Looking for a way to enclose your yard but hate the restrictive feel of tall privacy enclosures? Do you want security within your property but feel that stockade style fences are too plain for your landscape? Then lattice fences may be the right fence style for you. A lattice fence can offer privacy, security and help your backyard look more inviting to family and friends. We could alternatively use regular hexagons as the unit cells, but the x+ y shifts would still be required, so the simpler rhombus is usually preferred.Here are our best lattice fence design ideas. Notice that to generate this structure from the unit cell, we need to shift the cell in both the x- and y- directions in order to leave empty spaces at the correct spots. The unit cell of the graphite form of carbon is also a rhombus, in keeping with the hexagonal symmetry of this arrangement. As is shown more clearly here for a two-dimensional square-packed lattice, a single unit cell can claim "ownership" of only one-quarter of each molecule, and thus "contains" 4 × ¼ = 1 molecule. This means that an atom or molecule located on this point in a real crystal lattice is shared with its neighboring cells. Notice that in both of these lattices, the corners of the unit cells are centered on a lattice point. Although we could use a hexagon for the second of these lattices, the rhombus is preferred because it is simpler. Shown above are unit cells for the close-packed square and hexagonal lattices we discussed near the start of this lesson. In general, the best unit cell is the simplest one that is capable of building out the lattice. The one that is actually used is largely a matter of convenience, and it may contain a lattice point in its center, as you see in two of the unit cells shown here. Any number of primitive shapes can be used to define the unit cell of a given crystal lattice. The orange square is the simplest unit cell that can be used to define the 2-dimensional lattice.īuilding out the lattice by moving ("translating") the unit cell in a series of steps,Īlthough real crystals do not actually grow in this manner, this process is conceptually important because it allows us to classify a lattice type in terms of the simple repeating unit that is used to "build" it. The gray circles represent a square array of lattice points. These repeating units act much as a rubber stamp: press it on the paper, move ("translate") it by an amount equal to the lattice spacing, and stamp the paper again. Crystal lattices can be thought of as being built up from repeating units containing just a few atoms. The underlying order of a crystalline solid can be represented by an array of regularly spaced points that indicate the locations of the crystal's basic structural units. Adjacent sheets are bound by weak dispersion forces, allowing the sheets to slip over one another and giving rise to the lubricating and flaking properties of graphite. The coordination number of 3 reflects the sp 2-hybridization of carbon in graphite, resulting in plane-trigonal bonding and thus the sheet structure. The result is just the basic hexagonal structure with some atoms missing. Each carbon atom within a sheet is bonded to three other carbon atoms. The version of hexagonal packing shown at the right occurs in the form of carbon known as graphite which forms 2-dimensional sheets. This will, of course, be the hexagonal arrangement.ĭirected chemical bonds between atoms have a major effect on the packing. If the atoms are identical and are bound together mainly by dispersion forces which are completely non-directional, they will favor a structure in which as many atoms can be in direct contact as possible. If we go from the world of marbles to that of atoms, which kind of packing would the atoms of a given element prefer? If you are good at geometry, you can show that square packing covers 78 percent of the area, while hexagonal packing yields 91 percent coverage. It should also be apparent that the latter scheme covers a smaller area (contains less empty space) and is therefore a more efficient packing arrangement. The essential difference here is that any marble within the interior of the square-packed array is in contact with four other marbles, while this number rises to six in the hexagonal-packed arrangement. It turns out that there are two efficient ways of achieving this: How can you arrange them in a single compact layer on a table top? Obviously, they must be in contact with each other in order to minimize the area they cover. This will make it easier to develop some of the basic ideas without the added complication of getting you to visualize in 3-D - something that often requires a bit of practice. \)Ĭrystals are of course three-dimensional objects, but we will begin by exploring the properties of arrays in two-dimensional space.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |