Length change

The only tenn in this expression that we have not already seen is a, the vibration-rotation coupling constant. It accounts for the fact that as the molecule vibrates, its bond length changes which in turn changes the moment of inertia. Equation B1.2.2 can be simplified by combming the vibration-rotation constant with the rotational constant, yielding a vibrational-level-dependent rotational constant. 

Precise measurements of the dimensional stabiUty of low expansion materials indicate that vitreous siUcas, eg. Corning 7940 and Homosil, display a length change at 25°C of approximately 0.5 parts per biUion (ppb) per day (145). 

Dimensional Stability. Dimensional stabiHty refers to how a fiber changes length under the influence of load or heat. Conventionally described in terms of fiber shrinkage (ASTM D885-64) at a defined temperature, the term has also come to mean time dependent length change or creep. 

The gravity take-up must be used when handling hot materials in order to maintain chain and sprocket tooth engagement, as the chain length changes with thermal expansion. 

M. De Crescenzi. Phys. Rev. Letts. 30,1949,1987. Use of surface electron energy-loss fine structure (SEELFS) to determine oxygen-nickel bond length changes for oxygen absorbed on Ni (100) on a function of coverage from 0 to 1.0 monolayer. 

In this example, the two bond lengths changed only slightly, while the C-C-H bond angle increased by about 0.3 degrees. 

The IRC calculation confirms that the preceding transition structure does indeed connect these two minima. The C-Cl bond length increases as it proceeds in the forward direction along the reaction path, and this bond decreases in length in the reverse direction (naturally, the C-F bond length changes in the complementary manner). 

During the service life of a well, tubing can experience various combinations of pressures and temperatures that result in tubing length changes. The four basic effects to consider are as follows ... 

AL = length change necessary to bring the end of the tubing to the packer... 

The freely-jointed chain considered previously has no internal restraint, and hence, its internal energy is zero regardless of its present configuration. The entropy (S) is not constant, however, since the number of available configurations decreases with the chain end separation distance. The variation which follows from chain length change by a small amount (dr) at constant temperature (T) is given by the Boltzmann rule of statistical thermodynamics ... 

Molecular orbital calculations for the parent vinyl cation, Cj H3, were first reported by Hoffmann (161), who used the extended Hiickel method, and more recently by Yonezawa and co-workers (162), who used a semiempirical SCF procedure. Both treated the problem of classical, 172 (R = H), versus bridged structures, 173, but the methods suffered from their inability to account satisfactorily for bond-length changes, and neither discussed the question of linear, 172a, versus bent, 172b, structures. 

Dielectric elastomers are insulating, mbber-Uke structures, capable of undergoing reversible length change to a large extent and produce usable works. A dielectric elastomer actuator (DEA) works like an electrical motor by virtue of linear motion rather than rotation. 

AS = 2). Indeed, an average metal-ligand bond length change between the LS and HS states AR 0.17 A has been found for iron(II) complexes [6]. For... 

Bond length differences between HS and LS isomers have been determined for a number of iron(II), iron(III) and cobalt(II) complexes on the basis of multiple temperature X-ray diffraction structure studies [6]. The available results have been collected in Table 17. Average values for the bond length changes characteristic for a particular transition-metal ion have been extracted from these data and are obtained as AR 0.17 A for iron(II) complexes, AR 0.13 A for iron(III) complexes, and AR = 0.06 A for cobalt(II) complexes. These values may be compared with the differences of ionic radii between the HS and LS forms of iron(II), iron(III) and cobalt(II) which were estimated some time ago [184] as 0.16, 0.095, and 0.085 A, respectively. 

A quantum-mechanical description of spin-state equilibria has been proposed on the basis of a radiationless nonadiabatic multiphonon process [117]. Calculated rate constants of, e.g., k 10 s for iron(II) and iron(III) are in reasonable agreement with the observed values between 10 and 10 s . Here again the quantity of largest influence is the metal-ligand bond length change AR and the consequent variation of stretching vibrations. 

Length change of hardened hydraulic-cement mortar and... 

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