Growth Of Bicrystals Research Articles

Hot cracking susceptibility prediction from quantitative multi-phase field simulations with grain boundary effects

Hot cracks are notorious defects in casting, welding, and additive manufacturing. Grain boundaries play a key role in hot cracking formation. Still, their effects are often neglected in hot cracking susceptibility predictions, and thus a quantitative picture of hot cracking susceptibility and liquid fracture is still lacking. In this work, we construct a multi-order parameter phase-field model for binary alloy solidification to simulate attractive, neutral, and repulsive grain boundaries in the thin-interface limit. Phase-field simulations of different combinations of grain boundary and bi-crystal growth types are used to obtain solidification path data, which is then used as the input into the Rappaz, Drezet and Gremaud (RDG) model (Rappaz et al., 1999). We study the so-called Λ-shape variation of hot cracking susceptibility as a function of solute concentration, showing that the magnitude of the Λ curve peak shifts to higher values and to lower concentrations as grain boundary energy increases. Meanwhile, the peak magnitude becomes higher and shifts to a higher value and higher concentrations when convergent grain growth is applied. Furthermore, in all cases examined, the corresponding pressure drops predicted for hot cracking exceed the theoretical liquid rupture stress, consistent with experimental observations. These results demonstrate that quantitative phase-field simulations, when coupled with the RDG model, are capable of relatively accurately predicting liquid rapture states relevant to hot cracking since the large disparity between the predicted pressure drop and critical stress of liquid film is eliminated through the consideration of grain boundary effects in the solidification path calculation.

Multi-phase field model simulation based on MPI+OpenMP parallel: Evolution of seaweed and dendritic structure in directional solidification

A multi-phase model was established to imitate the growth of algal and dendritic grains during directional solidification. We studied the effects of temperature on the growth of bi-crystals and quantitatively analyzed the influence of anisotropic strength, thermal gradient, and pulling velocity on the evolution of bi-crystals. The results show that both weaker anisotropy strength and smaller pulling velocity can maintain the formation of seaweed tissue. The increase in the pulling velocity can degenerate the seaweed grains into dendrites and improve the growth rate of the dendrites, which make grain B produce more spindles, thereby accelerating the elimination of grain A. The thermal gradient is inversely proportional to the average initial spacing of dendrites. When the thermal gradient is too small, dendritic dendrites produce developed secondary dendrite arms, which, in turn, develop into tertiary dendrite arms to occupy the grain boundary, accelerating the elimination of seaweed grains. In addition, the multi-phase field model is solved by using central processing unit serial computation, single MPI (message passing interface) parallel programming method calculation, and MPI+OpenMP hybrid parallel programming structure, and the relevant factors affecting the efficiency of program operation are analyzed and tested. By comparing the computational efficiency of the three methods, it can be seen that the MPI+OpenMP hybrid parallel programming technology can make full use of computing resources in the case of large computing scale, further optimize the MPI parallel model, and obtain a higher acceleration ratio.

Non-uniplanar competitive growth of columnar dendritic grains during directional solidification in quasi-2D and 3D configurations

The competitive growth of bicrystals during directional solidification in both thin samples and three-dimensions (3D) was investigated by phase-field simulations. Unlike previous studies, which assumed the <001> orientation of the two competing grains to be in the same plane or in two parallel planes which are normal to the contacting plane of two grains, simulations in the present study focused on the more common configurations in which the <001> orientation of the two grains is non-uniplanar. Simulations of competitive growth in thin samples showed that the deviation of the <001> orientation of an unfavorably orientated grain from the sample plane caused difficulty in the generation of new primary arms from the unfavorably orientated grain. Therefore, the grain boundary orientation in thin samples may deviate from that in two-dimensions (2D), even though the bicrystal configuration observed in the thin-sample plane appeared similar to that in the 2D. It was found that in 3D, the new primary arms could develop from the favorably oriented dendrites along two directions to occupy the gap left by the unfavorably orientated grains, which led to a faster overgrowth rate of the unfavorably orientated grains than that in the case of diverging growth in 2D.

Features of bicrystal growth during the directional crystallization of metal melts

The factors responsible for the formation of different configurations of boundaries between adjacent crystallites during their growth from melt by Bridgman and Czochralski methods have been considered by an of example Fe–20 wt % Ga alloy and Ni bicrystals. It is found that the configuration of intercrystallite boundary is related to the features of crystallite growth, caused by the strained state of intercrystallite and interphase (crystal–melt) boundaries, the difference in the linear thermal expansion coefficients of the crystallite boundaries and bulk, and the shape (geometry) of the bicrystal cross section. It is suggested that the strained state of boundaries and the formation of substructure in crystallites during directional crystallization from metal melt are significantly affected by their deformation under the melt weight.

Liquid channel segregation and morphology and their relation with hot cracking susceptibility during columnar growth in binary alloys

The segregation and morphology of liquid channels at the last stage of solidification are closely related to hot cracking formation. We use Phase-Field (PF) simulations to investigate liquid channel characteristics during columnar growth of single-crystal and bi-crystal Al-Cu alloys. It is found that the back-diffusion is weak in Al-Cu alloys. Liquid channels in Al-2.0, 3.0 wt%Cu alloys coalesce into droplets above the eutectic temperature while the reduced Hot Cracking Susceptibility of Al-4.0 wt%Cu can be correlated to eutectic formation at the root of liquid channels. For bi-crystal growth, we demonstrate that non-equilibrium solute segregation at intergranular liquid channels (prospective Grain Boundaries (GBs)) depends on the convergent/divergent growth conditions between grains, and their misorientation angle. Divergent growth leads to stronger solute segregation as more solute diffuses laterally into divergent intergranular channels. It is thus expected that for the same GB energy, intergranular channels with higher solute composition can extend to lower temperatures, thus promote hot cracking. We introduce an approach for combining solid fraction vs. temperature curves calculated from microstructurally complex PF simulations with hot cracking models in the literature to predict the nominal composition with the highest HCS. Preliminary results from this work agrees well with experiments.

Features of growth of non-cubic bicrystals from the melt (example of leucosapphire and neodymium gallate)

Neodymium gallate (NdGaO3) and sapphire (Al2O3) are most suitable materials to produce bicrystal substrates for high-temperature superconducting (HTSC) films' microwaves Josephson junctions. Perfect bicrystal border is important for the devices, and it can be obtained in bicrystals grown directly from the melt. Unfortunately both materials have non-cubic symmetry and anisotropic thermophysical properties what complicates the bicrystal growth process. The experimental results of NdGaO3 bicrystals growth by Czochralski method using compound bicrystal seeds with different symmetries in the plane perpendicular to the growth axis are presented. The results proved to be very unstable and depended critically upon growth conditions and on bicrystal border orientation. The bicrystals with misorientation angle 180° which correspond to the natural (110) twins are grown. When bicrystal angles are within 22-28° range which is optimum for bicrystal Josephson junctions it is very difficult to grow the long bicrystals: the bicrystal border goes out of the crystal quickly. It is supposed that in the last case the symmetry of compound bicrystal seed in the plane perpendicular to the growth direction can differ from the heat field symmetry in the growth system. Requirements for growth of anisotropic crystals by Czochralski method are formulated. It is shown that the requirements of seed and heat field symmetry correspondence can be satisfied more easily in Stepanov's growth method (EFG). The sapphire bicrystal ribbons suitable for manufacturing of high quality substrates for HTSC film Josephson junctions using Stepanov's method are grown.

Crystal growth of Bi2WO6 single-domin crystals by Bridgeman method

Crystal growth of Bi2WO6 single-domin crystals by Bridgeman method

Growth of metallic bicrystals with high-energy grain boundary orientation

The growth of bicrystals containing high-energy grain boundaries is documented by the 45 ∘ [ 1 0 0 ] , { 0 k l } symmetrical interface in an Fe–Si base alloy. During the bicrystal growth by the floating zone technique, this general grain boundary tends to rotate along the sample axis thus changing its original orientation into an energetically more advantageous one. A detailed investigation of the dislocation and subgrain structures in the vicinity of the inclining grain boundary proves that other reasons for this continuous inclination are excluded.

Crystal growth of Bi 2(Sr xCa 3− x)Cu 2O y with traveling solvent floating zone method

The traveling solvent floating zone method was employed within an infrared radiation furnace to grow crystals of Bi 2(Sr x Ca 3− x )Cu 2O y , x=1.5–2. Crystals of various Sr/Ca ratios were obtained with lowest value approximately 1.32. The ratio of the temperature gradient G over the growth rate R, i.e. G/ R, directly relates to the occurrence of constitutional supercooling. The minimum critical value of G/ R in a stable growth condition is 4.5×10 11 K s/m 2 from this experimental result and fundamental estimation. A rotation rate of 30 rpm produced a slightly convex growth front and therefore enhanced the morphological stability of the growing crystal. Compositional analysis of the steady-state solvent zone indicated a primary crystallization field (PCF) located at the bismuth-rich and copper-deficient region relative to the 2 2 1 2 stoichiometry, and this compositional range equaled proximal to Bi 2.425Sr 1.911Ca 0.807Cu 1.857O y . Meanwhile this PCF composed a corresponding tie–line relationship with a slightly copper-deficient 2 2 1 2 single-phase region.

Oriented crystal growth in Bi(Pb)2223 bulks prepared with magnetic melt processing

A containerless melting-solidification process has been developed for Bi-Pb-Sr-Ca-Cu-O system by using a mixture of Bi(Pb)2212 and CaCuO/sub 2/ as precursors. Almost no solute liquid is spread out from the pellet during the melt processing and Bi(Pb)2212 is reformed after solidification without changing the composition, therefore bulks of high Bi(Pb)2223 content can be formed by a long time sintering. When a magnetic field of 8 T is applied during the melting-solidification process, an obvious texture is introduced in the reformed Bi(Pb)2212. We found that an oriented crystal growth of Bi(Pb)2223 is achieved from the textured Bi(Pb)2212. This indicates that the magnetic melt processing can be applied to obtain texture development in Bi(Pb)2223 bulks by orienting Bi(Pb)2212 grains firstly.

Effect of melt heat treatment on the solid/liquid interface morphology of directional solidification

A set of quadral-electrode DC input voltage measure equipment was built up to detect the electrical resistance of Sb–Bi single-phase alloy. The results suggest that Sb–5%wt Bi undergoes structural transition in the temperature range of 730–750°C. By overheating the melt to different temperatures and then cooling to 690°C after a period of time, the samples are directionally solidified in a Bridgeman-type furnace. It is found for the first time that after heat treatment of the melt, the solid/liquid interface morphology shows significant variation depending on the speciic heat treatment. Also, in Ag–Cu, Al–Cu systems, bicrystal growth with different orientation is found to have different interface morphologies after heat treatment. It is believed that the evolution of the cluster size distribution in the melt contributes to these phenomena.

Bicrystal growth and characterization of copper twist grain boundaries

Copper bicrystals with twist character were grown using the vertical Bridgman technique. Cu bicrystals were grown such that the grain boundary in each sample had a nominal twist misorientation consisting of either a low angle (10°), a special angle ( Σ5=36.87°), or a high angle (45°). The grain boundary plane in all cases was (1 0 0). The grain boundaries were grown using single-crystal seeds that were oriented to within ±0.5° using the Laue back-reflection X-ray diffraction method. The misorientation of each twist boundary was characterized using electron backscattering diffraction patterns in a scanning electron microscope. All grain boundary misorientations were determined to be within the limits defined by the Brandon criterion.

Epitaxial Growth of Co-Cr-M (M = Pt, Ta) Bicrystal Films

Magnetic anisotropy is one of the most basic and important properties determining the recording characteristics and thermal stability of magnetic recording media. In evaluating the anisotropy, most studies have commonly measured field dependence of rotational hysteresis by the torque magnetometry and subsequently determined the anisotropy field(Hκ). However, this method usually gives incorrect values of Hκ. In order to evaluate the anisotropy constant more accurately, we have sequentially grown Cr(001) single crystals and Co-Cr-M(M=Pt,Ta) bicrystals on (100) cleavage plane of sodium chloride single crystals and have investigated their magnetic properties. The pole figures of NaCl{220}, Cr{110}, and Co-Cr-M{10-10} indicate single crystal growth of Cr(001) on NaCl(001) and bicrystal growth of Co-Cr-M(11·0) on Cr(001), and the orientation relationship was found as (001)[100] NaCl//(001)[110]Cr//(11-20)[0001]Co-Cr-M. The magnetic properties showed fourfold symmetry in the film plane reflecting the bicrystal structures. It was found that Co-Cr-Pt films exhibit good epitaxial growth on Cr(001) and possess large coercivity. In contrast, very small amount of Ta considerably deteriorates the epitaxial growth, which may be due to the extremely small solubility limit of Ta in Co-Cr alloy. Torque magnetometry has revealed that Pt increases the anisotropy constants of Co-Cr alloys, while Ta decreases the anisotropy and the coercivity. Other experimental data on the additives' effects will be presented.

Kinetics and mechanisms of sintering: M.M. Ristic et al (Serbian Academy of Sciences, Belgrade, Yugoslavia) Science of Sintering, vol 26, no 2, 1994, 89–106

The segregation and morphology of liquid channels at the last stage of solidification are closely related to hot cracking formation. We use Phase-Field (PF) simulations to investigate liquid channel characteristics during columnar growth of single-crystal and bi-crystal Al-Cu alloys. It is found that the back-diffusion is weak in Al-Cu alloys. Liquid channels in Al-2.0, 3.0 wt%Cu alloys coalesce into droplets above the eutectic temperature while the reduced Hot Cracking Susceptibility of Al-4.0 wt%Cu can be correlated to eutectic formation at the root of liquid channels. For bi-crystal growth, we demonstrate that non-equilibrium solute segregation at intergranular liquid channels (prospective Grain Boundaries (GBs)) depends on the convergent/divergent growth conditions between grains, and their misorientation angle. Divergent growth leads to stronger solute segregation as more solute diffuses laterally into divergent intergranular channels. It is thus expected that for the same GB energy, intergranular channels with higher solute composition can extend to lower temperatures, thus promote hot cracking. We introduce an approach for combining solid fraction vs. temperature curves calculated from microstructurally complex PF simulations with hot cracking models in the literature to predict the nominal composition with the highest HCS. Preliminary results from this work agrees well with experiments.

Fractography of embrittled copper bicrystals

Abstract The grain boundaries of Σ33a copper bicrystals are examined by means of transmission electron microscopy. Two kinds of grain boundaries have been found in the as-grown bicrystals: one is the exact (118) 1 −(11 8 ) 2 boundary and the other is the zigzag boundary composed of (00 1 ) 1 −(334) 2 and (885) 1 −(11 4 ) 2 . Having been permeated with bismuth, the bicrystal is easily broken down in an intergranular mode. The fracture surfaces are examined by means of scanning electron microscopy, as well as reflection electron microscopy, using a conventional transmission electron microscope. The fractographic observations indicate that the grain boundary of an embrittled copper bicrystal has a well-developed facet structure and that the boundary is mainly composed of (001), (1 2 0) and (210) facets. Some macrofacets on the (010) plane, resulting from fluctuation during bicrystal growth, are also observed. The holes which appear at the grain boundary are related to titanium inclusions, which have an effect on the local orientations of the grain boundary near these holes. Experimental results show that reflection electron microscopy is a useful technique for the observation of the faceted fracture surfaces.

Growth Forms of Large Frost Crystals in the Antarctic

AbstractA variety of frost-crystal forms found growing from the vapor in ice caves and tunnels in the Antarctic are described and illustrated. Complex layered structures found within large, skeletal crystals are ascribed to the action of the temperature gradient. Some novelc-axis growth forms and a rare type of bicrystal growth – accelerated growth in a particular direction along a particular grain boundary – are also shown.

Growth Forms of Large Frost Crystals in the Antarctic

AbstractA variety of frost-crystal forms found growing from the vapor in ice caves and tunnels in the Antarctic are described and illustrated. Complex layered structures found within large, skeletal crystals are ascribed to the action of the temperature gradient. Some novel c-axis growth forms and a rare type of bicrystal growth – accelerated growth in a particular direction along a particular grain boundary – are also shown.

Silicon sheet bicrystal growth for the study of grain boundary effects in solar cells

Abstract A modification of the edge-supported pulling (ESP) technique is described for the growth of silicon bicrystals in sheet form. Two flat silicon seeds, 20–25 mm in width, are mounted side-by-side between parallel 0.5–1.5 mm diameter graphite filaments spaced 40–50 mm apart. The assembly is placed in a silicon melt where sheet growth is initiated at the seeds. A bicrystal grain boundary forms in the newly grown sheet where the two seeds are in contact, and this boundary is propagated as the assembly is pulled upward. The grain boundaries in these bicrystals are useful for the controlled study of grain boundary effects on photovoltaic devices. A series of [110] and [112] rotation boundaries have been grown from semiconductor-grade silicon. We present here the spreading resistance and solar cell data detailing the effects of these grain boundary defects on photovoltaic devices.

A new technique for the growth of bicrystals of refractory metals

A modified match-up seed method of growing bicrystals of refractory metals is described. Experimental results show that the new method eliminates some of the limitations of the Y-shaped seed method previously reported.

Bicrystal growth and grain boundary properties in the alkali halides

Bicrystals of sodium chloride and potassium bromide containing tilt boundaries have been pulled from the melt and differences in growth behaviour have been correlated with differences in the structure of grain boundaries in the two materials as revealed by electrodecoration. KBr boundaries have a strongly anisotropic pipeline structure, while NaCl boundaries have a less anisotropic two-dimensional structure. An examination of this difference is made.