1
X- Ray Crystallography:
Unlocking the structure of molecules
Presented By
Dhanashree Giridhar Kolhekar
M. Pharm (Pharmaceutical Analysis)
I Semester
Department of Pharmaceutical Sciences,
BBAU Lucknow
2
Contents
 Introduction 3
 History 4
 Principle 5
 Bragg’s law 8
 What is x ray and why they are used 10
 Crystals 11
 Types of crystals 12
 Why crystals are used 13
 Different x ray methods 14
 Procedure 24
 Instrumentation 25
 Applications 37
Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
3
Introduction
• X-ray Crystallography is a scientific method used to
determine the arrangement of atoms of a crystalline
solid in three dimensional space.
• A beam of x rays strikes a crystal and causes a beam of
light to diffract into many specific directions.
• The electron density , and the positions of atoms can be
contructed from the diffraction pattern to determine
the mean positions of the atoms in the crystal.
Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
4
History
• The English physicist sir William
Henry Bragg pioneered the
determination of crystal structure
by x ray diffraction methods.
• Using X ray crystal data , Dr.
James Watson and Dr. Francis
Crick determined the helix
structure of DNA in 1953.
Original Bragg x ray
spectrometer developed by
William Bragg
Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
5
Principle
It uses principle of diffraction into many specific
directions from crystal of the substance
This technique takes advantage of the interatomic
spacing of most crystalline solids by employing
them as a diffraction gradient for x ray light
A crystal can be described with the aid of grid or
lattice , defined by three axis and angles between
them.
Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
6
The diffraction pattern obtained helps to
generate the electron density map.
This map reveals where electrons are most
densely located, allowing researchers to build
an atomic model that accurately represents
the 3D arrangement of atoms in the crystal
structure.
Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
7
Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
8
Bragg’s law
• Diffraction of light as well as x ray obeyed by Bragg’s law,
which states that when the x ray is incident onto a crystal
suface , its angle of incidence , θ, will reflect back with a
same angle of scattering , θ. And when the path difference ,
d is equal to whole number, n of wavelength, a constructive
interference will occur . Thus
nλ = 2d sinθ
N is an integer
d is the spacing of the crystal layers
Θ is the incident angle
λ is the wavelength of x-ray
Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
9
10
What is x ray and why they are used?
Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
11
Crystals
• A crystal is a solid
whose atoms are
arranged in a highly
ordered repeating
pattern .
• these patterns are
called as crystal
systems .
Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
12
Types of crystals
Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
13
Why crystals are used?
• When sample is present in liquid form, the
bond angle keep changing, position of atoms
keep changing in every moment so it is very
hard to determine the structure of that
sample.
• In crystalline form the conformtion is fixed in
a single place so it makes easy to determine
the structure of crystal.
Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
14
Different x ray methods
x ray absorption method
Auger x ray emission method
X ray fluorescence method
X ray diffraction method
Rotating crystal method
Powder crystal method
Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
15
X ray absorption method
• Wavelength at which a
sudden change in
absorption occurs is used
to identify an element
present in a sample, and
the magnitude of the
change determines the
amount of particular
element present.
Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
16
Auger x ray emission method
• X-rays eject inner-shell
electrons.
• Instead of emitting a
characteristic X-ray, the
atom releases energy by
ejecting an outer electron,
called an Auger electron.
• The kinetic energy of this
electron provides element-
specific information.
Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
17
X ray fluorescence method
• The primary x ray ejects
electrons from inner
energy levels where the
wavelength is equal to
absorption edge.
• But when the
wavelength is shorter
than absorption edge it
emits secondary x ray
when electrons fall into
inner vacant levels.
Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
18
X ray diffraction method
• When a beam of monochromatic x radiation is
directed at a crystalline material, one observes
reflection or diffraction of the x rays at various
angle with respect to the primary beam.
• The relationship between the x radiation , angle
of diffraction and distance between each set of
atomic planes of crystal lattice is given by bagg’s
law
nλ = 2d sinθ
Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
19
Rotating crystal method
• This method involves rotating a single crystal
within an X-ray beam to obtain diffraction
patterns, which reveal information about the
arrangement of atoms within the crystal
lattice.
• As the crystal rotates, different sets of atomic
planes come into alignment with the incident
X-ray beam at various angles.
Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
20
• Each plane will produce a spot on
photographic plate.
• One can take photographs in two ways:
Complete rotation method
 oscillation method
Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
21
Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
22
Powder crystal method
• The powder crystal method, is an X-ray crystallography
technique used to study powdered samples.
• This method is ideal for samples that cannot be prepared as
single crystals.
• The sample is ground into a fine powder, so it contains many
small crystals with random orientations.
• This allows for a range of crystal planes to be exposed to the
X-ray beam at various angles.
Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
23
Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
24
Procedure
Structure determination
Data collection
Protein crystallization
Protein purificataion
It is a multistep process which can be outlined as
below:
Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
25
Instrumentation
1.Production of x rays
2.Collimator
3.Monochromator
4.Detectors
Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
26
Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
27
Production of x rays
• X rays are produced inside the x ray tube when high
energy projectile electrons from the filament interact
with the atoms of the anode.
• X ray also called as coolidge tube is a large vaccum
tube containing a heated cathode of tungsten filament
and copper or molybdenum target metal anode.
• Operated at higher voltage upto 60 kV.
Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
28
Cont….
• There is cathode which is a filament of tungsten metal
heated by a battery to emit the thermionic electrons.
• This beam of electrons moves towards anode target
and attain the kinetic energy and 99% of energy is
converted into heat via collision and remaining 0.5-1%
is converted to x rays.
• Generally the target gets very hot in use so this
problem has been solved to some extent by cooling
the tube with water.
Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
29
Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
30
Collimator
• X rays produced by the target material are randomly
directed.
• They form a hemisphere with a target at the centre. In
order to get a narrow beam of x rays, the x rays generated
by the target material are allowed to pass through a
collimator which consists of two sets of closely packed
metal plates separated by small gap.
• The collimator absorbs all the x rays except the narrow
beam that passes between the gaps.
Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
31
Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
32
Monochromator
They are of two types:
• Filter monochromator
A filter is a window of material that absorbs undesirable
radiation but allows the radiation of required wavelength
to pass.
• Crystal monochromator
A crystal monochromator is made up of a suitable
crystalline material positioned in the x ray beam so that
the angle of reflecting planes satisfies Braggs equation for
the required wavelength.
Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
33
Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
34
Detectors
1. Photographic method
• In order to record the position and intensity of
x ray beam a plane or cylindrical film is used.
• The film after exposing to x rays is developed.
The blackening of the developed film is
expressed in terms of density units D given by,
• D= Iog Io​
/I
Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
35
2. Counter methods
• The geiger tube is filled with an inert gas like argon and the
central wire anode is maintained at a potential of 800 to
2500V.
• when an X rays is entering the geiger tube, this ray
undergoes collision with the filling gas , resulting in the
production of an ion pair: the electron produced moves
towards the central anode while the positive ions move
towards outer electrode.
Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
36
• The electron is accelerated by the potential
gradient and causes the ionisation of large
number of argon atoms, resulting production
of an avalanche of electrons that are travelling
towards the central anode.
• The geiger tube is in expensive and is
relatively trouble free detector. This tube gives
the highest signal for given x ray intensity.
Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
37
Applications of crystallography
• Helps design drugs by revealing the 3D structure of
target proteins.
• used to determine the structure of minerals in geology.
• Helps to understand double-helix structure of DNA and
the organization of RNA.
• Used to study polymorphs of drugs to optimize their
solubility and bioavailability.
Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
38
• Differentiation of sugar
• X ray analysis of milk powder
Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
39
Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
40
References
• X-ray Crystallography - Chemistry LibreTexts
• https://www.slideshare.net/slideshow/xray-crystallography-1
18911634/118911634
• www.creativebiomart.net/resource/principle-protocol-x-ray-cr
ystallography-393.htm
• X-ray Crystallography: Definition, Principle, Steps, Data Analysi
s, Applications, and Limitations - The Science Notes
• Instrumental methods of analysis- williards, 7th
edition CBS
Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
41
Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow

X-_Ray_Crystallography_DHANASHREE KOLHEKAR[1].pptx

  • 1.
    1 X- Ray Crystallography: Unlockingthe structure of molecules Presented By Dhanashree Giridhar Kolhekar M. Pharm (Pharmaceutical Analysis) I Semester Department of Pharmaceutical Sciences, BBAU Lucknow
  • 2.
    2 Contents  Introduction 3 History 4  Principle 5  Bragg’s law 8  What is x ray and why they are used 10  Crystals 11  Types of crystals 12  Why crystals are used 13  Different x ray methods 14  Procedure 24  Instrumentation 25  Applications 37 Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
  • 3.
    3 Introduction • X-ray Crystallographyis a scientific method used to determine the arrangement of atoms of a crystalline solid in three dimensional space. • A beam of x rays strikes a crystal and causes a beam of light to diffract into many specific directions. • The electron density , and the positions of atoms can be contructed from the diffraction pattern to determine the mean positions of the atoms in the crystal. Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
  • 4.
    4 History • The Englishphysicist sir William Henry Bragg pioneered the determination of crystal structure by x ray diffraction methods. • Using X ray crystal data , Dr. James Watson and Dr. Francis Crick determined the helix structure of DNA in 1953. Original Bragg x ray spectrometer developed by William Bragg Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
  • 5.
    5 Principle It uses principleof diffraction into many specific directions from crystal of the substance This technique takes advantage of the interatomic spacing of most crystalline solids by employing them as a diffraction gradient for x ray light A crystal can be described with the aid of grid or lattice , defined by three axis and angles between them. Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
  • 6.
    6 The diffraction patternobtained helps to generate the electron density map. This map reveals where electrons are most densely located, allowing researchers to build an atomic model that accurately represents the 3D arrangement of atoms in the crystal structure. Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
  • 7.
    7 Dhanashree Kolhekar,M.Pharm- Isem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
  • 8.
    8 Bragg’s law • Diffractionof light as well as x ray obeyed by Bragg’s law, which states that when the x ray is incident onto a crystal suface , its angle of incidence , θ, will reflect back with a same angle of scattering , θ. And when the path difference , d is equal to whole number, n of wavelength, a constructive interference will occur . Thus nλ = 2d sinθ N is an integer d is the spacing of the crystal layers Θ is the incident angle λ is the wavelength of x-ray Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
  • 9.
  • 10.
    10 What is xray and why they are used? Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
  • 11.
    11 Crystals • A crystalis a solid whose atoms are arranged in a highly ordered repeating pattern . • these patterns are called as crystal systems . Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
  • 12.
    12 Types of crystals DhanashreeKolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
  • 13.
    13 Why crystals areused? • When sample is present in liquid form, the bond angle keep changing, position of atoms keep changing in every moment so it is very hard to determine the structure of that sample. • In crystalline form the conformtion is fixed in a single place so it makes easy to determine the structure of crystal. Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
  • 14.
    14 Different x raymethods x ray absorption method Auger x ray emission method X ray fluorescence method X ray diffraction method Rotating crystal method Powder crystal method Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
  • 15.
    15 X ray absorptionmethod • Wavelength at which a sudden change in absorption occurs is used to identify an element present in a sample, and the magnitude of the change determines the amount of particular element present. Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
  • 16.
    16 Auger x rayemission method • X-rays eject inner-shell electrons. • Instead of emitting a characteristic X-ray, the atom releases energy by ejecting an outer electron, called an Auger electron. • The kinetic energy of this electron provides element- specific information. Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
  • 17.
    17 X ray fluorescencemethod • The primary x ray ejects electrons from inner energy levels where the wavelength is equal to absorption edge. • But when the wavelength is shorter than absorption edge it emits secondary x ray when electrons fall into inner vacant levels. Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
  • 18.
    18 X ray diffractionmethod • When a beam of monochromatic x radiation is directed at a crystalline material, one observes reflection or diffraction of the x rays at various angle with respect to the primary beam. • The relationship between the x radiation , angle of diffraction and distance between each set of atomic planes of crystal lattice is given by bagg’s law nλ = 2d sinθ Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
  • 19.
    19 Rotating crystal method •This method involves rotating a single crystal within an X-ray beam to obtain diffraction patterns, which reveal information about the arrangement of atoms within the crystal lattice. • As the crystal rotates, different sets of atomic planes come into alignment with the incident X-ray beam at various angles. Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
  • 20.
    20 • Each planewill produce a spot on photographic plate. • One can take photographs in two ways: Complete rotation method  oscillation method Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
  • 21.
    21 Dhanashree Kolhekar,M.Pharm- Isem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
  • 22.
    22 Powder crystal method •The powder crystal method, is an X-ray crystallography technique used to study powdered samples. • This method is ideal for samples that cannot be prepared as single crystals. • The sample is ground into a fine powder, so it contains many small crystals with random orientations. • This allows for a range of crystal planes to be exposed to the X-ray beam at various angles. Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
  • 23.
    23 Dhanashree Kolhekar,M.Pharm- Isem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
  • 24.
    24 Procedure Structure determination Data collection Proteincrystallization Protein purificataion It is a multistep process which can be outlined as below: Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
  • 25.
    25 Instrumentation 1.Production of xrays 2.Collimator 3.Monochromator 4.Detectors Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
  • 26.
    26 Dhanashree Kolhekar,M.Pharm- Isem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
  • 27.
    27 Production of xrays • X rays are produced inside the x ray tube when high energy projectile electrons from the filament interact with the atoms of the anode. • X ray also called as coolidge tube is a large vaccum tube containing a heated cathode of tungsten filament and copper or molybdenum target metal anode. • Operated at higher voltage upto 60 kV. Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
  • 28.
    28 Cont…. • There iscathode which is a filament of tungsten metal heated by a battery to emit the thermionic electrons. • This beam of electrons moves towards anode target and attain the kinetic energy and 99% of energy is converted into heat via collision and remaining 0.5-1% is converted to x rays. • Generally the target gets very hot in use so this problem has been solved to some extent by cooling the tube with water. Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
  • 29.
    29 Dhanashree Kolhekar,M.Pharm- Isem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
  • 30.
    30 Collimator • X raysproduced by the target material are randomly directed. • They form a hemisphere with a target at the centre. In order to get a narrow beam of x rays, the x rays generated by the target material are allowed to pass through a collimator which consists of two sets of closely packed metal plates separated by small gap. • The collimator absorbs all the x rays except the narrow beam that passes between the gaps. Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
  • 31.
    31 Dhanashree Kolhekar,M.Pharm- Isem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
  • 32.
    32 Monochromator They are oftwo types: • Filter monochromator A filter is a window of material that absorbs undesirable radiation but allows the radiation of required wavelength to pass. • Crystal monochromator A crystal monochromator is made up of a suitable crystalline material positioned in the x ray beam so that the angle of reflecting planes satisfies Braggs equation for the required wavelength. Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
  • 33.
    33 Dhanashree Kolhekar,M.Pharm- Isem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
  • 34.
    34 Detectors 1. Photographic method •In order to record the position and intensity of x ray beam a plane or cylindrical film is used. • The film after exposing to x rays is developed. The blackening of the developed film is expressed in terms of density units D given by, • D= Iog Io​ /I Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
  • 35.
    35 2. Counter methods •The geiger tube is filled with an inert gas like argon and the central wire anode is maintained at a potential of 800 to 2500V. • when an X rays is entering the geiger tube, this ray undergoes collision with the filling gas , resulting in the production of an ion pair: the electron produced moves towards the central anode while the positive ions move towards outer electrode. Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
  • 36.
    36 • The electronis accelerated by the potential gradient and causes the ionisation of large number of argon atoms, resulting production of an avalanche of electrons that are travelling towards the central anode. • The geiger tube is in expensive and is relatively trouble free detector. This tube gives the highest signal for given x ray intensity. Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
  • 37.
    37 Applications of crystallography •Helps design drugs by revealing the 3D structure of target proteins. • used to determine the structure of minerals in geology. • Helps to understand double-helix structure of DNA and the organization of RNA. • Used to study polymorphs of drugs to optimize their solubility and bioavailability. Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
  • 38.
    38 • Differentiation ofsugar • X ray analysis of milk powder Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
  • 39.
    39 Dhanashree Kolhekar,M.Pharm- Isem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
  • 40.
    40 References • X-ray Crystallography- Chemistry LibreTexts • https://www.slideshare.net/slideshow/xray-crystallography-1 18911634/118911634 • www.creativebiomart.net/resource/principle-protocol-x-ray-cr ystallography-393.htm • X-ray Crystallography: Definition, Principle, Steps, Data Analysi s, Applications, and Limitations - The Science Notes • Instrumental methods of analysis- williards, 7th edition CBS Dhanashree Kolhekar,M.Pharm- I sem(Pharma'ceutical ANALYSIS) BBAU, Lucknow
  • 41.
    41 Dhanashree Kolhekar,M.Pharm- Isem(Pharma'ceutical ANALYSIS) BBAU, Lucknow