Crystal Structure Of NaCl And KCl
The three dimensional unit of atoms,ions and molecules within the crystal system is known as crystal lattice and the fundamental unit of crystal is known as unit cell.Weiss indices are the numbers that are to be multilpied with the intercept made by a unit plane so as to get the intercept made by a face.Miller indices are the reciprocal of Weiss indices.If Miller indices are known then interplanar distance can be easily calculated. Above note is about the crystal lattice,unit cell,laws of rational indices,Weiss indices,Miller indices and application of miller indices,bravais lattice and cryatal structure of NaCl.
Summary
The three dimensional unit of atoms,ions and molecules within the crystal system is known as crystal lattice and the fundamental unit of crystal is known as unit cell.Weiss indices are the numbers that are to be multilpied with the intercept made by a unit plane so as to get the intercept made by a face.Miller indices are the reciprocal of Weiss indices.If Miller indices are known then interplanar distance can be easily calculated. Above note is about the crystal lattice,unit cell,laws of rational indices,Weiss indices,Miller indices and application of miller indices,bravais lattice and cryatal structure of NaCl.
Things to Remember
The three dimensional unit of atoms,ions and molecules within the crystal system is known as crystal lattice and the fundamental unit of crystal is known as unit cell.Weiss indices are the numbers that are to be multilpied with the intercept made by a unit plane so as to get the intercept made by a face.Miller indices are the reciprocal of Weiss indices.If Miller indices are known then interplanar distance can be easily calculated.
The three dimensional unit of atoms,ions and molecules within the crystal system is known as crystal lattice and the fundamental unit of crystal is known as unit cell.Weiss indices are the numbers that are to be multilpied with the intercept made by a unit plane so as to get the intercept made by a face.Miller indices are the reciprocal of Weiss indices.If Miller indices are known then interplanar distance can be easily calculated.
The three dimensional unit of atoms,ions and molecules within the crystal system is known as crystal lattice and the fundamental unit of crystal is known as unit cell.Weiss indices are the numbers that are to be multilpied with the intercept made by a unit plane so as to get the intercept made by a face.Miller indices are the reciprocal of Weiss indices.If Miller indices are known then interplanar distance can be easily calculated.
The three dimensional unit of atoms,ions and molecules within the crystal system is known as crystal lattice and the fundamental unit of crystal is known as unit cell.Weiss indices are the numbers that are to be multilpied with the intercept made by a unit plane so as to get the intercept made by a face.Miller indices are the reciprocal of Weiss indices.If Miller indices are known then interplanar distance can be easily calculated.
The three dimensional unit of atoms,ions and molecules within the crystal system is known as crystal lattice and the fundamental unit of crystal is known as unit cell.Weiss indices are the numbers that are to be multilpied with the intercept made by a unit plane so as to get the intercept made by a face.Miller indices are the reciprocal of Weiss indices.If Miller indices are known then interplanar distance can be easily calculated.
The three dimensional unit of atoms,ions and molecules within the crystal system is known as crystal lattice and the fundamental unit of crystal is known as unit cell.Weiss indices are the numbers that are to be multilpied with the intercept made by a unit plane so as to get the intercept made by a face.Miller indices are the reciprocal of Weiss indices.If Miller indices are known then interplanar distance can be easily calculated.
The three dimensional unit of atoms,ions and molecules within the crystal system is known as crystal lattice and the fundamental unit of crystal is known as unit cell.Weiss indices are the numbers that are to be multilpied with the intercept made by a unit plane so as to get the intercept made by a face.Miller indices are the reciprocal of Weiss indices.If Miller indices are known then interplanar distance can be easily calculated.
The three dimensional unit of atoms,ions and molecules within the crystal system is known as crystal lattice and the fundamental unit of crystal is known as unit cell.Weiss indices are the numbers that are to be multilpied with the intercept made by a unit plane so as to get the intercept made by a face.Miller indices are the reciprocal of Weiss indices.If Miller indices are known then interplanar distance can be easily calculated.
The three dimensional unit of atoms,ions and molecules within the crystal system is known as crystal lattice and the fundamental unit of crystal is known as unit cell.Weiss indices are the numbers that are to be multilpied with the intercept made by a unit plane so as to get the intercept made by a face.Miller indices are the reciprocal of Weiss indices.If Miller indices are known then interplanar distance can be easily calculated.
The three dimensional unit of atoms,ions and molecules within the crystal system is known as crystal lattice and the fundamental unit of crystal is known as unit cell.Weiss indices are the numbers that are to be multilpied with the intercept made by a unit plane so as to get the intercept made by a face.Miller indices are the reciprocal of Weiss indices.If Miller indices are known then interplanar distance can be easily calculated.
The three dimensional unit of atoms,ions and molecules within the crystal system is known as crystal lattice and the fundamental unit of crystal is known as unit cell.Weiss indices are the numbers that are to be multilpied with the intercept made by a unit plane so as to get the intercept made by a face.Miller indices are the reciprocal of Weiss indices.If Miller indices are known then interplanar distance can be easily calculated.
The three dimensional unit of atoms,ions and molecules within the crystal system is known as crystal lattice and the fundamental unit of crystal is known as unit cell.Weiss indices are the numbers that are to be multilpied with the intercept made by a unit plane so as to get the intercept made by a face.Miller indices are the reciprocal of Weiss indices.If Miller indices are known then interplanar distance can be easily calculated.
The three dimensional unit of atoms,ions and molecules within the crystal system is known as crystal lattice and the fundamental unit of crystal is known as unit cell.Weiss indices are the numbers that are to be multilpied with the intercept made by a unit plane so as to get the intercept made by a face.Miller indices are the reciprocal of Weiss indices.If Miller indices are known then interplanar distance can be easily calculated.
The three dimensional unit of atoms,ions and molecules within the crystal system is known as crystal lattice and the fundamental unit of crystal is known as unit cell.Weiss indices are the numbers that are to be multilpied with the intercept made by a unit plane so as to get the intercept made by a face.Miller indices are the reciprocal of Weiss indices.If Miller indices are known then interplanar distance can be easily calculated.
The three dimensional unit of atoms,ions and molecules within the crystal system is known as crystal lattice and the fundamental unit of crystal is known as unit cell.Weiss indices are the numbers that are to be multilpied with the intercept made by a unit plane so as to get the intercept made by a face.Miller indices are the reciprocal of Weiss indices.If Miller indices are known then interplanar distance can be easily calculated.
The three dimensional unit of atoms,ions and molecules within the crystal system is known as crystal lattice and the fundamental unit of crystal is known as unit cell.Weiss indices are the numbers that are to be multilpied with the intercept made by a unit plane so as to get the intercept made by a face.Miller indices are the reciprocal of Weiss indices.If Miller indices are known then interplanar distance can be easily calculated.
The three dimensional unit of atoms,ions and molecules within the crystal system is known as crystal lattice and the fundamental unit of crystal is known as unit cell.Weiss indices are the numbers that are to be multilpied with the intercept made by a unit plane so as to get the intercept made by a face.Miller indices are the reciprocal of Weiss indices.If Miller indices are known then interplanar distance can be easily calculated.
The three dimensional unit of atoms,ions and molecules within the crystal system is known as crystal lattice and the fundamental unit of crystal is known as unit cell.Weiss indices are the numbers that are to be multilpied with the intercept made by a unit plane so as to get the intercept made by a face.Miller indices are the reciprocal of Weiss indices.If Miller indices are known then interplanar distance can be easily calculated.
The three dimensional unit of atoms,ions and molecules within the crystal system is known as crystal lattice and the fundamental unit of crystal is known as unit cell.Weiss indices are the numbers that are to be multilpied with the intercept made by a unit plane so as to get the intercept made by a face.Miller indices are the reciprocal of Weiss indices.If Miller indices are known then interplanar distance can be easily calculated.
The three dimensional unit of atoms,ions and molecules within the crystal system is known as crystal lattice and the fundamental unit of crystal is known as unit cell.Weiss indices are the numbers that are to be multilpied with the intercept made by a unit plane so as to get the intercept made by a face.Miller indices are the reciprocal of Weiss indices.If Miller indices are known then interplanar distance can be easily calculated.
The three dimensional unit of atoms,ions and molecules within the crystal system is known as crystal lattice and the fundamental unit of crystal is known as unit cell.Weiss indices are the numbers that are to be multilpied with the intercept made by a unit plane so as to get the intercept made by a face.Miller indices are the reciprocal of Weiss indices.If Miller indices are known then interplanar distance can be easily calculated.
The three dimensional unit of atoms,ions and molecules within the crystal system is known as crystal lattice and the fundamental unit of crystal is known as unit cell.Weiss indices are the numbers that are to be multilpied with the intercept made by a unit plane so as to get the intercept made by a face.Miller indices are the reciprocal of Weiss indices.If Miller indices are known then interplanar distance can be easily calculated.
The three dimensional unit of atoms,ions and molecules within the crystal system is known as crystal lattice and the fundamental unit of crystal is known as unit cell.Weiss indices are the numbers that are to be multilpied with the intercept made by a unit plane so as to get the intercept made by a face.Miller indices are the reciprocal of Weiss indices.If Miller indices are known then interplanar distance can be easily calculated.
The three dimensional unit of atoms,ions and molecules within the crystal system is known as crystal lattice and the fundamental unit of crystal is known as unit cell.Weiss indices are the numbers that are to be multilpied with the intercept made by a unit plane so as to get the intercept made by a face.Miller indices are the reciprocal of Weiss indices.If Miller indices are known then interplanar distance can be easily calculated.
The three dimensional unit of atoms,ions and molecules within the crystal system is known as crystal lattice and the fundamental unit of crystal is known as unit cell.Weiss indices are the numbers that are to be multilpied with the intercept made by a unit plane so as to get the intercept made by a face.Miller indices are the reciprocal of Weiss indices.If Miller indices are known then interplanar distance can be easily calculated.
- The three dimensional unit of atoms,ions and molecules within the crystal system is known as crystal lattice and the fundamental unit of crystal is known as unit cell.Weiss indices are the numbers that are to be multilpied with the intercept made by a unit plane so as to get the intercept made by a face.Miller indices are the reciprocal of Weiss indices.If Miller indices are known then interplanar distance can be easily calculated.
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Crystal Structure Of NaCl And KCl
Crystal lattice and unit cell
The three dimensional unit of atoms, ions or molecules within the crystal system is known as crystal lattice and the fundamental unit of crystal is known as unit cell.
Law of rational indices
the intercept made by a face of a crystal on a three crystallographic axes is difficult to calculate.So,to calculate the intercept made by the face, first of all intercept made by a unit plane is determined.Then,intercept made by a face is determined by using this law. This law states that 'the intercept made by a face
i)may be a simple whole number multiplied to these of unit plane.
ii)one or two intercept may be infinity if the face is parallel to axis.
Weiss Indices
Let a,b and c are the intercept made by a unit plane in crystallographic axes x,y and z respectively.Let p,q and r be the intercept made by a face on the respective axes.Then with the help of rational indices,p=na,q=n'b and r=n"c.Here,n,n' and n" are called as Weiss indices.These Weiss indices are defined as simply that are to be multiplied with the intercept made by a unit plane so as to get the intercept made by a face.
Miller Indices
Miller indices are the reciprocal of Weiss Indices which are converted into a whole number.Miller indices represent plane present in a crystal.If Weiss indices are known then Miller Indices can be easily calculated.Miller indices are represented by a symbol h,k and l.
Application of Miller Indices
If Miller indices are known,then interplanar distance can be calculated by using the expression
dhkl=a/√h2+k2+l2 ,where a=edge length.
Question:The Weiss indices are a,1 and 2/3.Find the Miller Indices of the plane.
We have,Weiss indices are 1,1 and 2/3.Taking reciprocal 1,1 and 3/2.To convert into whole numbers,these numbers are multiplied by 2.
∴Miller indices are 2,2 and 3.
Question:The Weiss indices of a face are 1,1 and 1/2.If edge length is 4.5,then calculate the interplanar distance.
Solution:
The whole numbers are 1,1 and 2.
given n=4.5
dhkl=a/√h2+k2+l2
=4.5/√12+12+22
=4.5/√6
=1.63 A°
Bravais Lattice
Initially,it was considered that the constituent particles are present only at the corners of the lattice system but later due to detail study of the internal structure of the crystal by bravais,it is believed that the constituent particles are present not only at the corners but the centre of body,centre of face and centre of end face of unit cell.Thus,each crystal system may be divided into same system or sub lattice.These sub lattice is called as Bravais Lattice.There are seven crystal system containing 14 Bravais lattice.
| S.N | Crystal System | Axial Characteristics | No. of Bravais lattice |
| 1. | Cubic | α=β=γ=90° | 3(Simple,face,centered and bod centered) |
| 2. | Tetragonal | α=β=γ=90° a=b≠c | 2(simpple and body centered) |
| 3. | Orthorhombic/ Rhombic | α=β=γ=90° a=b≠c | 4(simple,body centered,face centered and end centered) |
| 4. | Monaclinic | α=β=γ=90° and β≠90° a≠b≠c | 2(simple and end centered) |
| 5. | Triclinic | α≠β≠γ≠90° a≠b≠c | 1(simple) |
| 6. | Rhombohedral | α=β=γ≠90° a=b=c | 1(simple) |
| 7. | Hexagonal | α=β=90° γ≠120° a=b≠c | 1(simple) |
| Total crystal system=7 | |||
| Total Bravais lattice=14 |
Question:Draw the structure of simple face centered and body centered cubic system.Write their axial characteristics.
Question:Identify the crystal system having axial characteristics.
a)α=β=γ=90º b)α=β=90º,γ=120
a=b≠c a=b≠c
Number of net atoms in a cubic unit cell
i)An atom at the corner of unit cell is shared by eight unit cell.
ii)An atom at the body centre of unit cell belongs to that cell only.
iii)An atom at the face centre of unit cell is shared by two unit cells.
iv)An atom at the edge of unit cell is shared by four unit cell.
(There are 8 atoms present at the corner of unit cell)
The number of net atoms in a face centered cubic system=8×1/8+6×1/2=4
(There are 8 atoms at the corner and 6 atoms present at the centre of face)
The number of net atoms in body centered cubic system=8×1/8+1=2
(There are 8 atoms at the corner and 1 atom at the centre of body)
Question:The Weiss indices of aplane are 3/2,2 and 1.Find the miller indices.
Solution:
Given Weiss indices are 3/2,2 and 1.
The reciprocals of weiss indices are 2/3,1/2 and 1.
Then,multiplying by 6 we get Miller indices=4,3 and 6.
Crystal structure of sodium cloride (NaCl)
In the above structure,it is found that 14 Cl- ions and 13 Na+ ions present in the structure of NaCl.Out of 14 Cl- ions ,8 ions are present at the corner and 6 Cl- ions are present at the centre of face.We know that each corner is shared by 8 units cell and each face is shared by 2 unit cell.So,the number of net chloride ion = 8×1/8+6×1/2=1+3=4.
Similarly,out of 13 Na+ ions ,12 ions are present at the centre of edge and one ion is present at the centre of body i.e the number of net sodium ions=1+12×1/4=1+3=4 .Hence from above discussion ,we can conclude that each unit cell of NaCl contain 4 formula unit of NaCl in net.
Designation of plane and interplanar distance of cubic system.
There are 3 types of cubic lattice possible namely simple cubic,face centered cubic and body centered cubic.
For a simple cubic system,100,110 and 111 planers are possible.These planes can be represented as:
The interplanar distance ratio for a sim ple cubic system d100:d110:d111=a:a/√2:a/√3
d100:d110:d111=a/√22+0+0:a/√22+22+0:a/√12+12+12
=a/√2:a/2√2:a/√3
=1:1/√2:2/√3
∴d200:d220:d111=1:0.707:1.154
For a body centered cubic system 200,110 and 222 planes are possible and the interplanar distance ratio of these planes
d200:d110:d222=a/√22+0+0:a/√2:a/√2:a/√22+22+22
=a/2:a/√2:a/2√3
=1:√2:1/√3
d200:d110:d222=1:1.414:0.577
References
Prutton, S.H Maron & c. Principles of Physical Chemistry. Oxford & Pub. Co., 1992.
Crystal Strucyure of NaCl
Lesson
Solid State Chemistry
Subject
Chemistry
Grade
Bachelor of Science
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