Morphology crystal facets

The equilibrium shape of a crystal is, as described above, a polyhedron where the size of the crystal facets is inversely proportional to their surface energy, ysg. In the present section we will consider other types of interfaces as well and we will show that the interface energies determine the equilibrium morphology of interfaces in general. 

Crystals of NaA zeolite showed strong cubic habits typical of these structures (Figure 3). The surface morphology of the 0.3pm crystals of ZSM-5(9) was usually irregular (Figure 4) and seldom exhibited crystal facets. The 2pm crystals of ZSM-5(40) showed facets typical of ZSM-5 of moderate aluminum content (Figure 5). 

Louis Pasteur was the first scientist to study the effect of molecular chirality on the crystal structure of organic compoimds [23], finding that the resolved enantiomers of sodium ammonium tartrate could be obtained in a crystalline form that featured nonsuperimposable hemihedral facets (see Fig. 9.1). Pasteur was quite surprised to learn that when he conducted the crystallization of racemic sodium ammonium tartrate at temperatures below 28 °C, he also obtained crystals of that contained nonsuperimposable hemihedral facets. He was able to manually separate the left-handed crystals from the right-handed ones, and foimd that these separated forms were optically active upon dissolution. More surprising was the discovery that when the crystallization was conducted at temperatures exceeding 28 °C, he obtained crystals having different morphologies that did not contain the hemihedral crystal facets (also illustrated in Fig. 9.1). Later workers established that this was a case of crystal polymorphism. 

Activation and conductivity at room temperature are problems that can be addressed by the incorporation of other electronic structures that increase carrier transport. Crystal morphology is an important parameter in the boron doping process to determine uncompensated acceptors (Aa-Ad) for different crystal facets as a function of doping concentration. The temperature coefficient of resistance for a CVD diamond film can be changed by boron doping. As conductivity depends on the crystal phase, the combined electromechanical properties can be exploited in sensor applications both for resistive temperature detectors and for pressure transdu-cers. " As electrical conductivity is related linearly with boron concentration, a better-controlled process may allow for the development of better semiconductor devices improving crystal quality and operating limits. ... 

How does a support affect the morphology of a particle on top of it Which surface planes does the metal single crystal expose The thermodynamically most stable configuration of such small crystallites is determined by the free energy of the surface facets and the interface with the support, and can be derived by the so-called Wulff construction, which we demonstrate for a cross section through a particle-support assembly in two dimensions (Fig. 5.13). 

Figure 5. Relative fraction of the different surface atoms as a function of Log H, where Mis the number of atoms, for a (111) and (100) facetted f.c.c, crystal when the surface morphology is equilibriated, E. refers to the edges between the (inn) and (111) faces, to the edges between two (111) faces. The (111) curve is drawn using the axes to the right,...

Rg. 11.2 Single crystals of morphologically enantiomeric quartz. Note the mirror symmetry of the facets on the respective crystals. Unlike amino acids, the component silicon dioxide molecules have no chirality. The spontaneous resolution of quartz into crystals of opposite morphological handedness is an example of local symmetry breaking in the environment. 

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