Sapphire unit cell

Figure 2.5 A schematic diagram of the AI2O3 sapphire unit cell, there are six oxygen layers in the unit cell, the distances between the various atomic layers change as shown in the figure. The oxygen ions form a pseudohexagonal lattice. The small Al ions occupy the octahedral sites. (Courtesy of P. Ruterana.)...

The hybrid circuit 10 comprises a buffer structure 16 which is comprised of a material which accommodates the difference in thermal expansion coefficients of the HgCdTe detector array 12 and the silicon read-out chip 14. The buffer layer is made of sapphire which also has good thermal conductivity properties. The buffer structure has laser drilled vias 18 which are formed in registration with unit cells of the detector array and the read-out circuit. Each of the vias is provided with indium bumps 20 at opposing ends thereof. The buffer structure is interposed between the detector array and the read-out chip. Cold weld indium bump technology is employed to couple the bumps 20 to the buffer structure. The buffer structure is further... 

AIN buffer layer on (0001) sapphire. Composition was determined by help of X-ray diffraction. A continuous increase of the mode energy with x was observed. An AlxGai.xN/GaN/sapphire heterostructure grown with the AIN buffer layer technique was studied in infrared reflection and Raman spectroscopy by Wetzel et al [2] (FIGURE 2). From an X-ray analysis of the c-axis an AlN-ftaction of x = 0.15 was derived. Recently, however, it was shown that AIN layers in heterostructures with GaN are coherently strained up to a thickness of at least 350 nm. This leads to misinterpretation of the AIN fraction [8], Including the deformation of the unit cell in the pseudomorphic structure above, a value 50% smaller is concluded (x = 0.08). In backscattering off the c-plane the Ai(LO) mode was determined at 752 cm 1 (square with cross symbol) in excellent agreement with the infrared reflection data [2],... 

An enormous range of properties is found in oxides. The most successful and most widely used substrate for GaN to date is sapphire, AI2O3. Except for wurtzite materials, few of the unit cells in these materials match with GaN, but it is usually useful to think of these systems as having a close-packed nitrogen lattice in GaN matching to a near close-packed oxygen lattice in the oxide. 

Optical pumping experiments were first used to achieve lasing m GaN-based structures. Stimulated emission from GaN was observed as early as 1971 [17]. More recently, there have been a large number of reports on stimulated emission [18,19], without an intentionally formed cavity. This may partly be due to the well known difficulty of cleaving mirrors in the wurtzite nitrides grown on sapphire, due to the 30° tilt of the GaN unit cell with respect to the sapphire. 

Bulk sapphire has rhombohedral symmetry, which is usually treated as hexagonal (space group R3c), with 30 atoms (six AI2O3 units) per primitive unit cell. The lattice parameters (a=fe=4.7570 A, c=12.9877 A) and the internal coordinates (x=0.3063, z=0.3522) are taken from ref. [56]. The bulk unit cell consists of an alternated stacking, along the c-axis, of two Al planes (twelve in the unit cell) with one atom per plane, and one oxygen plane (six in the unit cell) with three O ions arranged with a threefold symmetry. 

FIGURE 1.17 View of the 0001 plane of sapphire. The projection of multiple unit cells is indicated by the dashed lines. (Reprinted from Kershner, R.J., Bullard, J.W., and Cima, M.J., Langmuir, 20, 4101, 2004. Copyright 2004 American Chemical Society. With permission.)... 

FIGURE 6.12 The sapphire crystal structure. (Top) [1120] view (bottom) [0001] view (left) atomic models (right) stacking octahedra. P, and P2 are two unoccupied octahedra. S is a triangle of more closely spaced 0 ions. Open circles in the lower left show the AB stacking of the anions. The unit cell is outlined for both projections. 

FIGURE 13.16 Sub-unit-cell surface steps on (a) sapphire and (b) spinel. The steps are 0.2 nm high in each case. 

Figure 9.9 Structure of sapphire viewed aiong (1100). The oxygen anion pianes are flat, but consist of linked larger and smaller triangles. The aluminum cation planes are puckered. The unit cell is outlined.

Contrary to the growth of c-plane GaN on c-plane sapphire, the lattice mismatch between the substrate and the film in the case of a-plane GaN growth on r-plane sapphire is not spatially isotropic but depends on the crystal direction and respective lattice plane distances. Figure 11.3 shows the projected surface of the r-plane sapphire and the surface unit cell associated to it. On top of this, 1.5-unit cells of a-plane GaN are superimposed. This representation visualizes the relatively small lattice mismatch in [1100] direction of about... 

Figure 11.3 Superposition of o-plane GaN and r-plane a-AfiOs gray filled and empty circles assign Al and O, respectively, and the black filled and empty circles assign Ga and N, respectively. The shaded rectangle indicates the surface unit cell of the r-plane sapphire.

Figure 2.6 The unit cell of sapphire (a) rhombohedral unit c (b) hexagonal unit cell. Smaller spheres are for O and large ones are for Al. (Courtesy of Q. Wang.)...

The calculated lattice mismatch between the basal ZnO before the in-plane rotation and the basal plane of sapphire is about 32%. However, the actual lattice mismatch of ZnO layers with sapphire is reduced by rotation of the ZnO lattice with respect to the substrate unit cell by 30°. Consequently, the lattice mismatch is reduced to 18.4%. This large mismatch would cause even the very thin layers to be fully relaxed at growth temperatures. When the samples are cooled down after the growth, a residual thermal strain is created. 

Figure 2.22 Schematic diagram of atom positions for basal ZnO grown on a-plane sapphire. The dots mark the O-atom positions and the dashed lines show the sapphire a-plane unit cells. The open circles markZn-atom positions and the solid lines show the ZnO basal-plane unit cell.

The equipment used in all experiments consisted basically of a C02 cylinder, a 20-mL view cell with three sapphire windows for visual observations, an absolute pressure transducer (Smar LD 301) with a precision of 0.012 MPa, a portable programmer (Smar HT 201) for pressure data acquisition, and a syringe pump (ISCO 260D). The equilibrium cell contained a movable piston, which permitted pressure control inside the cell. Figure 1 presents schematic diagram of the experimental unit. 

The phase equilibria unit shown in picture 3 is a useful completion for the SFE pilot units. It is built for measurements and detection of phase equilibria and phase transitions by optical and analytical means. The picture from the optical cell is transmitted through the sapphire windows by the directly connected camera system and is displayed on the monitor in the front panel. Whenever samples are drawn out of the cell the directly connected counterbalance piston moves, thus keeping the pressure in the cell constant even during sampling operations. 

Fig. 5 Cross-sectional diagram of high pressure vessel and s.f. unit. 1 rod made of AISI 316 2 lever to revolve rod 3 high pressure vessel 4 push-pull rod 5 receiver syringe 6 receiver-syringe piston 7 mixer and optical cell block 8 quartz 9 sapphire window 10 sapphire window holder 11 reactant syringe 12 reactant-syringe piston 13 high pressure vessel lid holder and 14 high pressure vessel lid.

The diamond anvils are typically gemstone quahty and weigh about 0.2 carat. Since pressure is simply force per unit area and the upper force hmit is determined by the strength limits of the components of the cell, the diameter of the diamond culet ultimately determines the maximum achievable pressure. No definitive relationship between the culet diameter and maximum pressure is available, but with a well-designed cell one can typically expect to reach pressures of 100 kbar with 700 pm culets, 500 kbar with 400 pm culets, and 1 Mbar with 200 pm culets [77]. Bevelled diamonds are recommended for pressures above 1 Mbar [77,80-82]. Sapphire [83,84] and cubic zirconia [85] are less expensive alternatives to diamond, but are not as strong and can be used only to 100 and 30 kbar, respectively. 

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