(2,0,0) plane for simple cubic lattice

In summary, in a simple cubic lattice, the plane (2,0,0) exists but has no physical meaning. When the X-ray diffraction is done, this plane may play a role.
  • #1
feiyangflash
4
0
Hi All,

Does the plane of miller index (2,0,0) exist in simple cubic lattice?

It is easy to understand that (1,0,0) plane exist. But for (2,0,0) plane, I feel confused.

If (2,0,0) plane exists, the plane intersect with the x-axis at 1/2*a, if a is the lattice constant; and the plane is parallel with y-axis and z-axis. However, there is no atoms deployed in this plane! Is there any physical meaning for this plane, since no atom is there? When the X-ray diffraction is done, does this plane ever play a role?

Thank you!

Fei
 
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  • #2
Hi Fei,

A simple cubic lattice can have a multiple-atom basis. For example, cesium chloride is simple cubic with a two atom basis. The atom at the center of the cell would create a diffraction at the (200) plane. In fact, for simple cubic, all reflections are possible due to the very high degree of symmetry.
 
  • #3
Hi UBY,

Thank you! Your explanation makes sense.

The alpha form of Polonium (Po) has a simple cubic crystal structure in a single atom basis. Does the plane (2,0,0) have a physical meaning for Polonium?


uby said:
Hi Fei,

A simple cubic lattice can have a multiple-atom basis. For example, cesium chloride is simple cubic with a two atom basis. The atom at the center of the cell would create a diffraction at the (200) plane. In fact, for simple cubic, all reflections are possible due to the very high degree of symmetry.
 
  • #4
For a single-atom basis, a (200) reflection will still exist, but only as a family member of the (100) reflection. In other words, its intensity would be related to the intensity of the (100) reflection by a geometric factor indicating the fraction of planes present (1/2).

In 2D, draw a series of parallel lines and pretend they are the (100) planes. Now draw a series of dashed lines in between these. The dashed lines AND the parallel lines represent all the equivalent (200) reflections, but only half are actually present in the crystal (the dashed lines are unoccupied).
 
  • #5


I can confirm that the (2,0,0) plane does indeed exist in a simple cubic lattice. While it may seem confusing at first that there are no atoms located within this plane, it is important to remember that the lattice points in a simple cubic lattice represent the centers of the atoms, not the actual positions of the atoms themselves. Therefore, the (2,0,0) plane does not necessarily need to have atoms located within it in order to exist in the lattice.

In terms of physical meaning, the (2,0,0) plane can still have an impact on the properties of the lattice. For example, it can affect the overall symmetry and diffraction patterns of the lattice. When X-ray diffraction is performed, the (2,0,0) plane may not directly contribute to the diffraction peaks, but it can still affect the overall diffraction pattern due to its presence in the lattice.

Overall, while it may seem counterintuitive that a plane with no atoms can exist in a lattice, it is a fundamental aspect of the structure and can still have an impact on its properties.
 

FAQ: (2,0,0) plane for simple cubic lattice

1. What is a simple cubic lattice?

A simple cubic lattice is a type of crystal lattice structure where the lattice points are arranged in a cube shape with each point at the corners of the cube. It is the simplest and most basic type of lattice and is commonly used in the study of crystals and materials science.

2. What does the (2,0,0) plane refer to in a simple cubic lattice?

The (2,0,0) plane refers to a specific crystal plane within a simple cubic lattice. It is parallel to the x-axis and contains lattice points at coordinates (2,0,0), (4,0,0), (6,0,0), and so on. This plane is important in understanding the atomic arrangement and properties of materials with a simple cubic lattice structure.

3. How is the (2,0,0) plane related to the unit cell of a simple cubic lattice?

The (2,0,0) plane is one of the six faces of the unit cell in a simple cubic lattice. The unit cell is the smallest repeating unit of a crystal lattice, and in a simple cubic lattice, it is a cube with lattice points at each corner. The (2,0,0) plane is a boundary of this unit cell, and it represents a specific orientation of the lattice points within the crystal.

4. What is the significance of studying the (2,0,0) plane in a simple cubic lattice?

Studying the (2,0,0) plane in a simple cubic lattice allows scientists to understand the atomic arrangement and properties of materials with this crystal structure. By analyzing the spacing and arrangement of atoms within this plane, researchers can gain insights into the physical, chemical, and mechanical properties of materials, which can be useful in various industries such as materials engineering and nanotechnology.

5. How does the (2,0,0) plane differ from other crystal planes in a simple cubic lattice?

The (2,0,0) plane is unique in that it is parallel to the x-axis and contains lattice points at coordinates that are multiples of 2. Other crystal planes in a simple cubic lattice, such as the (1,1,1) plane, have lattice points at coordinates that are multiples of different numbers. Each plane has its own set of properties and behaviors that contribute to the overall properties of the material, making the study of crystal planes in a simple cubic lattice important for understanding materials at the atomic level.

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