Big Chemical Encyclopedia

Chemical substances, components, reactions, process design ...

Articles Figures Tables About

Body-centred unit cell

The body-centred unit cell—symbol I—has a lattice point at each corner and one at... [Pg.23]

FIGURE 1.29 Packing diagram for a body-centred unit cell. [Pg.34]

Finally, we can square the result in (1) and equate this to (3) to obtain the relationship between r and a in a body-centred unit cell as ... [Pg.28]

X can be detennined easily if we look at the projection of two adjacent face-centred unit cells along c (Figure E3.2-E). Again, the dashed lines indicate the edges of two adjacent, face-centred unit cells, whereas the solid lines outline the new, body-centred unit cell. The fractional coordinates of selected, important lattice points have been indicated as well as original length a. You can see that the common lattice point (located at the centre of the two... [Pg.31]

There are two tungsten atoms in the body-centred unit cell, one at (0, 0, 0) and one at the cell centre, (A, A, A), (Figure 1.8). This structure is often called the body-centred cubic (bcc) structure, but the Strukturbericht symbol, A2, is a more compact designation. In this structure, each atom has 8 nearest neighbours and 6 next nearest neighbours at only 15% greater distance. If the atoms are supposed to be hard touching spheres, the fraction of the volume... [Pg.8]

Figure 6.13 Reflections from a body-centred unit cell (a) a body-centred unit cell (b) vector addition of waves for reflections h + k + l even, gives rise to a scattered amplitude (c) vector addition of waves for reflections h + k + l odd, gives rise to zero amplitude... Figure 6.13 Reflections from a body-centred unit cell (a) a body-centred unit cell (b) vector addition of waves for reflections h + k + l even, gives rise to a scattered amplitude (c) vector addition of waves for reflections h + k + l odd, gives rise to zero amplitude...
There are only 14 possible three-dimensional lattices, called Bravais lattices (Figure 5.1). Bravais lattices are sometimes called direct lattices. The smallest unit cell possible for any of the lattices, the one that contains just one lattice point, is called the primitive unit cell. A primitive unit cell, usually drawn with a lattice point at each comer, is labelled P. All other lattice unit cells contain more than one lattice point. A unit cell with a lattice point at each corner and one at the centre of the unit cell (thus containing two lattice points in total) is called a body-centred unit cell, and labelled I. A unit cell with a lattice point in the middle of each face, thus containing four lattice points, is called a face-centred unit cell, and labelled F. A unit cell that has just one of the faces of the unit cell centred, thus containing two lattice points, is labelled A-face-centred if the faces cut the a axis, B-face-centred if the faces cut the b axis and C-face-centred if the faces cut the c axis. [Pg.117]

There are two lattice points in the body-centred unit cell, and the motif is one atom at (0,0,0). The structure is adopted by tungsten, W (Figure 5.18)... [Pg.130]

Description of a cubic (primitive, body centred or face centred) unit cell (ac) in terms of the equivalent, primitive rhombohedral, (a,-, a) and triple-primitive hexagonal, cells (ah, ch). See Fig. 3.11. [Pg.108]

Transformation (deformation) of a face-centred cubic unit cell into a body-centred cubic cell. [Pg.109]

Fig. 11 Diffraction profile from Sc-II at 23 GPa obtained on beamline 9.5 at the SRS synchrotron using an exposure time of 25 min. The tick marks show the calculated peak positions for the bestfitting body-centred cubic cell [242]. The inset shows an enlarged view of the low-angle part of the profile, highlighting the doublet peak at 20 11.1° which is not accounted for by the cubic unit cell... Fig. 11 Diffraction profile from Sc-II at 23 GPa obtained on beamline 9.5 at the SRS synchrotron using an exposure time of 25 min. The tick marks show the calculated peak positions for the bestfitting body-centred cubic cell [242]. The inset shows an enlarged view of the low-angle part of the profile, highlighting the doublet peak at 20 11.1° which is not accounted for by the cubic unit cell...
The situation for body-centred cubic metals (A2) is more complicated, but related to the ccp arrangement. As shown in Figure 5.14 a tetragonal face-centred unit cell can be constructed around the central axis of four contiguous body-centred cells. The interstitial points in the transformed unit cell define an equivalent face-centred cell, as before, and the same sites also define a body-centred lattice (shown in stipled outline) that interpenetrates the original A2 lattice. Each metal site is surrounded by six fee interstices at an average distance d6 - four of them at a distance a/s/2 and two more at a/2. [Pg.191]

In additional to body-centred, there are also two possible types of face-centred unit cells. A lattice where all the faces have a centrally placed atom is given the symbol F. If only one pair of faces is centred, then the lattice is termed A, B or C depending on which face the centring occurs. For example, if the atom or ion lies on the face created by the a and b axes, the lattice is referred to as C-centred. Examples of face-centred lattices are given in Figure 1.6. [Pg.10]

Not all types of lattice are allowable within each crystal system, because the symmetrical relationships between cell parameters mean a smaller cell could be drawn in another crystal system. For example a C-centred cubic unit cell can be redrawn as a body-centred tetragonal cell. The fourteen allowable combinations for the lattices are given in Table 1.4. These lattices are called the Bravais lattices. [Pg.10]

Figure 6.15 Change in the symmetry of the FeCo cubic unit cell with temperature. Shaded atoms indicate the disordered body-centred unit ceil... Figure 6.15 Change in the symmetry of the FeCo cubic unit cell with temperature. Shaded atoms indicate the disordered body-centred unit ceil...
Figure Bl.21.1. Atomic hard-ball models of low-Miller-index bulk-temiinated surfaces of simple metals with face-centred close-packed (fee), hexagonal close-packed (licp) and body-centred cubic (bcc) lattices (a) fee (lll)-(l X 1) (b)fcc(lO -(l X l) (c)fcc(110)-(l X 1) (d)hcp(0001)-(l x 1) (e) hcp(l0-10)-(l X 1), usually written as hcp(l010)-(l x 1) (f) bcc(l 10)-(1 x ]) (g) bcc(100)-(l x 1) and (li) bcc(l 11)-(1 x 1). The atomic spheres are drawn with radii that are smaller than touching-sphere radii, in order to give better depth views. The arrows are unit cell vectors. These figures were produced by the software program BALSAC [35]-... Figure Bl.21.1. Atomic hard-ball models of low-Miller-index bulk-temiinated surfaces of simple metals with face-centred close-packed (fee), hexagonal close-packed (licp) and body-centred cubic (bcc) lattices (a) fee (lll)-(l X 1) (b)fcc(lO -(l X l) (c)fcc(110)-(l X 1) (d)hcp(0001)-(l x 1) (e) hcp(l0-10)-(l X 1), usually written as hcp(l010)-(l x 1) (f) bcc(l 10)-(1 x ]) (g) bcc(100)-(l x 1) and (li) bcc(l 11)-(1 x 1). The atomic spheres are drawn with radii that are smaller than touching-sphere radii, in order to give better depth views. The arrows are unit cell vectors. These figures were produced by the software program BALSAC [35]-...
In the face-centred cubic structure tirere are four atoms per unit cell, 8x1/8 cube corners and 6x1/2 face centres. There are also four octahedral holes, one body centre and 12 x 1 /4 on each cube edge. When all of the holes are filled the overall composition is thus 1 1, metal to interstitial. In the same metal structure there are eight cube corners where tetrahedral sites occur at the 1/4, 1/4, 1/4 positions. When these are all filled there is a 1 2 metal to interstititial ratio. The transition metals can therefore form monocarbides, niU ides and oxides with the octahedrally coordinated interstitial atoms, and dihydrides with the tetrahedral coordination of the hydrogen atoms. [Pg.182]

Figure 13.2 The cubic structure of skutterudite (C0AS3). (a) Relation to the ReOs structure (b) unit cell (only sufficient Co-As bonds are drawn to show that there is a square group of As atoms in only 6 of the 8 octants of the cubic unit cell, the complete 6-coordination group of Co is shown only for the atom at the body-centre of the cell) and (c) section of the unit cell showing CoAsg octahedra comer-linked to form AS4 squares. Figure 13.2 The cubic structure of skutterudite (C0AS3). (a) Relation to the ReOs structure (b) unit cell (only sufficient Co-As bonds are drawn to show that there is a square group of As atoms in only 6 of the 8 octants of the cubic unit cell, the complete 6-coordination group of Co is shown only for the atom at the body-centre of the cell) and (c) section of the unit cell showing CoAsg octahedra comer-linked to form AS4 squares.
Fig. 20.25 Unit cells of (a) the face-centred cubic (f.c.c.), (b) the close-packed hexagonal (c.p.h.) and (c) the body-centred cubic (b.c.c.) crystal structures... Fig. 20.25 Unit cells of (a) the face-centred cubic (f.c.c.), (b) the close-packed hexagonal (c.p.h.) and (c) the body-centred cubic (b.c.c.) crystal structures...

See other pages where Body-centred unit cell is mentioned: [Pg.359]    [Pg.109]    [Pg.34]    [Pg.141]    [Pg.238]    [Pg.3]    [Pg.27]    [Pg.32]    [Pg.34]    [Pg.25]    [Pg.359]    [Pg.220]    [Pg.359]    [Pg.109]    [Pg.34]    [Pg.141]    [Pg.238]    [Pg.3]    [Pg.27]    [Pg.32]    [Pg.34]    [Pg.25]    [Pg.359]    [Pg.220]    [Pg.118]    [Pg.264]    [Pg.31]    [Pg.189]    [Pg.301]    [Pg.281]    [Pg.1372]    [Pg.1374]    [Pg.158]    [Pg.176]    [Pg.236]    [Pg.86]    [Pg.71]    [Pg.1256]    [Pg.718]    [Pg.236]    [Pg.201]    [Pg.360]   
See also in sourсe #XX -- [ Pg.20 , Pg.28 ]




SEARCH



Body-centre

Body-centred

Cell body

Unit cell body-centred cubic

Unit cell body-centred cubic lattice

Unit cell centred

© 2024 chempedia.info