Diamond , thermodynamic properties

One of the first attempts to calculate the thermodynamic properties of an atomic solid assumed that the solid consists of an array of spheres occupying the lattice points in the crystal. Each atom is rattling around in a hole at the lattice site. Adding energy (usually as heat) increases the motion of the atom, giving it more kinetic energy. The heat capacity, which we know is a measure of the ability of the solid to absorb this heat, varies with temperature and with the substance.8 Figure 10.11, for example, shows how the heat capacity Cy.m for the atomic solids Ag and C(diamond) vary with temperature.dd ee The heat capacity starts at a value of zero at zero Kelvin, then increases rapidly with temperature, and levels out at a value of 3R (24.94 J-K -mol-1). The... 

Diamond, graphite, and the fullerenes differ in their physical and chemical properties because of differences in the arrangement and bonding of the carbon atoms. Diamond is the densest (3.51 vs 2.22 and 1.72 g cm-3 for graphite and Cw, respectively), but graphite is more stable than diamond, by 2.9 kJ mol-1 at 300 K and 1 atm pressure it is considerably more stable than the fullerenes (see later). From the densities it follows that to transform graphite into diamond, pressure must be applied, and from the thermodynamic properties of the two allotropes it can be estimated that they would be in equilibrium at 300 K under a pressure of —15,000 atm. Of course, equilibrium is attained extremely slowly at this temperature, and this property allows the diamond structure to persist under ordinary conditions. 

Mounet N, Marzari N (2005) First-principles determination of the structural, vibrational and thermodynamic properties of diamond, graphite, and derivatives. Phys Rev B 71 205214... 

Reassessment of the Si-B system was based primarily on the model parameters given by Fries and Lukas [25], Modifications have been made on the thermodynamic properties of the liquid and solid diamond phases Experimental liquidus data reported by Brosset and Magunsson [26], Armas et al. [27], and Male and Salanoubat [28], solid solubility data reported by Trum-bore [18], Hesse [29], Samsonov and Sleptsov [30], and Taishi et al. [52], as well as the boron activities in liquid phase measured by Zaitsev et al. [32], Yoshikawa and Morita [33], Inoue et al. [7], and Noguchi et al. [31] were all used to determine the model parameters. Figure 13.4 shows the new assessed phase equilibria in the Si-rich Si-B system. 

The direction of a chemical reaction or a phase transformation can be determined from the equilibrium thermodynamic properties of the phases involved. Note, though, that the speed of any transformation is not accessible from thermodynamics. Thermodynamics clearly states that diamond will transform into graphite at room temperature, but the rate of the reaction is insignificant. This chapter is concerned mainly with the kinetics of reactions, the speed at which they occur. Marrying this aspect with thermodynamics lies outside the scope of this chapter, but some introductory notes are given in Section S3.2. 

The effect was investigated of the nature and energy of the interatomic interaction on the structure and physical properties of crystals. Factors were studied which determine the thermodynamic properties and their temperature dependences. The effect of various parameters on the form of the frequency spectmm of phonons was investigated, taking, as an example, crystals with a diamond-type structure. The problem was also studied of the determination of the elastic constants as derivatives of the crystal energy in terms of the distribution functions of the electron density, represented by various approximations. 

Konings RJM, Benes O (2010) Thermodynamic properties of the f-elements tmd their compounds the lanthanide and actinide metals. J Phys Chem Refer Data 39 043102 Kleykamp H (2000) Thermal properties of beryllium. Thermochim Acta 345 179—184 Digonskii VV, Digonskii SV (1992) Laws of the diamond formation. Nedra, St. Peterbuig (in... 

Investigators must take care to read the foreword of the particular table they use so that they know which standard state has been employed, because most thermodynamic properties are calculated with respect to convenient scales. For example, the standard enthalpy of formation of a compound, AHf, is almost always quoted for a temperature of 298.15 K, and the enthalpy of formation of an element in its standard state must by definition be zero. It is therefore practically useful to look at a table and find, for an element, where a zero entry occurs. For example, the following values might appear C(graphite), A/ff = 0.000 kcalthmol" C(diamond), AHf = 0.4532 kcalthmol". It is clear that C(graphite) is the standard state adopted for carbon in the table under consideration. Entropy, on the other hand, is usually defined by taking as zero the entropy, at T = 0, of the crystalline form in which all the molecules are orientated regularly. Because many of the extant tables have used thermochemical calories, care will also have to be taken in the future to see that values taken from different tables are corrected to the same units. 

The table of thermodynamic properties [2] presents the standard enthalpies and Gibbs energies of formation for all materials as that of an ideal gas at298.15 K and 1 atm. That table does not include common solid minerals like NaCl, CaCOj, diamonds, or graphite. What difficulties might we encounter while attempting to insert these materials in that table ... 

Rozov, K. B., U. Berner, D. A. Kulik and L. W. Diamond (2011). Solubility and thermodynamic properties of carbonate-bearing hydrotalcite-pyroaurite solid solutions with a 3 1 Mg/(A1+Fe) mole ratio . Clays and Clay Minerals 59(3) 215-232. 

Solid carbon exists as graphite, diamond, and other phases such as the fullerenes, which have structures related to that of graphite. Graphite is the thermodynamically most stable of these allotropes under ordinary conditions. In this section, we see how the properties of the different allotropes of carbon are related to differences in bonding. 

Chapters 15 and 16 especially demonstrate the broad range of application of thermodynamics to chemical processes. In the discussions of the Haber cycle, synthesis of diamond, solubility of calcite, and the thermodynamics of metabolism, techniques are used to solve a specific problem for a particular substance. On the other hand, in the discussion of macrocyclic complexes, the description and interpretation involves the comparison of the properties of a number of complexes. This global approach is particularly helpful in the description of the energetics of ternary oxides in Chapter 15 and the stabilities of proteins and DNA in Chapter 16, where useful conclusions are obtained only after the comparison of a large amount of experimental data. 

Mechanical properties, electrical properties, thermodynamic stability, surface chemical activity, and other important parameters can all be discussed relative to the structure of the carbon network, composed of both aromatic layers and 3D-arranged (diamond-like) phases. 

The two allotropcs of carbon with particularly well defined properties are hexagonal graphite, as thermodynamically stable modification at ambient conditions, and its high-pressure, high-temperature allotrope. cubic diamond. Although both wcll-cryslalliscd forms with only very rarely be encountered in catalytic systems, it is important to recall some details about their prop-... 

The power of thermodynamics lies in its generality It rests on no particnlar model of the structure of matter. In fact, if the entire atomic theory of matter were to be found invalid and discarded (a very unlikely event ), the foundations of thermodynamics would remain nnshaken. Nonetheless, thermodynamics has some important limitations. Thermodynamics asserts that snbstances have specific mea-snrable macroscopic properties, but it cannot explain why a particular substance has particular numerical values for these properties. Thermodynamics can determine whether a process is possible, but it cannot say how rapidly the process will occur. For example, thermodynamics predicts that diamond is an unstable substance at atmospheric pressure and will eventually become graphite, but cannot predict how long this process will take. 

A thermodynamic system is in thermodynamic equilibrium if none of its macroscopic properties is changing over time. (Note Some states that appear not to be changing may not be true equilibrium states because the changes are too slow to be observed, for example, diamond turning into graphite.)... 

From thermodynamic principles, under specified conditions only one polymorph is the stable form (except at a transition point) [5], In practice, however, due to kinetic considerations, metastable forms can exist or coexist in the presence of more stable forms. Such is the case for diamond, which is metastable with regard to graphite, the thermodynamically stable form of carbon under ambient conditions. In practice, the relative stability of the various crystal forms and the possibility of interconversion between crystal forms, between crystals with a different degree of solvation and between an amorphous phase and a crystalline phase, can have very serious consequences on the life and effectiveness of a polymorphic product and the persistence over time of the desired properties (therapeutic effectiveness in the case of a drug, chromatic properties in the case of pigment, etc). 

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