Waldemar Wołczyński

The use of equilibrium phase diagram for the calculation of non-equilibrium precipitates in dendritic solidification. Validation

Abstract New model for solute redistribution in cellular/dendritic growth has been applied to predict the amount of non-equilibrium precipitates. Both real and theoretical redistribution of the Zn-solute within Al-75Zn alloy is taken into account to show the model application. The amount of non-equilibrium precipitates is determined for the explored morphology.

Concentration Micro-Field for Lamellar Eutectic Growth

A possibility of a modification of the Jackson-Hunt theory of an oriented structure formation is analysed. A new model for the formation of a concentration field ahead of growing regular lamellae with respect to the solid / liquid interface shape is presented. A coordinate system applied in the model is attached to the solid / liquid interface to be advancing in the z - direction, identically with interface moving at a constant velocity, v . The solution to a diffusion equation is given for the improved formulation of the boundary conditions. The boundary conditions are related to the interplay between the diffusion required for phase separation and the formation of the interphase between both lamellae. The boundary conditions are formulated to establish the stability of lamellar structure formation under steady-state conditions. It is assumed that stable growth of the lamellae is ensured by the separation of concentration fields within a boundary layer ahead of the solid / liquid interfaces of both the α and β phases. Coupled lamellar growth with the presence of a leading phase protrusion is defined. The general mass balance is analysed for a solute concentration in the liquid, taking into account a planar solid / liquid interface. A local mass balance is also ensured but it requires envisaging a protrusion of the minor eutectic phase. The existence of a lead distance is confirmed experimentally for the (Pb)-(Cd) eutectic system. The difference in undercooling is also considered as a phenomenon associated with the separation of concentration fields and the existence of a protrusion to relax the assumption of an isothermal interface (ideally coupled growth) given by the Hunt and Jackson theory.

Oscillatory Structure of the Zn-Cu-Ti Single Crystals

Structures obtained during Zn-Cu-Ti single crystal growth by the Bridgman method were investigated. The alloys of composition Zn-Cu0.1wt.%-Ti0.1wt.% were used for single crystals growth, which were produced at rate in the range of 1.8mm/h to 16mm/h. The Zn-Cu-Ti alloys were characterized by multiphase structure; in the solute-hardened matrix by Cu atoms exists a needle-shaped intermetallic phase Zn16Ti. The strong anisotropy of the hexagonal structure gives a significant influence on a second phase distribution in the matrix volume. In the range of the low growth rates (from 1.8mm/h to 10mm/h) oscillatory structures were observed. That effect vanished at the growth rates higher than 10mm/h. The observed oscillatory structures were characterized by existing periodic layers rich in the intermetallic phase of Zn16Ti interlaid with pure matrix (alpha phase Zn with Cu solute).

Transition of Flake into Fibre Structure in Eutectic Al-Si

The work presents microstructures of the Al-Si eutectic alloy obtained within the range of solidification rates at various temperature gradients at which the transition of flake into fibre structure could be expected. The solidification conditions applied were growth rates ν = 300÷800 μm/s and temperature gradients G = 40÷250 K/cm. An influence of temperature gradient onto structure parameters λ and R has not been observed. An influence of temperature gradient onto the range of the transition flake into fibre has not been noted neither.

Thermal Gradients Behaviour during the C-E Transition within Solidifying Massive Roll

Columnar or equiaxed structure selection and particularly the C→E transition in the solidifying massive rolls is shown as the result of changes in heat transfer. The numerical treatment of heat transfer allows to separate the temperature field for columnar structure formation from equiaxed structure formation. An area where transition from columnar into equiaxed structure occurs, C→E≡CET is also distinguished. The current model requires the transformation of the calculated temperature field into the thermal gradients’ field. Thermal gradients are approximately constant during the examined C→E transition according to the numerical simulation. This result is in accordance with the Hunt’s theoretical predictions. The localization of the structural transition (CET) in space and in time is also shown within the map which yields from the temperature field.

Space-Time-Structure Map for As Cast Massive Rolls

A thermal gradients’ field was studied for an as cast massive roll. Three ranges within the thermal gradients field were differentiated. The thermal gradient is constant along with the second range of thermal gradients’ field. Thus, columnar into equiaxed structure transition (CET) is to be expected within the second range. This statement is in good qualitative agreement with a similar observation given by Hunt’s theory. The columnar structure formation was significantly slowed down within the second range of thermal gradients field. At beginning of the second range the liquidus isotherm tears away from columnar structure / liquid interface. The columnar structure is still formed within the time adequate to the second range of thermal gradients but its growth vanishes due to lost competition, and at the end of the second range the equiaxed structure growth dominates, exclusively. In fact, the extrapolation of the velocity of the columnar structure / liquid interface to its value equal with zero confirms the appropriate location of the end of the second range within which the CET is observed. The detailed analysis of the solidus isotherm / liquidus isotherm movements allows a development of the Space-Time-Structure Map for a solidifying massive roll. The Map shows the location of the CET in time (solidification time) and in space (along the roll radius). Moreover a proper locations of structural zones are drawn in the Map. The simulation of the thermal gradients’ field is a very useful tool in the industrial practice. The results of simulation can be used to predict the Space-Time-Structure Map (STSM) for a given massive roll or a massive ingot. Additionally, the equation for solute redistribution after back-diffusion was formulated on the basis of the new theory for microsegregation. It allows formulating the so-called macrosegregation index dealing with the whole ingot/roll volume.Copyright

Columnar → Equiaxed Structure Transition in Solidifying Rolls

As the first step of simulation, a temperature field for solidifying cast steel and cast iron roll was created. The convection in the liquid is not comprised since in the first approximation, the convection does not influence the analysed occurrence of the C → E (columnar to equiaxed grains) transition in the roll. The obtained temperature field allows to study the dynamics of its behavior observed in the middle of the mould thickness. This midpoint of the mould thickness was treated as an operating point for the C → E transition. A full accumulation of the heat in the mould was postulated for the C → E transition. Thus, a plateau at the T(t) curve was observed at the midpoint. The range of the plateau existence tC ↔ tE corresponded to the incubation period, tC R ↔ tE R that appeared before fully equiaxed grains formation. At the second step of simulation, the thermal gradients field was studied. Three ranges were distinguished: a/ for the formation of the columnar structure (the C–zone): (T ≫ 0 and (G|t tER) ≈ 0). The columnar structure formation was significantly slowed down during incubation period. It resulted from a competition between columnar growth and equiaxed growth expected at that period of time. The (G|t=tC R − G|t=tE R ) ≈ 0) relationship was postulated to correspond well with the critical thermal gradient, Gcrit. . A simulation was performed for the cast steel and cast iron rolls solidifying as if in industrial condition. Since the incubation divides the roll into two zones (columnar and equiaxed) some experiments dealing with solidification were made on semi-industrial scale. A macrosegregation equation for both mentioned zones was formulated. It was based on a recent equation for redistribution after back-diffusion. The role of the back-diffusion parameter was emphasized as a factor responsible for the redistribution in columnar structure and equiaxed structure.© 2010 ASME

Segregation Profiles in Diffusion Soldered Ni/Al/Ni Interconnections

An Al foil of 25 µm thickness was used to produce a Ni/Al/Ni interconnection under isothermal conditions at 680°C. After dissolution of the Al filler metal in the Ni substrate, and Ni from the substrate in the Al liquid foil, a solidification process occurred. First of all, the solidification was stopped just at the disappearance of the Al liquid metal, but also at different steps of the progress of solidification. Sub-layers of the two phases Al3Ni2 and Al3Ni were revealed within the frozen joints. A solidification - segregation model was developed to describe the formation of the sub-layers of both mentioned phases. The model is able to predict solute segregation profiles across the sub-layers of the Ni/Al/Ni interconnection, taking into account a superposition of some phenomena like partitioning, back-diffusion into the solid and peritectic reactions. The value of the diffusion coefficient into the solid for the Al3Ni2 phase formation in the presence of the liquid is also estimated.

Control of the Single Crystal Reinforcement by the Intermetallic Compound Layers

. An improvement of the Brody & Flemings theory has been proposed to study not only the solute segregation but the solute redistribution during the single crystal growth as well. The redistribution is treated as a phenomenon superposed upon the segregation phenomenon. The crystal growth has been performed by the closed Bridgman system with a constant growth rate and an imposed temperature gradient. A hypo-eutectic Zn-Ti alloy has been subjected to oriented growth and precipitation of the Zn-16Ti intermetallic compound was observed. The precipitates have been placed as some layers distributed within the single crystal with a constant spacing. Some data from the Zn-Ti binary phase diagram was introduced into the theory to show possibility of the control the phenomenon of the reinforcement by precipitation during a single crystal growth.

Experimental Verification of the Solute Redistribution in Cellular/Dendritic Solidification of the Al-3.5Li and Fe-4.34Ni Alloys

Four specific methods for the measurements of the solute redistribution within selected cells or dendrites have been developed, which agree with the theoretical model of microsegregation. The methods allow for the verification of measurements by the model predictions in different ways. The samples of cellular structure have been obtained due to experiments of directional solidification carried out in both terrestrial conditions and aboard the space shuttle The method of neutron induced autoradiography has been applied for measurement of Li-concentration profile in the case of Al-3.5Li alloy quenched during solidification. The Ni-concentration profile has been determined in the case of Fe-4 34Ni alloys All methods allow for estimation of the back-diffusion parameter.