Allotropic transformation

Thin films (qv) of lithium metal are opaque to visible light but are transparent to uv radiation. Lithium is the hardest of all the alkaH metals and has a Mohs scale hardness of 0.6. Its ductiHty is about the same as that of lead. Lithium has a bcc crystalline stmcture which is stable from about —195 to — 180°C. Two allotropic transformations exist at low temperatures bcc to fee at — 133°C and bcc to hexagonal close-packed at — 199°C (36). Physical properties of lithium are Hsted ia Table 3. 

In the cP2-W type (CN 8) structure Vsph is 0.68 Vat (only a portion of the available space is occupied by the atomic sphere ). In the cF4-Cu type and in the ideal hP2-Mg type (CN 12) structures, Vsph is 0.74 Vat. Considering now the previously reported relationship between RCs n and i CN8, we may compute for a given element very little volume (Vat) change in the allotropic transformation from a form with CN 12 to the form with CN 8, because the radius variation is nearly... 

Table 5.8. Alkaline earth metals crystal structures, lattice parameters of their allotropes and calculated densities. When not differently indicated the allotropic transformations refer to room pressure.

Depending on the data available, Eqs (6.17)-(6.23) reproduce experimental pressure effects with considerable accuracy in many cases. In particular, Eq. (6.18) can be used to confirm entropy data derived using more conventional techniques and can also provide data for metastable allotropes. Ti again provides a leading example, as pressure experiments revealed that the u -phase, previously only detected as a metastable product on quenching certain Ti alloys, could be stabilised under pressure (Fig. 6.14). Extrapolation of the P/w transus line yields the metastable allotropic transformation temperature at which the / -phase would transform to w in the absence of the a-phase, while die slope of the transus lines can be used to extract a value for the relevant entropy via Eq. (6.18). 

The allotropy of elemental iron plays an important role in the formation of iron alloys. Upon solidification from the melt, iron undergoes two allotropic transformations (see Figure 2.9). At 1539°C, iron assumes a BCC structure, called delta-iron (5-Fe). Upon further cooling, this structure transforms to the FCC structure at 1400°C, resulting in gamma-iron (y-Fe). The FCC structure is stable down to 910°C, where it transforms back into a low-temperature BCC structure, alpha-iron (a-Fe). Thus, 5-Fe and a-Fe are actually the same form of iron, but are treated as distinct forms due to their two different temperature ranges of stability. 

T, is the temperature of allotropic transformation from a to 3 phase and Tm is the melting point. By combining with the effect of pressure we can construct a P-T diagram for a substance of interest. At a given pressure, say, the atmospheric pressure, Pa, as shown in the following diagram, as the a phase solid is heated, it transforms to the (3 phase at T and the (3 phase, upon further heating, melts at Tm, and the liquid boils at Tv. 

The following diagram (Fig A) shows the relation between a stable phase and an unstable phase in a given set of conditions. If cooling is carried out slowly from the liquid phase, the liquid solidifies at Tm to form solid p phase. An allotropic transformation from p to a phase occurs at T,. On slow heating the process will be reversed. 

Tin exists in two allotropic forms white tin (p) and gray tin (a). White tin, the form which is most familiar, crystallizes in the body-centered tetragonal system. Gray tin has a diamond cubic structure and may be formed when very high purity tin is exposed to temperatures well below zero. The allotropic transformation is retarded if the tin contains small amounts of bismuth, antimony, or lead. The spontaneous appearance of gray tin is a rare occurrence because the initiation of transformation requires, in some cases, years of exposure at —40°C. Inoculation with Ot-tin particles accelerates the... 

X49 Application to the allotropic transformation of a solid into another solid.— Formula (2) evidently applies almost without modification to the case in which a substance may exist in two distinct solid forms a and 6, resulting from an allotropic or isomeric transformation suppose that the form b passes into the form a with liberation of heat under the pressure P there exists a transformation point 0] at temperatures lower than 0 the form b passes over to a above 0, a chaneres to 6 When, at the temperature 0 and pressure P, a gramme of the form b passes into the form... 

X46. Law of Clapeyron and Clausius, 171.—147. Application to vaporization, 173.—X48. Application to fusion. Variation of fusing-point with pressure, 173.—X49. Application to the allotropic transformation of a solid into another solid, 175.—150. Application to dissociation, 178. ... 

No allotropic transformations, accompanied by marked changes in expansion rate, should occur in the metal over the range of temperature to which it may be subjected, either in making the seal or during its subsequent use. This range may be as extensive as -50°C to 2000°C. 

Consider a material that undergoes a first order phase transition such as fusion, vaporization, allotropic transformation, and the like. In each case two phases remain in equilibrium at a fixed temperature while heat flows in or out of the system during the transition. The theoretical background for characterizing this process will be provided in Chapter 2. 

For this reaction ( F/ )jr <0 and the affinity of the reaction increases with pressure. On the other hand for reactions in condensed phases the effect is usually extremely small. For example the allotropic transformation... 

Crystallized bodies which undergo no allotropic transformation, or at least no rapid one, can obviously be examined at once down to near the absolute zero. 

Chiotti, P., Dooley, G. J., Effect of carbon on the electrical resistivity and allotropic transformation of thorium, J. Nucl. Mater., 23, (1967), 45-54. Cited on pages 83,503. 

Pure titanium experiences an allotropic transformation from the hexagonal close-packed (hep) alpha (a) phase to the body-centered... 

Both first- and second-order transitions are observed in polymers. Melting and allotropic transformations are accompanied by latent-heat effects and are known as first-order transitions. During second-order transitions, changes in properties occur without any latent-heat effects. Below the second-order-transition temperature (glass transition temperature) a rubberlike material acts like a true solid (see Chapter 1). Above this temperature the fixed molecular structure is broken down partially by a combination of thermal expansion and thermal agitation. The glass transition temperature of polystyrene is 100°C below 100°C polystyrene is hard and brittle, and above 100°C it is rubberhke and becomes easily deformed. 

Phases with the same formulae but different space lattices (e.g. allotropic transformation) are distinguished by ... 

Each Pu allotrope transforms in contact with PU3C2 (C phase). Thermal analysis studies by Mulford et al (1960) have shown that PU3C2 decomposes into e-Pu -I- PuC at 575° while a metallographic technique places the temperature at 558° + 2° (Rosen et al, 1963). PU3C2 is apparently a line compound which forms slowly during cooling (Rosen et al, 1963). 

If we consider a substance undergoing an allotropic transformation in the solid state at temperature T, which melts at temperature 7> and boils at temperature Tsb, to integrate expressions [4.4] and [4.6], it is necessary to divide the temperature interval between the initial temperature To and the temperature T into slices. Each slice is characterized by a phase and therefore a function of the molar specific heat capacity at constant pressure with changing temperature. Thus, integration of equation [4.4] involves two t3 es of terms ... 

Shikhmanter et al. (1983b) have carried out TEM experiments in order to study the crystallization behavior of some R-Au (R=Gd, Tb, Dy and Er) vapor-deposited amorphous films (120 run thick). Crystallization takes places in the temperature range of 463-513 K, and further heating by an additional 50 K leads to the formation of the RAu alloys (CsCl strueture type). Further annealing at 533 K induces an allotropic transformation such as CsCl type (cubic structure) —+ CrB type (orthorhombic structure). The former is metastable, while the latter is, as in the bulk, more stable at low temperatures. The presence of R2O3 crystallites can act as catalyst for the transformation. It is concluded that conditions amenable to heterogeneous nucleation will appear on the R-Au films at higher temperatures than in the R-Cu films (413—423 K) or R-Ag films (388-398 K). 

Figure 2.4. Illustration of allotropic transformations exhibited by elemental sulfur. Shown are (a) cyclooctasulfur (Sg) at room temperature/pressure, (b) breaking apart of discrete S o rings at elevated temperature to form a viscous liquid, (c) formation of S o (catenasulfur or plastic sulfur ) via quenching in cold water, and (d) re-conversion of catenasulfur back to the thermodynamic stable Sg allotrope.

The change of the reference state has been made assuming that the enthalpies and entropies of fusion or of allotropic transformation do not vary with temperature. These values have been taken from Hultgren et al. (1973b) for the rare earths and from Getting et al. (1976) for the actinides. This choice was motivated by the fact that many authors have used these values to calculate the changes of the reference state (see for example Chiotti et al. 1981). 

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