Crystallographic planes atomic arrangements

Single crystal and bulk BaTiOs exhibits a sharp paraelectric-to-ferroelectric transition at 393K. In the presence of submicron grains, the transition becomes diffuse and can be absent for polycrystalline BaTiOs. Twin boundaries along the four crystallographically equivalent 11 planes constitute the main lattice defects. Junctions between such twin boundaries can be frequently observed within a grain. The local atomic arrangement of the core of twin intersections was studied by focal-series reconstruction (Jia etal. 1999). 

Keep in mind that this is for a uniform isotropic material. A lot of materials are not isotropic. Crystalline materials can be weaker or stronger along one crystallographic plane than another depending on the arrangement of atoms, relative strength of the bonds and the presence of defects. The modulus in each of these directions can also be different and we would have to write Hooke s law as (Equation 13-11) ... 

Since the various crystallographic planes differ not only in the number and geometrical arrangement of the surface atoms, but also in the number and spatial orientation of the orbitals emerging from one surface atom ), different behaviour can be expected from different surface planes. Numerous observations have been made at various coverages and in a wide range of temperatures. 

We have seen how sets of crystallographic planes may be defined by means of suitable indices of the type (hkl), that these planes an1 separated by a distance given by d = a/Vh2 + k2 + l 2f that in face-centred cubic lattices the sets of planes are defined by indices in which h, A and / are either all even or all odd, thus (111), (200), (220), etc. and that in body-centred cubic lattices the similarly defined sets of planes are found when the sum of h + k + l is an even number, e.g. (110), (200), (211), etc. In order to complete the discussion of crystal orientation we must now deal with the method of describing a crystallographic direction, i.e. a line which passes through the centres of atoms arranged in a crystallographic plane. 

The penta-, selenopenta-, and telluropentathionate ions have mirror plane symmetry in the crystals. This is crystallographically required in all four structure types except the triclinic one, but is realized even there. The ions thus have a cis form in these salts, with the terminal sulfonate groups on the same side of the plane through the three middle atoms. The occurrence of the cis form in the barium salts is perhaps due to the oxygencoordinating power of the barium ion, and favorable lattice conditions for the mirror-plane cis arrangement. 

The majority of substrate used for MEMS and microfiuidic devices or systems is silicon. Crystalline silicon forms a covalently bonded structure and has the same atomic arrangement as carbon in diamond. The crystallographic orientation in crystals of the cubic class is described in terms of Miller notation [1]. Any plane in the space satisfies the equation... 

The main characteristic of a crystalline arrangement consists in the existence of crystallographic planes, which, implicitly collect de periodicity of engagement of structural dots (atoms and assemblies of atoms) in all the directions in which the crystal expands the present discussion follows (Putz, 2006). 

Ferroelectricity was discovered in Rochelle salt in 1921. A ferroelectric crystal exhibits a spontaneous polarization P, in a certain temperature range and the direction of P, can be reversed by an external electric field. From a physical point of view, ferroelectric crystals are those crystalline compounds, which possess one or more ferroelectric phases. The ferroelectric phase is a particular state exhibiting spontaneous polarization, which can be reversed by an external field. A reversal ofpolarization is considered as a special case of the polarization reorientation. From a crystallographic point of view, ferroelectricity can be foimd in polar crystals. A polar crystal is a piezoelectric crystal (without center of symmetry) crystal whose point-group symmetry has a unique rotational axis, but does not have any mirror plane perpendicular to this axis. Along a unique rotational axis, the atomic arrangement at one end is different from that at the other (opposite end). Therefore, they display spontaneous polarization. Polar crystal, which can be found in ten point groups, are 1, 2, m, mm2,4, 4 mm, 3, 3 m, 6, 6 mm. 

Figure 10.3 Schematic of the atomic arrangement on different crystallographic planes (a) (0001) 4H-SiC ...

Schematic of the atomic arrangement on different crystallographic planes ...

The atomic arrangement for a crystallographic plane, which is often of interest, depends on the crystal structure. The (110) atomic planes for FCC and BCC crystal structures are represented in Figures 3.12 and 3.13, respectively. Reduced-sphere unit cells are also included. Note that the atomic packing is different for each case. The circles represent atoms lying in the crystallographic planes as would be obtained from a slice taken through the centers of the full-size hard spheres. 

The origin of such dissimilar interfaces has been analyzed based on the crystallographic relationships between BST and Pt. It is concluded that the atomic arrangement in the plane parallel to the interfacial plane plays an important role in determining the feature of the interfaces. For BST films, the directions perpendicular to the BST/Pt interfaces in the two cases are both determined to be [001], while for Pt electrodes the normal direction is [111], as illustrated in the insets in Figs. 1 (a) and (b). This indicates that the influence of the out-of-plane lattiee constants is negligible due to the same mismatch of lattice constants between BST and Pt in the normal direction in these two cases. However, the BST orientations parallel... 

Solution Bragg s law should be used to solve this problem (refer to Section 6.3.5 and eq. (6.3.11), Figure 6.20). In the equation mentioned, 9 is the incident angle and (p is the deflection angle. The picture is repeated here to make the situation clearer (Figure E6.14 an atomic arrangement is not depicted substituted by two reflected planes with interplanar distance d ). It is seen in the picture that cp = 26. The crystallographic plane s index is (600), in fact there is no such plane in the crystal this should be understood as a 6th order of reflection from the plane (100) (i.e., at distance... 

---