Determining Miller Indices of High Index Planes

In summary, Miller indices are a system used to describe the orientation of a crystal plane in a material, represented as three integers (hkl). The Miller indices of high index planes can be determined by finding the reciprocals of the intercepts with the axes and simplifying the fractions. High index planes have a large Miller index value, typically greater than 5, and are important in materials science and engineering due to their unique surface properties. Determining their Miller indices allows for a better understanding and control of a material's behavior and performance in various applications. Methods such as geometric construction, Laue diffraction, and X-ray diffraction can be used to determine the Miller indices of high index planes.
  • #1
beaverdam
1
0
Hi,

can anyone explain how miller indices can be determined for high index planes?
For example, why is it that

(544) = (S)-[ 9(111) x (100) ]

I tried to figure it out but i could no find a pattern

Thx in advance
 
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  • #2
3-component Miller Indices are defined in terms of cubic unit cells. Go back to the definition of a Miller Index. For (544) = (S)-[ 9(111) x (100) ], I cannot answer because I don't know what S is.

modey3
 
  • #3


Hi there,

Miller indices are used to describe the orientation of crystal planes in a crystal lattice. They are determined by taking the reciprocal of the intercepts of the plane on the crystal axes. In the case of high index planes, the intercepts may not be obvious and require some additional calculations.

In the equation you provided, (544) is the Miller index for a high index plane, and it is derived from the formula (hkl) = (S)-[ n(abc) x (uvw) ], where S is the smallest integer that makes all indices positive, n is the order of the plane, and (abc) and (uvw) are the normal vectors of the plane and the axes of the crystal, respectively.

In this case, (111) and (100) are the normal vectors of the plane and the crystal axes, respectively. By taking the cross product of these vectors, we get a vector that is perpendicular to both and represents the direction of the plane. This vector is then multiplied by the order of the plane, which in this case is 9, to account for the fact that it is a high index plane. Finally, the smallest integer S is chosen to make all indices positive, which in this case is 1.

I hope this explanation helps to clarify the process of determining Miller indices for high index planes. It may seem complex, but with practice, it becomes easier to identify patterns and apply the formula.
 

FAQ: Determining Miller Indices of High Index Planes

1. What are Miller Indices?

Miller indices are a system used to describe the orientation of a crystal plane in a material. They are represented as three integers (hkl) that indicate the intercepts of the plane with the x, y, and z axes, respectively.

2. How do you determine the Miller Indices of high index planes?

The Miller indices of a high index plane can be determined by finding the reciprocals of the intercepts of the plane with the x, y, and z axes, and then simplifying the resulting fractions. For example, if a plane intersects the x-axis at 2/3, the y-axis at 3/4, and the z-axis at 4/5, the Miller indices would be (3, 4, 5).

3. What are high index planes?

High index planes are crystal planes that have a large Miller index value, typically greater than 5. These planes are important in materials science and engineering because they often have unique surface properties that can affect the behavior and performance of a material.

4. Why is it important to determine the Miller Indices of high index planes?

Determining the Miller indices of high index planes is important because it allows scientists and engineers to understand the crystal structure of a material and how it may affect its properties. By knowing the orientation of high index planes, researchers can predict and control the behavior of a material, which is crucial in various applications, such as in electronic devices and coatings.

5. What methods are used to determine the Miller Indices of high index planes?

There are several methods that can be used to determine the Miller indices of high index planes, including geometric construction, Laue diffraction, and X-ray diffraction. These methods rely on the measurement of the angles and distances between crystal planes and can be performed using specialized equipment such as diffractometers.

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