Last time, we explained crystals, which are the arrangement of atoms that make up a substance, and crystal lattices, which are the smallest units of a crystal.
Furthermore, we explained two of the three representative crystal lattices of metallic bonding: body-centered cubic (BCC) and face-centered cubic (FCC).
This time, we will explain the hexagonal close-packed lattice, which is the last of the three representative crystal lattices of metallic bonding.
Hexagonal Close Packed Lattice (HCP)
First, let's look at the actual shape of the hexagonal close-packed lattice crystal lattice.
To begin with, let's review by looking at a simple, hypothetical diagram of a crystal and crystal lattice (the model used in the previous explanation of crystals and crystal lattices).
Basically, the hexagonal close-packed lattice is the same concept as this simple model, just with a different lattice shape.
The hexagonal close-packed lattice is easier to understand if you think of it in terms of stacking layers, so let's start by thinking about the first layer and then stacking it up to the second and third layers.
Let's start by considering the first level.
Please recall that the first layer of the body-centered cubic and face-centered cubic lattices, which we explained last time, consisted of atoms arranged in a 2x2 grid.
Next, let's broaden the scope a bit and consider a 3x3 atomic arrangement.
While this 3x3 atomic arrangement is fundamentally fine, nature is powerful, and there's a mechanism at work that encourages more atoms to fit into a given area, resulting in a more efficient arrangement.
Specifically, atoms arranged in a 3x3 grid move as shown in the following diagram.
This results in a dense hexagonal arrangement of atoms, as shown in the following diagram.
In other words, it becomes a dense hexagonal structure. This hexagon becomes the first layer.
This hexagon is the origin of the name "hexagonal close-packed lattice."
Next, let's consider the second row.
From here on, I will explain using a model made from BB pellets.
First up is the hexagonal model in the first layer.
Let's use this model as a basis to design the second layer.
As I mentioned before, nature is magnificent, and the atoms in the second layer are arranged to be denser than the atoms in the first layer (atoms are more comfortable when they are close together and densely packed).
Based on that principle, the arrangement of atoms in the second layer, which is the closest to the first layer, will be as follows.
This arrangement can be represented in a model as follows.
Three atoms are arranged in the second layer to create this dense arrangement.
Next, let's consider the third level.
The third layer is very simple, with atoms arranged in the exact same hexagonal pattern as the first layer, covering it like a lid.
When made into a model, it would look like this.
Since we're here, let's take a look at the model from the other side.
In this way, a hexagonal arrangement of six atoms is sandwiched above and below a triangular arrangement of three atoms.
This forms a hexagonal close-packed lattice.
This can be illustrated as follows:
This is just my personal impression.The atomic arrangement that makes up the first and third layers is hexagonal.with accommodation.The densest structurewith accommodation.hexagonal close-packed latticeI think so.
It is generally called a hexagonal close-packed lattice, but some people refer to it as a dense hexagonal lattice or hexagonal close-packed structure, all of which refer to the same thing.
I might get scolded by scholars and professors for this, but my image of it is that of three body-centered cubic lattices joined together at an angle.
The English name is also important.Hexagonal, Close, and Packed are collectively called HCP..
A crystal like the one shown in the following diagram is formed when many of these hexagonal close-packed lattices (HCPs) come together.
The shape is important here as well, so I will explain the detailed characteristics later.
Well-known examples of materials with this crystal lattice or crystal structure include magnesium (Mg), zinc (Zn), cobalt (Co), and titanium (Ti).
However, since the shape of the crystal lattice of each substance changes depending on the temperature and other conditions and treatments, I don't think it's necessary to memorize them.
Many common explanations state that "a hexagonal close-packed lattice is the structure in which atoms are packed most densely," but that's not actually the case.
I will explain the detailed reasons for using numbers later."Why is a hexagonal close-packed lattice not the densest structure?"I will explain this using images.
Hexagonal close-packed lattice and face-centered cubic lattice (in fact, the degree of atomic density is the same)
As I've already mentioned in the title, the degree of atomic density is actually the same for hexagonal close-packed lattices (HCP) and face-centered cubic lattices (FCC).
First, let's compare the diagrams of the face-centered cubic lattice (FCC) and hexagonal close-packed lattice (HCP) that we have explained so far.
Judging from the diagram, it seems that the hexagonal close-packed lattice (HCP) is definitely the denser state.
In reality, the degree of density is the same, but we will use a model to explain why this is the case.
First, let's recall the diagram of a hexagonal close-packed lattice (HCP) with two layers stacked on top of each other.
This can be represented in a diagram as follows.
When made into a model, it would look like this.
In a hexagonal close-packed lattice (HCP), the second layer is covered with atoms arranged in the same hexagonal configuration as the first layer.
But this time, let's change our approach a bit and consider a different atomic arrangement that would be denser in the third layer.
The following diagram shows the locations where atoms can be densely arranged on top of the second layer of atoms, which consists of three atoms.
The idea is to place an atom on top of the space between two connected atoms.
Therefore, since each atom is composed of three parts, the second layer can accommodate three atoms.
When made into a model, it would look like this.
I think you now have a clearer image of it.
Those with a keen eye may have already noticed, but I'm going to try changing the way I paint the models.
Let's take another look at the face-centered cubic lattice illustrated here.
Yes, it becomes a face-centered cubic lattice (FCC) with the cubes slightly tilted.
To explain it in words, the first two layers are stacked in the same way as a hexagonal close-packed lattice (HCP), but if you slightly change the way you stack the third layer, you get a face-centered cubic lattice (FCC).
SoBoth hexagonal close-packed lattices (HCP) and face-centered cubic lattices (FCC) are densely packed, so the degree of density of atoms within the lattice is the same.
Incidentally, in the world of materials science, this degree of density is called packing efficiency, and it can be expressed numerically as the ratio of the volume occupied by atoms to the volume of the lattice.
I will explain the details later.
In any case, what I want you to keep in mind here is that the degree of density of atoms in a lattice is the same for face-centered cubic lattices and hexagonal close-packed lattices.
Summary
Let's summarize the three basic types of crystal lattices that metal atoms and metallic bonds possess.
Even with the same substance (metal), the properties can change significantly depending on the crystal structure and the shape of the crystal lattice.
Metal atoms and metallic bonds primarily have three types of crystal lattices.
One of the most representative metallic crystals is the body-centered cubic (BCC) lattice.
One of the most common types of metallic crystals is the face-centered cubic (FCC) lattice.
One of the most representative metallic crystals is the hexagonal close-packed lattice (HCP).
The degree of atomic density within the lattice is the same for face-centered cubic (FCC) and hexagonal close-packed (HCP) lattices.
I apologize for always repeating the same thing, but understanding is more important than memorization (though I apologize to students and exam takers, as memorization is also necessary).
Even if you don't remember, you can figure it out yourself if you understand the mechanism, and if you forget, you can just look it up (please feel free to use this site as a memo pad).
This concludes our explanation of the basic crystal lattices of metals.
In particular, the degree of atomic density within a face-centered cubic lattice and a hexagonal close-packed lattice is the same. As will be explained in more detail later, because the degree of density is the same, the properties of face-centered cubic lattices and hexagonal close-packed lattices are quite similar.
This is extremely important, so I really want you to understand it.
Next time, I'll explain the characteristics of each crystal and crystal lattice (lattice constant, coordination number, etc.), although it might not be very interesting.
Finally, I'd like to introduce something different and unusual.
We've discussed some typical crystal lattices, but for those who want a deeper understanding, I recommend trying to build a model like I did (it's simple). This time, we're dealing with a slightly more complex hexagonal close-packed lattice, so building a model is very effective for understanding it. In particular, the relationship between face-centered cubic lattices and hexagonal close-packed lattices becomes much clearer when you use a model.
Anything will do as long as you have a ball and some adhesive, but I'll introduce what I used.
Tokyo Marui BBs 0.2g 1600 rounds
The manufacturer, weight, and precision don't really matter, but I recommend white.
Loctite instant adhesive
Any adhesive will do, but it's best to use a branded one as it will be difficult to work with if it doesn't have a certain level of performance.
To those who found this article helpful in understanding design:
While there is basically no textbook covering this content, and it is my own original work, I will introduce the textbook that I have been using since I was a student.
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