If we write everything in terms of the radius of an atom, you can see that every face-centered cubic crystal will have the same packing factor regardless of the actual element. The volume of a sphere is. That is exactly the same value as face-centered cubic FCC crystals, because both HCP and FCC are close-packed structures with the maximum possible APF although it is possible to have higher packing if you use multiple kinds of atoms with different sizes.
In addition to FCC and HCP, it is possible to have other close-packed structures such as the close-packed rhombohedral structure found in samarium. It all comes down to stacking order. I already mentioned this before, but both the conventional and primitive HCP cells are commonly used.
The conventional cell has advantages because it is highly symmetric and easy for humans to understand. The primitive cell is smaller which can make mathematical manipulation easier. If you are interested in primitive cells, you can read all about them in this article. Interstitial sites are the spaces inside a crystal where another kind of atom could fit.
HCP has two types of interstitial sites: octahedral and tetrahedral. Technically trigonal sites are also possible, but they are not practically useful. HCP has 6 octahedral sites, which means that a small interstitial atom could fit in 6 positions such that it is equally surrounded by 6 HCP lattice atoms. These octahedral interstitial sites have a radius of 0. HCP also has 12 tetrahedral sites, which means that a small interstitial atom could fit in 12 positions such that it is equally surrounded by 4 HCP lattice atoms.
Slip systems are the way that atoms slide past each other when deforming. Slip systems determine many mechanical properties of materials, and is the main reason why a material will be ductile or brittle.
You can see in this plane, there are 3 slip directions: [], [], and []. However, since [] can be made by the linear combination of [] and [], there are actually only 2 independent slip systems. There are also prismatic and pyramidal slip systems in HCP. These systems, however, are not necessarily close-packed, and may need to be thermally activated.
Because not all HCP metals have all at least 5 independent slip systems active at room temperature, not all HCP metals are ductile at room temperature. In other metals, the slip systems can be thermally activated to provide ductility. The Hexagonal Close-Packed HCP crystal structure is one of the most common ways that atoms can be arranged in pure solids.
If you want to know more about the basics of crystallography, check out this article about crystals and grains. I also mentioned atomic packing factor APF earlier in this article.
This is an important concept in your introductory materials science class, so if you want a full explanation of APF, check out this page.
If you want to learn about specific crystal structures, here is a list of my articles about Bravais lattices and some related crystal structures for pure elements. Adding the volumes of these 6 atoms, gives a volume that is equivalent to that of 3 full atoms. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group.
Create a free Team What is Teams? Learn more. Asked 5 years, 8 months ago. Active 3 years, 6 months ago. Viewed 25k times. Can somebody explain why this objection is incorrect? Improve this question. Quaternion Quaternion 1 1 gold badge 2 2 silver badges 10 10 bronze badges. I was forgetting to include the spherical caps from middle-layer atoms whose centres lie in adjacent unit cells.
When a single layer of spheres is arranged into the shape of a hexagon, gaps are left uncovered. The hole formed between three spheres is called a trigonal hole because it resembles a triangle.
In the example below, two out of the the six trigonal holes have been highlighted green. Once the first layer of spheres is laid down, a second layer may be placed on top of it. The second layer of spheres may be placed to cover the trigonal holes from the first layer. Holes now exist between the first layer the orange spheres and the second the lime spheres , but this time the holes are different. The triangular-shaped hole created over a orange sphere from the first layer is known as a tetrahedral hole.
A hole from the second layer that also falls directly over a hole in the first layer is called an octahedral hole. In a hexagonal closest packed structure, the third layer has the same arrangement of spheres as the first layer and covers all the tetrahedral holes. Since the structure repeats itself after every two layers, the stacking for hcp may be described as "a-b-a-b-a-b.
Similar to hexagonal closest packing, the second layer of spheres is placed on to of half of the depressions of the first layer. The third layer is completely different than that first two layers and is stacked in the depressions of the second layer, thus covering all of the octahedral holes. The spheres in the third layer are not in line with those in layer A, and the structure does not repeat until a fourth layer is added.
The fourth layer is the same as the first layer, so the arrangement of layers is "a-b-c-a-b-c. A unit cell is the smallest representation of an entire crystal. All crystal lattices are built of repeating unit cells.
0コメント