Lattice disordering

Radiation Damage. It has been known for many years that bombardment of a crystal with energetic (keV to MeV) heavy ions produces regions of lattice disorder. An implanted ion entering a soHd with an initial kinetic energy of 100 keV comes to rest in the time scale of about 10 due to both electronic and nuclear coUisions. As an ion slows down and comes to rest in a crystal, it makes a number of coUisions with the lattice atoms. In these coUisions, sufficient energy may be transferred from the ion to displace an atom from its lattice site. Lattice atoms which are displaced by an incident ion are caUed primary knock-on atoms (PKA). A PKA can in turn displace other atoms, secondary knock-ons, etc. This process creates a cascade of atomic coUisions and is coUectively referred to as the coUision, or displacement, cascade. The disorder can be directiy observed by techniques sensitive to lattice stmcture, such as electron-transmission microscopy, MeV-particle channeling, and electron diffraction. 

CoUision cascades (see Fig. 1) lead to a distribution of vacancies, interstitial atoms, and other types of lattice disorder in the region around the ion... 

Draw ratio Degree of crystallinity Lattice disorder coefficient (k) Average crystallite size perpendicular to the crystallographic plane (hkl) Dhki (nm) ... 

B) The model of De Wolff disorder gives no explanation for the line broadening of reflections which are not affected by this type of lattice disorder. Chabre and Pannetier ascribed this effect to a micro twinning of the ramsdel-lite/rutile lattice on the planes [0 2 1] and [0 6 1], These faces are believed to be growth planes of EMD [45, 46],... 

The mean-field phase diagram in the WSL calculated by Matsen et al. [138] predicts a transition from C to the disordered state via the bcc and the fee array with decreasing /N. This was not followed here. Transitions from the C to S (at 115.7 °C), to the lattice-disordered sphere - where the bcc lattice was distorted by thermal fluctuations - and finally to the disordered state (estimation > 180 °C but not attained in the study) were observed. It was reasoned to consider the lattice-disordered spheres as a fluctuation-induced lattice disordered phase. This enlarges the window for the disordered one and causes the fee phase to disappear. Even if the latter should exist, its observation will be aggravated by its narrow temperature width of about 8 K and its slow formation due to the symmetry changes between fee and bcc spheres. 

Once the cluster expansion of the partition function has been made the remaining thermodynamic functions can be obtained as cluster expansions by taking suitable derivatives. Of particular interest are the expressions for the equilibrium concentrations of intrinsic point defects for the various types of lattice disorder. Since the partition function is a function of Nx, N2, V, and T, it is convenient for the derivation of these expressions to introduce defect chemical potentials for each of the species in the set (Nj + N2) defined, by analogy with ordinary Gibbs chemical potentials (cf. Section I), by the relation... 

By taking the minimum in Eq. (69) subject to the restrictions specified and using Lagrange undetermined multipliers (see, for example, Ref. 6), one finds a set of relationships satisfied by the defect chemical potentials. The results for the three basic types of intrinsic lattice disorder are as follows ... 

The final crystals that ultimately constitute the crude pigment product are known as primary particles. These are true single crystals with the typical lattice disorders or combinations of several lattice structures that appear as units under X ray. 

Measurements of x ) as a function of temperature should also establish whether or not static disorder dominates the apparent dynamics in a crystalline protein. If the lattice disorder term is the major con-... 

Figure 18. Lattice disorder, percent of lithium sites occupied by nickel ions in LiNijMn2Coi-y-/)2- Materials synthesized at 800 °C for Whittingham and 900 °C for Oh,278 Dahn,216.236 Kim284 unless otherwise stated.

Figure 18. Schematic model of the structure of Pt particles on an voltammogram in relation to the electrode potential. The hydrogen, double layer, and oxide regions are based on cyclic voltammetry. The lattice disorder decreases in the order D>A>C>B." (Reproduced with permission from ref 40. Copyright 1993 ElsevierSequoia S.A., Lausanne.)...

Scherrer equation is typically within 10% of that observed directly by TEM (Table 27.1), indicating that lattice disorder in the LP particles does not significantly broaden the X-ray diffraction lines. 

Obviously, the lattice disorder and the Kramer effect remain to be analyzed. An X-ray study showed that the lattice disorder in aluminum increased slightly when milled and did not change with time. Consequently, lattice disorder is not the main cause of the mechanochemical activity. 

The specimen intensity transform X is a type of convolution product of the particle intensity transform Ip and the particle orientation density function ( 1,2). The procedure that we have used to simulate Ip involves firstly the calculation of the intensity transform for an infinite particle, with appropriate allowances for random fluctuations in atomic positions and for matrix scattering. A mapping of Xp is then carried out which includes the effects of finite particle dimensions and of intraparticle lattice disorder, if this is present. A mapping of Is is then obtained from Tp by incorporating the effects of imperfect particle orientation. 

The spread of the reflections around the reciprocal lattice points due to the finite particle dimensions and to cumulative lattice disorders of the "ideally paracrystalline" type is calculated according to the formula given by Hosemann and Wilke (7). They showed that for a one-dimensional crystal the integral breadth (8) varies with the Miller index (h) of the reflection and can be approximated by the expression... 

Methods for estimating lattice distortion generally require two or more orders of a particular reflection to be present, and most polymers have only one order available. A method for estimating both crystallinity and lattice disorder, which does not need higher orders of a reflection, and indeed takes into account the whole of the diffraction trace, is that due to Buland (27). This method has been applied to many different fibres by Sotton and his colleagues, who have discussed their results both here (28) and elsewhere (12). The major problem with Ruland s method is that an arbitrary separation of the crystalline scatter from the non-crystalline scatter must be made other restrictions are that the method cannot be used to measure crystallite size and cannot give any indication of the presence of paracrystalline or intermediate-phase material. 

While many researchers believe that the above mentioned three ingredients for rl behavior to appear are more or less independent, we have argued since long [6] that the primary cause of RL behavior is the lattice disorder, which is at the origin of the occurrence of polar nanodomains and their fluctuations within the highly polarizable lattice. In order to describe disordered systems and to explore their basic thermodynamic behavior simple spin models are frequently used. The model Hamiltonian... 

The existence of free interstitial point defects forming the complements to the vacancy centers is generally not observed following irradiation at room temperature. At these temperatures the interstitials cluster together to form interstitial aggregates and dislocation loops. However, lattice disorder can slow down or prevent the aggregation process due to interstitial trapping. 

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