure development in laser surface-melted superalloy single crystals. Mathematical modeling of single-crystal growth in a melt pool (Part II)
Abstract The mathematical model developed for single-crystalline solidification in laser surface melting (LSM) described in Part I [Acta Mater 2004;52:4833–4847] was used to compute the dendrite growth pattern and velocity distribution in the 3D melt pool for various substrate orientations. LSM experiments with single-crystal nickel-base superalloys were conducted for different orientations to verify the computational results. Results show that the substrate orientation has a predominant effect on crystal growth pattern, and simultaneously influences the magnitude and distribution of dendrite growth velocity in the melt pool. The selected 〈1 0 0〉 growth variants and the number of the chosen growth variants are dependent on the substrate orientation. The maximum velocity ratio (dendrite growth velocity over the beam velocity, V/Vb) in the melt pool is a function of melt-pool geometrical parameters and the substrate orientation. The largest maximum velocity-ratio among the symmetric orientations is 1.414 for the (0 0 1)/[1 1 0] and ( 0 1 1 ) / [ 0 1 1 ¯ ] orientations, while that value for asymmetric orientations is 1.732 for the ( 0 1 1 ) / [ 1 1 1 ¯ ] orientation. Good agreement was obtained between the predicted and experimentally observed microstructures. The results are discussed with the susceptibility to stray grain formation as a function of substrate orientations and melt-pool geometrical parameters. These findings have some important implications for single-crystal surface processing.
The crystal structure of stilpnomelane. Part II. The full cell
Summary The structural formula of stilpnomelane averaged from 37 representative literature analyses and based on the determined structure is (Ca,Na,K)4(Ti0·1Al2·3Fe35·5Mn0·8Mg9·3)[Si63Al9](O,OH)216·nH2O. Ferrostilpnomelanes have up to 12 R 3+ cations in the octahedral sheet, ferristilpnomelanes commonly have between 24 and 30 R 3+ cations, rarely up to 37. The two groups can be distinguished by accurate X-ray powder diffraction, ferrostilpnomelanes having d 001 less and a greater than have ferristilpnomelanes. The unit cell is triclinic, a = b∼21·8 Å, γ = 120°, d 001∼12·2 Å, P . Hexagonal groups or ‘islands’ of 24 silicon-oxygen tetrahedra co-ordinate to the octahedral sheet, the centres of the ‘islands’ are displaced by 5a/12, 8b/12 on either side of the octahedral sheet as a result of warping of this sheet to permit articulation with the smaller tetrahedral sheet. The 24-tetrahedra ‘islands’ are linked laterally by 6-member rings of inverted tetrahedra, which in turn link at their apices to like rings connecting the next sheet of ‘islands’. Thus a single tetrahedral layer is 4 tetrahedra thick and has symmetry 6/m. The 6-member rings of tetrahedra act as hinges permitting up to 0·5 Å extension or contraction of the tetrahedral sheet to accommodate variations in the octahedral sheet dimensions with varying R 2+/R 3+ ratio.