Atomic Vacancy Formation

As an element of structural defects, atomic vacancies, or point defects are very important in materials and have remarkable effect on the physical properties of a material such as electrical resistance, heat capacity, and mechanical strength. A vacancy formation is associated with local strain, densification, quantum entrapment, and polarization. 

Atomic vacancy formation needs energy to break all the bonds of the specific atom to its surroundings, which is the same to the atomic E though structure deformation or relaxation is involved upon vacancy formation. However, the structural deformation or relaxation costs no additionally external energy. Vacancy volume should be greater than the atomic size because of the atomic CN imperfection induced contraction of bonds surrounding the vacancy. The measured Eb is subject to accuracy. For instance, the Eb of a Mo atom varies from 2.24 to 3.30 eV [8]. 

Theoretical efforts can predict the Eb of limited numbers of metals and alloys, but the theories are rather complicated [9]. 

Brooks [10] assumed the crystal is isotropic and considered the formation of a vacancy as an equivalent to creating new surface, equal to the area of one unit cell, being approximately the spherical surface of the atomic volume. He also assumed that the surface tension of the hole would shrink the vacancy size by distorting the rest of the crystal elastically. Then, the for atomic vacancy formation inside a bulk solid equals the minimum of the sum of the increased surface energy and distortion energy, 

G is the shear modulus and yo the surface energy per unit area surrounding the vacancy. Introducing the size effect to the do, G, and yo, the relative change in the mean in a nanoparticle becomes. 

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In addition, Xie et al. [11] derived an expression for the size dependence of surface energy of nanostructures y = nS with d being the mean atomic radius and E- the atomic vacancy formation energy [12]. 

The diffusion coefficient corresponding to the measured values of /ch (D = kn/4nRn, is the reaction diameter, supposed to be equal to 2 A) equals 2.7 x 10 cm s at 4.2K and 1.9K. The self-diffusion in H2 crystals at 11-14 K is thermally activated with = 0.4 kcal/mol [Weinhaus and Meyer 1972]. At T < 11 K self-diffusion in the H2 crystal involves tunneling of a molecule from the lattice node to the vacancy, formation of the latter requiring 0.22 kcal/mol [Silvera 1980], so that the Arrhenius behavior is preserved. Were the mechanism of diffusion of the H atom the same, the diffusion coefficient at 1.9 K would be ten orders smaller than that at 4.2 K, while the measured values coincide. The diffusion coefficient of the D atoms in the D2 crystal is also the same for 1.9 and 4.2 K. It is 4 orders of magnitude smaller (3 x 10 cm /s) than the diffusion coefficient for H in H2 [Lee et al. 1987]. 

Another example of the use of neutron diffraction to understand the role of atomic vacancies in producing a superconducting metal oxide phase is work that has been performed on Bao Kq 4fii03. This work demonstrates that at the synthesis temperature (700° C), under the proper conditions, oxygen vacancies are created to allow the formation of the parent phase with bismuth largely in the +3 oxidation state. The presence of the vacancies allows the incorporation of potassium in the... 

Table 4 Tight-binding vacancy formation energies compared to first-principles calculations and experiment. Energies were computed using a 108 atom supercell. The experimental column shows a range of energies if several experiments have been tabulated. Otherwise the estimated error in the experiment is given.

The anodic dissolution of metals on surfaces without defects occurs in the half-crystal positions. Similarly to nucleation, the dissolution of metals involves the formation of empty nuclei (atomic vacancies). Screw dislocations have the same significance. Dissolution often leads to the formation of continuous crystal faces with lower Miller indices on the metal. This process, termed facetting, forms the basis of metallographic etching. 

By definition, the rate at which the tracer atom is displaced by a surface vacancy is the product of the vacancy density at the site next to the tracer times the rate at which vacancies exchange with the tracer atom. For the case where the interaction between the tracer atom and the vacancy is negligible, the activation energy obtained from the temperature dependence of the total displacement rate equals the sum of the vacancy formation energy EF and the vacancy diffusion barrier ED. When the measurements are performed with finite temporal resolution and if there is an interaction present between the vacancy and the indium atom, this simple picture changes. 

The importance of the measurements that we have presented so far for the diffusion of embedded tracer atoms becomes evident when we now use these measurements and the model discussed in Section 3 to evaluate the invisible mobility of the Cu atoms in a Cu(00 1) terrace. The results presented in Section 2 imply that not just the tracer atom, but all atoms in the surface are continuously moving. From the tracer diffusion measurements of In/Cu(0 0 1) we have established that the sum of the vacancy formation energy and the vacancy diffusion barrier in the clean Cu(0 01) surface is equal to 717 meV. For the case of self-diffusion in the Cu(0 01) surface we can use this number with the simplest model that we discussed in Section 3.2, i.e. all atoms are equal and no interaction between the vacancy and the tracer atom. In doing so we find a room temperature hop rate for the self-diffusion of Cu atoms in a Cu(00 1) terrace of v = 0.48 s-1. In other words, every terrace Cu atom is displaced by a vacancy, on average, about once per two seconds at room temperature and about 200times/sec at 100 °C. We illustrate this motion by plotting the calculated average displacement rate of Cu terrace atoms vs. 1 /kT in Fig. 14. 

The energetics of non-stoichiometric surfaces can be characterized in two different ways. One consists in defining the vacancy formation energy Evf. It is the energy required to extract one neutral oxygen atom from the... 

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