Lattice impurities

The thermal strain measurements described above have the common feature of anisotropic behaviour in a supposed isotropic state (cubic structure). These observations go well beyond the short-range, static strain fields associated with the lattice impurities responsible for Huang scattering. This then raises the question of the temperature at which the lattice symmetry changes and the implications of this for the central mode scattering. 

While there is evidence in support of a lattice impurity or defect-induced, strain-field mechanism, this model has not enjoyed wide support. 

The presence of a defect in the lattice (impurity, surface, vacancy...) breaks the symmetry and induces perturbations of the electronic structure in its vicinity. Thus it is convenient to introduce the concept of local density of states (LDOS) at site i ... 

As described above, the electrons in a semiconductor can be described classically with an effective mass, which is usually less than the free electron mass. When no gradients in temperature, potential, concentration, and so on are present, the conduction electrons will move in random directions in the crystal. The average time that an electron travels between scattering events is the mean free time, Tm. Carrier scattering can arise from the collisions with the crystal lattice, impurities, or other electrons. However, during this random walk, the thermal motion is completely random, and these scattering processes will therefore produce no net motion of charge carriers on a macroscopic scale. 

Hamiltonians formally similar to Eq. (2.4) are encountered not only in the central problems of lattice dynamics and electron propagation, but also in a large variety of other problems. Among them we mention the Frenkel theory of excitons, the coupled electron-lattice impurities in the entire range of coupling, the Jahn-Teller (or pseudo-Jahn-Teller) systems, interacting spins, and so on. 

Hydrogen in metals is trapped by all maimer of lattice impurities, including other interstitials and lattice defects. Trapping reduces the mobility of hydrogen but its solubility is usually improved. This prevents precipitation, and the crystal degradation that it causes is avoided. 

Local crystal defects called point defects, appear as either impurity atoms or gaps in the lattice. Impurity atoms can occur in the lattice either at interstitial sites (between atoms in a non-lattice site) or at substitutional sites (replacing an atom in the host lattice). Lattice gaps are called vacancies and arise when an atom is missing fi om its site in the lattice. Vacancies are sometimes called Schottky defects. A vacancy in which the missing atom has moved to an interstitial position is known as a Frenkel defect. 

Diamond does have impurities which impair the optical performance. These impurities can be either a form of inclusion, or a lattice impurity such as nitrogen or boron, which are adjacent to carbon in the periodic table, have similar atomic radii and therefore, easily fit into the diamond structure. Nitrogen tends to form a nitrogen pair where the nitrogen atoms are adjacent within a unit cell or, alternatively, the nitrogen could form platelets. 

The migration of Ge as a lattice impurity was studied by using specimens which were annealed at 1149 to 166IK. The concentration profiles were evaluated by means of secondary ion mass spectrometry. The diffusion coefficients were found to range from 2.0 x 10"19 to 7.7 x lO l cm /s, and the data could be described by ... 

Lattice impurities which consist of foreign elements incorporated in the lattice, the foreign atom replacing a CEufion atom. 

The two major lattice impurities found in diamond are nitrogen and boron. Tnese two elements are the neighbors of carbon in the periodic table. They have small atomic radii and fit readily within the diamond structure. Other elemental impurities may also be present but only in extremely small amounts and their effect on the properties of the material is still uncertain... 

Measurements of the nuclear magnetic resonance (NMR) (201,202) and the electron spin resonance (ESR) (156,183,203-205) of cBN treated under various conditions have been reported. The temperature dependence of the magnetic susceptibility of cBN was studied to evaluate the contribution of the lattice impurities and defects (206). 

In general, then, anion-forming adsorbates should find p-type semiconductors (such as NiO) more active than insulating materials and these, in turn, more active than n-type semiconductors (such as ZnO). It is not necessary that the semiconductor type be determined by an excess or deficiency of a native ion impurities, often deliberately added, can play the same role. Thus if Lr ions are present in NiO, in lattice positions, additional Ni ions must also be present to maintain electroneutrality these now compete for electrons with oxygen and reduce the activity toward oxygen adsorption. 

After some typical time, r, the electron will scatter off a lattice imperfection. This imperfection might be a lattice vibration or an impurity atom. If one assumes that no memory of the event resides after the scattering... 

Materials that contain defects and impurities can exhibit some of the most scientifically interesting and economically important phenomena known. The nature of disorder in solids is a vast subject and so our discussion will necessarily be limited. The smallest degree of disorder that can be introduced into a perfect crystal is a point defect. Three common types of point defect are vacancies, interstitials and substitutionals. Vacancies form when an atom is missing from its expected lattice site. A common example is the Schottky defect, which is typically formed when one cation and one anion are removed from fhe bulk and placed on the surface. Schottky defects are common in the alkali halides. Interstitials are due to the presence of an atom in a location that is usually unoccupied. A... 

A coprecipitated impurity in which the interfering ion occupies a lattice site in the precipitate. 

Precipitate particles grow in size because of the electrostatic attraction between charged ions on the surface of the precipitate and oppositely charged ions in solution. Ions common to the precipitate are chemically adsorbed, extending the crystal lattice. Other ions may be physically adsorbed and, unless displaced, are incorporated into the crystal lattice as a coprecipitated impurity. Physically adsorbed ions are less strongly attracted to the surface and can be displaced by chemically adsorbed ions. 

Example of copredpitation (a) schematic of a chemically adsorbed inclusion or a physically adsorbed occlusion in a crystal lattice, where C and A represent the cation-anion pair comprising the analyte and the precipitant, and 0 is the impurity (b) schematic of an occlusion by entrapment of supernatant solution (c) surface adsorption of excess C. 

Theoretical studies of diffusion aim to predict the distribution profile of an exposed substrate given the known process parameters of concentration, temperature, crystal orientation, dopant properties, etc. On an atomic level, diffusion of a dopant in a siUcon crystal is caused by the movement of the introduced element that is allowed by the available vacancies or defects in the crystal. Both host atoms and impurity atoms can enter vacancies. Movement of a host atom from one lattice site to a vacancy is called self-diffusion. The same movement by a dopant is called impurity diffusion. If an atom does not form a covalent bond with siUcon, the atom can occupy in interstitial site and then subsequently displace a lattice-site atom. This latter movement is beheved to be the dominant mechanism for diffusion of the common dopant atoms, P, B, As, and Sb (26). 

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