Miller indices practice examples: planes and directions

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MrClean1796

#khanacademytalentsearch. Many thanks to Krithika Chandrasekar, who inspired and encouraged me to make this video.

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Arkadeep Kumar

I am going to create a wtsapp group for guidance and doubt clearing, learning new concepts in easy ways with mutual benefits. kindly drop your details at:
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MANEES MEHTA

Tutorial on how to sketch the crystallographic direction vector when given the Miller indices of the direction vector.

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Linda Vanasupa

This video is about Working with Crystallographic Planes and Miller Indices

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Scott Ramsay

full video on Miller Indices very important for all competitive exams GATE,ESE and PSUs

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Sri Digital Gurukul

This video addresses the issues students commonly have with planes, Miller indices, and planar packing density.
To download the slide set from this video, visit this site:
http://www.slideshare.net/mseasuslides/23-muddiest-point2
To study the vocab used in this video, visit this site:
http://quizlet.com/21414859/23-crystal-structure-iii-planes-and-miller-indices-flash-cards/
This work was supported by NSF Grants #0836041 and #1226325.

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MaterialsConcepts

Structure of Materials by Prof. Sandeep Sangal & Dr. Anandh Subramaniam,Department of Metallurgy and Material Science,IIT Kanpur.For more details on NPTEL visit http://nptel.ac.in

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nptelhrd

Materials science problem that shows how to determine the indices of a plane in a cubic unit cell.

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Engineering and Design Solutions

This is lecture 7 in the series of chapter-1:crystal structure of course SOLID STATE PHYSICS.
here we will learn what is miller indices of planes ,and we will do some very good questions,
this lecture will be helpful to those who are preparing for iit-jam,iit-jee, neet, aiims, GATE,CSIR-NET, etc and physics enthusiasts .
link to last lecture on miller indices of directions is given here,
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#millerindicesplanes #gatephysics #netphysics #millerindices #iitjam #iitjee

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raystudies

Miller Indices for Planes

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Introduction to Materials Science and Engineering

Practice problems for miller indices want to comes to planes directions and structures of a unit cell

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MrClean1796

Explains the Miller indices notation used to label planes in a crystal structure. Made by faculty at the University of Colorado Boulder Department of Chemical and Biological Engineering. Reviewed by faculty from other academic institutions.
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LearnChemE

In this lecture we will discuss about crystallographic directions we will do few problems on it and then about angles in two crystallographic directions. book used is,
solid state physics by puri and babbar .
please visit the channel and subscribe if you want to help grow this channel.

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raystudies

Tutorial for indexing crystal planes and drawing planes given a miller index.
Video lecture for Introduction to Materials Science & Engineering (MSEN 201/MEEN 222), Texas A&M University, College Station, TX.
http://engineering.tamu.edu/materials

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Patrick Shamberger

Exclusive range of revision notes & video lessons available on our site |||--- ClicK LINK To ViSiT ---||| http://www.studyyaar.com/index.php/module/81-crystal-structure
Learn about Miller Indices and Planes, Calculating Miller Indices, Steps for Drawing Planes using Miller Indices, Family of Planes, Interplanar Distance, Numericals
http://www.studyyaar.com/index.php/module-video/watch/288-crystal-planes

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StudyYaar.com

Miller Indices of Directions

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Introduction to Materials Science and Engineering

detail explanation of miller indices for ESE,GATE,PSUs,with diffrent questions asked in ESE,GATE, and PSUs

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Sri Digital Gurukul

Finding miller indices of a crystal plane and drawing a plane for given miller indices

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meenakshi sonth

The application of a set of rules leads to the assignment of the Miller Indicesa set of numbers which quantify the intercepts and thus may be used to uniquely identify the plane or surface. ... So the surface/plane illustrated is the plane of the cubic crystal.Miller indices, group of three numbers that indicates the orientation of a plane or set of parallel planes of atoms in a crystal. If each atom in the crystal is represented by a point and these points are connected by lines, the resulting lattice may be divided into a number of identical blocks, or unit cells; the intersecting edges of one of the unit cells defines a set of crystallographic axes, and the Miller indices are determined by the intersection of the plane with these axes. The reciprocals of these intercepts are computed, and fractions are cleared to give the three Miller indices lengths equal to the edges of a unit cell has Miller indices of (111). This scheme, devised by British mineralogist and crystallographer William Hallowes Miller, in 1839, has the advantage of eliminating all fractions from the notation for a plane. In the hexagonal system, which has four crystallographic axes, a similar scheme of four Bravais-Miller indices is used.Phase, in thermodynamics, chemically and physically uniform or homogeneous quantity of matter that can be separated mechanically from a nonhomogeneous mixture and that may consist of a single substance or of a mixture of substances. The three fundamental phases of matter are solid, liquid, and gas (vapour), but others are considered to exist, including crystalline, colloid, glassy, amorphous, and plasma phases. When a phase in one form is altered to another form, a phase change is said to have occurred.• A vector r passing from the origin to a lattice point can be written as: r = r1 a + r2 b + r3 c where, a, b, c → basic vectors and Miller Indices for Planes: Procedure 1. Identify the plane intercepts on the x, y and z-axes. 2. Specify intercepts in fractional coordinates. 3. Take the reciprocals of the fractional intercepts. In Materials Science it is important to have a notation system for atomic planes since these planes influence • Optical properties • Reactivity • Surface tension • Dislocations
We've now seen how crystallographic axes can be defined for the various crystal systems. Two important points to remember are that
The lengths of the crystallographic axes are controlled by the dimensions of the unit cell upon which the crystal is based.
The angles between the crystallographic axes are controlled by the shape of the unit cell.
We also noted last time that the relative lengths of the crystallographic axes control the angular relationships between crystal faces. This is true because crystal faces can only develop along lattice points. The relative lengths of the crystallographic axes are called axial ratios, our first topic of discussion.
Axial Ratios
Axial ratios are defined as the relative lengths of the crystallographic axes. They are normally taken as relative to the length of the b crystallographic axis. Thus, an axial ratio is defined as follows:
Axial Ratio = a/b : b/b : c/b
where a is the actual length of the a crystallographic axis, b, is the actual length of the b crystallographic axis, and c is the actual length of the c crystallographic axis.
For Triclinic, Monoclinic, and Orthorhombic crystals, where the lengths of the three axes are different, this reduces toModern crystallographers can use x-rays to determine the size of the unit cell, and thus can determine the absolute value of the crystallographic axes. For example, the mineral quartz is hexagonal, with the following unit cell dimensions as determined by x-ray crystallography:
a1 = a2 = a3 = 4.913Å
c = 5.405Å
where Å stands for Angstroms = 10-10 meter.
Thus the axial ratio for quartz is
1 : 1 : 1 : 5.405/4.913
or
1: 1 : 1 : 1.1001
which simply says that the c axis is 1.1001 times longer than the a axes.
For orthorhombic sulfur the unit cell dimensions as measured by x-rays are:
a = 10.47Å
b = 12.87Å
c = 24.39Å
Thus, the axial ratio for orthorhombic sulfur is:
10.47/12.87 : 12.87/12.87 : 24.39/12.87
or
0.813 : 1 : 1.903
Because crystal faces develop along lattice points, the angular relationship between faces must depend on the relative lengths of the axes. Long before x-rays were invented and absolute unit cell dimensions could be obtained, crystallographers were able to determine the axial ratios of minerals by determining the angles between crystal faces. So, for example, in 1896 the axial ratios of n name, or index faces of crystals and define directions within crystals.Crystal faces can be defined by their intercepts on the crystallographic axes. For non-hexagonal crystals, there are three cases

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Pankaj Physics Gulati

Explanation of Miller indices in Hindi
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RQ physics

HOW TO DRAW PLANES IN MATERIAL SCIENCE

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Aniket Kolekar

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Study Hard until success

How to calculate miller indices of planes and directions in a crystal structure

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Matthew Araujo

Worked tutorial example showing how to identify a plane containing 3 points. We show two methods of solving this problem. The first is to sketch the points and plane and try to identify graphically where the plane intersects the x, y, and z axes. The second approach is to determine two directions in the plane by taking final-initial of the three points and then taking a cross-product to determine the normal vector which will be the same as the miller indices of the plane (ONLY in a cubic crystal system)

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Taylor Sparks

https://www.fiberoptics4sale.com
So what are Miller indices? They are a set of whole numbers to represent a plane or a direction inside a single crystal. In many semiconductor processing steps precise surface orientation is critical and directly affects the devices’ characteristics. We need a systematic way to represent different crystallographic planes and directions within a single crystal. And Miller indices are for this purpose.
This picture shows that single crystal silicon wafers’ surface is carefully aligned to lie in a specific crystallographic plane. And a ‘flat’ cut is ground along the edge to identify a reference direction within the surface plane. The top surface is represented by its Miller indices “(100)”. And the upward direction perpendicular to this plane is represented by its Miller indices “[001]”.
Then how do we get these Miller indices numbers? Here is the procedure for a crystallographic plane. In the next slide we will talk about the procedure for a direction.
We follow a very simple step by step procedure to get the Miller indices for a plane within a single crystal.
First, we need a coordinate system, so we set up coordinate axes along the edges of the unit cell. In this simple cubic cell, it’s the x, y, z axes.
Then let’s look at the plane of interest. And write down the values where it intercepts the axes. For this example, it is ‘a’ for x axis, ‘one half of b’ for y axis, and ‘3c’ for z axis.
Then we divide these values by the unit cell length along the respective axis. So ‘a’ divided by ‘a’ is 1 for x axis, ‘one half of b divided by b’ is one half for y axis, and ‘3c divided by c’ is 3 for z axis.
Now we need to invert the values, so 1 over 1 is 1 for x axis, 1 over one-half is 2 for y axis, and 1 over 3 is one-third for z axis.
Then we multiply these numbers by a minimum possible integer so these numbers become the smallest possible whole numbers. For this particular case, we need to multiply with the number 3, and we get 3, 6, 1 as the final numbers.
Lastly enclose this set of whole numbers inside a pair of curly brackets, so “(3,6,1)” is the Miller indices for this plane.
This picture shows more examples of Miller indices for different planes. There are two special cases we need to take care of.
First, if the plane is parallel to an axis, the “intercept” along that axis is marked as infinity. When you invert infinity, you get the number zero. This is why you see zeros such as “(100)” which is parallel to y and z axis, “(110)” which is parallel to z axis, etc.
Second, If the plane intercepts an axis in the negative portion, the minus sign is placed on top of the corresponding number, such as this “minus 1, zero, zero” plane.
The Miller indices for a direction are established by decomposing a vector in the direction into its components. Let’s look at the [120] direction in this example.
This vector’s x axis projection value is “one half”, y axis projection value is “1”, z axis projection value is “0”.
We then multiply these numbers by “2” so the results will be a set of smallest possible whole numbers. Thus we get 1, 2, 0.
We then enclose them inside a pair of square brackets. This is the convention for Miller indices of a direction.
We take care of directions parallel to axes and negative numbers the same way as for planes as we pointed out in the last page.
Lastly, here are some more direction examples and you can practice getting their Miller indices.

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FOSCO CONNECT

This lecture is useful for 10+2, Mechanical engineering, B.Sc. and B.Tech. students. If any questions please contact me WhatsAp number 9416939577

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If a face PQR makes intercepts p, q and r on the three axes and the intercepts made by the unit plane are a, b and c then we have,p = na, q = n’b and r = n’’c Where n, n’ and n’’ are simple whole numbers or infinity. Then the face PQR may be presented by (n, n’, n’’). The numbers used to represent a face are called Weiss indices.
Miller indices may be defined as the reciprocal of the coefficients of the intercepts, expressed as integers.Thus the intercept made by plane PQR can be expressed as, Then the Miller indices of the plane are (h, k, l). Obviously, the miller indices of a face are inversely proportional to the intercept of that face on the crystallographic axes.
Examples of Miller indices:
(i) If the intercepts made by plane PQR are 2a, 2b, 3c. The reciprocals of the coefficients of a, b, c are, and LCM of 2, 2, 3 = 6. Multiplying the reciprocals by 6 we have 3, 3, 2. Therefore the miller indices for the plane PQR is (3, 3, 2)
(ii) If the intercepts made by plane PQR are a, b, c. The reciprocals of the coefficients of a, b, c are, and LCM of 1, 1, 1 = 1. Therefore the miller indices for the plane PQR is (1, 1, 1)
(iii) If the intercepts made by plane PQR are 2a, 3b, ∞c. That means plan is not cutting the z axis. The reciprocals of the coefficients of a, b, c are, and LCM of 2 and 3 = 6. Multiplying the reciprocals by 6 we have 3, 2, 0. Therefore the miller indices for the plane PQR is (3, 2, 0)
(iv) If the intercepts made by plane is negative i.e. the face is cut by the axis when extended in the opposite direction, it is represented by putting a bar over it.
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Cepek Media

Introducción de los índices de Miller en un sistema de panos cristalográficos.
Para ver ejemplos de indices de Miller, haz click el siguiente link:
https://youtu.be/zN0AyXHsWAM

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Ciencia y tecnología

Crystal structure :
Classification of solids based on arrangement
Elements of crystal forms
Miller indices
Common forms in Crystallograpy
Elements of symmetry
Classification of Solid based on symmetry

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Geology Concepts

Tutorial example solutions for labeling and drawing crystal planes with Miller Indices. In addition, we show why you can select any origin or convert planes to smallest integers using crystal diagram software VESTA

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Taylor Sparks

Miller-Bravais for hexagonal crystals

Here we review Miller index notation.

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Scott-WSU Beckman

Tutorial for indexing crystal planes and drawing planes given a miller index.
Video lecture for Introduction to Materials Science & Engineering (MSEN 201/MEEN 222), Texas A&M University, College Station, TX.
http://engineering.tamu.edu/materials

Views: 64758
Patrick Shamberger

Determines the four-parameter Miller-Bravais indices for an hexagonal unit cell.
Made by faculty at the University of Colorado Boulder Department of Chemical and Biological Engineering. Reviewed by faculty from other academic institutions.
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Are you using a textbook? Check out our website for videos organized by textbook chapters: http://www.learncheme.com/screencasts

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LearnChemE

*Miller indices
*Crystal Planes
*Direction of planes
*Family of planes
*Family of directions
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Physics and Technology

Miller Indices for a plane and its normal in Cubic Crystal

How to find Miller Indices and distance between two parallel plane in crystal using miller indices.

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gkbit

How to find out miller indices for 3a : 2b : 3c
Step 1 - remove letters
3 2 3
Step 2 - take reciprocal
1 1 1
-- -- --
3 2 3
Step 3 - multilpy all denominator
3 X 2 X3 = 18
Step 4 - put 18 on every numerator (multiple all numerator with ans) here 1X18 =18
now - 18 18 18
--- --- ---
3 2 3
Step 5 - devide all numerator by denominator
6 9 6
Step 6 - if valuse can furthur be divided then divide by a common no
6 9 6
--- --- --- = 3 2 3
3 3 3
so miller indices for 3a : 2b : 3c is ==== 3 2 3
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Exclusive Geology

How to calculate miller indices for HCP

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Matthew Araujo

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Here the plane intersects x axis at a and is parallel to y and z axis.
Therefore, Miller Indices of plane is (100).
Here the plane intersects y axis at b and is parallel to x and z axis.
Therefore, Miller Indices of plane is (010).
Here the plane intersects z axis at c and is parallel to x and y axis.
Therefore, Miller Indices of plane is (001).
Here the plane intersects x axis at a and y axis at b and is parallel to z axis. Therefore, Miller Indices of plane is (110).
Here the plane intersects x axis at a and z axis at c and is parallel to y axis. Therefore, Miller Indices of plane is (101).
Here the plane intersects y axis at b and z axis at c and is parallel to x axis.Therefore, Miller Indices of plane is (011).
Here the plane intersects x axis at a, y axis at b and z axis at c..
Therefore, Miller Indices of plane is (111).
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Cepek Media

This is the "Talking Head" version of this topic, including three examples.
I have posted three versions of this topic (1.Annotated Tablet, 2.Talking Head, 3. Chalkboard) and I'm interested to learn which version people find most useful.

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Scott Ramsay