Lattice deformations

Structures of the f.c.c. parent and b.c.t. martensite phases are shown in Fig. 24.3. The f.c.c. parent structure contains an incipient b.c.t. structure with a c/a ratio which is higher than that of the final transformed b.c.t. martensite. The final b.c.t. structure can be formed in a very simple way if the incipient b.c.t. cell in Fig. 24.3a is extended by factors of rji = 772 = 1.12 along x[ and x 2 and compressed by 773 = 0.80 along x 3 to produce the martensite cell in Fig. 24.36. This deformation, which converts the parent phase homogeneously into the martensite phase, is known in the crystallographic theory as the lattice deformation-1 Unfortunately, 

The OA, OB, OC, and OD in the martensite remain unchanged in length in the deformation. The figure has circular symmetry around the x z axis, and all of the vectors in the system that satisfy this condition fall on two cones centered on the 3 axis with their apexes at O and passing through OA, OB, OC, and OD, respectively. To find these same vectors in the parent phase, we make use of the 

The angle 6 may be found from the equation for the AOB cone, which can be obtained by setting the equation for the unit sphere, x + x 2 + =1, equal to 

2 Undistorted Plane by Application of Additional Lattice-Invariant Deformation 

These operations do not occur separately and in any particular sequence but are simply a convenient way to conceptualize the transformation as a series of operations, each of which can be analyzed separately, but which working together produce a martensitic structure containing an invariant plane. As such, they can be imagined to occur in any sequence. For purposes of analysis, it is convenient to imagine that the lattice-invariant deformation occurs first, followed by the lattice deformation, followed finally by the rigid-body rotation. We now show that a lattice-invariant shear by slip followed by the lattice deformation analyzed above can produce an undistorted plane. 

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Regarding the emission properties, AM I/Cl calculations, performed on a cluster containing three stilbene molecules separated by 4 A, show that the main lattice deformations take place on the central unit in the lowest excited state. It is therefore reasonable to assume that the wavefunction of the relaxed electron-hole pair extends at most over three interacting chains. The results further demonstrate that the weak coupling calculated between the ground state and the lowest excited state evolves in a way veiy similar to that reported for cofacial dimers. 

More recently, D. Emin [24] developed an alternative analysis of activated hopping by introducing the concept of coincidence. The tunneling of an electron from one site to the next occurs when the energy state of the second site coincides with that of the first one. Such a coincidence is insured by the thermal deformations of the lattice. By comparing the lifetime of such a coincidence and the electron transit time, one can identify two classes of hopping processes. If the coincidence lime is much laigcr than the transit lime, the jump is adiabatic the electron has lime to follow the lattice deformations. In the reverse case, the jump is non-adia-batic. 

Central damage region, corresponding to the site where a particle first contacts with the surface, undergoes the greatest stress, which leads to crystal lattice deformation. 

Due to particles extrusion, crystal lattice deformation expands to the adjacent area, though the deformation strength reduces gradually (Figs. 10(a)-10(other hand, after impacting, the particle may retain to plow the surface for a short distance to exhaust the kinetic energy of the particle. As a result, parts of the free atoms break apart from the substrate and pile up as atom clusters before the particle. The observation is consistent with results of molecular dynamics simulation of the nanometric cutting of silicon [15] and collision of the nanoparticle with the solid surface [16]. 

When particle impacts with a solid surface, the atoms of the surface layer undergo crystal lattice deformation, and then form an atom pileup on the outlet of the impacted region. With the increase of the collision time, more craters present on the solid surface, and amorphous transition of silicon and a few crystal grains can be found in the subsurface. 

Positron annihilation spectroscopy (PAS) was first applied to investigate [Fe(phen)2(NCS)2] [77]. The most important chemical information provided by the technique relates to the ortho-positronium lifetime as determined by the electron density in the medium. It has been demonstrated that PAS can be used to detect changes in electron density accompanying ST or a thermally induced lattice deformation, which could actually trigger a ST [78]. 

Response time which can be controlled by taking into account the origin of the transition (1) fs for pure electronic transition, (2) addition of molecular deformation leads to ps response time, (3) further addition of lattice deformation leads to a slower response time > ps. 

Response temperature (operating temperature) may decrease in the foUowing order bond formation and cleavage —> molecular deformation lattice deformation —> electronic deformation such as SDW and charge-order melting. 

With mixed-valence compounds, charge transfer does not require creation of a polar state, and a criterion for localized versus itinerant electrons depends not on the intraatomic energy defined by U , but on the ability of the structure to trap a mobile charge carrier with a local lattice deformation. The two limiting descriptions for mobile charge carriers in mixed-valence compounds are therefore small-polaron theory and itinerant-electron theory. We shall find below that we must also distinguish mobile charge carriers of intennediate character. 

Fig. 4a-c Hole population, for a stationary state formed by interaction with a lattice deformation only, b environment only, c both (After Basko and Conwell [64])... 

Figure 24.4 Deformation ellipsoids involved in the lattice deformation in the...

Figure 24.9 Stereographic representation of undistorted plane produced by the lattice-invariant deformation and lattice deformation illustrated in Fig. 24.8. Traces h and h" represent initial and final positions of the undistorted plane, respectively. Their poles are at h and h". Figure referred to f.c.c. axes. After Wayman [5],...

The plane containing a and c in Fig. 24.9 is the plane in the f.c.c. phase that initially contained the vectors a" and c". If the b.c.t. phase is now given a rigid-body rotation so that a" —> a and c" —> c, the undistorted plane in the b.c.t. phase will be returned to its original inclination in the f.c.c.-axis system and will therefore be an invariant plane of the overall deformation. In the present case, this can be achieved by a rotation around the axis indicated by u in Fig. 24.9 (see Exercise 24.3). The solution of the problem is now complete. The invariant plane is known, and the orientation relationship between the two phases and total shape change can be determined from the combined effects of the known lattice-invariant deformation, lattice deformation, and rigid-body rotation. 

The problem above can also be solved analytically using tensor methods—the preferred technique when higher accuracy is required. In general, any homogeneous deformation can be represented by a second-rank tensor that operates on any vector in the initial material and transforms it into a corresponding vector in the deformed material. For example, in the lattice deformation, each vector, Ffcc, in the initial f.c.c. structure is transformed into a corresponding vector in the b.c.t. structure, Vbct, by... 

The input data for the model consist of the description of the lattice deformation and the choice of the slip system in the lattice-invariant shear. The model has successfully predicted the observed geometrical features of many martensitic transformations. The observed and calculated habit planes generally have high indices that result from the condition that they be macroscopically invariant. 

We now describe briefly martensitic transformations in three contrasting systems which illustrate some of the main features of this type of transformation and the range of behavior that is found [15]. The first is the In-Tl system, where the lattice deformation is relatively slight and the shape change is small. The second is the Fe-Ni system, where the lattice deformation and shape change are considerably larger. The third is the Fe-Ni-C system, where the martensitic phase that forms is metastable and undergoes a precipitation transformation if heated. 

Upon cooling, an In-Tl (19% Tl) alloy undergoes an f.c.c. solid solution —> f.c.t. solid solution martensitic transformation in which the lattice deformation is relatively slight, corresponding to... 

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