Dendritic grain growth simulation in weld molten pool based on CA‐FD model

The finite difference model is coupled with a cellular automaton (CA) model to simulate dendrite growth in TIG (tungsten inert‐gas) weld molten pool of nickel‐based alloys. Based on the macro finite difference computation of the thermal field of the whole weldment, the micro CA model is used to simulate grain formation process in 2‐dimension area within weld molten pool. The results illustrate that the complicated thermal field and solute field can lead to complex grain morphologies in weld molten pool. The primary dendrite spacing changes during welding solidification process and the final primary dendrite spacing is decided by the thermal field, solute field and other parameters. And it is indicated that the grain boundary segregation has important relationship with welding speed. The grain boundary segregations become more severe as the welding speed increases when the other parameters are kept unchanged. (© 2007 WILEY ‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Phase‐field simulation of dendrite growth under forced flow conditions in an Al–Cu welding molten pool

A quantitative phase‐field model for directional solidification is applied to study dendrite growth under forced flow conditions in an Al‐Cu Gas Tungsten Arc (GTA) welding molten pool. Evolution of the dendrite morphology and the solute field under forced flow conditions is simulated. Growth of columnar grains goes through three periods, including the initial instability period, the competitive growth period and the relatively stable period. The solute segregation, the solute redistribution and the solute concentration in the liquid side of the interface are investigated, respectively. For the given conditions, simulation results are in good agreement with experimental findings.     

Columnar grain growth pattern with fluid flowing in molten pool

A coupled model was used to simulate columnar grain growth in TIG (tungsten inert‐gas) molten pool of nickel base alloy. The cellular automaton algorithm for dendritic growth is incorporated with solute transport model to take fluid flow into consideration. The results indicate that shear flow changes the solute distribution at the S/L (Solid/Liquid) interface, leading to asymmetrical growth of columnar grains. The dendrite arms on the upstream side grow fast, while the growth of dendrite arms on the downstream side is much delayed. However, dendrite arms on both sides are not as well‐developed as the grain growth without flow. With inlet flow velocity increasing, the phenomenon becomes more obvious. In addition, shear flow also results in more severe coring segregation. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of a vertical magnetic field on the dendrite morphology during Bridgman crystal growth of Al–4.5 wt% Cu

The effect of a vertical high magnetic field (up to 10 T) on the dendrite morphology has been investigated during Bridgman growth of Al–4.5 wt%Cu alloys experimentally. It is found that the field causes disorder in dendrites and their tilt in orientation. Along with the increase of the magnetic field and decrease of the growth velocity, the dendrites became broken and orientated in 1 1 1 along the direction of solidification instead of 1 0 0. The field also enlarged the primary dendrite spacing and promoted the branching of the dendrites to form high-order arms. Above phenomena are attributed to the thermoelectromagnetic convection effect and orientation caused by the high magnetic field.     

Phase field investigation on sidebranching dynamics in transient growth

A computationally efficient quantitative phase field formulation is used to investigate the sidebranching dynamics under different transient conditions in directional solidification for realistic parameters of a dilute alloy. The sidebranch growths where the pulling speed or temperature gradient increases with constant increasing rates are simulated and discussed by using the noise amplification theory. The results show that in transient growth, the tip shape can rapidly adjust with the instantaneous conditions, and the tip velocity changes continuously due to the change of tip undercooling. Therefore, under our given transient conditions, the sidebranch spacing or sidebranching frequency depends strongly on the transient conditions and transient history, which is different with that in steady‐state conditions where the sidebranching frequency is found to be independent of the temperature gradient and primary spacing, but varies as a power law of pulling speed.     

Growth of equiaxed dendritic crystals settling in an undercooled melt,Part 1: Tip kinetics

Experiments are conducted to measure the dendrite tip growth velocities of equiaxed crystals of the transparent model alloy succinonitrile–acetone that are settling in an undercooled melt. The tip velocities are measured as a function of the crystal settling speed and the Eulerian angle between the dendrite arms and the flow direction relative to the crystal. The ratio of the settling speed (or flow velocity) to the tip growth velocity ranges from 62 to 572. The ratio of the measured tip velocity to that predicted from a standard diffusion theory for free dendritic growth ranges from almost zero for dendrite tips growing in the wake of the crystal, about unity for dendrite tips with an orientation close to normal to the flow direction, and up to two for dendrite tips growing into the flow. Despite the relatively strong flow relative to the crystal, the average tip growth velocity of the six primary dendrite arms of an equiaxed crystal is found to be in excellent agreement with the standard diffusion theory result. The individual tip velocities are correlated using a boundary layer model of free dendritic growth in the presence of melt flow that is modified to account for the flow angle dependence. Using the same dendrite tip selection parameter, σ^*, as established previously under purely diffusive conditions (0.02), good agreement is achieved between the measured and predicted tip velocities. The model is also found to predict well the variations in the tip velocity that occur during settling due to crystal rotation and settling speed changes.     

Measurement of three‐dimensional concentration gradients around a crystal growing from its aqueous solution using laser schlieren

Schlieren measurements of the gradients of the concentration field around a KDP crystal growing from its aqueous solution are reported. The measurement of the concentration gradient field is important for crystal growth because it controls the rate of solute transport from the bulk of the solution to the crystal surface. In the crystal vicinity, the concentration gradients have a three dimensional distribution. The concentration gradient field has been imaged using monochrome schlieren technique. Four view angles, namely 0, 45, 90 and 135° have been utilized. By interpreting the schlieren images as projection data of solute concentration gradient, the three‐dimensional concentration gradient field around the crystal has been determined using an algebraic reconstruction technique. At low supersaturation levels, the growth process is accompanied by weak fluid movement during which diffusion effects are significant. At higher levels of supersaturation and large crystal size, a well‐defined convective plume around the growing crystal is observed. Reconstruction of concentration gradients around the crystal explains the preferential growth rates of various faces of the crystal. The non‐circular shape of the crystal is seen to affect the symmetry of the distribution of concentration gradients in its vicinity. The effect of crystal morphology on the orientation of convection currents rising from the crystal surface has also been brought out on the basis of the reconstructed concentration gradients distribution in the growth chamber. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Measurements of dendrite tip growth and sidebranching in succinonitrile–acetone alloys

Experiments are carried to investigate free dendritic growth of succinonitrile–acetone alloys in an undercooled melt. The measurements include the steady dendrite tip velocity and radius, the non-axisymmetric amplitude coefficient of the fins near the tip, and the envelope width, projection area, and contour length of the sidebranch structure far from the tip. It is found that the measured dendrite tip growth Péclet numbers agree well with the predictions from a stagnant film model that accounts for thermosolutal convection in the melt. The measured tip selection parameter, σ^?, is verified to be independent of the alloy composition, but shows a strong dependence on the imposed undercooling. The universal amplitude coefficient, A₄, is measured to be equal to 0.004, independent of the undercooling, but the early onset of sidebranching prevents its accurate determination for more concentrated alloys. For the self-similar sidebranch structure far from the tip, scaling laws are obtained for the measured geometrical parameters. While melt convection causes some widening of the sidebranch envelope, and the early onset of sidebranching for alloy dendrites results in a 25% upward shift of the envelope width, the projection area and, hence, the mean width of a sidebranching dendrite, as well as its contour length in the sidebranch plane, obey universal power laws that are independent of the convection intensity and the alloy composition.     

Development of dendrite array growth during alternately changing solidification condition

To investigate competitive growth in a dendrite array a directional solidification study was carried out on a succinonitrile–acetone alloy. In the experiment the temperature gradient G applied is alternately altered over a wide range, increased from a lower to a higher limit, and then decreased back to the lower one. It was found that source dendrites, i.e. parent dendrites, are not superior to derived dendrites in terms of growth competition. The orientation deviation between neighbouring dendrites impacts both local dendrite creation and elimination. At lower gradients, the new dendrites grow out from the ternary arms, while at the higher gradients new dendrites originate directly from the secondary arms. During increasing and decreasing G, average primary dendrite spacing λ measured traces out different paths, revealing an unclosed hysteresis loop in the λ–G-diagram.     

Solidification behavior and microstructural evolution of the Cr‐Nb eutectic alloy

A series of microstructures including fully coupled eutectic, both α‐Cr and β‐Cr₂Nb primary dendrites embedded in eutectic and only β‐Cr₂Nb primary dendrites plus eutectic were observed in the arc‐melted Cr‐Cr₂Nb eutectic alloy. By employing EPMA analysis performed at the eutectic regions, the eutectic composition of the Cr‐Cr₂Nb system was indicated to contain less than 18 at.%Nb. Based on the solidification phase selection involving phase competitive nucleation and growth, the α‐Cr phase was predicted to be the primary nucleating phase and the β‐Cr₂Nb the primary growing phase. Under large undercooling conditions, the solidification process was controlled by nucleation, which led to the formation of α‐Cr primary particles. With the decrease in undercooling, the solidification process developed into growth controlling, which caused the occurrence of β‐Cr₂Nb primary phase since the actual solidification path of the alloy lay within the hypereutectic region. The explanation was confirmed by the experimental composition analysis.     

Rapid crystallization and growth mechanisms of highly undercooled Ag–Cu–Ge ternary alloy

Crystallization from undercooled melt of Ag-33.4 wt% Cu-28.1 wt% Ge ternary alloy was carried out with glass fluxing method under different undercoolings and the nucleation and growth characteristics of the primary phase, two-phase eutectic, and ternary eutectic are investigated. It is found that both the solidification microstructures and the size of primary phase (Ge) and intermetallic compound η vary significantly with undercooling, whereas the ternary eutectic structure has no apparent variation. With the increase of undercooling, macrosegregation of primary (Ge) phase becomes weak and this phase experiences a “large block/strip→small particle” morphology transition. Moreover, the ((Ge)+η) two-phase eutectic can nucleate in preference to the primary (Ge) phase within a large undercooling regime. The intermetallic compound phase η grows competently with (Ge) phase and it can directly form alloy melt. The experimental results of the containerless processing by a 3 m drop tube indicate that in order to make the ternary eutectic nucleate in preference to the (Ge) primary phase and the ((Ge)+η) two-phase eutectic with the glass fluxing method, the undercooling should be at least larger than 195 K.     

Growth and characterization of nanostructured Al2O3/YAG/ZrO2 hypereutectics with large surfaces under laser rapid solidification

The preparation of large bulk oxide eutectics with homogeneous and dense structure in nano-scale by melt growth method is a difficult challenge. Fully dense, homogeneous and crack-free ternary nanostructured Al₂O₃/YAG/ZrO₂ hypereutectic plate with large surface is successfully obtained by laser remelting. The hypereutectic in selected composition presents an ultra-fine eutectic-like microstructure consisting of alternating interpenetrating Al₂O₃, YAG and ZrO₂ lamellae with mean interphase spacing of about 150 nm, which is much smaller than the ternary eutectic composition grown at the same growth conditions. With the increase of laser scanning rate, the lamellar spacing is rapidly decreased. The minimum value obtained is 50 nm. The analysis indicates that the strong faceted growth behavior and cooperative branching of the component phases related with high entropies of fusion and large kinetic undercooling during laser rapid solidification are the primary formation reasons for the irregular eutectic growth morphology. Furthermore, the unique cellular microstructure with complex structure is also observed at high growth rate, and their formation mechanism and effect of the composition on the microstructure are discussed.     

Microstructural evolution of decagonal quasicrystal in the undercooled Al72Ni12Co16 alloy melts

The microstructure evolution of decagonal quasicrystals in Al₇₂Ni₁₂Co₁₆ alloy was investigated by the electromagnetic melting and cyclic superheating method. Single-phase decagonal quasicrystals have been obtained when the undercoolings were larger than 60 K. The decagonal quasicrystals formed at various undercoolings show different microstructural morphologies. Furthermore, grain refinement was found near the undercooling of 120 K. Based on current thermodynamic and dendrite growth theories, a dimensionless superheating parameter was adopted to explain the effect of processing conditions on the microstructure of Al₇₂Ni₁₂Co₁₆ alloy. The result indicate that the fine equiaxied microstructure of decagonal quasicrystal (D-phase) formed near on undercooling of 120 K originates from the break-up of dendrites.     

On the morphology of <100>-textured Germanium Crystallites in Zn—Ge Eutectic Alloy

Different geometry parameters for the cross-like germanium crystallites (eutectic dendrites) of the Zn-Ge eutectic alloys unidirectionally solidified have been related to the growth rate R and liquid temperature gradient G using linear regression analysis. It has been found that for eutectic dendrite spacing λ, balk length d and balk thickness b follow the relationship of the type w = C_wR^−rwG^−gw; C_w is a constant. The spacing relationship of eutectic dendrites (r_λ = 0.21; g_λ = 0.48) shows a similarity with published experimental and theoretical results on primary dendrite arm spacing (r_λ = 0.25; g_λ = 0.5). It has been shown in terms of a profile ration λ/d that for geometrical similar morphologies the relationship λ²R = const. is valid.     

Cover Picture: Cryst. Res. Technol. 4/2009

The cover picture shows simulated columnar dendritic grain morphologies at different times in a weld pool of Al‐Cu alloy (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Diffusion-controlled crystal growth in K2OSiO2 compositions

The growth of cristobalite dendrites in two K₂OSiO₂ glasses containing 10.3 and 15.0 mol% K₂O has been studied over a wide range of temperature. The kinetics of crystallization were linear; i.e. the growth rates were independent of time. The observed crystallization rates were consistent with a diffusion-controlled mechanism. Measurements of the tip radii of curvature of the dendrites are consistent, at low undercoolings, with the predictions of Horvay and Cahn for the growth of an isolated dendrite. However, at lower temperatures at which the dendrites are closely spaced, the predicted radii are seriously in error. A model is described which takes account of the overlapping diffusion fields of neighboring dendrites and gives improved agreement with the observed growth rates.The presence of a maximum in each of the crystal growth rate versus temperature curves has not been explained. This phenomenon is apparently related to changes in the size, shape and spacing of the dendrites, which occur in the same temperature range.     

Investigation of directional solidified Al–Ti alloy

Al–1 wt% Ti alloy was directionally solidified upwards under argon atmosphere under the two conditions; with different temperature gradients (G = 2.20–5.82 K/mm) at a constant growth rate (V = 8.30 μm/s) and with different growth rates (V = 8.30–498.60 μm/s) at a constant temperature gradient (G = 5.82 K/mm) in a Bridgman furnace. The dependence of characteristic microstructure parameters such as primary dendrite arm spacing (λ₁), secondary dendrite arm spacing (λ₂), dendrite tip radius (R) and mushy zone depth (d) on the velocity of crystal growth and the temperature gradient were determined by using a linear regression analysis. A detailed analysis of microstructure development with models of dendritic solidification and with previous similar experimental works on dendritic growth for binary alloys were also made.     

Dendrite spacing in unidirectionally solidified Al-Cu alloy

Directional solidification experiments have been carried out to study the variation in primary and secondary arm spacings with solidification parameters in the Al-Cu system. It is found that the primary arm spacing Z₁ obeys the common correlation Z₁ = KG^-aV^-b in the high velocity regime or low temperature gradient regime, where a and b are constants, the value of K included the composition dependence, G is the temperature gradient in the liquid and V the growth rate; however, it does not obey this correlation for the low velocity regime or high temperature gradient regime but goes through a maximum or a catastrophe as a function of V or G at V = V_cs/k or G = kG_cs, where k is the equilibrium distribution coefficient, and V_cs and G_cs are the critical velocity and temperature gradient at the limit of constitutional undercooling respectively. The initial secondary arm spacings Z₂₀ are nearly independent of G and mainly depended on V, Z₂₀ = 0.016 V^-0.54 (mm). The secondary arm spacing Z₂ tends to c oarsen with time and thus is a function of coarsening time t_f, Z₂ = 0.016t^0.34_f (mm). Theoretical analyses of the primary arm spac ing and the initial secondary arm spacing have been proposed, and the derived relationships agree reasonably well with the above experimental results.