SlideShare a Scribd company logo
DIRECTIONS, PLANES AND
MILLER INDICES
By Srilakshmi B
UCST, Tumkur
CONTENTS
• INTRODUCTION
• NEED OF DIRECTIONS AND PLANES
• GENERAL RULES AND CONVENTION
• MILLER INDICES FOR DIRECTIONS
• MILLER INDICES FOR PLANES
• IMPORTANT FEATURES OF MILLER INDICES
INTRODUCTION
The crystal lattice may be regarded as made
up of an infinite set of parallel equidistant
planes passing through the lattice points
which are known as lattice planes.
In simple terms, the planes passing through
lattice points are called ‘lattice planes’.
For a given lattice, the lattice planes can be
chosen in a different number of ways.
• The orientation of planes or faces in a crystal can
be described in terms of their intercepts on the
three axes.
• Miller introduced a system to designate a plane
in a crystal.
• He introduced a set of three numbers to specify
a plane in a crystal.
• This set of three numbers is known as ‘Miller
Indices’ of the concerned plane.
NEED OF DIRECTIONS AND PLANES
• Deformation under loading (slip) occurs on
certain
crystalline planes and in certain crystallographic
directions.
• Before we can predict how materials fail, we need
to know what modes of failure are more likely to
occur. Other properties of materials (electrical
conductivity, thermal conductivity, elastic
modulus) can vary in a crystal with orientation.
GENERAL RULES FOR LATTICE
DIRECTIONS, PLANES AND MILLER
INDICES
• Miller indices used to express lattice planes and
directions
• x, y, z are the axes (on arbitrarily positioned
origin)
• a, b, c are lattice parameters (length of unit cell
along a side) h, k, l are the Miller indices for
planes and directions -
expressed as planes: (hkl) and directions: [hkl]
CONVENTION FOR NAMING
• There are NO COMMAS between numbers
• Negative values are expressed with a bar over
the number
Example: -5 is expressed 5
MILLER INDICES FOR DIRECTIONS
• Draw vector, and find the coordinates of the
head, h1,k1,l1 and the tail h2,k2,l2.
• subtract coordinates of tail from coordinates
of head
• Remove fractions by multiplying by smallest
possible factor
• Enclose in square brackets
The direction can also be
determined by giving
the coordinates of the
first whole numbered
point (x,y) through
which each of the
direction passes.
In this figure direction of
OA is[110] and OB is
[520]
IMPORTANT DIRECTIONS IN A CRYSTAL
MILLER INDICES FOR PLANES
• If the plane passes through the origin, select
an equivalent plane or move the origin
• Determine the intersection of the plane with
the axes in terms of a,b, and c
• Take the reciprocal (1/∞ = 0)
• Convert to smallest integers
• Enclose by parentheses
EXAMPLE
• Here x,y and z
intercepts are 1,1,1.
• Therefore (111) is the
miller indices of the
plane
• DETERMINATION OF ‘MILLER
INDICES
• Step 1:The intercepts are 2,3 and
2 on the three axes.
• Step 2:The reciprocals are 1/2,
1/3 and 1/2.
• Step 3:The least common
denominator is ‘6’. Multiplying
each reciprocal by lcd, we get, 3,2
and 3.
• Step 4:Hence Miller indices for
the plane ABC is (3 2 3)
IMPORTANT FEATURES OF MILLER
INDICES
• A plane passing through the origin is defined in
terms of a parallel plane having non zero
intercepts.
• All equally spaced parallel planes have same
‘Miller indices’ i.e. The Miller indices do not only
define a particular plane but also a set of parallel
planes. Thus the planes whose intercepts are 1,
1,1; 2,2,2; -3,-3,-3 etc., are all represented by the
same set of Miller indices.
• It is only the ratio of the indices which is
important in this notation. The (6 2 2) planes
are the same as (3 1 1) planes.
• If a plane cuts an axis on the negative side of
the origin, corresponding index is negative. It
_
is represented by a bar, like (1 0 0). i.e. It
indicates that the plane has an intercept in
the –ve X –axis.
Planes and their negatives are
equivalent
In the cubic system, a plane and a
direction with the same indices are
orthogonal
Here the direction is
[001]
and plane is (001)
SOME IMPORTANT PLANES
BIBLIOGRAPHY
• SOLID STATE PHYSICS BY S.O.PILLAI, FIFTH
EDITION BY NEW AGE INTERNATIONAL
PUBLICATION
Directions, planes and miller indices

More Related Content

What's hot

Crystal structure
Crystal structureCrystal structure
Crystal structure
nagaraju kondrasi
 
MILLER INDICES FOR CRYSTALLOGRAPHY PLANES
MILLER INDICES FOR CRYSTALLOGRAPHY PLANESMILLER INDICES FOR CRYSTALLOGRAPHY PLANES
MILLER INDICES FOR CRYSTALLOGRAPHY PLANES
Manipal Academy of Higher Education (MAHE)
 
crystalstructure
crystalstructurecrystalstructure
Space lattice and crystal structure,miller indices PEC UNIVERSITY CHD
Space lattice and crystal structure,miller indices PEC UNIVERSITY CHDSpace lattice and crystal structure,miller indices PEC UNIVERSITY CHD
Space lattice and crystal structure,miller indices PEC UNIVERSITY CHDPEC University Chandigarh
 
UCSD NANO106 - 03 - Lattice Directions and Planes, Reciprocal Lattice and Coo...
UCSD NANO106 - 03 - Lattice Directions and Planes, Reciprocal Lattice and Coo...UCSD NANO106 - 03 - Lattice Directions and Planes, Reciprocal Lattice and Coo...
UCSD NANO106 - 03 - Lattice Directions and Planes, Reciprocal Lattice and Coo...
University of California, San Diego
 
Brillouin zones newton sow
Brillouin zones newton sowBrillouin zones newton sow
Brillouin zones newton sow
Soundar Rajan
 
Crystal structures in material science
Crystal structures in material scienceCrystal structures in material science
Crystal structures in material science
Sachin Hariprasad
 
Crystal systems
Crystal systemsCrystal systems
Crystal systems
onlinemetallurgy.com
 
Crystal structure
Crystal structureCrystal structure
Crystal structure
Gabriel O'Brien
 
Imperfections in solids
Imperfections in solidsImperfections in solids
Imperfections in solids
Nitika Sharma
 
Point defect in solids
Point defect in solidsPoint defect in solids
Point defect in solids
neelusharma39
 
Engineering Physics - Crystal structure - Dr. Victor Vedanayakam.S
Engineering Physics - Crystal structure - Dr. Victor Vedanayakam.SEngineering Physics - Crystal structure - Dr. Victor Vedanayakam.S
Engineering Physics - Crystal structure - Dr. Victor Vedanayakam.S
Madanapalle Institute of Technology and Science
 
Crystal structures
Crystal structuresCrystal structures
Crystal structures
Ratnadeepsinh Jadeja
 
Crystal structure
Crystal structureCrystal structure
Crystal structure
Parth Patel
 
Solid state__physics (1)by D.Udayanga.
Solid  state__physics (1)by D.Udayanga.Solid  state__physics (1)by D.Udayanga.
Solid state__physics (1)by D.Udayanga.damitha udayanga
 
Crystal structure notes
Crystal structure notesCrystal structure notes
Crystal structure notes
Praveen Vaidya
 
Crystal imperfections dislocations
Crystal imperfections dislocationsCrystal imperfections dislocations
Crystal imperfections dislocationsGulfam Hussain
 
Imperfections in solids con
Imperfections in solids conImperfections in solids con
Imperfections in solids con
Nimisha I K
 

What's hot (20)

Crystal structure
Crystal structureCrystal structure
Crystal structure
 
MILLER INDICES FOR CRYSTALLOGRAPHY PLANES
MILLER INDICES FOR CRYSTALLOGRAPHY PLANESMILLER INDICES FOR CRYSTALLOGRAPHY PLANES
MILLER INDICES FOR CRYSTALLOGRAPHY PLANES
 
crystalstructure
crystalstructurecrystalstructure
crystalstructure
 
Space lattice and crystal structure,miller indices PEC UNIVERSITY CHD
Space lattice and crystal structure,miller indices PEC UNIVERSITY CHDSpace lattice and crystal structure,miller indices PEC UNIVERSITY CHD
Space lattice and crystal structure,miller indices PEC UNIVERSITY CHD
 
Packing Factor
Packing Factor Packing Factor
Packing Factor
 
UCSD NANO106 - 03 - Lattice Directions and Planes, Reciprocal Lattice and Coo...
UCSD NANO106 - 03 - Lattice Directions and Planes, Reciprocal Lattice and Coo...UCSD NANO106 - 03 - Lattice Directions and Planes, Reciprocal Lattice and Coo...
UCSD NANO106 - 03 - Lattice Directions and Planes, Reciprocal Lattice and Coo...
 
Brillouin zones newton sow
Brillouin zones newton sowBrillouin zones newton sow
Brillouin zones newton sow
 
Crystal structures in material science
Crystal structures in material scienceCrystal structures in material science
Crystal structures in material science
 
Crystal Physics
Crystal PhysicsCrystal Physics
Crystal Physics
 
Crystal systems
Crystal systemsCrystal systems
Crystal systems
 
Crystal structure
Crystal structureCrystal structure
Crystal structure
 
Imperfections in solids
Imperfections in solidsImperfections in solids
Imperfections in solids
 
Point defect in solids
Point defect in solidsPoint defect in solids
Point defect in solids
 
Engineering Physics - Crystal structure - Dr. Victor Vedanayakam.S
Engineering Physics - Crystal structure - Dr. Victor Vedanayakam.SEngineering Physics - Crystal structure - Dr. Victor Vedanayakam.S
Engineering Physics - Crystal structure - Dr. Victor Vedanayakam.S
 
Crystal structures
Crystal structuresCrystal structures
Crystal structures
 
Crystal structure
Crystal structureCrystal structure
Crystal structure
 
Solid state__physics (1)by D.Udayanga.
Solid  state__physics (1)by D.Udayanga.Solid  state__physics (1)by D.Udayanga.
Solid state__physics (1)by D.Udayanga.
 
Crystal structure notes
Crystal structure notesCrystal structure notes
Crystal structure notes
 
Crystal imperfections dislocations
Crystal imperfections dislocationsCrystal imperfections dislocations
Crystal imperfections dislocations
 
Imperfections in solids con
Imperfections in solids conImperfections in solids con
Imperfections in solids con
 

Similar to Directions, planes and miller indices

Directions & planes
Directions & planesDirections & planes
Directions & planes
onlinemetallurgy.com
 
MILLER INDICES FOR CRYSTALLOGRAPHY PLANES
MILLER INDICES FOR CRYSTALLOGRAPHY PLANESMILLER INDICES FOR CRYSTALLOGRAPHY PLANES
MILLER INDICES FOR CRYSTALLOGRAPHY PLANES
Manipal Academy of Higher Education (MAHE)
 
Miller indices
Miller indicesMiller indices
Miller indices
Kaushal Gandhi
 
SSP UNIT-I CRYSTAL STRUCTURE ENGINEERING PHYSICS.pdf
SSP UNIT-I CRYSTAL STRUCTURE ENGINEERING PHYSICS.pdfSSP UNIT-I CRYSTAL STRUCTURE ENGINEERING PHYSICS.pdf
SSP UNIT-I CRYSTAL STRUCTURE ENGINEERING PHYSICS.pdf
sooriyaprakash334
 
Directions & planes 2
Directions & planes 2Directions & planes 2
Directions & planes 2
onlinemetallurgy.com
 
Crystallographic planes
Crystallographic planesCrystallographic planes
Crystallographic planes
sandhya sharma
 
Solid state chemistry
Solid state chemistrySolid state chemistry
Solid state chemistry
PRAVIN SINGARE
 
Crystallographic points directions and planes.pdf
Crystallographic points directions and planes.pdfCrystallographic points directions and planes.pdf
Crystallographic points directions and planes.pdf
DrJayantaKumarMahato1
 
ANALYTIC-GEOMETRY(4).pptx
ANALYTIC-GEOMETRY(4).pptxANALYTIC-GEOMETRY(4).pptx
ANALYTIC-GEOMETRY(4).pptx
BercasioKelvin
 
Bell 301 unit II
Bell 301 unit IIBell 301 unit II
Bell 301 unit II
Prashant Kumar
 
Classification of Surveying.pptx
Classification of Surveying.pptxClassification of Surveying.pptx
Classification of Surveying.pptx
ivargarud
 
lecture3.pptx
lecture3.pptxlecture3.pptx
lecture3.pptx
ivargarud
 
Structure of Solid Materials
Structure of Solid MaterialsStructure of Solid Materials
Structure of Solid Materials
MUHAMMAD MUSTAFEEZ ALAM
 
Crystallography
Crystallography Crystallography
Crystallography
AvinashAvi110
 
8.Charts
8.Charts8.Charts
8.Charts
AmenBAL
 
Meeting 1
Meeting 1Meeting 1
Meeting 1
Meiva Lestari
 
ppt 1.pptx
ppt 1.pptxppt 1.pptx
ppt 1.pptx
ShasidharaniD
 
02 vertex, min, max, intercepts - graphing
02 vertex, min, max, intercepts - graphing02 vertex, min, max, intercepts - graphing
02 vertex, min, max, intercepts - graphingmajapamaya
 
Chapter 3b miller_indices
Chapter 3b miller_indicesChapter 3b miller_indices
Chapter 3b miller_indices
chenna raidu c
 
Three dimensional space dfs
Three dimensional space dfsThree dimensional space dfs
Three dimensional space dfs
Farhana Shaheen
 

Similar to Directions, planes and miller indices (20)

Directions & planes
Directions & planesDirections & planes
Directions & planes
 
MILLER INDICES FOR CRYSTALLOGRAPHY PLANES
MILLER INDICES FOR CRYSTALLOGRAPHY PLANESMILLER INDICES FOR CRYSTALLOGRAPHY PLANES
MILLER INDICES FOR CRYSTALLOGRAPHY PLANES
 
Miller indices
Miller indicesMiller indices
Miller indices
 
SSP UNIT-I CRYSTAL STRUCTURE ENGINEERING PHYSICS.pdf
SSP UNIT-I CRYSTAL STRUCTURE ENGINEERING PHYSICS.pdfSSP UNIT-I CRYSTAL STRUCTURE ENGINEERING PHYSICS.pdf
SSP UNIT-I CRYSTAL STRUCTURE ENGINEERING PHYSICS.pdf
 
Directions & planes 2
Directions & planes 2Directions & planes 2
Directions & planes 2
 
Crystallographic planes
Crystallographic planesCrystallographic planes
Crystallographic planes
 
Solid state chemistry
Solid state chemistrySolid state chemistry
Solid state chemistry
 
Crystallographic points directions and planes.pdf
Crystallographic points directions and planes.pdfCrystallographic points directions and planes.pdf
Crystallographic points directions and planes.pdf
 
ANALYTIC-GEOMETRY(4).pptx
ANALYTIC-GEOMETRY(4).pptxANALYTIC-GEOMETRY(4).pptx
ANALYTIC-GEOMETRY(4).pptx
 
Bell 301 unit II
Bell 301 unit IIBell 301 unit II
Bell 301 unit II
 
Classification of Surveying.pptx
Classification of Surveying.pptxClassification of Surveying.pptx
Classification of Surveying.pptx
 
lecture3.pptx
lecture3.pptxlecture3.pptx
lecture3.pptx
 
Structure of Solid Materials
Structure of Solid MaterialsStructure of Solid Materials
Structure of Solid Materials
 
Crystallography
Crystallography Crystallography
Crystallography
 
8.Charts
8.Charts8.Charts
8.Charts
 
Meeting 1
Meeting 1Meeting 1
Meeting 1
 
ppt 1.pptx
ppt 1.pptxppt 1.pptx
ppt 1.pptx
 
02 vertex, min, max, intercepts - graphing
02 vertex, min, max, intercepts - graphing02 vertex, min, max, intercepts - graphing
02 vertex, min, max, intercepts - graphing
 
Chapter 3b miller_indices
Chapter 3b miller_indicesChapter 3b miller_indices
Chapter 3b miller_indices
 
Three dimensional space dfs
Three dimensional space dfsThree dimensional space dfs
Three dimensional space dfs
 

Recently uploaded

platelets_clotting_biogenesis.clot retractionpptx
platelets_clotting_biogenesis.clot retractionpptxplatelets_clotting_biogenesis.clot retractionpptx
platelets_clotting_biogenesis.clot retractionpptx
muralinath2
 
ESR_factors_affect-clinic significance-Pathysiology.pptx
ESR_factors_affect-clinic significance-Pathysiology.pptxESR_factors_affect-clinic significance-Pathysiology.pptx
ESR_factors_affect-clinic significance-Pathysiology.pptx
muralinath2
 
Nutraceutical market, scope and growth: Herbal drug technology
Nutraceutical market, scope and growth: Herbal drug technologyNutraceutical market, scope and growth: Herbal drug technology
Nutraceutical market, scope and growth: Herbal drug technology
Lokesh Patil
 
4. An Overview of Sugarcane White Leaf Disease in Vietnam.pdf
4. An Overview of Sugarcane White Leaf Disease in Vietnam.pdf4. An Overview of Sugarcane White Leaf Disease in Vietnam.pdf
4. An Overview of Sugarcane White Leaf Disease in Vietnam.pdf
ssuserbfdca9
 
Seminar of U.V. Spectroscopy by SAMIR PANDA
 Seminar of U.V. Spectroscopy by SAMIR PANDA Seminar of U.V. Spectroscopy by SAMIR PANDA
Seminar of U.V. Spectroscopy by SAMIR PANDA
SAMIR PANDA
 
Structures and textures of metamorphic rocks
Structures and textures of metamorphic rocksStructures and textures of metamorphic rocks
Structures and textures of metamorphic rocks
kumarmathi863
 
Citrus Greening Disease and its Management
Citrus Greening Disease and its ManagementCitrus Greening Disease and its Management
Citrus Greening Disease and its Management
subedisuryaofficial
 
What is greenhouse gasses and how many gasses are there to affect the Earth.
What is greenhouse gasses and how many gasses are there to affect the Earth.What is greenhouse gasses and how many gasses are there to affect the Earth.
What is greenhouse gasses and how many gasses are there to affect the Earth.
moosaasad1975
 
erythropoiesis-I_mechanism& clinical significance.pptx
erythropoiesis-I_mechanism& clinical significance.pptxerythropoiesis-I_mechanism& clinical significance.pptx
erythropoiesis-I_mechanism& clinical significance.pptx
muralinath2
 
Comparing Evolved Extractive Text Summary Scores of Bidirectional Encoder Rep...
Comparing Evolved Extractive Text Summary Scores of Bidirectional Encoder Rep...Comparing Evolved Extractive Text Summary Scores of Bidirectional Encoder Rep...
Comparing Evolved Extractive Text Summary Scores of Bidirectional Encoder Rep...
University of Maribor
 
Mammalian Pineal Body Structure and Also Functions
Mammalian Pineal Body Structure and Also FunctionsMammalian Pineal Body Structure and Also Functions
Mammalian Pineal Body Structure and Also Functions
YOGESH DOGRA
 
filosofia boliviana introducción jsjdjd.pptx
filosofia boliviana introducción jsjdjd.pptxfilosofia boliviana introducción jsjdjd.pptx
filosofia boliviana introducción jsjdjd.pptx
IvanMallco1
 
In silico drugs analogue design: novobiocin analogues.pptx
In silico drugs analogue design: novobiocin analogues.pptxIn silico drugs analogue design: novobiocin analogues.pptx
In silico drugs analogue design: novobiocin analogues.pptx
AlaminAfendy1
 
general properties of oerganologametal.ppt
general properties of oerganologametal.pptgeneral properties of oerganologametal.ppt
general properties of oerganologametal.ppt
IqrimaNabilatulhusni
 
GBSN- Microbiology (Lab 3) Gram Staining
GBSN- Microbiology (Lab 3) Gram StainingGBSN- Microbiology (Lab 3) Gram Staining
GBSN- Microbiology (Lab 3) Gram Staining
Areesha Ahmad
 
Richard's aventures in two entangled wonderlands
Richard's aventures in two entangled wonderlandsRichard's aventures in two entangled wonderlands
Richard's aventures in two entangled wonderlands
Richard Gill
 
Lateral Ventricles.pdf very easy good diagrams comprehensive
Lateral Ventricles.pdf very easy good diagrams comprehensiveLateral Ventricles.pdf very easy good diagrams comprehensive
Lateral Ventricles.pdf very easy good diagrams comprehensive
silvermistyshot
 
RNA INTERFERENCE: UNRAVELING GENETIC SILENCING
RNA INTERFERENCE: UNRAVELING GENETIC SILENCINGRNA INTERFERENCE: UNRAVELING GENETIC SILENCING
RNA INTERFERENCE: UNRAVELING GENETIC SILENCING
AADYARAJPANDEY1
 
Cancer cell metabolism: special Reference to Lactate Pathway
Cancer cell metabolism: special Reference to Lactate PathwayCancer cell metabolism: special Reference to Lactate Pathway
Cancer cell metabolism: special Reference to Lactate Pathway
AADYARAJPANDEY1
 
Hemoglobin metabolism_pathophysiology.pptx
Hemoglobin metabolism_pathophysiology.pptxHemoglobin metabolism_pathophysiology.pptx
Hemoglobin metabolism_pathophysiology.pptx
muralinath2
 

Recently uploaded (20)

platelets_clotting_biogenesis.clot retractionpptx
platelets_clotting_biogenesis.clot retractionpptxplatelets_clotting_biogenesis.clot retractionpptx
platelets_clotting_biogenesis.clot retractionpptx
 
ESR_factors_affect-clinic significance-Pathysiology.pptx
ESR_factors_affect-clinic significance-Pathysiology.pptxESR_factors_affect-clinic significance-Pathysiology.pptx
ESR_factors_affect-clinic significance-Pathysiology.pptx
 
Nutraceutical market, scope and growth: Herbal drug technology
Nutraceutical market, scope and growth: Herbal drug technologyNutraceutical market, scope and growth: Herbal drug technology
Nutraceutical market, scope and growth: Herbal drug technology
 
4. An Overview of Sugarcane White Leaf Disease in Vietnam.pdf
4. An Overview of Sugarcane White Leaf Disease in Vietnam.pdf4. An Overview of Sugarcane White Leaf Disease in Vietnam.pdf
4. An Overview of Sugarcane White Leaf Disease in Vietnam.pdf
 
Seminar of U.V. Spectroscopy by SAMIR PANDA
 Seminar of U.V. Spectroscopy by SAMIR PANDA Seminar of U.V. Spectroscopy by SAMIR PANDA
Seminar of U.V. Spectroscopy by SAMIR PANDA
 
Structures and textures of metamorphic rocks
Structures and textures of metamorphic rocksStructures and textures of metamorphic rocks
Structures and textures of metamorphic rocks
 
Citrus Greening Disease and its Management
Citrus Greening Disease and its ManagementCitrus Greening Disease and its Management
Citrus Greening Disease and its Management
 
What is greenhouse gasses and how many gasses are there to affect the Earth.
What is greenhouse gasses and how many gasses are there to affect the Earth.What is greenhouse gasses and how many gasses are there to affect the Earth.
What is greenhouse gasses and how many gasses are there to affect the Earth.
 
erythropoiesis-I_mechanism& clinical significance.pptx
erythropoiesis-I_mechanism& clinical significance.pptxerythropoiesis-I_mechanism& clinical significance.pptx
erythropoiesis-I_mechanism& clinical significance.pptx
 
Comparing Evolved Extractive Text Summary Scores of Bidirectional Encoder Rep...
Comparing Evolved Extractive Text Summary Scores of Bidirectional Encoder Rep...Comparing Evolved Extractive Text Summary Scores of Bidirectional Encoder Rep...
Comparing Evolved Extractive Text Summary Scores of Bidirectional Encoder Rep...
 
Mammalian Pineal Body Structure and Also Functions
Mammalian Pineal Body Structure and Also FunctionsMammalian Pineal Body Structure and Also Functions
Mammalian Pineal Body Structure and Also Functions
 
filosofia boliviana introducción jsjdjd.pptx
filosofia boliviana introducción jsjdjd.pptxfilosofia boliviana introducción jsjdjd.pptx
filosofia boliviana introducción jsjdjd.pptx
 
In silico drugs analogue design: novobiocin analogues.pptx
In silico drugs analogue design: novobiocin analogues.pptxIn silico drugs analogue design: novobiocin analogues.pptx
In silico drugs analogue design: novobiocin analogues.pptx
 
general properties of oerganologametal.ppt
general properties of oerganologametal.pptgeneral properties of oerganologametal.ppt
general properties of oerganologametal.ppt
 
GBSN- Microbiology (Lab 3) Gram Staining
GBSN- Microbiology (Lab 3) Gram StainingGBSN- Microbiology (Lab 3) Gram Staining
GBSN- Microbiology (Lab 3) Gram Staining
 
Richard's aventures in two entangled wonderlands
Richard's aventures in two entangled wonderlandsRichard's aventures in two entangled wonderlands
Richard's aventures in two entangled wonderlands
 
Lateral Ventricles.pdf very easy good diagrams comprehensive
Lateral Ventricles.pdf very easy good diagrams comprehensiveLateral Ventricles.pdf very easy good diagrams comprehensive
Lateral Ventricles.pdf very easy good diagrams comprehensive
 
RNA INTERFERENCE: UNRAVELING GENETIC SILENCING
RNA INTERFERENCE: UNRAVELING GENETIC SILENCINGRNA INTERFERENCE: UNRAVELING GENETIC SILENCING
RNA INTERFERENCE: UNRAVELING GENETIC SILENCING
 
Cancer cell metabolism: special Reference to Lactate Pathway
Cancer cell metabolism: special Reference to Lactate PathwayCancer cell metabolism: special Reference to Lactate Pathway
Cancer cell metabolism: special Reference to Lactate Pathway
 
Hemoglobin metabolism_pathophysiology.pptx
Hemoglobin metabolism_pathophysiology.pptxHemoglobin metabolism_pathophysiology.pptx
Hemoglobin metabolism_pathophysiology.pptx
 

Directions, planes and miller indices

  • 1. DIRECTIONS, PLANES AND MILLER INDICES By Srilakshmi B UCST, Tumkur
  • 2. CONTENTS • INTRODUCTION • NEED OF DIRECTIONS AND PLANES • GENERAL RULES AND CONVENTION • MILLER INDICES FOR DIRECTIONS • MILLER INDICES FOR PLANES • IMPORTANT FEATURES OF MILLER INDICES
  • 3. INTRODUCTION The crystal lattice may be regarded as made up of an infinite set of parallel equidistant planes passing through the lattice points which are known as lattice planes. In simple terms, the planes passing through lattice points are called ‘lattice planes’. For a given lattice, the lattice planes can be chosen in a different number of ways.
  • 4. • The orientation of planes or faces in a crystal can be described in terms of their intercepts on the three axes. • Miller introduced a system to designate a plane in a crystal. • He introduced a set of three numbers to specify a plane in a crystal. • This set of three numbers is known as ‘Miller Indices’ of the concerned plane.
  • 5. NEED OF DIRECTIONS AND PLANES • Deformation under loading (slip) occurs on certain crystalline planes and in certain crystallographic directions. • Before we can predict how materials fail, we need to know what modes of failure are more likely to occur. Other properties of materials (electrical conductivity, thermal conductivity, elastic modulus) can vary in a crystal with orientation.
  • 6.
  • 7. GENERAL RULES FOR LATTICE DIRECTIONS, PLANES AND MILLER INDICES • Miller indices used to express lattice planes and directions • x, y, z are the axes (on arbitrarily positioned origin) • a, b, c are lattice parameters (length of unit cell along a side) h, k, l are the Miller indices for planes and directions - expressed as planes: (hkl) and directions: [hkl]
  • 8. CONVENTION FOR NAMING • There are NO COMMAS between numbers • Negative values are expressed with a bar over the number Example: -5 is expressed 5
  • 9. MILLER INDICES FOR DIRECTIONS • Draw vector, and find the coordinates of the head, h1,k1,l1 and the tail h2,k2,l2. • subtract coordinates of tail from coordinates of head • Remove fractions by multiplying by smallest possible factor • Enclose in square brackets
  • 10.
  • 11. The direction can also be determined by giving the coordinates of the first whole numbered point (x,y) through which each of the direction passes. In this figure direction of OA is[110] and OB is [520]
  • 13. MILLER INDICES FOR PLANES • If the plane passes through the origin, select an equivalent plane or move the origin • Determine the intersection of the plane with the axes in terms of a,b, and c • Take the reciprocal (1/∞ = 0) • Convert to smallest integers • Enclose by parentheses
  • 14. EXAMPLE • Here x,y and z intercepts are 1,1,1. • Therefore (111) is the miller indices of the plane
  • 15. • DETERMINATION OF ‘MILLER INDICES • Step 1:The intercepts are 2,3 and 2 on the three axes. • Step 2:The reciprocals are 1/2, 1/3 and 1/2. • Step 3:The least common denominator is ‘6’. Multiplying each reciprocal by lcd, we get, 3,2 and 3. • Step 4:Hence Miller indices for the plane ABC is (3 2 3)
  • 16. IMPORTANT FEATURES OF MILLER INDICES • A plane passing through the origin is defined in terms of a parallel plane having non zero intercepts. • All equally spaced parallel planes have same ‘Miller indices’ i.e. The Miller indices do not only define a particular plane but also a set of parallel planes. Thus the planes whose intercepts are 1, 1,1; 2,2,2; -3,-3,-3 etc., are all represented by the same set of Miller indices.
  • 17. • It is only the ratio of the indices which is important in this notation. The (6 2 2) planes are the same as (3 1 1) planes. • If a plane cuts an axis on the negative side of the origin, corresponding index is negative. It _ is represented by a bar, like (1 0 0). i.e. It indicates that the plane has an intercept in the –ve X –axis.
  • 18. Planes and their negatives are equivalent
  • 19. In the cubic system, a plane and a direction with the same indices are orthogonal Here the direction is [001] and plane is (001)
  • 20.
  • 22. BIBLIOGRAPHY • SOLID STATE PHYSICS BY S.O.PILLAI, FIFTH EDITION BY NEW AGE INTERNATIONAL PUBLICATION