Galvanized surface with visible crystallites (grains) of zinc.

A grain boundary is the interface between two grains in a polycrystalline material. Grain boundaries disrupt the motion of dislocations through a material so reducing crystallite size is a common way to improve strength, as described by the Hall-Petch relationship. Since grain boundaries are defects in the crystal structure they tend to decrease the electrical and thermal conductivity of the material. Grain Boundary impedes dislocation motion. The high interfacial energy and relatively weak bonding in most grain boundaries often makes them preferred sites for the onset of corrosion and for the precipitation of new phases from the solid. They are also important to many of the mechanisms of creep. Image:Galvanized surface. ... Image:Galvanized surface. ... Galvanization or galvanisation refers to any of several electrochemical processes named after the Italian scientist Luigi Galvani. ... General Name, Symbol, Number zinc, Zn, 30 Chemical series transition metals Group, Period, Block 12, 4, d Appearance bluish pale gray Atomic mass 65. ... A crystallite is a domain of solid-state matter that has the same structure as a single crystal. ... This article lacks information on the subject matters importance. ... Quartz crystal Copper(II) sulfate and iodine crystal Synthetic bismuth crystal Insulin crystals Gallium, a metal that easily forms large single crystals A huge monocrystal of potassium dihydrogen phosphate grown from solution by Saint-Gobain for the megajoule laser of CEA. In chemistry and mineralogy, a crystal is a solid... Electrical conductivity is a measure of a materials ability to conduct an electric current. ... In physics, thermal conductivity, k, is the intensive property of a material that indicates its ability to conduct heat. ... Look up creep in Wiktionary, the free dictionary. ...

Types of boundary

It is convenient to separate grain boundaries by the extent of the misorientation between the two grains. low angle grain boundaries (LAGBs) are those with a misorientation less than about 11 degrees. Generally speaking they are composed of an array of dislocations and their properties and structure are a function of the misoriention. In contrast the properties of high angle grain boundaries (HAGBs) whose misorientation is greater than about 11 degrees (the transition angle varies from 10-15 degrees depending on the material) are normally found to be independent of the misorientation. However there are 'special boundaries' at particular orientations whose interfacial energies are notably lower than those of general HAGBs. For the syntaxic operation, see Dislocation (syntax) For the medical term, see Dislocation (medicine) In materials science a dislocation is a linear crystallographic defect, or irregularity, in crystal structure. ...

Schematic representations of a tilt boundary (with an array of edge dislocations) and a twist boundary

Consider the simplest case of a tilt boundary where a single, contiguous crystallite or grain is gradually bent by some external force. The energy associated with the elastic bending of the lattice can be reduced by inserting a dislocation, which is essentially a half-plane of atoms that act like a wedge. As the grain is bent further, more and more dislocations must be introduced to accommodate the deformation resulting in a growing wall of dislocations - a low-angle boundary. The grain can now be considered to have split into two sub-grains of related crystallography but notably different orientations. Eventually, as the density of dislocations increases, the cores of the dislocations will begin to overlap and the ordered nature of the boundary will begin to breakdown. At this point the boundary can be considered to be high-angle and the original grain to have separated into two entirely separate grains. Image File history File links Download high-resolution version (1675x1078, 51 KB) Made by Slinky Puppet 03-07-06. ... Image File history File links Download high-resolution version (1675x1078, 51 KB) Made by Slinky Puppet 03-07-06. ... A crystallite is a domain of solid-state matter that has the same structure as a single crystal. ...

An alternative is a twist boundary where the misorientation occurs around and axis that is perpendicular to the boundary. This type of boundary incorporates two sets of screw dislocations. If the Burgers vectors of the dislocations are orthogonal then the dislocations do not strongly interact and form a square network. In other cases the dislocations may interact to form a more complex hexagonal structure. In materials science, a dislocation is a crystallographic defect, or irregularity, within a crystal structure. ... In materials science, a dislocation is a linear crystallographic defect, or irregularity, within a crystal structure. ...

High angle boundary structure

High angle boundaries were originally thought to be some form of amorphous or even liquid layer but this conflicted with evidence from electron diffraction and could not explain the observed strength of grain boundaries. It is now accepted that a boundary consists of structural units which depend on both the misorientation of the two grains and on the plane of the interface. The types of structural unit that exist can be related to the concept of the coincidence site lattice. The degree of fit (Σ) between the structures of the two grains is described by the reciprocal of the ratio of CSL sites to the total number of sites. Thus a boundary with high Σ might be expected to have a higher energy than one with low Σ. Low-angle boundaries, where the distortion is entirely accommodated by dislocations, are Σ1. Some other low Σ boundaries have special properties especially when the boundary plane is one that contains a high density of coincident sites. Examples include coherent twin boundaries (Σ3) and high-mobility boundaries in FCC materials (Σ7). Deviations from the ideal CSL orientation may be accommodated by local atomic relaxation or the inclusion of dislocations into the boundary. In mathematics, the reciprocal, or multiplicative inverse, of a number x is the number which, when multiplied by x, yields 1. ...

Describing a boundary

A boundary can be described by the orientation of the boundary with respect to the two grains and the 3-D rotation required to bring the grains into coincidence. Thus a boundary has 5 macroscopic degrees of freedom. However, it is common to describe a boundary only in terms of the orientation relationship of the neighbouring grains. Generally, the convenience of ignoring the boundary plane orientation, which is very difficult to determine, outweighs the reduced information. The relative orientation of the two grains is described using the rotation matrix: The phrase degrees of freedom is used in three different branches of science: in physics and physical chemistry, in mechanical and aerospace engineering, and in statistics. ... A rotation matrix is a matrix which when multiplied by a vector has the effect of changing the direction of the vector but not its magnitude. ...

The characteristic distribution of boundary misorientations in a completely randomly oriented set of grains.

Using this system the rotation angle θ is: Image File history File links Download high-resolution version (2834x2180, 57 KB) Made by Slinky Puppet. ... Image File history File links Download high-resolution version (2834x2180, 57 KB) Made by Slinky Puppet. ...

while the direction [uvw] of the rotation axis is:

The nature of the crystallography involved limits the misorientation of the boundary. A completely random polycrystal, with no texture, thus has a characteristic distribution of boundary misorientations (see figure). However, such cases are rare and most materials will deviate from this ideal to a greater or lesser degree. Crystallography (from the Greek words crystallon = cold drop / frozen drop, with its meaning extending to all solids with some degree of transparency, and graphein = write) is the experimental science of determining the arrangement of atoms in solids. ...

Boundary energy

The energy of a tilt boundary and the energy per dislocation as the misorientation of the boundary increases.

The energy of a low-angle boundary is dependent on the degree of misorientation between the neighbouring grains up to the transition to high-angle status. In the case of simple tilt boundaries the energy of a boundary made up of dislocations with Burgers vector b and spacing h is predicted by the Read-Shockley equation: Image File history File links Download high-resolution version (2834x2237, 53 KB) Made by Slinky Puppet, 1-07-06. ... Image File history File links Download high-resolution version (2834x2237, 53 KB) Made by Slinky Puppet, 1-07-06. ...

where θ = b/h, γ₀ = Gb/4 π(1-ν), A = 1 + ln(b/2 πr₀), G is the shear modulus, ν is possions ratio, and r₀ is the radius of the dislocation core. It can be seen that as the energy of the boundary increases the energy per dislocation decreases. Thus there is a driving force to produce fewer, more misoriented boundaries (i.e grain growth). Grain growth refers to the increase in size of grains (crystallites) in a material at high temperature. ...

The situation in high-angle bounadries is more complex. Although theory predicts that the energy will be a minimum for ideal CSL configurations, with deviations requiring dislocations and other energetic features, empirical measurements suggest the relationship is more complicated. Some predicted troughs in energy are found as expected while others missing or substantially reduced. Surveys of the available experimental data have indicated that simple relationships such as low Σ are misleading [1]:

It is concluded that no general and useful criterion for low energy can be enshrined in a simple geometric framework. Any understanding of the variations of interfacial energy must take account of the atomic structure and the details of the bonding at the interface. : - Sutton and Balluffi

Boundary migration

The movement of grain boundaries (HAGB) has implications for recrystallization and grain growth while subgrain boundary (LAGB) movement strongly influences recovery and the nucleation of recrystallization. Insulin crystals Recrystallization is an essentially physical process that has meanings in chemistry, metallurgy and geology. ... Grain growth refers to the increase in size of grains (crystallites) in a material at high temperature. ... Recovery is the first e-book and seventh installment of The New Jedi Order series set in the Star Wars galaxy. ...

A boundary moves due to a pressure acting on it. It is generally assumed that the velocity is directly proportional to the pressure with the constant of proportionality being the mobility of the boundary. The mobility is strongly temperature dependent and often follows an Arrhenius type relationship: The Arrhenius equation is a simple, but remarkably accurate, formula for the temperature dependence of a chemical reaction rate. ...

The apparent activation energy (Q) may be related to the thermally activated atomistic processes that occur during boundary movement. However, there are several proposed mechanisms where the mobility will depend on the driving pressure and the assumed proportionality may break down.

It is generally accepted that the mobility of low-angle boundaries is much lower than that of high-angle boundaries. The following observations appear to hold true over a range of conditions:

• The mobility of low-angle boundaries is proportional to the pressure acting on it.
• The rate controlling process is that of bulk diffusion
• The boundary mobility increases with misorientation.

Since low-angle boundaries are composed of arrays of dislocations and their movement may be related to dislocation theory. The most likely mechanism, given the experimental data, is that of dislocation climb, rate limited by the diffusion of solute in the bulk [2]. A rate is a special kind of ratio, of two measurements with different units. ... This article or section does not cite its references or sources. ...

The movement of high-angle boundaries occurs by the transfer of atoms between the neighbouring grains. The ease with which this can occur will depend on the structure of the boundary, itself dependent on the crystallography of the grains involved, impurity atoms and the temperature. It is possible that some form of diffusionless mechanism (akin to diffusionless phase transformations such as martensite) may operate in certain conditions. Some defects in the boundary, such as steps and ledges, may also offer alternative mechanisms for atomic transfer. Martensite, named after the German metallurgist Adolf Martens, is a class of hard minerals occurring as lathe- or plate-shaped crystals. ...

Since a high-angle boundary is imperfectly packed compared to the normal lattice it has some amount of free space or free volume where solute atoms may possess a lower energy. As a result a bounadry may be associated with a solute atmosphere that will retard its movement. Only at higher velocities will the boundary be able to break free of its atmosphere and resume normal motion.

Both low- and high-angle boundaries are retarded by the presence of partilces via the so-called zener pinning effect. This effect is often exploited in commercial alloys to minimise or prevent recrystallization or grain growth during heat-treatment. Zener pinning is the influence of a dispersion of fine particles on the movement of low- and high angle grain boundaries through a polycrystalline material. ... Insulin crystals Recrystallization is an essentially physical process that has meanings in chemistry, metallurgy and geology. ... Grain growth refers to the increase in size of grains (crystallites) in a material at high temperature. ... Anneal may refer to: Annealing (metallurgy), a heat treatment wherein the microstructure of a material is altered, causing changes in its properties such as strength and hardness. ...

References

1. AP Sutton, RW Balluffi (1987). "Overview no. 61: On geometric criteria for low interfacial energy". Acta Metallurgica 35 (9): 2177–2201. 
2. FJ Humphreys, M Hatherly (2004). Recrystallisation and related anealing phenomena. Elsevier. 
3. RD Doherty; DA Hughes; FJ Humphreys; JJ Jonas; D Juul Jenson; ME Kassner; WE King; TR McNelley; HJ McQueen; AD Rollett (1997). "Current Issues In Recrystallisation: A Review". Materials Science and Engineering A238: 219–274. 

See also

• Crystal
• Crystallography