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Defects in Metals

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Cambridge University Press978-1-107-40997-2 - Materials Research Society Symposium Proceedings: Volume 209:Defects in MaterialsEditors: Paul D. Bristowe, J. Ernest Epperson, Joseph E. Griffith and Zuzanna Liliental-WeberExcerptMore information

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DEFECTS IN MATERIALS: THEIR CHARACTERIZATION AND SIMULATION.

COLIN G.WINDSORNational Non-Destructive Testing Centre,AEA Technology,B521.2, Harwell Laboratory, 0X11 ORA, UK.

ABSTRACT

Materials research does not necessarily need to eliminate defects, but rather tocharacterize them, and to understand and control their effects. In most caseschacterization of defects means making structural or dynamic measurements oftheir properties. To understand these measurements in order to predict materialand defect properties outside the range of the measurements is a much harderproblem. Ideally a theory is required. However in the materials examplesconsidered in this review, point defects in uranium oxide, copper clusters in steel,grain boundary aggregations, and stress concentrations, a true analytic theory isbeyond our capabilities. Here computer modelling is often able to make theprogress needed. This review considers the complementary nature ofexperimental characterization and computer simulation in our understanding ofdefects in materials.

INTRODUCTION

Defects are a fact of life. As Dr Marshall said to our UK House of Commons SelectCommittee on Energy, "The central point is that you cannot make anything without havingsome defect in it. It may be very tiny or it may be very large, and you have to assess howimportant that defect is."

Defects can be classified in many ways. Size is an obvious classifier, and will be usedin this review, but there are many others. Dimensionality is a vital axis. Some defects areessentially point-like, others volumetric, others planar or linear. Grain boundaries will bediscussed as representative of planar defects. The interface between two polymer blendsrepresents another planar defect. Defects can be dangerous, they can be advantageous, or theycan be benign. The tiny copper clusters found in pressure vessels may certainly be dangerous,but the clusters found in many aged hardened alloys are beneficial.

Temperature plays a key role for many defects. The atomic defects which give rise tosuperionicity appear with increasing temperature as the thermal energy becomes comparablewith their energy of formation. Many volumetric defects, such as alloy clusters, break up athigh temperatures, but represent a condensed state of matter which becomes stable atintermediate temperatures. Macroscopic defects may be the hardest to characterize. A regionof high residual strain in a structure can be more dangerous than many more easily locateddefects. Figure 1 illustrates these axes for some types of defect which will be discussed here.

Mat. Res. Soc. Symp. Proc. Vol. 209. ©1991 Materials Research Society




Volume

Figure 1Some of the variablesused to characterizedefects. In italics aresome of the defectsconsidered in thisreview.

Planar

Line

Point

b&corvcLasvu,

bZvrvaL

vn&sxpxca,

Advantageous

NanometreDangerous

Micron Millimetre

POINT DEFECTS: SUPERIONICTTY IN UO 2 + X , ZrO2 and SrCl2.

The detailed understanding of the high temperature properties of uranium dioxide isvital to the safety studies of many reactor systems. As an example of point defect studies thecase of oxygen defects in UO2+X is considered. Its fluorite structure may be viewed as a asimple cubic lattice of oxygen anions with alternate cube centres filled by uranium cations.One might expect any thermally excited or excess oxygen to occupy the empty cube centres.However single crystal neutron diffraction, which gives the time averaged occupation of theunit cell, has shown that these sites are not appreciably occupied. Instead, the diffractionresults are consistent with the defect cluster, proposed by Willis[l]. This cluster takes theform shown in figure 2, known as the 2:2:2 cluster. To understand such a defect and predictits effect on bulk properties, essential tools are computer codes such as the HarwellAutomatic Defect Examination System (HADES) [2]. Such codes must be given a potentialbased on measured properties such as the phonon dispersion curves, the dielectric properties,and the anion and cation migration energies. In the case of UO2+X work by Catlow[3] wasable to show that the 2:2:2 cluster, with appropriate interactions and relaxation, was indeedenergetically stable.

Figure 2A typical atomic cluster defect - the2:2:2 cluster in UO2+X- Excess anioninterstitials are located at positions"I". The nearest neighbour anionssites are relaxed to sites "R", leavingvacancies "V" on their regular sites.This gives rise to the notation

T site interstitial

Relaxed I D Anion vacancyA | . s j t e j n t e r s t i t iQ lAnion

© Cation# Anion




At high temperatures the excess oxygen atoms become mobile, jumping from one siteto another. The effect is important technologically because an increase in the oxygendiffusion constant can have a strong effect on the thermal conductivity. The characterizationof the oxygen interstitial defect has come historically from diffraction - both X-ray andneutron. Neutron diffraction has been specially useful because of the good resolution in theoxygen positions it gives, and because of the ability of neutron diffraction furnaces to reachthe temperatures of order 3000K necessary to study the superionicity of these materials. Theclassic tool for studying the detail of the defect scattering pattern has been the reactordiffractometer. Bragg scattering intensity gives the time averaged occupation of sites, whilethe diffuse scattering shows the time-averaged correlations between the ions and vacanciesin the defect. The coherent diffuse scattering from anion excess fluorites has now beenmeasured. It is possible to calculate the scattering using specific cluster models and so testthe computed predictions. As can be seen from figure 3 the experimental data from UO2J3at 858K is in good agreement with the computed profiles from the 8:2:8 cluster, which is the2:2:2 cluster with third neighbour relaxation. Indeed it is possible to fit the parameters of themodel directly from the data [4].

Raduccd Wfemvtctor. {

Figure 3The diffuse scattering in UO2J3 as measured at 858K on a reactordiffractometer {left) It may be compared with the computed map for the 8:2:8cluster (right) [4]. The contours represent scattering intensity as a function ofposition in the reciprocal lattice.

Figure 4The diffuse scatteringfrom yttria dopedzirconia measured onthe pulsed singlecrystal diffractometeron the ISIS pulsedneutron source. Theplane over reciprocalspace is produced bycovering a range ofboth scattering anglesand wavelengthssimultaneously. [5]

30 40 50Time (ms)

6 0




Now very detailed diffuse scattering patterns are being obtained from pulsed neutron sources.Figure 4 shows results from ZrO2 doped with Y2C>3 which forms a model system for ananion deficient fluorite, such as UO2.X. These measurements have been taken on the SingleCrystal Diffractometer of the ISIS pulsed neutron source [5]. The two-dimensional positionsensitive counter gives the scattering intensity over a whole volume of reciprocal spacesimultaneously. The figure shows only results for the plane containing the reciprocal latticepoints. The diffuse scattering is clearly seen as the foothills of intensity forming a ridgebetween the allowed Bragg peaks like 224 and the forbidden peaks like 114, which are due toa tetragonal phase. This scattering can be compared with detailed models of the defectstructure.

The defects in these structures must not be thought of as being static. Indeed inUO2+X the defects are always dynamic in the sense that they have only has a limited lifetimebefore they jump to another equivalent position in the lattice. These lifetimes can bemeasured by quasi-elastic neutron scattering where small energy transfers about elasticscattering are measured. [6] Figure 5 shows measurements made on incoherent diffusescattering from the strontium yttrium chloride system using the IRIS instrument at the ISISpulsed neutron source . The incoherent scattering is related directly to the self correlation andcan be used to determine the diffusion constant of the anions.

Figure 5The quasi-elastic scattering fromstrontium chloride doped withYttrium chloride measured on theIRIS instrument at the ISISpulsed neutron source. Thedifferent energy widths betweenthe scans at the two temperaturesenables the lifetime of the defectsto be estimated. [6]

-0.05 0 0.05Energy transfer E1-E2 («eY)

COPPER CLUSTERS IN PRESSURE VESSEL STEELS

The pressure vessel of a pressurised water reactor can be embrittled by the combinedeffects of irradiation and thermal ageing if there is a presence of impurity copper. This inturn can lead to the growth of cracks. Because of the importance of being able to understandand model these effects a wide variety of techniques have been applied, but a completeunderstanding is still awaited [7,8]. Figure 6 shows the problem illustrated for a model alloyof Fel.3w%Cu. The hardness of the alloy increases to give a peak either with irradiation at aneutron dose around 1019 n cm"2 or with thermal ageing at 550C for around 2 hours.

Figure 6The problem of copperclustering in ferritic steels.The figure shows thehardness of the steel as afunction of ageing time at550C and of irradiationdose[7].

1 10 100AGEING TIME AT 550"c thrs)

1.10" 1.1020

DOSE (n.cnf2)




Small angle neutron scattering (SANS) was among the first techniques to show thatthe effect correlated with the formation of copper clusters. The left hand part of figure 7shows the SANS particle size distribution for the alloy at 2 and 10 hours ageing at 55OC. Theclusters are seen to be around 5 nm in diameter at 2 hours and give a bimodal distribution at10 hours.

Figure 7The defect sizedistribution functionmeasured after 2 and10 hours ageing at550C measured by(left) Small AngleNeutron Scattering(SANS), and (right) byTransmission ElectronMicroscopy (TEM)[7]

F«Cu -. 550* C.

0-4

0-3

02

0-1

r

Fe/Cu

— 2—-10

n

j S

hrshrs

Precipitate diam*t*r(nm)10 20

DIAMETER (nm)

Transmission electron microscopy (TEM) can observe the clusters in both cases asshown on the right of figure 7. The 5 nm clusters are seen as characteristic "black-white"images which can be identified as copper rich clusters from energy dispersive X-raymeasurements (EDX). These measurements are shown inset in figure 8, which shows theTEM images from the alloy aged at 2 hours. All these measurements are consistent with 5nm diameter clusters composed of coherent body centred cubic copper. The 12 nm diameterclusters aged for longer times are face centred cubic.

Figure 8High resolutionimages of the copperrich clusters. Inset areshown some of theenergy dispersive x-ray spectra thatidentify thecomposition of theclusters. On the upperright is an enlargedview of a "black andwhite" cluster. On thelower right are shownlattice images with theplane spacing of bcccopper[8].




Recent high resolution electron microscopy (HREM) has been able to confirm this by directlattice imaging as shown in figure 8 [8]. It is now clear that during ageing the copper clusterschange from a coherent bcc to an incoherent fee structure. These transformations have nowbeen confirmed by extended X-ray absorption fine structure (EXAFS) measurements whichare able to measure the local environment of the copper atoms alone from the local structurearound the copper absorption edge [8]. Figure 9 shows the fourier transform of the edgecompared with results from pure bcc iron and pure fee eopper.Essentially these monitor thedensity of atomic shells around copper ions as a function of distance. The results confirmunambiguously that the 2 hour aged copper clusters have a bcc structure while the 10 houraged clusters have a fee structure.

Figure 9Extended X-ray Absorption FineStructure (EXAFS) measurementsof copper clusters in steel. Themeasurements have been Fouriertransformed to reveal the nearneighbour atomic shells [8].

E

ICD

I

2 4 6 8

Radius (A)

10

Field ion microscopy (FIM) was the first technique to give evidence of thecomposition of the copper rich clusters. The method is able to analyse the atoms layer bylayer as they are peeled off by the field. The first measurements suggested that the clusters at2 hour ageing had a low copper concentration, but this has now been revised. Furtherevidence on this can be obtained from the SANS cross section in the presence of an appliedmagnetic field sufficient to saturate the magnetization of pure iron. The ratio the crosssection parallel and perpendicular to the field should be about 10 for a pure copper clusterbut only 1.3 for voids in iron. The values are in the range 5 to 10 so that they are not yet ableto confirm the exact composition of the clusters [7,8].

Molecular dynamics has been applied to obtain the properties of bcc copper in theiron matrix [8]. In molecular dynamics each atom is allowed to move freely under anassumed potential, and at a given temperature. No assumption is made about any latticewhich the atoms may choose to cluster on. In this case the computer code MOLDY was usedin conjunction with the potential of Ackland [9]. It was shown that bcc copper is unstablebelow 12.5 GPa, when it its shear modulus drops to zero allowing it to transform to a faultedfee structure. In the iron matrix the bcc phase becomes stable under the pressure caused bythe copper atoms being larger than the iron atoms. This gives a lattice misfit of 3.3%. Aparticularly valuable contribution of the simulation was to predict the shear modulus for bcccopper shown in figure 10. At the expected misfit pressure the modulus is a good dealsmaller than for fee copper or for bcc iron.




These studies of model alloys have allowed the behaviour of practical pressure vesselsteels to be modelled with much lower copper contents than in the alloys whose results arereported here.

Figure 10A molecular dynamicscomputation of the shear modulusof copper in a body centred cubic(bcc) lattice under the internalpressure from the lattice misfit.The bcc iron and fee coppermoduli at zero pressure are alsoshown.

z

I

•s~\

\\\

MPrc

\

\

V\

Isfitssure

fee

_bcc

\

\

Cu

Cu

5 10 15

External Pressure (GPa)

20

SURFACES AND INTERFACES

There are numerous techniques available for characterising exposed surfaces [10].They can be viewed in up to atomic detail by microscopes, their composition can bemeasured by spectroscopy of excited states. However characterization is not so easy if thesurface is not exposed. Examples are liquid-liquid interfaces, liquid-solid interfaces, theinterface between polymer blends, and the interface between polymers and coatings. Suchinterfaces can now be studied by neutron reflectometry [11]. The method is illustrated insetin figure 11. A collimated neutron beam is incident at glancing angles onto the interface. Thebeam penetrates the layer and its reflectivity may be measured as a function of scatteringangle or of wavelength. Figure 11 shows results of Burgess[12] from a thin layer of siliconsputtered on to a polyimide substrate.The difference in scattering length density between themedia may be found from the critical angle where the reflectivity becomes perfect. Thethickness, density and perfection of the evaporated layer may be found from the interferencepattern giving rise to the fringes shown.

GRAIN BOUNDARIES

"Grain boundary engineering" is the phrase which expresses the key role which thedetails of the grain boundary microstructure play in the performance of a finished material. A"perfect" grain boundary would be outside the scope of this review, but these never exist in







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