Non-stoichiometric phases

1 Introduction Several special problems of nomenclature for non-stoichiometric phases have arisen with the improvements in the precision with which their structures can be determined. Thus, there are references to homologous series, non-commensurate and semi-commensurate structures, Vernier structures, crystallographic shear phases, Wadsley defects, chemical twinned phases, infinitely adaptive phases and modulated structures. Many of the phases that fall into these classes have no observable composition ranges although they have complex structures and formulae an example is Mo17047. These phases, despite their complex formulae, are essentially stoichiometric and possession of a complex formula must not be taken as an indication of a non-stoichiometric compound (cf. Section IR-11.1.2). 

2 Modulated structures Modulated structures possess two or more periodicities in the same direction of space. If the ratio of these periodicities is a rational number, the structures are called commensurate  

The structure is of the fluorite type with extra sheets of atoms inserted into the parent YX2 structure. When these are ordered, a homologous series of phases results. When they are disordered, there is a non-commensurate, non-stoichiometric phase, while partial ordering will give a Vernier or semi-commensurate effect. Other layer structures can be treated in the same way. 

Misfit structures consist of two or more different, often mutually non-commensurate, units which are held together by electrostatic or other forces no basic stmcture can be defined. The composition of compounds with misfit structures is determined by the ratio of the periodicities of their structural units and by electroneutrality. 

Sr1 pCr2S4 p with p = 0.29, where chains of compositions Sr3CrS3 and Sr3 xS lie in tunnels of a framework of composition Cr2iS36 the three units are mutually non-commensurate. 

---

While Cordfuncke [997] believes that there are only four stable compounds in the U03—NH3—H20 system, the results of Stuart et al. [998, 999] indicate the existence of a continuous non-stoichiometric phase containing the NH4 ion and possessing zeolitic properties U02(0H)2 x (ONH4 )x yH20. 

Analyses of the defect chemistry and thermodynamics of non-stoichiometric phases that are predominately ionic in nature (i.e. halides and oxides) are most often made using quasi-chemical reactions. The concentrations of the point defects are considered to be low, and defect-defect interactions as such are most often disregarded, although defect clusters often are incorporated. The resulting mass action equations give the relationship between the concentrations of point defects and partial pressure or chemical activity of the species involved in the defect reactions. 

The configurational entropy term, given by the degeneracy, gc, is included in AfG but not in AfGc. Let us assume the existence of two compounds with different formal oxidation states for the B atom, ABO3 and ABO2.5. The two compounds have the same (perovskite-type) structure and the non-stoichiometric phase... 

In Fig. 2.19, on the contrary, we observe that intermediate solid phases with a variable composition are formed (non-stoichiometric phases). In the diagrams shown here we see therefore examples both of terminal and intermediate phases. (For instance, the Hf-Ru diagram shows the terminal solid solutions of Ru in a and (3Hf and of Hf in Ru and the intermediate compound containing about 50 at.% Ru). These phases are characterized by homogeneity ranges (solid solubility ranges), which, in the case of the terminal phases, include the pure components and which, generally, have a variable temperature-dependent extension. 

A more complex notation is needed for non-stoichiometric phases. Selected simple examples are given below, and more detailed information will be reported when discussing crystal coordination formulae ... 

Pt3Cdo.6Zn4.4 ( Pt5CdZn7) (non-stoichiometric phase with partial substitution of Cd and Zn atoms) Hexagonal, a = 705.0pm, c = 279.2pm space groupP31 m, N. 157. 

Above 1127°C, a single oxygen-rich non-stoichiometric phase of UO2 is found with formula U02+, ranging from UO2 to U02.25- Unlike FeO, where a metal-deficient oxide was achieved through cation vacancies, in this example the metal-deficiency arises from interstitial anions. 

Titanium and oxygen form non-stoichiometric phases which exist over a range of composition centered about the stoichiometric 1 1 value, from TiOo.es to TiOi.25. We shall look at what happens in the upper range from TiOi 00 to TiOi.25. 

There are a number of solid phases of the types MScCl and ScCl where the formal oxidation state of scandium is less than three. They are usually made by direct combination at elevated temperatures of MCI, ScCl3 and metallic scandium. Their structures often show evidence of Sc—Sc bonds. Thus CsScCl3 is made by action of Sc on Cs3Sc2Cly at 700 °C. The shiny blue product has the hexagonal perovskite CsNiCl3 structure. This is similar to the Cs3Sc2Cl9 structure but with all Sc positions filled. Non-stoichiometric phases exist between the two end structures.128 When scandium is heated with ScCl3 at 940-960 °C in a sealed Ta... 

X-ray examination of the products of the thermal decomposition of Pb02 discloses two intermediate, non-stoichiometric phases between Pb02 and PbgO. The a-phase is close to Pb O j and the /3-phase to PbgOg (Butler and Copp, 1956). 

The metals V, Nb, and Ta have b.c.c. structures. The a solid solution of H in this kructure extends to VHq.os, NbH(,., and TaHo.2. The next distinct phase is the/3 hydride, a non-stoichiometric phase which is a (tetragonal) distorted version of the b.c.c. solid solution and is stable over a wide range of composition (for example. 

For the formulae of solid solutions and non-stoichiometric phases, see Chapter IR-11. 

IR-11.1.2 Stoichiometric and non-stoichiometric phases IR-11.2 Names of solid phases IR-11.2.1 General IR-11.2.2 Mineral names IR-11.3 Chemical composition IR-11.3.1 Approximate formulae IR-11.3.2 Phases with variable composition IR-11.4 Point defect (Kroger-Vink) notation IR-11.4.1 General... 

IR-11.4.5 Defect clusters and use of quasi-chemical equations IR-11.5 Phase nomenclature IR-11.5.1 Introduction IR-11.5.2 Recommended notation IR-11.6 Non-stoichiometric phases IR-11.6.1 Introduction IR-11.6.2 Modulated structures IR-11.6.3 Crystallographic shear structures IR-11.6.4 Unit cell twinning or chemical twinning IR-11.6.5 Infinitely adaptive structures IR-11.6.6 Intercalation compounds IR-11.7 Polymorphism IR-11.7.1 Introduction IR-11.7.2 Use of crystal systems IR-11.8 Final remarks IR-11.9 References... 

---