Growth grain

For grain growth, dependence of grain size on time 

For many polycrystalline materials, the grain diameter d varies with time t according to the relationship 

The mechanical properties at room temperature of a fine-grained metal are usually superior (i.e., higher strength and toughness) to those of coarse-grained ones. If the 

Computation of Grain Size after Heat Treatment 

When a hypothetical metal having a grain diameter of 8.2 X 10 mm is heated to 500°C for 12.5 min, the grain diameter increases to 2.7 x 10 mm. Compute the grain diameter when a specimen of the original material is heated at 500°C for 100 min. Assume the grain diameter exponent n has a value of 2. 

For 2D grain growth, kinetic models generally predict a parabolic growth law of the form [13] 

Solution Starting with the parabolic grain growth law (Equation 7.16), we can explicitly incorporate the Arrhenius-type temperature dependence of the growth kinetics into the growth constant C, giving 

The next subject we will discuss is that of grain growth. The simplest way to illustrate this factor is through the sintering behavior of aggregates, as shown in the following diagram  

Even where a metal is melted and then cast, nucleation leads to formation of many fine particles in the sub-solidus (partially solidified) state. This leads to grain growth in the solid metal, thereby lowering its strength. Sometimes, special additives are added to the melt to slow nucleation 

Note that this involves a precipitation mechanism where aggregates form. Grain boundaries form junctions between grains within the particle, due to vacancy and line-defect formation. This situation arises because of the 2nd Law of Thermodynamics (Entropy). Thus, if crystallites are formed by precipitation from solution, the product will be a powder consisting of many small particles. Their actual size will depend upon the methods used to form them. Note that each crystallite can be a single-crystal but, of necessity, will be limited in size. 

Another example is our old friend, BaCDs. If we fire this solid compound in air at a very high temperature for a long time, we get several changes. First, it decomposes to very fine particles of BaO. These fine particles 

Let us now consider the thermodynamics of sintering. There are two types of sintering which are distinguished by the change in volume which occurs. These are  

The above analyses were restricted to transport across a free surface. However, the Gibbs-Thomson equation is applicable to grain boundaries as well as free surfaces. The application to grain growth in polycrystalline materials is described in the next section. 

Therefore there is a driving force for the transport of matter from grain 1 to grain 2 such that grain 1 will shrink and grain 2 will grow. 

A simple kinetic analysis [5] gives the change in the average grain size with time as 

The reduction in the free surface energy of the system is achieved by reducing the surface area by one or a combination of the following three processes  

Methods that can be used to produce a large grain structure in UO2 can be divided into the following categories [5]  

The simplest model of grain growth considers the movement of a single grain boundary in a pure, dense material. There is a free energy difference AG across a curved grain boundary  

AG is the difference in free energy ri, T2 are the principal radii of curvature y is the surface energy  

Vm is the molar volume of atoms moving across the boundary. 

As the energy of the interfaces has the form yA, where y is the specific energy of the interface and A is the surface area of the interface, the system s energy can be reduced using two borderline cases  

In addition to the possibility of being homogenous or, on the contrary, heterogenous, the microstracture can be more or less isotropic. For the simple case of a mono-phased polycrystal, we can distinguish four cases  

The majority of ceramics are multiphased materials that comprise both ciystallized and vitreous phases. Porcelain thus consists of silicate glass reinforced by acicular crystals of crystallized muUite, but we can also observe millimetric ciystal agglomerates with a very porous microstracture (iron and steel refiactoiy materials), or fine grained polycrystals ( 10 pm) without vitreous phases and with very low porosity (hip prosthesis in alumina or zirconia). It should be reiterated that, in addition to the chemical nature of the compound(s) in question, it is the microstracture of the material (size and shape of the grains, rate and type of porosity, distribution of the phases) that controls the properties. 

In addition to its role in the coupling between densification and grain growth, the size of the grains (d ) of the sintered ceramics is, together with the porosity, the essential microstructural parameter. We can give five examples  

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Unlike melting and the solid-solid phase transitions discussed in the next section, these phase changes are not reversible processes they occur because the crystal stmcture of the nanocrystal is metastable. For example, titania made in the nanophase always adopts the anatase stmcture. At higher temperatures the material spontaneously transfonns to the mtile bulk stable phase [211, 212 and 213]. The role of grain size in these metastable-stable transitions is not well established the issue is complicated by the fact that the transition is accompanied by grain growth which clouds the inteiyDretation of size-dependent data [214, 215 and 216]. In situ TEM studies, however, indicate that the surface chemistry of the nanocrystals play a cmcial role in the transition temperatures [217, 218]. 

To confirm that the matrix is amorphous following primary solidification, isothermal dsc experiments can be performed. The character of the isothermal transformation kinetics makes it possible to distinguish a microcrystalline stmcture from an amorphous stmcture assuming that the rate of heat released, dH/dt in an exothermic transformation is proportional to the transformation rate, dxjdt where H is the enthalpy and x(t) is the transformed volume fraction at time t. If microcrystals do exist in a grain growth process, the isothermal calorimetric signal dUldt s proportional to, where ris... 

The stmcture of the polysihcon depends on the dopants, impurities, deposition temperature, and post-deposition heat annealing. Deposition at less than 575°C produces an amorphous stmcture deposition higher than 625°C results in a polycrystalline, columnar stmcture. Heating after deposition induces crystallization and grain growth. Deposition between 600 and 650°C yields a columnar stmcture having reasonable grain size and (llO)-preferred orientation. 

Lead—silver alloys show significant age hardening when quenched from elevated temperature. Because of the pronounced hardening which occurs using small amounts of silver, the content of silver as an impurity in pure lead is restricted to less than 0.0025 wt % in most specifications. Small additions of silver to lead produces high resistance to recrystaUization and grain growth. 

Wrought or extmded lead—teUurium (0.035—0.10 wt %) aUoys produce extremely fine grains. The binary aUoy is, however, susceptible to recrysta11i2ation. The addition of copper or sUver reduces grain growth and retains the fine grain si2e. Because teUurium is a poison for sealed lead—acid batteries, the teUurium content of lead and lead aUoys used for such purposes is usuaUy restricted to less than 1 ppm. 

In the General Electric—Allegheny Ludlum (GE—AT,) process (18), boron and nitrogen with sulfur or selenium are used as grain-growth inhibitors. 

H. H. Hausner "Grain Growth During Sintering" in Special Report No. 58 of the Iron and Steel Institute, London, 1954, pp. 102—112. 

The matte can be treated in different ways, depending on the copper content and on the desired product. In some cases, the copper content of the Bessemer matte is low enough to allow the material to be cast directly into sulfide anodes for electrolytic refining. Usually it is necessary first to separate the nickel and copper sulfides. The copper—nickel matte is cooled slowly for ca 4 d to faciUtate grain growth of mineral crystals of copper sulfide, nickel—sulfide, and a nickel—copper alloy. This matte is pulverized, the nickel and copper sulfides isolated by flotation, and the alloy extracted magnetically and refined electrolyticaHy. The nickel sulfide is cast into anodes for electrolysis or, more commonly, is roasted to nickel oxide and further reduced to metal for refining by electrolysis or by the carbonyl method. Alternatively, the nickel sulfide may be roasted to provide a nickel oxide sinter that is suitable for direct use by the steel industry. 

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