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INTEGRATED PROJECT REPORTON
“DETERMINING MILLER INDICES & INTERPLANAR DISTANCE USING ‘C’
Department of ELECTRONICS & COMMUNICATION ENGINEERING
Chitkara University, Baddi Campus, HP, INDIA
DECEMBER 2012
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Submitted by:
1. ABHI MARKANDEY (B120020007)
2. AGAM KAPOOR (B120020018)
3. AKANKSHA SHARMA (B120020023)
4. AKASHDEEP SINGH (B120020024)
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TABLE OF CONTENTS:-
CHAPTER 1:
INTRODUCTION
MILLER INDICES................................................................................................................................
CHAPTER 2 : HISTORY
HISTORY BEHIND MILLER INDICES...........................................................................................
CHAPTER 3 : STRUCTURE ..............................................................................................................
CRYSTAL STRUCTURE ....................................................................................................................
CHAPTER 4 : CUBIC STRUCTURE………………………………………………………………
CASE OF CUBIC STRUCTURE…………………………………………………………................
'C' CODING OF MILLER INDICES & INTERPLANAR DISTANCE.........................................
SOURCE CODE .........................................................................................................................................
CONCLUSION ……………………………………………………………………………………….
FUTURE PLANS……………………………………………………………………………………..
REFERENCES………………………………………………………………………………………..
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LIST OF FIGURES:
Figure No. Description Page
Figure 1 Output screen[1] . 11
Figure 2 Output screen[2] . 12
Figure 3 Output screen[3] . 13
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CHAPTER 1: INTRODUCTION
Miller Indices
1. Miller Indices form a notation system in crystallography for planes in crystal lattices.
2. In particular, a family of lattice planes is determined by three integers h, k, and ℓ. 3. The notation {hkℓ} denotes the set of all planes that are equivalent to (hkℓ) by the
symmetry of the lattice.4. The notation ⟨hkℓ⟩ denotes the set of all directions that are equivalent to [hkℓ] by
symmetry.
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CHAPTER 2: HISTORY
HISTORY BEHIND MILLER INDICES
1. Miller indices were introduced in 1839 by the British mineralogist William Hallowes Miller.
2. The method was also historically known as the Millerian system, and the indices as Millerian.
3. The precise meaning depends upon a choice of lattice vectors for the crystal.
4. Usually, three primitive lattice vectors are used. However, for cubic crystal systems, the cubic lattice vectors are used even when they are not primitive.
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CHAPTER 3: STRUCTURE
CRYSTAL STRUCTURE
1. It is a unique arrangement of atoms/molecules in a crystalline liquid/solid2. Composed of a pattern, a set of atoms arranged in a particular way of & a lattice
exhibiting long range-order & symmetry.3. Patterns are located upon the points of a lattice, which is an array of points repeating
periodically in 3D. 4. They are grouping of crystal according to axial system used to describe their lattices.5. Each lattice Consists of a set three axes in a particular geometrical arrangement.6. They are similar to but not quite the same as seven crystals.
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CHAPTER 4: CUBIC STRUCTURE
CASE OF CUBIC STRUCTURE
1. For the special case of simple cubic crystals, the lattice vectors are orthogonal and of equal length similar to the reciprocal lattice.
2. The Miller indices (hkℓ) and [hkℓ] both simply denote normals /directions in Cartesian coordinates.
3. For cubic crystals with lattice constant a, the spacing d between adjacent (hkℓ) lattice planes is:-
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PROGRAMMING OF MILLER INDICES & INTERPLANAR DISTANCE USING ‘C’ LANGUAGE
The Following Is The Source Code:
[Using C Complier example: Dave C++.]
#include<stdio.h>
#include<conio.h>
#include<math.h>
main()
{
float a,b,c,h,k,l,d,e,i;
printf("Enter the 3 Intercept\n");
scanf("%f\n%f\n%f",&a,&b,&c);
if(a==b==c)
{
h=a;
k=a;
l=a;
}
else if(a==b||b==c||a==c)
{
if(a==b)
{
h==c;
k==a;
l==a;
}
if(b==c)
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{
h==b;
k==a;
l==a;
}
if(a==c)
{
h==b;
k==a;
l==b;
}
}
else
{
h=b*c;
k=a*c;
l=a*b;
}
printf("\nmiller indices are =%f:%f:%f",h,k,l);
printf("\nenter the value of a=");
scanf("%f",&i);
e=sqrt((h*h)+(k*k)+(l*l));
d=i/e;
printf("\n interplaner distance d=%f",d);
getch();
}
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Figures :
Output of the program:
1.
This is the first output screen shot.
In this user has to enter the intercepts.
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2.
After the user enters the intercepts, the program gives the miller indices.
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3.
After the user enters the value of lattice constant, the interplanar distance is showed up.
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CONCLUSION:
We can determine miller indices interplanar distance. Similarly, we can calculate different formula unit involved material science. It can be very useful in determining different formula units with ease.
FUTURE PLANS
To develop a Miller indices counter which can perform the whole lot of operations whether its related to Miller Indices (including miller indices, interplanar distance in a single machine itself which is compact, cheap, efficient, reliable, accurate and easy to handle.
REFRENCES:
1. Let us C – by Yashavant P. Kanetkar (12th edition), BPB Publications.2. Engineering Physics by H.K. Malik 2010 edition3. www.chem.qmul.ac.uk/surfaces/scc/scat1_1b.htm
4. en.wikipedia.org/wiki/Miller_index
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