SCIENCE REPORTER, DECEMBER 2012 8

PARESH R. VAIDYA

A Century ofX-ray

Diffraction

MUCH of the solid matter we see

around us is made up of crystals,

including rocky planets such as

ours. Crystals may be solid, but they are by

no means inscrutable. Scientists have

always tried to peer into this solid matter,

down to the micro level formations. When

Max von Laue registered the first diffraction

pattern from a crystal a century ago, he

took the first step to satisfy this urge of

scientists to see the atom level

configurations. The discovery of X-ray

diffraction was a central event in modern

science.

While the technique of X-ray

diffraction (XRD) began by identifying the

symmetries in the crystals of minerals, it

eventually evolved into a unique and

powerful method of finding even the

molecular structures in chemistr y and

biology. The observation of X-ray diffraction

by Friedrich, Knipping and Laue is one of

the most important discoveries in the history

of science, and one with monumental

consequences. It opened the path for the

development of modern solid-state physics

and materials science, including

mineralogy, chemistr y and molecular

The year 2012 marks the 100th anniversary of thediscovery of X-ray diffraction and its use as a probe ofthe structure of matter. Einstein called the discovery ofX-ray diffraction in crystals as one of the most beautifuldiscoveries in physics. Here is an account of how it cameabout.

X-ray diffraction began by identifying symmetries in thecrystals of minerals

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SCIENCE REPORTER, DECEMBER 20129

biology. In fact, all the science describing

the material world around us has use for

XRD and there is hardly any field in basic or

applied research that has not employed

XRD for achieving its ends. It continues to

widen its net even today.

Though the mysterious radiation

discovered by Roentgen was named ‘X-

ray ’, the debate was on for a few years

whether they were waves or corpuscles

(i.e. particles). A wave is expected to

provide diffraction. Roentgen worked hard

to get such an effect but could not.

Frustrated, he wrote in March 1897:

“…using narrow slits I observed

phenomena which looked very much like

diffraction. But in each case a change in

experimental conditions undertaken to test

the correctness of the explanation, failed

to confirm it. And in many cases I was able

to show that the phenomena had arisen in

an entirely different way than by diffraction.

I have not succeeded to register a single

experiment from which I could gain the

conviction of the existence of diffraction

of X-rays that satisfies me.”

DiffractionWhen a wave hits an object, they cannot

reach the region immediately behind that

object. Shadows are formed due to this.

Since the waves of light are blocked, the

region immediately behind the object is

darker.

But shadows are sharper close to an

object than they are further from it. This is

due to diffraction. Waves that pass the

object change their direction of travel

slightly. The wave that just missed the object

spreads in a circle or sphere, into the space

behind the object. This is why shadows

become more blurred further away from

the object that casts them. Eventually the

spherically spreading waves from each

edge of the obstacle may even meet up.

This remained valid till 1912 when Laue

cracked the jinx. Laue was at the Munich

University (the same university where

Roentgen was the chair in Experimental

Physics), and was working with X-rays to

understand their nature. Laue worked

under A. Sommerfeld who was the chair in

the theoretical physics department. Laue

had a simple logic: the optical light gets

diffracted using gratings if the spacing

between grating lines is of the order of the

wavelength of the light. Going by the

similarity, X-rays can be diffracted if only

you have a diffracting element spaced at

about a wavelength apart.

The wavelength of X-rays was not

known then, obviously, because it was not

even decided if they were waves at all!

Rutherford had then given the estimate of

the atomic dimensions in the range of

angstrom units (1 angstrom unit A0 = 10-8

cm.). If so, a crystal made up of an array

of atoms may work as a grating. Laue

guessed the wavelength of X-rays around

the lattice dimensions and took a simple

plunge.

Walter Friedrich and a doctoral

student Paul Knipping, his associates

borrowed from Roentgen’s lab, were put

on the job. Preliminary trials using copper

sulphate crystal yielded a patchy picture

indicating diffused dots, which did not

appear to mean anything. But the shrewd

physicists saw a promising pattern therein.

Soon an improved picture with zinc

sulphide crystal was

taken along three-

fold and four-fold

symmetry axes. The

outcome was

almost l ike a

miracle. A thin

cr ystal, nearly

transparent to X-

rays, was expected

to result in a dark

patch on the film.

Instead, the

polychromatic X-ray

beam divided itself

into many tiny

fractions that

created a

r e m a r k a b l e

symmetric design of

dots with different blackness. They had

proved that the X-rays were waves and

also that the lattice spacing had

dimensions comparable with X-ray

wavelength.

As was the practice those days, the

results were presented to a group of

scientists of the Bavarian Academy of

Sciences before the printed publication

by their boss Sommerfeld, who was a

Fellow of the Academy, on 8 June and 6

July 1912. Simultaneously, Laue presented

them to the Berl in Physical Society.

Publication of the proceedings came later

in October in the names of Laue, Friedrich

and Knipping. It was indeed a

breakthrough. The dots, their pattern and

distances could give the unit cell

dimensions of the cr ystal and the

symmetries involved. Thus far, X-rays were

known to give a view of the internals of an

assembly or a body. Now they also

permitted a view inside a tiny crystal and

promised to show the atomic

configurations!

Of course, attempts for the latter did

not succeed uniformly as it was more of

an art of imagination than a method. Very

The mysteriousradiationdiscovered byRoentgen wasnamed ‘X-ray”but it was notsure whetherthey werewaves orparticles

Max von Laue registeredthe first diffraction

pattern from a crystal ahundred years ago

In fact, today’scrystallographer does nothave to work as hard asthose in yesteryears becausetens of thousands ofstructures of organic andinorganic compounds as wellas of various metals andalloys are already workedout and stored digitally.

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SCIENCE REPORTER, DECEMBER 2012 10

soon, the Braggs gave a systematic

approach to observe the reflections and

get precise values.

Making the Art a Science:

X-ray SpectrometryThe stage for act two of the crystallography

play now moved from Munich in Germany

to Leeds and Cambridge Universities in

England. The two lead actors were W.H.

Bragg and W.L. Bragg, a British father and

son scientist pair. William Henry Bragg,

often called Bragg Senior, had returned

from Australia where he had been

teaching at Adelaide University since the

past 22 years. He joined research at the

Leeds University.

He was a unique scientist whose

research career began at the late age of

43 years. It was when he obtained the first

ever X-ray tube of Australia in his

department in Adelaide. Within three years

he came to England to pursue work in this

line. The Laue results came shortly after

that. Bragg explained these results in a

more specific manner and developed an

instrument, an X-ray spectrometer, which

could provide more precise information

about the lattice parameters than the

Laue photos could.

Meanwhile, Bragg Junior was

admitted to the Cambridge University on

arrival from Australia to complete his

graduation. He was lucky to pursue his

research training at the Cavendish Lab

under the famous J.J. Thomson, who had

discovered electron just ten years back in

1897.

In 1912, when Laue’s results came in,

W.L. Bragg was still at Cambridge and

followed his father ’s work when he visited

his home at Leeds. He felt interested in this

research, and collaborated with him. W.H.

Bragg Diffraction

To understand Braggs’ equation, let us look at an imaginary lattice array withatoms as shown in the figure here. Let a narrow beam of monoenergetic X-rays fall on this array of atoms. Monoenergetic signifies that the beam hasonly one wavelength ë, unlike the experiments of Laue where the X-ray beamwas a mixture of rays of various wavelengths. This can be obtained byappropriate filters. For X-rays, wavelength and energy are related; thus asingle energy beam also means a single wavelength beam.

Diffraction is a two-step process: first a scattering and then interferenceof the scattered waves, either constructively or destructively. The single rayAO hits an atom and gets scattered in the direction OB; the ray A´O´ goes inO´B´ direction. Notice the small cut marks on these waves which indicatelocation of a crest of the wave; the distance between two consecutive marksis wavelength ë of the x-rays. The way marks placed on AO and A´O´ showthat both the rays are in phase – their crests occur at the same time along thejourney. Scattered waves OB and O´B´ are also in phase. This is because thedelay MO´ + O´N is equal to one or more integer multiple of a wavelength. Sothe phase of the scattered ray is not disturbed and being at same phase OBand O´B´ add the intensities on the way ahead. That gives a dark spot on theX-ray film or a peak in intensity of X-rays in a meter.

Scattering can happen in any direction and thus OP or O´Q are alsoscattered waves as well. But here the crests of the rays (the cut marks) do notoccur in synchronous manner. Thus leaving them out of phase and therebysubtracting their intensities. This scattering fails to produce a spot. Fromthis, Bragg deducted a very simple condition for noticeable diffraction. As MO´ = O´ N = d sinè, the condition is

2d sinè = an integer times ë = n ë

This is the famous Bragg equation. It was first published in the book X-rays and Crystal Structure (Bell, London 1915) by W.H. Bragg and W.L Bragg.

Hence, it can becredited to bothof them and iscalled Braggs’formula.

Please notethat this was at w od i m e n s i o n a lsituation. In areal crystal the

atomic array and the rays are in three dimensions. Appropriate formulae arethere to determine the lattice parameters in three dimensions.

The approach to deriveBragg Formula

The Bragg father and son duo

X-raytube

Leadscreen

10,000-40,000volts

Crystaline solid

Spot from incident beam

Spot from diffracted X-rays

Photographic plate

Graduallythere wereimpro-vementsandrefinementsin instru-mentation.

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SCIENCE REPORTER, DECEMBER 201211

Bragg was more interested in X-ray

spectroscopy, finding intensities at different

wavelengths in the output from X-ray tubes.

For this he built a spectrometer.

It was during this period that the

famous formula of X-ray diffraction (n ë =

2d sinè) was evolved (see attached box

for explanations of the formula ). The

formula has three parameters (ë, è and d)

and you can find any one if the other two

are known. W.H. Bragg used his

spectrometer that employed a rotating

turntable (later christened as goniometer),

which had angular markings to measure

è. When you use a single crystal, lattice

parameter ‘d’ is constant and you have

relationship between ë and è. (Single

crystal is such a crystal where the lattice is

uniform through out the crystal without a

change in lattice spacing or a break).

Different wavelengths get received at their

corresponding angles around the circle.

The photographic film of Laue was

replaced by an ionization chamber so that

accurate X-ray intensit ies could be

measured. Instead of dots of Laue you now

had intensity peaks.

While W.H. Bragg determined spectra,

his son preferred to work on crystallography

and determine the lattice spacing ‘d’. For

this the X-ray beam with nearly f ixed

wavelength ë was used; by finding the

corresponding angle è where X-ray

intensity peaks, spacing d can be found

from the formula. Lattice spacing in all

directions will give the idea of the shape

and size of the unit cell of the particular

type of material.

Thei r s tudy of diamond latt ice

showed how diamond is different from

graphite. Laue’s results on how NaCl and

KCl cr ystals are bui l t could now be

reconfirmed. The Braggs presented their

Laue’s methodcan be used inthe reflectionmode as shownat the left.

Original spectrometer used by the Braggs (left) and right a modern spectrometer

Structure of a NaCl crystal. Notice that the planes indifferent orientation contain different combination of

atoms and yield different peaks

Film

X-rays

Crystal

Mounting

Goniometer

Film

Na+

Cl-

work at the Royal Society of London on

13 Apr i l 1913 ent i t led “About the

reflection of X-rays by crystals” where the

members learnt for the first time that the

atoms in a rock sal t cr ystal were

arranged in a particular way (which today

is called “NaCl pattern”) and how to find

it. This was published in the Society ’s

proceedings in the Fal l of 1913. By

November they were ready with the

structures of fluorite, sphalerite and pyrite

for presenting to the Society ’s meeting.

Gradually there were improvements

and refinements in instrumentation. For

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SCIENCE REPORTER, DECEMBER 2012 12

example, if you take a fine powder

sample, it will contain crystallites (fine

grains) in all likely orientations. A diffraction

pattern from this can be obtained without

the need to rotate the sample, as is

needed for a crystal. A special camera

for taking diffractograms from powder

samples was developed by A. Hull and

later by many people including Peter

Debye and Scherrer. All these different

methods of peeping into crystals to find

atomic locations were a dream come

true and the scientific community was

thrilled using them.

The Nobel PrizeSo important was this new technique that

it yielded a Nobel Prize in just two years

after the discovery! Laue got the prize in

Physics in 1914 for his work done in 1912

and Braggs jointly got the prize in 1915 for

the XRD technique given in 1913.

By then the First World War was

brewing. Bragg senior devoted his time to

detection of submarines and the younger

Bragg was taken for his part of compulsory

mil itar y service. When the prize was

announced in November, W.L. Bragg was

serving in the horse artillery somewhere in

France. At 25, he is the youngest Noble

Prize winner till date, not only in physics but

also across all the subjects in which the

Prizes are given. Besides, this is also the

only occasion where father and son have

shared the same prize, though there are

three more cases where father and son

both are prize winners at different times.

Sadly, the joy of receiv ing the

celebrated prize was taken away by the

untimely death of his younger brother in

the war field in the month of September

1915. There was no prize in physics for

the year 1916; once again in 1917 the

prize went to X-rays – this time to Barkla

for explaining the X-ray spectrum with

character is t ic X-ray peaks

superimposed. These peaks (Ká) were

later used as the source of

monochromatic X-rays by filtering out the

spectrum up to the peak. This was very

useful in the Bragg method and opened

further vistas into X-ray diffraction for all

times to come.

Applications in other FieldsThis new and ingenious method of

crystallography found favour with scientists

in other disciplines also. From the results of

the work a realization was growing about

the connection between the structure of

materials and their properties as well as

reactions. This was true for metallurgy and

chemistry; somewhat later biology also

joined the pursuit.

Nobel laureate Ada Yonath with X-ray diffraction equipment and a modern X-raydiffraction machine (left)

The molecular model of DNA was based on X-rayphotos taken by Rosalind Franklin and Maurice

Wilkins at the King’s College London

X-raydiffractioninspiredscientists toexplorediffractionusingelectrons andneutrons.With the DeBrogliehypothesis ofwave-particleduality, it wasaccepted thatthe beams ofboth theseparticlescould betreated aswaves.

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SCIENCE REPORTER, DECEMBER 201213

All Coincidence?

While declaring that particles and waves are the two sides of the same coin,Lois De Broglie also gave a formula to find the wavelength of the associatedwave from the energy of the particle. It is given as ë = h/p where h is thePlanck’s constant and p is the particle momentum. This applies to electronsand neutrons; for X-rays it can be modified to get ë = 12.4 / Energy in keV

To have wavelength in the range of 1 Ao, which is the order of magnitudeof the atomic distances in a lattice, following energies would be needed:

X-rays 12.4 keVElectrons 150 eVNeutrons 0.1 eV

Electrons of any energy can be produced by applying e.m.f. between twoelectrodes. But what about monoenergetic X-rays in the given range? It is acoincidence that the Ká lines of many abundant metallic elements lie in thisrange. See this:

Mo: 17.4 keV Cu: 8.04 keV Ni: 7.47 keVCo: 6.93 keV Fe: 6.4 keV Cr: 5.41 keV

Mosley found a method to use these metals as targets as well as filters toobtain nearly monoenergetic X-ray beams. Similarly, neutrons in a nuclearreactor have a broad range of energies but the thermal neutrons, which aremost abundant in a reactor, have the energy suitable for the diffraction work.Are all these coincidences or the ingenuity of scientists in locating theuseful radiation?

Cellulose structure was seen in 1920.

The first organic structure determined was

Hexamethylene Tetramine in 1923 (by

Dickinson and Raymond). The nature of

bonds in molecules could be understood

from diffraction studies. The Benzene

structure was understood in 1928 by

Kathleen Lonsdale. C.G. Darwin (grandson

of the famous Charles Darwin) gave a

method to determine valency from the

crystal structure. Later, a separate branch

in chemistry called structural chemistry

evolved.

Metallurgy has derived maximum

benefits from the application of XRD. Alloys

could be better understood if the crystal

structures were known. Graphical

representations of alloy compositions at

different temperatures are called phase

diagrams; they are highly valuable tools

to understand an alloy ’s behavior. These

could be generated with the help from

the XRD.

The modern XRD units facil itate

dynamic study of structures by observing

the changes in metallic phases in real time

with changing temperatures. Even creating

new alloys of desired properties is possible

with the help of XRD and electron

microscopes. If the material or a

component is under stress – applied or

left over after fabrication sequence – the

lattice gets distorted. This results in a

change in parameter ‘d ’ and can be

detected easily by XRD. This is a popular

application of XRD in residual stress

measurement in engineering.

Applications in BiologyBioscientists were the last to get on board

the XRD train. This is because XRD and

crystallography were synonymous in those

days. No biological substance, except

bone, appeared to be crystalline, though

later it came to be known that the X-ray

techniques could be used for amorphous

materials also.

But biologists entered through a

different route. They worked on crystallizing

the proteins to study them. J.D. Bernal in

England was the first to get X-ray photos of

proteins in 1934, published in Nature (Vol.

133, p 794). Several biochemicals in our

body are actually proteins: enzymes,

hormones, haemoglobin or antibodies.

X-ray picture of A and B form of DNA taken by RosalindFranklin

A B

Laue pattern of the Zinc blende crystal

In the last hundred years, thebranch of crystallography hasearned more than 20 Nobelprizes, indicating its deeprelevance. To commemorate thehundred years of the twindiscoveries of crystallographyand X-ray diffraction, theinternational community ofscientists is arranging variousprogrammes.

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They are large molecules and finding their

structure was challenging. Sometimes it

took five to seven years after obtaining the

X-ray pictures to determine the exact

structure in three dimensions.

After Bernal, his colleague Dorothy

Crowfoot Hodgkin pursued this field of

biomolecules throughout her l i fe,

deciphering Cholesterol, Penicillin and

Vitamin B-12 etc. Her decoding of insulin

came after she won the Nobel Prize in

1964. Credit for solving haemoglobin

goes to John Kendrew and Max Perutz,

whose efforts were aided by improved

instrumentation and evolved

mathematics.

In this chain of workers came

Rosalind Franklin at the King’s College

London, as well as James Watson and

Francis Crick at Cavendish Lab at

Cambridge. The latter two gave the

model of the hereditar y material DNA

(deoxyribonucleic acid). The molecular

model was built up based on X-ray photos

taken by Rosalind and Maurice Wilkins,

though Watson and Crick did not

acknowledge this fact till Rosalind was

alive. It is an old and lively debate in the

history of science. It is really a tribute to

the long career of W.L. Bragg that he was

the Head of Cavendish Lab when this most

SCIENCE REPORTER, DECEMBER 2012 14

important molecule was reconstructed

using the technique he invented 40 years

earlier!!

The major impact of XRD work on

human life has come through the

achievements in biological science more

than any other branch of science. The

functioning of various proteins in the body

depends on their shape; they connect to

other chemicals at the open ends of the

molecule to give effect to many a

biological process. Thus, knowing their

structure helps us to understand many

processes and enables intervention.

Take for instance drug design.

Knowing the physiological basis of any

ailment, one can construct a drug that

has a molecular structure of one’s choice

to go and nul l i fy the malfunctioning

molecule. Scientists at Squibb Institute of

Medical Research were the f i rst to

collaborate with cr ystallographers for

drug development, by targeting an

enzyme for intentional latching. The first

drug to come out this way was Captopril

in 1975, used to alleviate hypertension. A

branch of science cal led structural

biology opened up to determine target

structures responsible for morbidity,

including enzymes, protein receptors,

zones of DNA, RNA etc. These days, many

drugs are designed in this way rather than

invented by an accident or iterative trials.

This became feasible because of

better instrumentation for XRD technique,

mathematical tools such as Fourier analysis

and, above all, the progress in computer

technology that permitted scientists to avail

of the new theoretical concepts in a

shorter time span. While Vitamin B-12 (C63

H

88N14

O14

P Co) with 181 atoms took eight

years to resolve, today molecules

comprising thousands of atoms can be

resolved in a matter of months, thanks to

help from computers.

In fact, today’s crystallographer does

not have to work as hard as those in

yesteryears because tens of thousands of

structures of organic and inorganic

compounds as well as of various metals

and alloys are already worked out and

stored digitally. Most times the equipment

itself guides you to the identity of the

reflection. Young scientists do not have to

reinvent the wheel. In addition, with

improved X-ray sources (l ike the

synchrotron) and radiation detectors, data

collection time has reduced drastically

and signal-to-noise ratios have improved.

This obviously widens the scope of

applications.

X-ray diffraction inspired scientists to

explore diffraction using electrons and

neutrons. With the De Broglie hypothesis

of wave-particle duality, it was accepted

that the beams of both these particles

could be treated as waves. Neutron

diffraction particularly broke new grounds

in nuclear physics. They had a clear

advantage in two situations: X-rays do not

show adequate scattering by low atomic

number nuclei and neutrons happen to

have selectively better scattering by such

nuclei. Hence, the presence of l ight

atoms in a lattice can be studied better

by neutrons. Secondly, unl ike X-ray

photons, neutrons have magnetic

moment that makes them very unique

tools to study their interaction with

ferromagnetic (or paramagnetic) atoms

in the latt ices. These methods were

developed in the second half of the 20th

century.

In the last hundred years, the branch

of crystallography has earned more than

20 Nobel pr izes, indicating i ts deep

relevance. To commemorate the

hundred years of the twin discoveries of

crystallography and X-ray diffraction, the

international community of scientists is

arranging various programmes. In

December 2012, the Universi ty of

Adelaide in Australia will hold a Bragg

Symposium as W.H. Bragg once worked

there. The International Union of

Cr ystal lography, of which Dorothy

Hodgkin was one of the founders, has

declared 2014 as the Year of

Crystallography and has requested the

UN to declare it so internationally. All this

wi l l put the technique on the wider

pedestal of awareness.

When laser was invented in 1960 it was

touted as a ‘solution in search of a

problem’. Contrar y to its enormous

potential, lasers waited very long before

their applications came. X-ray diffraction,

on the other hand, turned out to be a

technique for which applications were

waiting.

Dr Paresh R. Vaidya Retired as Scientific Officer(H) and Head, Quality Control Section, BARC,Trombay, Mumbai. Address: Flat No 3, NishantSurabhi, Plot 110, Sector 28, Vashi (Navi Mumbai)-400703; Email: prvaidya@gmail.com

Schematic of theBraggSpectrometer

XRD patterns from pearls. Left one is natural pearl whilethe one on right is cultured pearl.

X-ray detector

Incident X-ray beam20

Crystal

When Max von Laue registered the first diffractionpattern from a crystal a century ago, he took thefirst step to satisfy this urge of scientists to see theatom level configurations. The discovery of X-raydiffraction was a central event in modern science.The observation of X-ray diffraction by Friedrich,Knipping and Laue is one of the most importantdiscoveries in the history of science, and one withmonumental consequences. It opened the path forthe development of modern solid-state physics andmaterials science, including mineralogy, chemistryand molecular biology.

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