Neutrons vs X-rays

X -ray s are scattered by the electrons o f the atom and the intensity o f diffraction is th erefo re prop ortio nal to the atom ic num ber. L ight atom s, such as hydrogen and m ore im portantly in this project oxygen, are very difficult to locate accurately using X -ray d iffractio n. N eu tron s on the other hand d iffract from the nucleus so the scatterin g factor is not d epend en t on atom ic num ber but can vary dram atically betw een elem ents, and indeed betw een different isotopes o f the same element. In the scop e o f th is th esis this m eans th a t n eu tro n d iffractio n afford better positional p aram eters for oxygen atom s in com plex structures such as N b ,2 0 29" A nother ad v an tag e neu tron d iffractio n has over X -rays rad iatio n is that the scattering is

isotopic and does not dim inish w ith increasing 2 6 as in the case o f X -ray diffraction.

T his is because the X -rays are scattered from the electron cloud and interference takes place betw een X -rays scattered from different parts o f the atom. By contrast neutrons, being scattered by the nucleus, a point source, and thus interference does n o t take place. N eutron diffraction is a pow erful technique for solving the m agnetic structure o f solids. N eutrons have spin w hich interacts w ith any unpaired electrons on the nucleus giving detailed info rm atio n on the m agnetic ordering. A lthough n eu tro n d iffra c tio n has m any ad v an tag es o v er X -ray d iffrac tio n for structure determ ination. X -ray diffraction as a laboratory technique is invaluable particularly for fo llow ing p ro d u ct fo rm ation d urin g synthesis and for prelim inary structure solution. It has the advantage o f generally having m uch higher diffraction intensities and therefore needing sm aller sample sizes.

3.1.2 X-ray Diffraction

Pow der X -ray diffraction data w ere collected using a Siem ens D 500 diffractom eter operating in B ragg-B rentano geom etry w ith Cu K a l radiation, selected by use o f a prim ary m o nochrom ator. S am ples w ere m ounted on p lates, the pow der being pressed into a recess and m ade flush w ith the surface o f the plate using a glass

m icro scop e slide. M easu rem en ts w ere o f tw o types: short m easu rem ents for prelim inary assessm ent o f sam ple purity, and longer ones for final assessm ent and prelim inary R ietveld refinem ent. The shorter m easurem ents w ere taken over the range 5 < 20 /° < 70 w ith a step size o f 0.04° and a counting tim e o f 1 or 2 seconds. The longer scans w ere taken over the range 5 < 20/° < 100 w ith a step size o f 0.02°

and a co unting tim e o f b etw een 10 an d 40 seconds. The d iffracto m eter was

controlled using the Siem ens D iffrac-A T software package.

3.1.3 Neutron Diffraction

All the neutron diffraction experim ents carried out in this thesis w ere firom constant w avelength reactor sources, either at the Institut L aue-L angevin (ILL), G renoble, France or the N ational Institute o f Standards and Technology, G aithersburg, USA. The w hite beam o f neutrons, extracted through a hole in the reactor, is collim ated by

a 2 to lim it the spread o f incident directions. From here the beam is directed to a

single crystal m onochrom ator w hich selects a band o f w avelengths

NklX

these neutrons (som etim es v ia a second collim ator) on to the sam ple. The beam is then scattered into a detector w here the divergence o f the scattered beam is governed by a third collim ator and the position and intensity o f the scattering are recorded.

3.1.3.1 Institut Laue-Langevin, Grenoble, France.

A t ILL two high resolution diffractom eters w ere used: D IA and D2B. The high flux reactor operates at a therm al pow er o f 58 M W using a single fuel elem ent w ith an

operating cycle o f 50 days. The neutrons are m oderated and cooled using D2O in a

3.1.3.2D2B

D 2B is characterised by a high m onochrom ator tak e-o ff angle o f 135°. A Ge [335] m onochrom ator w ith a w avelength o f 1.594Â and a Ge [331] m onoehrom ator w ith a w avelength o f 2.398Â w ere used. The beam is 300m m high, focusing vertically onto about 50m m at the sample position, 3 m etres from the m onochrom ator. A com plete diffraction pattern is obtained after 100 steps o f 0.025° in 2 0 . Since the 64 He^ deteetors are spaced at 2.5° intervals these seans take about 30 m inutes and w ere

repeated to im prove statistics so a com plete data set took around 1 2 hours.

Monochromator Collimator 5' Collimator 5' Sample 2 0 Multidetector Reactor

3.1.3.3 DIA

D IA is a m edium resolution diffractom eter w ith a slightly sm aller take o ff angle o f 122°. The Ge [115] m onochrom ator, giving a w avelength o f 1.911Â, focusses the 250m m high beam to 30m m at the sam ple. There are 25 high efficiency collim ators and detectors w hich are show n in the figure below. A com plete diffraction pattern is tak en up to 160° 2 0 w ith a step size o f 0.05°. This instrum ent w as used for a

diffraction pattern o f TiN b^O ^g, the scan took 1 2 hours.

M o n o ch ro m ato r R eacto r 60m

25 co llim ato r d etecto r b an k

3.1.3.4 National Institute o f Standards and Technology, NIST, Gaithersburg, USA

The reactor operates using uranium fuel elem ents producing a thermal flux o f4 x l Q i4

neutron cm '^s'^ at a rated pow er o f 20 M W , w ith a 7 w eek operating cycle. The

reactor is D2O m oderated, cooled and reflected.

3.I.3.5BT-I

BT-1 is a 32 detector high resolution pow der diffractom eter that can be used w ith three different m onochrom ators; Ge [311], Cu [311] or Si [531], w ith either 15’ or 7 ’ collim ation. The take o ff angles for the different m onochrom ators are shown in figure 3.3. The C u [311], w avelength 1.5401Â, has the optim al balance betw een intensity and resolution and w as used for m ost o f the sam ples. The Ge [311], w avelength 2.077Â , m onochrom ator yields the highest neutron intensity and best resolution but only at low er scattering angles.

Reactor Collimator 15' g c (311)Cu (311) Si (531)

Sampli

32 Detectors

3.2 Magnetism

3.2.1 SQUID magnetometers

The m ost sen sitiv e m e th o d in th e m easu rem en t o f m ag netisation is to use a Superconducting Q uantum Interference D evice or SQUID, the m ain com ponents o f

w h ich are sh o w n in fig u re 3.4. T he S Q U ID m ag n eto m eter co n sists o f a

superconducting ring containing tw o Josephson ju nctio ns w hich are thin regions o f non-superconducting m aterial through w hich the superconducting current can tunnel. W hen a current is applied to bias the SQ U ID , it divides betw een the two ju nctions and, if it is greater than the critical current, then the ring has a non-zero resistance and voltage is produced across it. The product o f the area o f the ring and the m agnetic field enclosed by it is called the m agnetic flux and is quantised. The critical current is a m axim um w hen an integer num ber o f flux quanta are contained and a m inim um w hen a non integer num ber o f flux quanta are contained. Consequently, changes in the m agnetic field give rise to changes in the critical current and hence in the voltage m easured across the SQ U ID . As the v oltage change across the SQ U ID is the quantity m easured, it is possible to m easure a change in flux sm aller than the flux quantum and thereby m aking the technique extrem ely sensitive.

current _current

- Voltage -

Josephson