A liquid when cooled solidifies. Alternatively, it may solidify when the pressure is decreased or increased, 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 the enthalpy of the solid is less than that of the liquid. Similarly, solute may partition into the liquid if its solubility in the solid is less than that in the liquid.
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Computer simulated image of dendritic growth using a cellular automata technique. Notice the branching on the dendrites. Photograph courtesy of the Institute of Materials, based on the work of U. Dilthey, V. Pavlik and T. Reichel, Mathematical Modelling of Weld Phenomena 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 which the liquid in front of the solidification front is supercooled. The interface thus becomes unstable and in appropriate circumstances solidification becomes dendritic. The mechanism of this instability is discussed elsewhere.
A dendrite tends to branch because the interface instability applies at all points along its growth front. The branching gives it a tree-like character which is the orgin of the term dendrite.
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Computer simulated image of the dendritic solidification of pure nickel. The simulation is of "free growth", i.e., the solid is growing without contact with anything but the liquid. The degree of undercooling of the liquid in front of the interface is indicated by the adjacent scale. Photograph courtesy of the Institute of Materials, based on 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 directions which are generally <100> for cubic metals. |
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The alloy has a chemical composition Fe-34Cr5Nb-4.5C wt.%. During cooling, niobium carbide dendrites are the first to solidify. Their shape can be revealed by attacking the sample with an acid which removes the matrix iron-rich phase Figure. In this particular case, the solid/liquid interfacial energy is varies with orientation so the minimum energy shape is that with crystallographic facets. The fast growth direction is still <100> as can be deduced from the symmetry of the dendrite.
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Scanning electron micrograph of a niobium carbide (cubic-F) dendrite in an iron-base hardfacing alloy. Photograph by courtesy of Berit Gretoft, Central Research Laboratories, ESAB AB, Sweden. |
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Transmission electron micrograph of a cobalt-rich "blobby" dendrite which is in a hard eutectic (dark). The eutectic is a mixture of carbides and matrix. The solid-liquid interface energy is not very anisotropic so the dendrite adopts the smooth shape. Nevertheless, the fast growth directions are along <100>. Micrograph by courtesy of S. Atamert and H. K. D. H. Bhadeshia. See also "Comparison of the Microstructures and Wear Properties of Stellite Hardfacing Alloys Deposited by Arc Welding and Laser Cladding" Metallurgical Transactions A, Vol. 20A, 1989, pp. 1037-1054. S. Atamert and H. K. D. H. Bhadeshia |
| An optical micrograph showing a typical banded microstructure in steel. The solute-depleted regions have transformed in the solid state into bainite whereas the solute-enriched regions are martensitic. Photograph courtesy of S. A. Khan and H. K. D. H. Bhadeshia. See also, "The Bainite Transformation in Chemically Heterogeneous 300M High-Strength Steel" Metallurgical Transactions A, Vol. 21A, 1990, pp. 859-875. S. A. Khan and H. K. D. H. Bhadeshia |
The following photographs show dendrites of zinc obtained by withdrawing the solid from a melt of impure zinc. The photographs are of samples collected by Professor Paul Howell, Pennsylvania State University.
Dendrites of zinc rescued from partially solidified melt. |
Dendrites of zinc rescued from partially solidified melt. |
When the weather outside is cold, moisture in a warm room can condense on the inner surface to form a thin film of moisture. If the temperature outside is sufficiently low, ice nucleates and grows. The region around the ice crystal becomes depleted in moisture. Moisture then has to arrive to the ice crystal by diffusion through the depleted zone, from the remaining moisture far from the interface. Suppose a small part of the ice crystal accidentally advances further then the rest of the interface. The diffusion distance for that perturbation decreases, and hence the perturbation grows faster. This leads to the formation of a branch, and a branching instability is said to have formed. This leads to the formation of ice dendrites as illustrated below. These pictures were taken at the Harbin Institute of Technology - the temperature outside can be below -20oC. The mechanism described here is essentially how snow-flakes are supposed to form, by the diffusion of water molecules through air on to the ice crystals. Snow-flakes have the dendritic morphology in three dimensions.
Ice dendrites on inner surface of cold window. |
Ice dendrites. |
Ice dendrites. |
Ice dendrites. |
When a sheet of ice undergoes internal melting, dendrites of water form inside the ice. It is now the liquid which advances into the solid with an unstable interface. Furthermore, since ice has a lower density than water, a bubble forms inside each dendrite of the water.
The following transmission electron micrographs have kindly been provided by Andrew Fairbank with copyright clearance from the University of Wollongong. They show the early stages of dendrites of α-(Fe,Si) growing in the solid-state, from the amorphous Fe82Si4B14 metallic glass during annealing at 433 °C for 60 min.
 Dendrites forming in Fe82Si4B14 metallic glass. |
 Dendrites forming in Fe82Si4B14 metallic glass. |
 Dendrites forming in Fe82Si4B14 metallic glass. |
 Dendrites forming in Fe82Si4B14 metallic glass. |
 Dendrites forming in Fe82Si4B14 metallic glass. |
Some materials cannot be welded by conventional techniques because the high temperatures involved would destroy their properties. For such materials, diffusion bonding is an attractive solution because it is a solid state joining technique, which is normally carried out at a temperature much lower than the melting point of the material.
Diffusion bonding is a candidate process for joining many aluminium based materials including a 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 is a site for impurity segregation, where oxide particles may also be trapped. In addition, there can be problems in ensuring the continuity of the metallic bond.
 | Equipment used for temperature gradient diffusion bonding |
Shirzadi and Wallach (Materials Science and Metallurgy, University of Cambridge) invented a disarmingly simple method of breaking up the planar bond into an unstable interface which develops into a three-dimensionally 'sinusoidal' or cellular surface. A small temperature gradient was applied at the bond, causing the interface instability. This concept is taught in many undergraduate courses but it took imagination and foresight on the part of Shirzadi and Wallach 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 the Institute of Materials.
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