Miller Indices

1. MILLER INDICES
DEPARTMENT OF CHEMISTRY
Date: 26 June, 2023 NIT
SRINAGAR
Zeeshan Nazir

2. Table of Contents
• Introduction
• Lattice Plane
• Miller Indices
• How to calculate
• Points to remember
• Numericals
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3. What is Miller Indices ?
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4. Lattice Plane
Before that, let’s know what is a
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5. Lattice Plane
• The plane which passes through crystal lattice and intersects lattice points is
called “Lattice plane”.
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6. Miller Indices
Miller Indices are set of three numbers used to specify lattice plane.
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7. How to calculate?
1. Find intercepts made by the plane in X, Y, Z axis.
Here X= ∞, Y= 1 and Z= ∞.
2. Take reciprocal of:
x intercept = 1/∞ = 0
y intercept = 1/1 = 1
z intercept = 1/∞0 =0
3. Miller Indices of this plane are: (010)
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8. Remember
• Miller Indices are written without use of Commas.
(010) ✔️
(0,1,0) ❌
• Values of Miller Indices is not written in fractions either.
(2/3,1,0) ❌
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9. Example
• Here: X intercept= 2
Y intercept=3
Z intercept=1
• Reciprocal = 1/2 1/3 1
• Since Miller indices cannot be fraction multiply
LCM of denominator(2⛌3= 6) throughout the
numerator.
• Therefore Miller Indices = (326)
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10. What if plane passes through origin?
• In this case Y intercept is “0” therefore reciprocal of
intercept is 1/0.
• Which is not possible.
• In such a situation you need to shift the "origin" to the
nearest lattice point of parallel face.
• Now Y= -1, X= ∞, Z= ∞
• Therefore Miller Indices can be represented as (0 1 0)
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11. ?
Thank you so much!

12. Special Thanks to Dr. Shrikant S Maktedar (Sir)
Linkedin.com/ZeeshanNazir
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