Polytypism

Polytypism in layered silicates has been well characterized. There are as many as 19 polytypes known among micas. The repeat unit in muscovite mica, [KAl2(OH)2(Si3Al)0 o], for instance, consists of a sheet of octahedrally coordinated aluminium ions sandwiched between two identical sheets of (Si, AOO tetrahedra, the large ions being located in interlayer positions. Surface oxygens of the tetrahedra in 

Several ABO3 oxides, where A is a large cation like Ba and B is a small cation of the d-transition series, are known to exhibit polytypism. These oxides consist of close-packed, ordered, AO3 layers which are stacked one over the other and the B cations 

Staeking faults and sometimes proper polytypism are found in many inorganic compounds - to pick out just a few, zinc sulphide, zinc oxide, beryllium oxide. Interest in these faults arises from the present-day focus on electron theory of phase stability, and on eomputer simulation of lattice faults of all kinds investigators are attempting to relate staeking-fault concentration on various measurable character-isties of the compounds in question, such as ionicity , and thereby to cast light on the eleetronic strueture and phase stability of the two rival structures that give rise to the faults. 

5 Crystal structure, crystal defects and chemical reactions. Most chemical reactions of interest to materials scientists involve at least one reactant in the solid state examples inelude surfaee oxidation, internal oxidation, the photographie process, electrochemieal reaetions in the solid state. All of these are critieally dependent on crystal defects, point defects in particular, and the thermodynamics of these point defeets, especially in ionic compounds, are far more complex than they are in single-component metals. I have spaee only for a superficial overview. 

Two German physical chemists, W. Sehottky and C. Wagner, founded this branch of materials seience. The story is very clearly set out in a biographical memoir of Carl Wagner (1901 1977) by another pioneer solid-state chemist, Hermann Schmalzried (1991), and also in Wagner s own survey of point defects and their interaction (Wagner 1977) - his last publieation. Sehottky we have already briefly met in connection with the Pohl school s study of colour centres 

The number in the notation of the resulting crystal structure determines the number of layers before the sequence repeats itself, and the letter determines the resulting structure of the crystal C for cubic, H for hexagonal, and R for rhomohedral. 

All polytypes are SIC of equal proportions of silicon and carbon atoms, but due to the fact that the stacking sequence between the planes differs, the electronic and optical properties differ. The bandgap is, for instance, 2.39 eV for 3C-SiC, 3.023 eV for 6H-SiC, and 3.265 eV for 4H-SiC [2]. 

The unit cell for the different polytypes will naturally vary, as will the number of atoms per unit cell. This will affect the number of electronic bands and the phonon branches for a given polytype. 

---

Figure C2.16.2 shows tire gap-lattice constant plots for tire III-V nitrides. These compounds can have eitlier tire WTirtzite or zincblende stmctures, witli tire wurtzite polytype having tire most interesting device applications. The large gaps of tliese materials make tliem particularly useful in tire preparation of LEDs and diode lasers emitting in tire blue part of tire visible spectmm. Unlike tire smaller-gap III-V compounds illustrated in figure C2.16.3 single crystals of tire nitride binaries of AIN, GaN and InN can be prepared only in very small sizes, too small for epitaxial growtli of device stmctures. Substrate materials such as sapphire and SiC are used instead.

MOLE, however, is more sensitive than ETIR (<1 samples compared to about 100 p.m ). With surface-enhanced Raman spectroscopy the Raman signal is enhanced by several orders of magnitude. This requires that the sample be absorbed on a metal surface (eg, Ag, Cu, or Au). It also yields sophisticated characterization data for the polytypes of siUcon carbide, graphite, etc. 

Table 1 Hsts the properties of several semiconductors relevant to device design and epitaxy. The properties are appropriate to the 2incblende crystal stmcture in those cases where hexagonal polytypes exist, ie, ZnS and ZnSe. This first group of crystal parameters appHes to the growth of epitaxial heterostmctures the cubic lattice constant, a the elastic constants, congment sublimation temperature, T. Eor growth of defect-free...

The properties of siHcon carbide (4—6) depend on purity, polytype, and method of formation. The measurements made on commercial, polycrystalline products should not be interpreted as being representative of single-crystal siHcon carbide. The pressureless-sintered siHcon carbides, being essentially single-phase, fine-grained, and polycrystalline, have properties distinct from both single crystals and direct-bonded siHcon carbide refractories. Table 1 Hsts the properties of the hiUy compacted, high purity material. 

Crystal Structure. Sihcon carbide may crystalline in the cubic, hexagonal, or rhombohedral stmcture. There is a broad temperature range where these stmctures may form. The hexagonal and rhombohedral stmcture designated as the a-form (noncubic) may crystalline in a large number of polytypes. 

A number of theories have been put forth to explain the mechanism of polytype formation (30—36), such as the generation of steps by screw dislocations on single-crystal surfaces that could account for the large number of polytypes formed (30,35,36). The growth of crystals via the vapor phase is beheved to occur by surface nucleation and ledge movement by face specific reactions (37). The soHd-state transformation from one polytype to another is beheved to occur by a layer-displacement mechanism (38) caused by nucleation and expansion of stacking faults in close-packed double layers of Si and C. 

A progressive etching technique (39,40), combined with x-ray diffraction analysis, revealed the presence of a number of a polytypes within a single crystal of sihcon carbide. Work using lattice imaging techniques via transmission electron microscopy has shown that a-siUcon carbide formed by transformation from the P-phase (cubic) can consist of a number of the a polytypes in a syntactic array (41). 

Semiconducting Properties. Sihcon carbide is a semiconductor it has a conductivity between that of metals and insulators or dielectrics (4,13,46,47). Because of the thermal stabiUty of its electronic stmcture, sihcon carbide has been studied for uses at high (>500° C) temperature. The Hall mobihty in sihcon carbide is a function of polytype (48,49), temperature (41,42,45—50), impurity, and concentration (49). In n-ty e crystals, activation energy for ioniza tion of nitrogen impurity varies with polytype (50,51). 

Sihcon carbide whiskers typically have diameters of a few micrometers and lengths up to 5 cm. They may be composed of either P SiC or a-SiC, the latter in one or more polytypes, and occur mosdy as hair- or ribbonlike crystals. Despite many attempts to produce SiC whiskers on a large scale at low cost, they have never acquired a wide importance. SiC whiskers have been reviewed (111—120). 

The analysis of siUcon carbide involves identification, chemical analysis, and physical testing. For identification, x-ray diffraction, optical microscopy, and electron microscopy are used (136). Refinement of x-ray data by Rietveld analysis allows more precise deterrnination of polytype levels (137). 

GIAB studies of sputtered thin films of different composition for tribological applications have been reported [4.157-4.159]. The technique has been used to study the structure of very thin GdS layers (deposited by chemical bath deposition) for photovoltaic applications in combination with 6-26 diffraction it enabled identification of their polytype structure [4.160]. Glancing angle diffraction in the GIAB geometry... 

The different forms of carbynes were assumed to be polytypes with different numbers of carbon atoms in the chains lying parallel to the hexagonal axis and different packing arrangements of the chains within the crystallite. Heimaim et al [23] proposed that the sizes of the unit cells were determined by the spacing between kinks in extended carbon chains, Fig. 3A. They were able to correlate the Cg value for the different carbyne forms with assumed numbers of carbon atoms, n (in the range n = 6 to 12), in the linear parts of the chains. 

Polymorphism in nonmetals has also received a great deal of study and is particularly clearly discussed in a book by two Indian physicists (Verma and Krishna 1966) which also links to the phenomenon of polytypism, discussed in Section 3.2.3.4. 

On silicon carbide, it is easier to see and measure step heights than in crystals like beryl, because SiC has polytypes, first discovered by the German crystallog-rapher Baumhauer (1912). The crystal structure is built up of a succession of close-packed layers of identical structure, but stacked on top of each other in alternative ways (Figure 3.24). The simplest kind of SiC simply repeats steps ABCABC, etc., and the step height corresponds to three layers only. Many other stacking sequences... 

McLT81 McLarnen, T. J. Mathematics tools for counting polytypes. Z. fur Kristal. 155 (1981) 227-245. 

Fig. 1.5 The (rhombohedral) 3R and (hexagonal) 2H stacking polytypes of M0S2. Adjacent layers in the 2H polytype are rotated by 60°, whereas those in the 3R polytype can be superimposed with a translation only. (Reproduced with permission from [77], Copyright 2009, American Chemical...

However, SiC also exhibits other stacking sequences, as shown in 6.15.6., given on the next page. These arranged layers are called "polytypes" and are prevalent where simple compounds such as SiC and SiN are involved. In many cases, the properties of such compounds depend, to a large extent, upon the specific stacked layers obtained during formation. 

Polymorphic forms with structures having different stacking sequences of like layers are called polytypes. 

Other stacking sequences than these are also possible, for example AaBpAaCy... or statistical sequences without periodic order. More than 70 stacking varieties are known for silicon carbide, and together they are called a-SiC. Structures that can be considered as stacking variants are called polytypes. We deal with them further in the context of closest-sphere packings (Chapter 14). 

In addition to this cubic Laves phase, a variant with magnesium atoms arranged as in hexagonal diamond exists in the MgZn2 type, and further polytypes are known. 

The structure of wurtzite corresponds to a hexagonal closest-packing of S atoms in which half of the tetrahedral interstices are occupied by Zn atoms. In addition, any other stacking variant of closest-packings can have occupied tetrahedral interstices. Polytypes of this kind are known, for example, for SiC. 

The familiar diamond structure, with each atom covalently bonded in a perfect tetrahedral fashion to its four neighbors, is adopted not only by C but also by Si and Ge. Silicon can also adopt a wurtzite structure (see below), an example of a polytype (one of several crystal structures possible for a substance having an identical chemical composition but differing in the stacking of layers, and which may exist in a metastable state after its formation at some different temperature or pressure). 

---