Dendritic Solidification

Dendritic Solidification

H. K. D. H. Bhadeshia

Solidification

A liquid when cooled solidifies. Alternatively, it may solidify when the pressure is decreased orincreased, depending on the sign of the density change. Once nucleation has occurred,solidification proceeds by the movement of an interface. The process may generate heat if theenthalpy of the solid is less than that of the liquid. Similarly, solute may partition into the liquidif its solubility in the solid is less than that in the liquid.

Computer simulated image of dendritic growth using acellular automata technique. Notice the branching onthe dendrites. Photograph courtesy of the Institute ofMaterials, based on the work of U. Dilthey, V. Pavlikand T. Reichel, Mathematical Modelling of WeldPhenomena III, eds H. Cerjak and H. Bhadeshia,Institute of Materials, 1997.

The accumulation of solute and heat ahead of the interface can lead to circumstances in whichthe liquid in front of the solidification front is supercooled. The interface thus becomes unstableand in appropriate circumstances solidification becomes dendritic. The mechanism of thisinstability is discussed elsewhere.

A dendrite tends to branch because the interface instability applies at all points along itsgrowth front. The branching gives it a tree-like character which is the orgin of the term dendrite.

Computer simulated image of the dendritic solidificationof pure nickel. The simulation is of "free growth", i.e.,the solid is growing without contact with anything butthe liquid. The degree of undercooling of the liquid infront of the interface is indicated by the adjacent scale.Photograph courtesy of the Institute of Materials, basedon the work of U. Dilthey, V. Pavlik and T. Reichel,Mathematical Modelling of Weld Phenomena III,Institute of Materials, 1997.

Growth tends to occur along fast growth directionswhich are generally <100> for cubic metals.

Technological Consequences

We first consider the solidification of a "hardfacing alloy" which is deposited as liquid onsubstrates which require wear resistance. Typical applications include earth movingequipment, heavy farm equipment and rock crushers used in the mining industry.

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The alloy has a chemical composition Fe-34Cr5Nb-4.5C wt.%. During cooling, niobiumcarbide dendrites are the first to solidify. Their shape can be revealed by attacking thesample with an acid which removes the matrix iron-rich phase Figure. In this particularcase, the solid/liquid interfacial energy is varies with orientation so the minimum energyshape is that with crystallographic facets. The fast growth direction is still <100> as canbe deduced from the symmetry of the dendrite.

niobium carbide

Scanning electron micrograph of a niobium carbide(cubic-F) dendrite in an iron-base hardfacing alloy.Photograph by courtesy of Berit Gretoft, CentralResearch Laboratories, ESAB AB, Sweden.

The second example deals with a cobalt-base alloy known as "Stellite". This is muchmore expensive than the iron-base alloy described above but is considerably tougherbecause it has a much finer microstructure. Thus, it is necessary to use transmissionelectron microscopy to study the fine structure Figure.

cobalt dendrite

Transmission electron micrograph of a cobalt-rich"blobby" dendrite which is in a hard eutectic (dark). Theeutectic is a mixture of carbides and matrix. The solid-liquid interface energy is not very anisotropic so thedendrite adopts the smooth shape. Nevertheless, thefast growth directions are along <100>. Micrograph bycourtesy of S. Atamert and H. K. D. H. Bhadeshia. Seealso "Comparison of the Microstructures and WearProperties of Stellite Hardfacing Alloys Deposited byArc Welding and Laser Cladding" MetallurgicalTransactions A, Vol. 20A, 1989, pp. 1037-1054. S.Atamert and H. K. D. H. Bhadeshia

Dendritic solidification frequently occurs under conditions which are far from equilibrium.Given these circumstances, regions of solute-rich liquid can be trapped between thedendrite arms, and solidify eventually to solute-rich solid regions. This in turn leads to thedevelopment of a "banded" microstructure when the material is subsequently processedby rolling or other mechanical fabrication methods. The banded microstructure Figure canbe detrimental to the mechanical properties.

banded microstructure

An optical micrograph showing a typical bandedmicrostructure in steel. The solute-depleted regionshave transformed in the solid state into bainite whereasthe solute-enriched regions are martensitic. Photographcourtesy of S. A. Khan and H. K. D. H. Bhadeshia. Seealso, "The Bainite Transformation in ChemicallyHeterogeneous 300M High-Strength Steel"Metallurgical Transactions A, Vol. 21A, 1990, pp.859-875. S. A. Khan and H. K. D. H. Bhadeshia

Dendrites of Zinc

The following photographs show dendrites of zinc obtained by withdrawing the solid from amelt of impure zinc. The photographs are of samples collected by Professor Paul Howell,Pennsylvania State University.


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http://www.msm.cam.ac.uk/phase-trans/2004/z/zinc Dendrites

Dendrites of zinc rescued from partiallysolidified melt.

http://www.msm.cam.ac.uk/phase-trans/2004/z/zinc Dendrites

Dendrites of zinc rescued from partiallysolidified melt.

Dendrites of Ice

When the weather outside is cold, moisture in a warm room can condense on the inner surfaceto form a thin film of moisture. If the temperature outside is sufficiently low, ice nucleates andgrows. The region around the ice crystal becomes depleted in moisture. Moisture then has toarrive to the ice crystal by diffusion through the depleted zone, from the remaining moisture farfrom the interface. Suppose a small part of the ice crystal accidentally advances further thenthe rest of the interface. The diffusion distance for that perturbation decreases, and hence theperturbation grows faster. This leads to the formation of a branch, and a branching instability issaid to have formed. This leads to the formation of ice dendrites as illustrated below. Thesepictures were taken at the Harbin Institute of Technology - the temperature outside can bebelow -20oC. The mechanism described here is essentially how snow-flakes are supposed toform, by the diffusion of water molecules through air on to the ice crystals. Snow-flakes havethe dendritic morphology in three dimensions.

Ice dendrites on inner surface of cold window.

DSCN4008.JPGIce dendrites.

DSCN4009.JPGIce dendrites.

Ice dendrites.

Negative Dendrites

When a sheet of ice undergoes internal melting, dendrites of water form inside the ice. It is nowthe liquid which advances into the solid with an unstable interface. Furthermore, since ice hasa lower density than water, a bubble forms inside each dendrite of the water.

Dendrites in Metallic Glass

The following transmission electron micrographs have kindly been provided by AndrewFairbank with copyright clearance from the University of Wollongong. They show the earlystages of dendrites of α-(Fe,Si) growing in the solid-state, from the amorphous Fe82Si4B14


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metallic glass during annealing at 433 °C for 60 min.

aDendrites forming in Fe82Si4B14 metallic

glass.

bDendrites forming in Fe82Si4B14 metallic

glass.c

Dendrites forming in Fe82Si4B14 metallicglass.

dDendrites forming in Fe82Si4B14 metallic

glass.e

Dendrites forming in Fe82Si4B14 metallicglass.

Interface Stability and Diffusion Bonding

Some materials cannot be welded by conventional techniques because the high temperaturesinvolved would destroy their properties. For such materials, diffusion bonding is an attractivesolution because it is a solid state joining technique, which is normally carried out at atemperature much lower than the melting point of the material.

Diffusion bonding is a candidate process for joining many aluminium based materials includinga variety of artificial composites. Unfortunately, the method has been beset by difficulties,particularly that the bond line remains a plane of weakness. This is because the bond plane isa site for impurity segregation, where oxide particles may also be trapped. In addition, therecan be problems in ensuring the continuity of the metallic bond.

Equipment used for temperature gradient diffusionbonding

Shirzadi and Wallach (Materials Science and Metallurgy, University of Cambridge) invented adisarmingly simple method of breaking up the planar bond into an unstable interface whichdevelops into a three-dimensionally 'sinusoidal' or cellular surface. A small temperaturegradient was applied at the bond, causing the interface instability. This concept is taught inmany undergraduate courses but it took imagination and foresight on the part of Shirzadi andWallach to apply it to transient liquid phase bonding. The method is incredibly successful,leading to a vast increase in bond strength, and has been granted a UK patent, No. 9709167.2,the Granjon Prize of the International Institute of Welding and the Cook-Ablett Award of theInstitute of Materials.

Movies

Movies about dendritic and cellular solidification.Computer-generated movies of dendritic solidification.

Battery Fires

Professor Clare Grey and her team at Cambridge University have concluded that metal fibres inthe form of dendrites grow within lithium batteries which are charged rapidly. These causeshort circuits, overheating and in some cases, fires.

Superalloys Titanium Bainite Martensite Widmanstätten ferriteCast iron Welding Allotriomorphic ferrite Movies SlidesNeural Networks Creep Stainless Steels Theses TRIP

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Dendritic Solidification