Lattice volume

The XRD data and Zn/Cu ratio are also given for a reference aurlchalclte specimen reported In the literature ( ). All d-spaclngs In the mineral and synthetic aurlchalclte matched the literature values within the lattice volume changes (<2%) reported In Table 1. Over 30 XRD peaks were used In the XRD comparisons. The XRD analysis established that the structure of the mineral and synthetic aurlchalclte was essentially Identical. The only distinguishing features were the higher Cu content and the 1.6Z smaller unit cell volume of the mineral sample compared to the synthetic sample. 

A Japanese group [297] measured the hyperfine field at Ir nuclei in the alloys Feo.yPto.aJrx (0.03 < x < 0.2) using the Ir (73 keV) Mossbauer transition, in order to understand the mechanism associated with the decrease of the magnetic moment (and negative hyperfine field) in these alloys. The isomer shift was found to increase with increasing x, which could be rationalized by the contraction of the lattice volume. 

The equilibrium, room temperature structure of pure cobalt is hep. The fee structure is stable at high temperatures (422 °C to 1495 °C) and has been retained at room temperature by rapid solidification techniques [101], X-ray diffraction analysis was used to probe the microstructure of bulk Co-Al alloy deposits containing up to 25 a/o Al and prepared from solutions of Co(II) in the 60.0 m/o AlCfi-EtMelmCl melt. Pure Co deposits had the hep structure no fee Co was observed in any of the deposits. The addition of aluminum to the deposit caused a decrease in the deposit grain size and an increase in the hep lattice volume. A further increase in the aluminum content resulted in amorphization of the deposit [44], Because the equilibrium... 

According to the relationship between the lattice volume and Tc as described, cubic CssCgo would be an ultimate candidate for a higher Tc superconductor, but the conventional vapor-solid reaction affords only the thermodynamically stable CsCso and CS4C60 phases. In 1995, noncubic CssCgo was obtained by a solution process in liquid ammonia, and the superconductivity was observed below 40 K under an applied hydrostatic pressure of 1.4 GPa [311]. 

Interestingly, the standard entropies (and in turn heat capacities) of both phases were found to be rather similar [69,70]. Considering the difference in standard entropy between F2(gas) and the mixture 02(gas) + H2(gas) taken in their standard states (which can be extracted from general thermodynamic tables), the difference between the entropy terms of the Gibbs function relative to HA and FA, around room temperature, is about 6.5 times lower than the difference between enthalpy terms (close to 125 kJ/mol as estimated from Tacker and Stormer [69]). This indicates that FA higher stability is mostly due to the lower enthalpy of formation of FA (more exothermic than for HA), and that it is not greatly affected by entropic factors. Jemal et al. [71] have studied some of the thermodynamic properties of FA and HA with varying cationic substitutions, and these authors linked the lower enthalpy of formation of FA compared to HA to the decrease in lattice volume in FA. 

Mo are single phase, supersaturated solid solutions having an fee structure very similar to that of pure Al. Broad reflection indicative of an amorphous phase appears in deposits containing more than 6.5 atom% Mo. As the Mo content of the deposits is increased, the amount of fee phase in the alloy decreases whereas that of the amorphous phase increases. When the Mo content is more than 10 atom%, the deposits are completely amorphous. As the Mo atom has a smaller lattice volume than Al, the lattice parameter for the deposits decreases with increasing Mo content. Potentiodynamic anodic polarization experiments in deaerated aqueous NaCl revealed that increasing the Mo content for the Al-Mo alloy increases the pitting potential. It appears that the Al-Mo deposits show better corrosion resistance than most other aluminum-transition metal alloys prepared from chloroaluminate ionic liquids. 

For isotropic glasses, the activation volume tensor has two independent components. These are the bulk activation volume, which is equal to the lattice volume v, and the shear activation volume Q12. The activation volumes in uniaxial tension and compression are found to be [30]... 

Figure 8.14(a) shows the results [83] of positron lifetime measurements in a series of rare earth borocarbides. The lifetime is seen to increase linearly with the lattice volume, as obtained from x-ray diffraction measurements. Calculations [83, 84] of positron density distribution in these rare earth borocarbides indicate that the positron samples the unit cell uniformly (unlike many of the cuprate superconductors) and the calculated lifetime is seen to increase slightly with the unit cell volume as shown in the top panel. It is also noted from Figure 8.14(a) that the lifetime in YNi2B2C is significantly larger than this linear trend. 

It is also appropriate to return briefly to the work by Poser and Sanchez of which the theory just discussed was a variant. The liquid consists of r-mers and vacancies, randomly mixed, with next neighbour interactions. This energy, together with the lattice volume and r define the fluid. For the Interface Cahn-... 

Activation enthalpies for the lattice (volume) diffusion were derived between 586 and 628 kJ mol for single crystals and between 502 and 586kJ mol" for polycrystalline tungsten. Accordingly, the following equations were set up [1.79] ... 

At lower temperatures the reaction is restricted to the surfrice, and at higher temperatures die rather unstable nitrides decompose. There is no attack by anunonia from there up to the melting point. Due to the very low solubility of nitrogen in the tungsten crystal lattice, volume reactions proceed mainly via grain boundary difrusion. 

Asa one-dimensional example this was seen in Eq. (4.30) where the transformation coefficients contain the inverse square root of the total numher N of lattice atoms which is proportional to the lattice volume. 

The use of a CTE is often insufficient for an adequate description of solids when substantial amounts of defects are formed at elevated temperatures. As an example, this is the case of mixed-conducting oxides where the lattice volume is a function of both temperature and oxygen vacancies concentration. Such strain variations can often be quantified in terms of both the standard volumetric CTE (a y) and volumetric chemical expansivity (Uc) induced by the vacancy formation [26]... 

The quantity b is considered a "quasi-lattice" volume, and (V-b) is then the "free volume," vf, for the system. Bagley, Nelson, and Scigliano (37) used their experimental results to show that on mixing two components the thermodynamics of the mixing is described to the accuracy of the data by... 

In order to decide whether a reflection is partial or not for a given crystal orientation the sample reflection rocking width A or a spherical reciprocal lattice volume of radius E can be compared with a unit Ewald sphere these are given by ... 

The formation of supported MoP can be explained as follows. First, PH3 decomposes on the surface of the Mo particles to form P atoms, which chemisorb on the Mo particles and form a thin MoP layer. At the low phosphiding temperature (523 K), the P atoms cannot migrate easily into the metallic particles and will remain on the outer surface of the Mo particles. When the sample is heated to 723 K, the P atoms migrate into the Mo particles and ciystallization take place, resulting in the formation of crystalline MoP. The incorporation of phosphorus into the Mo particles resulted in an increase in the particle size from 9 to 13 nm on silica and from 6 to 8 nm on alumina, as shown by XRD (Figs. 1 and 2). Considering that the lattice volumes of Mo and MoP are 31.2 and 29.0 respectively and that there are two Mo atoms and one MoP per unit cell, the diameter of a MoP particle must be 1.23 times larger than the diameter of the Mo particle for the same number of Mo atoms. This value is close to the value we obtained. 

Braga and Grepioni have undertaken a series of analyses of the crystal structures of metal carbonyl clusters, 7t-arene complexes, mixed carbonyl n-arene complexes and some substituted derivatives [170]. Their analyses are based on examination of the packing details and motifs in the crystal structures, recognition of specific interactions, calculation of the packing potential energy for the crystal and consideration of contributions to the lattice volume. Their objective, to investigate the interplay between molecular structure and crystal structure, is very similar to the perspective in this article. 

Due to these interactions, the macroscopic swelling results in crystal lattice, which in turn affects the lattice parameter. The swelling may be associated with plastic flow (irradiation creep) that occurs in response to the ion implantation stress (Primak 1976, Volkert 1991, Brenier 1993). Expansion of lattice volumes in association with macroscopic swelling is already evidenced from the XRD results that the lattice parameter increases with irradiation fluence. However, phase transition does not occur for the present irradiation dosages investigated in the present study. 

COMMENT. The precision of this method depends strongly on just how constant the lattice volume really is. 

ITEM. MEAN CONCENTRATIOTi (g/lifcer) HEIGHT OF LATTICE, h TEMPERATURE (°C) DjO REFLECTOR nilCKNESS (cm) MEAN LATTICE RADIUS. R (cm) LATTICE VOLUME, V (liters) CRITICAL MASS OF U (g) UTTICE AS IN FIGURE... 

By interpolating the results of a series of total energy calculations in a range of different lattice volumes, the curves of enthalpy (Figure 30) and the V vs P isothermal (Figure 31) can be plotted in any pressure range easily. 

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