X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure...

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X-Ray Diffraction

Transcript of X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure...

Page 1: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

X-Ray Diffraction

Page 2: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

IntroductionIntroduction

• X-ray diffraction techniques are very useful for crystal X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of structure analysis and identification of different types of crystals.crystals.

• Experimental study of crystalline materials became possible Experimental study of crystalline materials became possible

only after the discovery of only after the discovery of X-raysX-rays. .

• Diffraction occurs when waves traveling through an object Diffraction occurs when waves traveling through an object whose dimensions are order of whose dimensions are order of wavelengthwavelength..

• Typical inter atomic spacing in crystals is Typical inter atomic spacing in crystals is 2-3°A2-3°A..

• The x-rays have wavelengths The x-rays have wavelengths (0.02°A to 100°A) (0.02°A to 100°A) in this range . in this range . Hence x-ray diffraction is utilized to study the crystal Hence x-ray diffraction is utilized to study the crystal structures.structures.

Page 3: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

Bragg’s law

• Bragg’s law states that, the path difference between the two reflected rays by the crystal planes should be an integral multiple of wavelength of incident x-rays for producing maxima or constructive interference.

Page 4: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

Plane 1

Plane 2

Plane 3

A

B

C D

P

Q

R

S

d90° ө 90°ө

Page 5: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

The path difference between these two rays is CB+BDThe path difference between these two rays is CB+BD

n sin 2d

sin dBDCB

nBDCB

Where n = 1,2,3,…..first , second …order etc.Where n = 1,2,3,…..first , second …order etc.

• For 1For 1stst order sin order sinθθ11 = = λλ/2d./2d.

• For 2For 2ndnd order sin order sinθθ22 = 2 = 2λλ / 2d. / 2d.

• For 3For 3rdrd order sin order sinθθ3 3 = 3= 3λλ / 2d. / 2d.

• where where θθ11, , θθ22 and and θθ33 are the glancing angles for n=1,2 are the glancing angles for n=1,2

and 3 respectively.and 3 respectively.

Page 6: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

The Bragg equation can be used for determining the lattice parameters of cubic crystals.

Let us consider the first order spectrum from three planes of cubic crystal system. 2

3:2:1

d

1:

d

1:

d

1FCCfor

3:2

1:1

d

1:

d

1:

d

1BCCfor

3:2:1d

1:

d

1:

d

1SCCfor

sinθ:sinθ:sinθd

1:

d

1:

d

1

sinθ2dsinθ2dsinθ2dλλ

2sinθ

d

1

1)n(λ2dsinθ

111110100

111110100

111110100

321111110100

311121101100

Hence by knowing the values of glancing angles ratio, the ratio of interplanar spacing hence the type of lattice can be identified.

Importance of Braggs law

Page 7: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

X-Ray Diffraction Techniques

There are two main experimental X-Ray diffraction There are two main experimental X-Ray diffraction methods by which the crystal structure can be methods by which the crystal structure can be analyzed.analyzed.

1.Laue Method.1.Laue Method.

2.Powder Method.2.Powder Method.

Page 8: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

Laue Method

Consider heterogeneous beam of X-Rays in the wavelength of Consider heterogeneous beam of X-Rays in the wavelength of 0.2°A to 2°A 0.2°A to 2°A originating from a suitable source.originating from a suitable source.

In this technique, the crystal stationary in a In this technique, the crystal stationary in a heterogeneousheterogeneous beam of X-Rays.beam of X-Rays.

The diffraction pattern consists of The diffraction pattern consists of a a bright central spot bright central spot and a and a set of spots arranged in a definite pattern about the central spot.set of spots arranged in a definite pattern about the central spot.

TheThe symmetrical pattern symmetrical pattern caused by diffraction of X-Rays by caused by diffraction of X-Rays by crystal planes is called the Laue patterncrystal planes is called the Laue pattern..

Page 9: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

Crystal

Photographic Plate

Laue Pattern

X-Rays

Slits

Page 10: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

Photographic film

P

o

θ

X-Rays

Crystal

2θ D

Page 11: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

• If The Crystal is fixed, for an incident angle ‘θ’, the diffracted angle becomes ‘2θ’.

• Consider, ‘D’ is the distance between the crystal and photographic film and OP = R.

Tan2θ = OP/OC OP = OC tan2θ R = D tan2θ

• This method is used to study theThis method is used to study the orientation orientation of the of the crystal and verifycrystal and verify Crystal symmetryCrystal symmetry..

Page 12: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

Powder ( Debye – Scherer) Method

• The Powder Method is applicable to finely divided Crystalline The Powder Method is applicable to finely divided Crystalline powder.powder.

• It is used for accurate determination of lattice parameters in It is used for accurate determination of lattice parameters in crystals.crystals.

• The powdered specimen is kept inside a small capillary tube.The powdered specimen is kept inside a small capillary tube.

• A narrow pencil of monochromatic X-Ray is diffracted from the A narrow pencil of monochromatic X-Ray is diffracted from the powder and recorded by the Photographic film as a series of lines powder and recorded by the Photographic film as a series of lines of varying curvature.of varying curvature.

• The full opening angle of the diffraction cone ‘4The full opening angle of the diffraction cone ‘4θθ’ is determined ’ is determined by measuring the distance ‘s’ between two corresponding arc.by measuring the distance ‘s’ between two corresponding arc.

Page 13: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

r2θ

2θ

Incident X-Ray beam S

Crystal Powder 4r

sθ

rs4θ

Where r is the Where r is the specimen to film specimen to film distance.distance.

Page 14: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

Applications of Powder Method

• Study of d-spacing.• Study of mixtures.• Study of alloys.• Stress determination in metals. • Determination of particle size.

Page 15: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

Defects in Crystals

Page 16: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

IntroductionIntroduction

• In an ideal crystal, the atomic arrangement iIn an ideal crystal, the atomic arrangement is perfectly regular and continuous but real crystals perfectly regular and continuous but real crystals never perfect.never perfect.

• They always contain a considerable density defects They always contain a considerable density defects and imperfections that affect theand imperfections that affect their physical, r physical, chemical ,mechanical and electronic properties.chemical ,mechanical and electronic properties.

• Crystalline imperfections can be classified on they Crystalline imperfections can be classified on they basis of their geometry under four main divisions basis of their geometry under four main divisions namelynamely

Page 17: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

1.Vacancies or Schottky2.Interstitialcies or Frenkel3.Compositional defects.

a. Substitutionalb. interstitial

4.Electronic defects

Defects

Point defects (0-dimensional)

Line defects (1-dimensional)

Surface defects (2-dimensional)

Volume defects (3-dimensional)

1.Edge dislocation2.Screw dislocation

1.Grain boundaries2.Tilt boundaries3.Twin boundaries4.Stacking faults

1.Cracks2.Voids or air bubbles

Page 18: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

Point Point Defectsefects

Point imperfections are also Point imperfections are also called zero dimensional called zero dimensional imperfections. imperfections.

One or two atomic diameters One or two atomic diameters is the typical size of a point is the typical size of a point imperfection.imperfection. Perfect Crystal

Page 19: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

Vacancy:A Vacancy refers to an atomic site from where the atom is missing.

Page 20: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

Compositional defects

• A Substitutional impurity is a point imperfection and it refers to a foreign atom that substitutes for or replaces a parent atom in the crystal.

• A small sized atom occupying the void space in the parent crystal disturbing the parent atoms from their regular sites is a interstitial impurity.

Page 21: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

Frenkel Defect: An atom leaves the regular site and occupies interstitial position. Such defects are called Frenkel defects.

The point imperfections in silver halides and CaF2 are of the Frenkel type.

Page 22: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

Schottky defect: A pair of one cataion and one anion can be missing from an ionic crystal as shown in a figure. such a pair of vacant ion sites is called Schottky defect.

Page 23: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

Electronic defects

• Errors in charge distribution in solids are called electronic defects.

• These defects are produced, when the composition of an ionic crystal does not correspond to the exact Stoichiometric formula.

Page 24: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

Calculation of number of vacancies at a given temperature.

• All most in all crystals vacancies are present and the main cause for these defects is thermal agitation.

• Let us consider Ev is the energy required to move an atom from lattice site inside the crystal to lattice site on the surface.

• Therefore the amount of energy required to produce n number of isolated vacancies can be written as

vnEU

Page 25: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

The total number of ways to move n number of atoms out of N number of atoms in a crystal on to its surface will be

!)!(

!

nnN

NP

The increase in entropy due to formation of n vacancies can be written as

}log{

log

!)!(!

nnNN

B

B

K

PKS

Page 26: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

But the free energy TSUF

}logn!n)!log(NT{logN!KnEF

)n!n)!(N

N!Tlog(KnEF

Bv

Bv

Using Stirling is a approximation, log x! = x log x - x

nlogn}n)n)log(N(NT{NlogNKnEF Bv

Page 27: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

At thermal equilibrium, free energy is constant and minimum with respect to n, hence

}TK

ENexp{n

Nnif

}TK

Eexp{

n

nN

}n

nNTlog{KE

logn}1n)log(NT{1KE

0nlogn})n)n)log(N(NT{NlogNK(nEdn

d

odn

dF

B

v

B

v

Bv

Bv

Bv

Hence equilibrium concentration of vacancies decreases with temperature.

Page 28: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

Calculation of number Schottky defects at a given temperature:

• In ionic crystals, the number of schottky defects at a given temperature, can be calculated assuming an equal number of positive and negative ion vacancies are present.

• Let us consider Ep is the energy required to move an ion Pair from lattice site inside the crystal to a lattice site on the surface.

• Therefore the amount of energy required to produce n number of isolated ion pair vacancies will be

pnEU

Page 29: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

• The total number of ways that to move n numbers of ion pairs out of N number of ionic molecules in a crystal on to the surface will be

2

2

]!)!(

!log[

log

]!)!(

![

nnN

NKS

PKS

nnN

NP

B

B

Page 30: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

The free energy2

Bp ]n!n)!(N

N!Tlog[KnEF

TSUF

Using stirling approximation xxxx log!log

nlogn]n)n)log(N(NT[NlogN2KnEF

n]nlognn)n)log(N(N2[NlogN]n!n)!(N

N!log[

n]nlognn)(Nn)n)log(N(NN2[NlogN]n!n)!(N

N!log[

Bv

2

2

Page 31: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

At thermal equilibrium, free energy is constant and minimum with respect to n, hence

}T2K

ENexp{n

Nnif

}T2K

En)exp{(Nn

]n

nNlog[

T2K

E

]n

nNTlog[2KE

0]dn

dF[

B

p

B

p

B

p

BP

T

Page 32: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

Calculation of number of Frenkel Defects at given temperature: In ionic crystal an ion may be displaced from the regular lattice into an interstitial site or void space. If it is so, then a vacancy and an interstitial defect will be formed.

A Frenkel imperfections in silver halides and calcium fluoride are of the Frenkel type.

Frenkel and Schottky defects together are called Intrinsic defects.

Page 33: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

• Let us consider Ei is the energy required to move an atom from lattice site inside the crystal to a lattice site on the surface.

• The amount of energy required to produce ‘n’ number of isolated vacancies…

inEU

Page 34: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

• The total number of ways to move n numbers of ions out of N number ionic molecules in a crystal on to the surface will be,

]}n!n)!(N

!N][

n!n)!(N

N!Tlog{[KnEF

TSUfreeenergy

]}n!n)!(N

!N][

n!n)!(N

N!log{[KS

logpKentropy

]n!n)!(N

!N][

n!n)!(N

N![p

i

iBi

i

iB

B

i

i

Page 35: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

}log2)log()()log()(loglog{

log2)log()()log()(loglog

]}!)!(

!][

!)!(

!log{[

nnnNnNnNnNNNNNTKnEF

nnnNnNnNnNNNNN

nnN

N

nnN

N

iiiiBi

iiii

i

i

Page 36: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

At equilibrium, the free energy is constant and minimum with respect to n, hence

TK

ENNn

TK

ENNn

nNNTKEn

NNTK

nNnNn

nNnNTKE

dn

dF

B

ii

Bi

iBi

iB

i

iBi

T

2exp)(

2}log{

2

1log

]log2}[log{

}log{

,

}))((

log{

0][

2

1

2

2

Hence it is concluded that number of Frenkel defects, is proportional (NNi)1/2

Page 37: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

Line defects

• Line defects are one dimensional imperfections in the geometrical sense.

• There are in general two types of dislocations:

1. Edge dislocation

2. Screw dislocation

Page 38: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

Edge dislocation

• In a perfect crystal, atoms are arranged in both vertical and horizontal planes parallel to the side faces.

• If one of these vertical planes does not extended to full length but ends in between, within the crystal as shown in figure, it is called edge dislocation.

• Edge dislocations are symbolically represented by ┴ or ┬ or depending on whether the incomplete plane starts from the top or from the bottom of the crystal.

• These two configurations are referred to as positive and negative edge dislocations.

Page 39: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

Perfect Crystal

An incomplete plane in aCrystal results in an edge dislocation

Page 40: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

Perfect crystal

Edge dislocated crystal

Extra half plane

Slip plane

Page 41: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

• The edge dislocation containing an extra plane of atoms lying above the positive slip plane (or) Burgers plane are conventionally called the positive edge dislocation.

• If the extra half plane of atoms containing below

the slip plane called the negative edge dislocation.

Page 42: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

Positive and negative dislocations

Page 43: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

Burgers vector

• The magnitude and the direction of the displacement are defined by a vector called the Burgers vector.

• Consider two crystals one perfect and another with edge dislocation.

Page 44: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

Perfect crystal

P

An incomplete plane in aCrystal results in an edgedislocation

Fig 1. Fig 2.

PQb

Page 45: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

• From fig. 1. Starting from the point P, we go up by 6 steps, then move

towards right by 5 steps, and move down by 6 steps and finally move towards left by 5 steps to reach the starting point P, the burgers circuit gets closed.

• From fig 2. We end up at Q instead of the starting point P.

Now we have to move an extra step QP to return to ‘P’ in order to close the burgers circuit.The magnitude and the direction of the step defines the Burgers vector (BV)

BV = QP = b

The Burgers vector is perpendicular to the edge dislocation line.

Page 46: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

Screw dislocation

• The second basic type of dislocation is the Screw or Burgers dislocation.

• In this, the atoms are displaced in two separate planes perpendicular to each other.

• In a figure the plane ABCD is the slipped area. • The upper portion of the crystal has been sheared by

an atomic distance to the right relative to the lower portion.

• No slip has taken place to the right of AD and AD is a dislocation line.

Page 47: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

A

B

CD

Shear vector

• Here, the dislocation is parallel to its Burgers vector or shear vector.

• The designation ‘screw’ for this lattice defect is derived from the fact that the lattice planes of the crystal spiral the dislocation line AD.

Page 48: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

Surface defects

• Surface defects arise from a change in the stacking of atomic planes (or) across a boundary.

• The change may be one of the orientations (or) of the stacking sequence of the planes.

• Surface defects are two types.

1. External surface imperfections

2. Internal surface imperfections

Page 49: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

External surface defects

Since these surface atoms are not entirely surrounded by others, they posses higher energy than that of internal atoms.

Page 50: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

Internal surface imperfections

• Internal surface defects are four types.

1. Grain boundaries

2. Tilt boundaries

3. Twin boundaries

4. Stacking faults

Page 51: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

1. Grain boundary

• The boundary between two miss oriented crystalline material is called grain boundary.

• During nucleation or crystallization this may happen.

• Grain boundaries also known as high angle boundaries.

Page 52: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

Grain boundaries

Poly crystal

Page 53: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

2. Tilt (angle) boundaries

• This is called low-angle boundary as the orientation difference between two neighboring crystals is less than 10º.

• Low angle boundaries can be described by suitable array of edge dislocations.

• A low angle tilt boundary is composed of edge dislocation lying one above the other in boundary.

Page 54: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

Tilt boundaryθ

b

D

D

bThe low angle (or) tilt will be θ=

b Magnitude of burger’s vector

D Average vertical distance between dislocations

=b/θ

b

D

θ

Page 55: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

3. Stacking faults

• Stacking faults are planar surface imperfections caused by faults in the stacking sequence of atomic planes (or) layers in crystals.

• In FCC crystal we have three different stacking layers ABC while in HCP stacking we have only two different layers BC.

• Hence when FCC crystal grows we have the stacking as …….ABCABCABC……..

Page 56: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

A

B

C

A

Stacking sequence of ABC ABC…..in FCC

Page 57: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

STACKING SEQUENCE IN HCP AB AB….

A

B

A

Page 58: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

• While growing if the plane A indicated by arrow above is missing then we get the sequence

………….ABCABCBCABC…………….

• Thus we find that the stacking in the missing region becomes HCP.

• This thin region is a surface imperfection and is called a stacking fault.

Page 59: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

4.Twin boundary

• The atomic arrangement on one side of a twin boundary is a mirror reflection of the arrangement on the other side, such a boundary and the region between the pair of boundaries is called twinned region.

• Twin boundaries are easily identified under an optional microscope.

Page 60: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

Twin boundary

Fig: The atomic arrangement in a twin boundary

Page 61: X-Ray Diffraction. Introduction X-ray diffraction techniques are very useful for crystal structure analysis and identification of different types of crystals.X-ray.

Volume defects

• Volume defects such as cracks may arise when there is only small electrostatic dissimilarity between the stacking sequences of close packed planes in metals.

• When clusters of atoms are missing ,a largeVacancy or void is got which is also a volume imperfection.

• Foreign particle inclusions, large voids or non crystalline regions which have the dimensions of the order of 0.20nm are also called volume imperfection.

• We can study the volume defects by using interferometric techniques and optical microscopes.


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X-Ray Diffraction - B.D.cullITY

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X Ray Diffraction (XRD), Powder X Ray Diffraction (PXRD ... · Heidari A (2018) X–Ray Diffraction (XRD), Powder X–Ray Diffraction (PXRD) and Energy– Dispersive X–Ray Diffraction

X Ray Diffraction (XRD), Powder X Ray Diffraction (PXRD ... · Heidari A (2018) X–Ray Diffraction (XRD), Powder X–Ray Diffraction (PXRD) and Energy– Dispersive X–Ray Diffraction