Lattice atoms

The lattice atoms in the simulation are assumed to vibrate independently of one another. The displacements from the equilibrium positions of the lattice atoms are taken as a Gaussian distribution, such as... 

Fig. 5. An ion incident on a crystal lattice is deflected in nuclear coUisions with the lattice atoms and also loses energy in coUisions with electrons (7).

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. 

Phase Trigonal prismatic void in 2c Metal host lattice atoms in 12k -f- 6h(l) -1- 6h(2) Icosahedral center in 2a Octahedral void in 6g ... 

Phase Octahedral void I in 16c Octahedral void 11 in 8a Icosahedral center in 16d Metal host lattice atoms in 48f + 32e... 

Summary. Coherent optical phonons are the lattice atoms vibrating in phase with each other over a macroscopic spatial region. With sub-10 fs laser pulses, one can impulsively excite the coherent phonons of a frequency up to 50THz, and detect them optically as a periodic modulation of electric susceptibility. The generation and relaxation processes depend critically on the coupling of the phonon mode to photoexcited electrons. Real-time observation of coherent phonons can thus offer crucial insight into the dynamic nature of the coupling, especially in extremely nonequilibrium conditions under intense photoexcitation. 

Interstitial Vacant lattice Atom in normal atom site lattice site... 

J. C. Meyer, C. Kisielowski, R. Erni, M. D. Rosseii, M. F. Crommie, A. Zetti, Direct imaging of lattice atoms and topological defects in graphene membranes, Nano Lett., vol. 8, pp. 3582-3586, 2008. 

The interaction of tin oxide and water also leads to a decrease of the sensor resistance, for which several reaction mechanisms were proposed. The first mechanism involves tin and oxygen lattice atoms reacting with water [1] ... 

The dispersion curves of surface phonons of short wavelength are calculated by lattice dynamical methods. First, the equations of motion of the lattice atoms are set up in terms of the potential energy of the lattice. We assume that thejxitential energy (p can be expressed as a function of the atomic positions 5( I y in the semi-infinite crystal. The location of the nth atom can be... 

The clean siuface of solids sustains not only surface relaxation but also surface reconstruction in which the displacement of surface atoms produces a two-dimensional superlattice overlapped with, but different from, the interior lattice structure. While the lattice planes in crystals are conventionally expressed in terms of Miller indices (e.g. (100) and (110) for low index planes in the face centered cubic lattice), but for the surface of solid crystals, we use an index of the form (1 X 1) to describe a two-dimensional surface lattice which is exactly the same as the interior lattice. An index (5 x 20) is used to express a surface plane in which a surface atom exactly overlaps an interior lattice atom at every five atomic distances in the x direction and at twenty atomic distances in the y direction. 

CO is oxidized into CO2 over perovskites during CO-TPD experiments (Table 7) and this CO oxidation is promoted by Cu substitution leading to an enhancement in CO2 desorption. It was reported that CO oxidation happens via a suprafacial catalytic process involving a surface lattice atomic oxygen (0 )[5]. The CO oxidation therefore was proposed as the following step ... 

States due to different biographical structural defects existing on any real surface and playing the part of local disturbances in the strictly periodic structure of the surface (Sec. IX,A). These include vacant lattice sites in the surface layer of the lattice, atoms or ions of the lattice ejected onto the surface, and foreign atomic inclusions in the surface of the lattice (surface impurities). 

One must distinguish between macroscopic and microscopic imperfections existing on a real surface. Macroscopic imperfections are perturbations of the periodic structure covering a region of dimensions considerably greater than the lattice constant. They include cracks on the surface of the crystal, pores, and various macroscopic inclusions. We shall not deal with such imperfections here. Microscopic imperfections are perturbations of dimensions of the order of a crystallc raphic cell. Microscopic imperfections include vacancies in the surface layer of the crystal, foreign atoms or lattice atoms on the surface, different groups of such atoms (ensembles), etc. We shall limit ourselves to a consideration of this kind of imperfection. 

Fig. 5 Montage image combining an STM image of the Ag oxide structure (from bottom left) superimposed over the proposed oxide structure (from top right). The numbers, n = 1-5, correspond to the symmetrically different positions within the middle silver layer sandwiched between two O layers. Agi and Ag2 have metallic character, as they are exclusively bonded to silver atoms in the substrate below, whereas Ags, Ag4, and Ags are directly bonded to oxygen inside the oxide rings and are ionic in nature. Both Ag4 and Ags sites sit above threefold sites of the underlying (111) lattice atoms, whereas Ags occupies a top site. Reprinted with permission from Bocquet et at.. Journal of the American Chemical Society, 2003, 125, 3119. 2003, American Chemical Society.

The second type of point defect is called an impurity. Impurities can occur in two ways as an interstitial impurity, in which an atom occupies an interstitial site (see Figures 1.21, 1.22, and 1.29) or when an impurity atom replaces an atom in the perfect lattice (see Figure 1.29). In the first instance, either the same atom as in the lattice, or an impurity atom, can occupy an interstitial site, causing considerable lattice strain as the atomic planes distort slightly to accommodate the misplaced atom. The amount of strain created depends on how large the atom is relative to lattice atoms. It... 

The second type of impurity, substitution of a lattice atom with an impurity atom, allows us to enter the world of alloys and intermetallics. Let us diverge slightly for a moment to discuss how control of substitutional impurities can lead to some useful materials, and then we will conclude our description of point defects. An alloy, by definition, is a metallic solid or liquid formed from an intimate combination of two or more elements. By intimate combination, we mean either a liquid or solid solution. In the instance where the solid is crystalline, some of the impurity atoms, usually defined as the minority constituent, occupy sites in the lattice that would normally be occupied by the majority constituent. Alloys need not be crystalline, however. If a liquid alloy is quenched rapidly enough, an amorphous metal can result. The solid material is still an alloy, since the elements are in intimate combination, but there is no crystalline order and hence no substitutional impurities. To aid in our description of substitutional impurities, we will limit the current description to crystalline alloys, but keep in mind that amorphous alloys exist as well. 

When the applied electric field reaches a few volts per angstrom range, atoms on a surface, irrespective of whether they are lattice atoms or adsorbed atoms and of whether the surface temperature is high or low, may start to emit out of the surface in the form of ions. This high electric field produced evaporation phenomenon is usually called field evaporation if the surface atoms are lattice atoms, and is called field desorption if they are adsorbed atoms. From a theoretical point of view there are no fundamental differences. We will use the term field desorption for general purposes, especially for theoretical discussions, since desorption is the term used in many other adsorption-desorption phenomena. When we specifically mean removal of lattice atoms by electric field the term field evaporation will be used. Sometimes field evaporation is used where it may mean both field evaporation and field desorption. 

Map showing the exchange of an adatom with a lattice atom in cross channel adatom diffusion on the fee 110 plane. 

For much of the discussion in this chapter, the BOA is assumed valid so that the bond making/breaking is simply described by motion of nuclei on a multidimensional ground state PES. For example, dissociation of a molecule from the gas phase is described as motion on the PES from a region of phase space where the molecule is far from the surface to one with the adsorbed atoms on the surface. Conversely, the time-reversed process of associative desorption is described as motion on the PES from a region of phase space with the adsorbed atoms on the surface to one where the intact molecule is far from the surface. For diatomic dissociation/associative desorption, this PES is given as V(Z, R, X, Y, ft, cp, < ), where Z is the distance of the diatomic to the surface, R is the distance between atoms in the molecule, X and Y are the location of the center of mass of the molecule within the surface unit cell, ft and cp are the orientation of the diatomic relative to the surface normal and represent the thermal distortions of the hh metal lattice atom... 

The importance of lattice coupling in direct molecular dissociation is at present poorly understood. However, there are at least two ways in which inclusion of the lattice can affect direct dissociative adsorption. First, conversion of Et to Eq competes with translational activation in dissociation. Second, thermal distortion of lattice atoms from their equilibrium positions may affect the PES, e.g., the barriers to dissociation V ( ). These two effects can be most simply thought of as a phonon induced modulation of the barrier along the translational coordinate and in amplitude, respectively. 

---