Translation of atoms

Long-range order is the most distinct characteristic of crystalline materials and is simply the regnlar or periodic repetition (by means of translation) of atoms or molecnles in three dimensions. Long-range order determines the structural anisotropy and macroscopic properties of crystalline solids. 

Initially the pseudo-elastic material is in its austenitic phase at room temperature. Initially the material in the austenitic phase deforms like a conventional material linear elastic under load. With increasing loads a stress-induced transformation of the austenitic to the martensitic phase is initiated at the pseudo-yield stress Rpe- This transformation is accompanied with large reversible strains at nearly constant stresses, resulting in a stress plateau shown in Fig. 6.53. At the end of the stress plateau the sample is completely transformed into martensite. Additional loading passing the upper stress plateau causes a conventional elastic and subsequently plastic deformation of the martensitic material. If the load is decreased within the plateau and the stress reaches the lower stress level a reverse transformation from martensite to austenite occurs. Since the strains are fully reversible the material and the sample respectively is completely recovered to its underformed shape. These strains are often called pseudo-elastic because the reversible deformation is caused by a reversible phase transformation and is not only due to a translation of atoms out of their former equilibrium position [74]. 

Although a diatomic molecule can produce only one vibration, this number increases with the number of atoms making up the molecule. For a molecule of N atoms, 3N-6 vibrations are possible. That corresponds to 3N degrees of freedom from which are subtracted 3 translational movements and 3 rotational movements for the overall molecule for which the energy is not quantified and corresponds to thermal energy. In reality, this number is most often reduced because of symmetry. Additionally, for a vibration to be active in the infrared, it must be accompanied by a variation in the molecule s dipole moment. 

The length or dimension of the RDF code is independent of the number of atoms and the size of a molecule, unambiguous regarding the three-dimensional arrangement of the atoms, and invariant against translation and rotation of the entire molecule. 

Coordin ates of atom s can he set by n orm al translation orrotation of HyperCh cm molecules, fo set initial velocities, however, it is necessary to edit th e H l. file explicitly. The tin it o f velocity in the HIN file is. An gstrom s/picosecon d.. Areact.hin file and a script react.scr are in eluded with HyperChem to illustrate one simple reacting trajectory. In order to have these initial velocities used in a trajectory the Restart check box of the Molecular Dynamics Option s dialog box must he checked. If it is n ot, the in itial velocities in the HIN file will be ignored and a re-equilibration to the tern peratiire f of th e Molecular Dyn am ics Option s dialog box will occur. This destroys any imposed initial conditions on the molecular dynamics trajectory. 

From the information on the right side of the C3v eharaeter table, translations of all four atoms in the z, x and y direetions transform as Ai(z) and E(x,y), respeetively, whereas rotations about the z(Rz), x(Rx), and y(Ry) axes transform as A2 and E. Henee, of the twelve motions, three translations have A and E symmetry and three rotations have A2 and E symmetry. This leaves six vibrations, of whieh two have A symmetry, none have A2 symmetry, and two (pairs) have E symmetry. We eould obtain symmetry-adapted vibrational and rotational bases by allowing symmetry projeetion operators of the irredueible representation symmetries to operate on various elementary eartesian (x,y,z) atomie displaeement veetors. Both Cotton and Wilson, Deeius and Cross show in detail how this is aeeomplished. 

Electronic spectroscopy is the study of transitions, in absorption or emission, between electronic states of an atom or molecule. Atoms are unique in this respect as they have only electronic degrees of freedom, apart from translation and nuclear spin, whereas molecules have, in addition, vibrational and rotational degrees of freedom. One result is that electronic spectra of atoms are very much simpler in appearance than those of molecules. 

Molecular Nature of Steam. The molecular stmcture of steam is not as weU known as that of ice or water. During the water—steam phase change, rotation of molecules and vibration of atoms within the water molecules do not change considerably, but translation movement increases, accounting for the volume increase when water is evaporated at subcritical pressures. There are indications that even in the steam phase some H2O molecules are associated in small clusters of two or more molecules (4). Values for the dimerization enthalpy and entropy of water have been deterrnined from measurements of the pressure dependence of the thermal conductivity of water vapor at 358—386 K (85—112°C) and 13.3—133.3 kPa (100—1000 torr). These measurements yield the estimated upper limits of equiUbrium constants, for cluster formation in steam, where n is the number of molecules in a cluster. 

S. V. EUnson and K. L. Petrov, Zirconium, Chemical and Physical Methods of Analysis, Main Administration on the Use of Atomic Energy at the Council of Ministers, Moscow, 1960 English translation. Office of Technical Services, Dept, of Commerce, Washington, D.C., 1962. 

The other major defects in solids occupy much more volume in the lattice of a crystal and are refeiTed to as line defects. There are two types of line defects, the edge and screw defects which are also known as dislocations. These play an important part, primarily, in the plastic non-Hookeian extension of metals under a tensile stress. This process causes the translation of dislocations in the direction of the plastic extension. Dislocations become mobile in solids at elevated temperamres due to the diffusive place exchange of atoms with vacancies at the core, a process described as dislocation climb. The direction of climb is such that the vacancies move along any stress gradient, such as that around an inclusion of oxide in a metal, or when a metal is placed under compression. 

Figure 18.12 The electron-density map is interpreted by fitting into it pieces of a polypeptide chain with known stereochemistry such as peptide groups and phenyl rings. The electron density (blue) is displayed on a graphics screen in combination with a part of the polypeptide chain (red) in an arbitrary orientation (a). The units of the polypeptide chain can then be rotated and translated relative to the electron density until a good fit is obtained (b). Notice that individual atoms are not resolved in such electron densities, there are instead lumps of density corresponding to groups of atoms. [Adapted from A. Jones Methods Enzym. (eds. H.W. Wyckoff, C.H. Hirs, and S.N. Timasheff) 115B 162, New York Academic Press, 1985.]...

In the latter the surfactant monolayer (in oil and water mixture) or bilayer (in water only) forms a periodic surface. A periodic surface is one that repeats itself under a unit translation in one, two, or three coordinate directions similarly to the periodic arrangement of atoms in regular crystals. It is still not clear, however, whether the transition between the bicontinuous microemulsion and the ordered bicontinuous cubic phases occurs in nature. When the volume fractions of oil and water are equal, one finds the cubic phases in a narrow window of surfactant concentration around 0.5 weight fraction. However, it is not known whether these phases are bicontinuous. No experimental evidence has been published that there exist bicontinuous cubic phases with the ordered surfactant monolayer, rather than bilayer, forming the periodic surface. 

Crystals are sohds. Sohds, on the other hand can be crystalhne, quasi-crystal-hne, or amorphous. Sohds differ from liquids by a shear modulus different from zero so that solids can support shearing forces. Microscopically this means that there exists some long-range orientational order in the sohd. The orientation between a pair of atoms at some point in the solid and a second (arbitrary) pair of atoms at a distant point must on average remain fixed if a shear modulus should exist. Crystals have this orientational order and in addition a translational order their atoms are arranged in regular lattices. 

---