Phase transformations,

Phase transitions are processes where small causes have large effects. Small changes in intensive variables (P, T,nt) can result in large changes of the extensive macroscopic properties of a system. Some specific quantities exhibit singularities at the transition point. 

These two different ways of ordering require different driving forces. In case 1), macroscopic transport occurs. The driving force is therefore the chemical potential 

Most chemical reactions occur by a change in the configurational order (AS 0). Compared to fluids, crystalline reactants already have a low entropy and thus solid state reactions are normally exothermic In this sense, order-disorder reactions are in no way special, except that they occur in homophase crystals. 

It is always convenient to use intensive thermodynamic variables for the formulation of changes in energetic state functions such as the Gibbs energy G. Since G is a first order homogeneous function in the extensive variables V, S, and rtk, it follows that [H. Schmalzried, A.D. Pelton (1973)] 

The foregoing classification is not without ambiguity. For example, it is common practice to call the reaction A - B +C° (see Fig. 6-1) induced by decreasing the temperature a phase transformation. The similar (peritectoid) reaction C = a+fi (Fig. 12-2) induced by a temperature increase, however, is named a decomposition reaction. In addition, the isothermal reaction AO = A+j02, which occurs if the intensive variable fio2 is decreased so that AO decomposes, is called a metal oxide reduction. It is thus categorized as a genuine heterogeneous solid state reaction (the 

All of our analysis of the Cu crystal structure has been based on the reasonable idea that the crystal structure with the lowest energy is the structure preferred by nature. This idea is correct, but we need to be careful about how we define a materials energy to make it precise. To be precise, the preferred crystal structure is the one with the lowest Gibbs free energy, G G(P, T). The Gibbs free 

In solids, the first two terms tend to be much larger than the entropic contribution from the last term in this expression, so 

In Sections 2.1 -2.3 we interpreted the minimum in a plot of the DFT energy as a function of the lattice parameter as the preferred lattice parameter for the crystal structure used in the calculations. Looking at Eqs. (2.8) and (2.11), you can see that a more precise interpretation is that a minimum of this kind defines the preferred lattice parameter at P 0 and T 0. 

An interesting consequence of Eq. (2.10) is that two crystal structures with different cohesive energies can have the same Gibbs free energy if A coh — P AT. Comparing this condition with Eq. (2.11), you can see that 

Perform calculations to determine whether Pt prefers the simple cubic, fee, or hep crystal structure. Compare your DFT-predicted lattice parameter ) of the preferred structure with experimental observations. 

The effect of such a transformation on a pressure-volume relation and on wave profiles is shown in Fig. 2.12. Above the transformation, its characteristics dominate the wave profile. At sufficiently high pressure, the peak pressure wave will move at higher speeds and a strong shock regime can be encountered. 

When the pressures to induce shock-induced transformations are compared to those of static high pressure, the values are sufficiently close to indicate that they are the same events. In spite of this first-order agreement, differences between the values observed between static and shock compression are usually significant and reveal effects controlled by the physical and chemical nature of the imposed deformation. Improved time resolution of wave profile measurements has not led to more accurate shock values rather. 

Above the critical pressure, a transformation is initiated, but, unlike isothermal equilibrium transitions, a finite pressure and volume change is typically required to complete the transition. Such a behavior is clear evidence for nonequilibrium behavior. 

We can anticipate that the highly defective lattice and heterogeneities within which the transformations are nucleated and grow will play a dominant role. We expect that nucleation will occur at localized defect sites. If the nucleation site density is high (which we expect) the bulk sample will transform rapidly. Furthermore, as Dremin and Breusov have pointed out [68D01], the relative material motion of lattice defects and nucleation sites provides an environment in which material is mechanically forced to the nucleus at high velocity. Such behavior was termed a roller model and is depicted in Fig. 2.14. In these catastrophic shock situations, the transformation kinetics and perhaps structure must be controlled by the defective solid considerations. In this case perhaps the best published succinct statement 

Reviews of shock-induced phase transformations are summarized in Table 2.4. The review of Duvall and Graham [77D01] emphasizes the thermo- 

Due to the imaging conditions, only the regions with the alpha (a) stacking display lattice fringes. The terminations of the fringes show the mophology of 

With the CaO additions has been obtained a ceramic of mullite + zirconia + anorthite showing Kic values of 4.5 MPa m / in which HREM has been carried out [25]. The observation by conventional TEM depicts twinned crystals in both zirconia grains and anorthite precipitated from the glassy phase produced via reaction sintering. There are two types of zirconia composing the microstructure of these ceramics, viz intergranular with 1-3 yum size located between the mullite crystals and intragranular with very small (0.1-0.5 um size) rounded crystals. 

At higher magnifications in HREM, the mullite lattice fringes (d(llO) = 0.55 nm) corresponding to the periodicity of (110) planes have been observed (Fig. 7). Similarly, the cross fringes of 0.508 nm corresponding to (010) planes of the monoclinic zirconia are shown in Fig. 7. 

The zirconia/mullite interphase has been examined indicating a coherent relation between both types of crystals, as is shown in Fig. 8. Only the A labeled grain shows this coherency while the B grain oriented with respect to the other does not show this effect. Therefore, the HREM allows us to distinguish the critical orientations of crystals at interphases. Domains of closure interpenetrating into the zirconia are visible at the boundary [25]. 

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It is noted in Sections XVII-10 and 11 that phase transformations may occur, especially in the case of simple gases on uniform surfaces. Such transformations show up in q plots, as illustrated in Fig. XVU-22 for Kr adsorbed on a graphitized carbon black. The two plots are obtained from data just below and just above the limit of stability of a solid phase that is in registry with the graphite lattice [131]. 

Chandler D, Weeks J D and Andersen H C 1983 The van der Waals picture of liquids, solids and phase transformations Science 220 787... 

Riter J R Jr 1973 Shock-induced graphite.far.wurtzite phase transformation in boron nitride and implications for stacking graphitic boron nitride J. Chem. Phys. 59 1538... 

Sheu S-Y, Mou C-Y and Lovett R 1995 How a solid can be turned into a gas without passing through a first-order phase transformation Phys. Rev. E 51 R3795-8... 

Kumar K P, Keizer K and Burggraaf A J 1994 Stabiiization of the porous texture of nanostructured titania by avoiding a phase transformation J. Mater. Sc/. Lett. 59... 

Penn R L and Banfieid J F 1999 Formation of rutiie nuciei at anatase (112) twin interfaces and the phase transformation mechanism in nanocrystaiiine titania Am. Miner. 84 871... 

This class of smart materials is the mechanical equivalent of electrostrictive and magnetostrictive materials. Elastorestrictive materials exhibit high hysteresis between strain and stress (14,15). This hysteresis can be caused by motion of ferroelastic domain walls. This behavior is more compHcated and complex near a martensitic phase transformation. At this transformation, both crystal stmctural changes iaduced by mechanical stress and by domain wall motion occur. Martensitic shape memory alloys have broad, diffuse phase transformations and coexisting high and low temperature phases. The domain wall movements disappear with fully transformation to the high temperature austentic (paraelastic) phase. 

Crack Reflection. Crack deflection can result when particles transform ahead of a propagating crack. The crack can be deflected by the locali2ed residual stress field which develops as a result of phase transformation. The force is effectively reduced on the deflected portion of the propagating crack resulting in toughening of the part. 

Table 16. Phase Transformations in Binary Aluminum Alloys...

In engineering appHcations, the transport processes involving heat and mass transfer usually occur in process equipment involving vapor—gas mixtures where the vapor undergoes a phase transformation, such as condensation to or evaporation from a Hquid phase. In the simplest case, the Hquid phase is pure, consisting of the vapor component alone. 

Aging. When a gel is maintained in its pore Hquid, the stmcture and properties continue to change long after the gel point. This process is called aging. Four aging mechanisms can occur, singly or simultaneously polycondensation, syneresis, coarsening, and phase transformation (9,21). 

Eor the ferrite grades, it is necessary to have at least 12% chromium and only very small amounts of elements that stabilize austenite. Eor these materials, the stmcture is bcc from room temperature to the melting point. Some elements, such as Mo, Nb, Ti, and Al, which encourage the bcc stmcture, may also be in these steels. Because there are no phase transformations to refine the stmcture, brittieness from large grains is a drawback in these steels. They find considerable use in stmctures at high temperatures where the loads are small. 

Pure barium is a silvery-white metal, although contamination with nitrogen produces a yellowish color. The metal is relatively soft and ductile and may be worked readily. It is fairly volatile (though less so than magnesium), and this property is used to advantage in commercial production. Barium has a bcc crystal stmcture at atmospheric pressure, but undergoes soHd-state phase transformations at high pressures (2,3). Because of such transformations, barium exhibits pressure-induced superconductivity at sufftciendy low temperatures (4,5). 

Research. A significant impact on research at high pressure has come about with the use of gem quaHty diamonds as Bridgman-type anvils in a smaU compact high pressure device (40—42). With this type of apparatus, pressures greater than those at the center of the earth (360 GPa = 3.6 Mbars) have been reached, and phase transformations of many materials have been studied. Because of the x-ray transparency of diamond, it is possible to determine the stmcture of the phases under pressure. Because of the strenuous environment, crystals selected for this appHcation have to be of very high quaHty. 

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