PTOT structures

ReB3 has a very similar hexagonal structure, with boron atoms added at the comers of the cell at 0 and 50. The added boron atoms are at the centers of octahedral sites. We can treat this as a PTOT structure or consider the three closely spaced boron layers (95,0,5 and 45, 50, 55) as a triple layer (Section 8.3.1). 

We have noted that a PTOT structure based on an hep sequence of P layers is not expected if all layers are filled because of repulsion between close layers as in Tb Pc Tb or Tc Pb To ReB3 is a notable exception because of the triple boron layers. Bonding among the three boron layers results in height separations of 50 between Tb and Tb or Tc and Tc layers. 

Water has a complex structure determined by hydrogen bonding of molecules. In view of the above discussion we assume now that a dipole is not rigid. Introducing some changes in our recent works [6, 8], we represent a total dipole moment ptot as a superposition of the constant part p and of a small decaying component p(f) due to fast vibration of the H-bonded molecules ... 

We have seen examples of the 1 1 stoichiometry corresponding to NaCl (3-2PO) and ZnS (3-2PT or 2-2PT). Rutile (Ti02) has P layers filled by O2 with Ti4+ in O sites. The stoichiometry is 1 2 and this is clear from the notation 2-2POi/2. Only 1/2 of the sites in the O layer are filled and the P layers are hep. Later we will examine a more systematic treatment of applications of the PTOT notation. It applies to thousands of inorganic crystal structures including more complex structures. It is not limited to metals and MX, MX2 and M2X com-... 

All P, O, and T layers have the same hexagonal close-packed arrangement within each layer. The two T layers are equivalent for ccp and hep, and for ccp, only P and O layers are interchangeable, and together they are equivalent to the two T layers (considered together). Because of these similarities, ccp, hep, the simple cubic structure, and even bcc structures can be handled in the PTOT system. It also applies to much more complex structures. The PTOT system provides a framework for considering the mechanism of formation and transformation of crystal structures. The transformations of structures of metals, ccp, hep, and bcc, are of particular interest. These are considered in detail in Chapter 4. 

In this book we are particularly interested in simple descriptions of structures that are easily visualized and providing information of the chemical environment of the ions and atoms involved. For metals, there is an obvious pattern of structures in the periodic table. The number of valence electrons and orbitals are important. These factors determine electron densities and compressibilities, and are essential for theoretical band calculations, etc. The first part of this book covers classical descriptions and notation for crystals, close packing, the PTOT system, and the structures of the elements. The latter and larger part of the book treats the structures of many crystals organized by the patterns of occupancies of close-packed layers in the PTOT system. 

The sequence and spacings given for close packing are not artificial descriptions or approximations, as these are determined by geometry. The PTOT system is the most detailed and definitive treatment presented for close-packed structures, and many other structures can be described in this system. 

In Figure 3.7, we can see that P and T layers occupy only A and B positions. Let us focus on a Pg layer. Just below and above the Pg layer there are Ta layers. These T sites are very close, with no shielding. For hep structures no examples are encountered for PTT or PTOT with both T layers filled without unusual features (pp. 139-144). Partial filling of both T layers avoids repulsion involving adjacent T sites. 

In the introductory chapters the examples using the PTOT notation have been simple inorganic compounds. Most of these structures have a close-packed arrangement of anions with cations occupying T and / or O sites. Most of the elements are monatomic, and close packing is expected. The structures of most elements with diatomic molecules and even those with larger molecules can be described also in the PTOT system. 

Again, the complex structure is greatly simplified in terms of the PTOT system. 

The structure of p-quartz is unique and much different from those of tridymite and cristobalite. It does not follow the rules for the PTOT system, but the notation can be applied with some qualification. In general, for close-packed structures between packing layers there are two T layers, and half way between the P layers there is an O layer. The... 

K2PtCl6 illustrates the versatility of the PTOT system. It can be handled as a 2 1 salt (Li20 structure) treating PtCljj as a unit (3 3PTT, Section 6.3.3, Figure 6.14). If we consider it as a PO structure, the P layers are three-quarters filled by Cl and one-quarter by K. The Pt atoms are in alternate layers, occupying one-quarter of the O sites, only those sites surrounded by Cl atoms. This gives the notation 3 3Pi/4 3/4P1/4 3/4O1/4. 

Books using the close-packing description missed the important overall general PTOT pattern. The P, T, and O layers are obvious in hep structures when we look for them, because the layers are packed along the c axis. The layers are not obvious in ccp structures because the common models and drawings show one axis horizontal and one vertical. Layers are packed along the body diagonal of the cell. 

The general PTOT scheme predicts similar stabilities of hep and ccp structures using P layers only and those using P layers and one set of the two T layers. For many metals the ccp (3P) and hep (2P) structures have nearly the same stability and have both structures under different conditions. For ZnS, both zinc blende (3 2PT, ccp) and wurtzite (2 2PT, hep) occur as minerals. Because of similar stabilities of ccp (3P) and hep (2P) structures of metals and for 3PT and 2PT structures of ZnS, we might expect similarities in other combinations of layers for ccp and hep structures, but this is not the case. The expected compounds using... 

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