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IT9700344 INFN - LABORATORi NAZIONALI DI FRASCATI XRPD ÌSCHOOL LNF - 96/049 (IR) 17 Settembre 1996 V School on X-ray Diffraction from Polycristalline Materials THIN FILM CHARACTERISATION ADVANCED X-RAY DIFFRACTION TECHNIQUES October 2 -5, 1996 Frascati (Rome) - ITALY Organised by: Associazione Italiana di Cristallografia C.N.R. - Comitato Tecnologico C.N.R. - Istituto Strutturistica Chimica Consorzio Interuniversitario Nazionale di Chimica dei Materiali I.N.F.N. - Laboratori Nazionali di Frascati Università di Tor Vergata Sponsored by: Ital Structures Siars Philips Analytical Sistec Editors Rich. Seifert Web Power Giorgio Cappuccio and M. Letizia Terranova INFN - LABORATORI NAZIONALI Dl FRASCATI LNF - 96/049 (IR) 17 Settembre 1996 V School on X-ray Diffraction from Polycrystallme Materials THIN FILM CHARACTERISATION BY ADVANCED X-RAY DIFFRACTION TECHNIQUES Frascati, October 2 - 5,1996 Editors Giorgio Cappuccio and Maria Letizia Terranova SIS - Pubblicazioni Laboratori Nazionali di Frascati P. O. Box 13,1-00044 Frascati (Italy) 28 te 1 3 Sponsored by: Associazione Italiana di Cristallografia C.N.R. - Comitato Tecnologico (Roma -1) C.N.R. - Istituto di Strutturistica Chimica (Montelibretti -1) Consorzio Interuniversitario Nazionale di Chimica dei Materiali I.N.F.N. - Laboratori Nazionali di Frascati (Roma -1) Universita' di Tor Vergata (Roma -1) Ital Structures (Riva del Garda -1) Philips Analytical (Monza -1) Rich Seifert & Co (Ahrensburg - G) Siars (Roma -1) Sistec (Rocca di Papa -1) Web Power (Trento -1) Organising Committee: G. Artioli (Univ. Milano -1) M. Bellotto (CTG - Paris - F) G. Berti (Univ. Pisa-I) E. Burattini (Univ. Verona & INFN - LNF - Frascati -1) G. Cappuccio (CNR - ISC - Montelibretti & INFN - LNF - Frascati -1) G. Chiari (Univ. Torino -1) N. Masciocchi (Univ. Milano -1) V. Massarotti (Univ. Pavia -1) P. Scardi (Univ. Trento -1) M.L. Terranova (Univ. Tor Vergata - Roma -1) Scientific Supervision: G. Cappuccio (CNR - ISC - Montelibretti & INFN - LNF - Frascati -1) M.L. Terranova (Univ. Tor Vergata - Roma -1) Secretary: V. Sessa (Univ. Tor Vergata - Roma -1) " Sine qua (i.e. scientia) mortalium vita non regitur Uberaliter " From a letter by Federico II of Svevia to the students of the University of Bologna. (XIII Century) PREFACE The aim of this School series is to promote the use of modern X-ray diffraction techniques, with special attention paid to polycrystalline materials characterisation. The present volume collects the contributions to the V Edition of the School: "Thin-Film Characterisation by Advanced X-ray Diffraction Techniques", which was held in Frascati, 2 - 5 October 1996. X-ray diffraction is a powerful analytical method for characterising materials and understanding their structural features. The 1996 School wants to illustrate the fundamental contribution of modern diffraction techniques (grazing incidence, surface analysis, standing waves, etc.) to the characterisation of thin and ultra-thin films, which have become so important in many advanced technological fields. X-ray diffraction, using both conventional and non-conventional sources (synchrotron radiation) allows phase identification, layer thickness evaluation, grain-size determination, microstrain and residual stress analysis, etc. We hope that the above aims have been fulfilled by the exhaustive treatment and logical succession of the various topics, in any case, we leave final judgement to the reader. Giorgio Cappuccio Maria Letizia Terranova CONTENTS C. Giacovazzo BASICS OF X-RAY DIFFRACTION 1 C. Giacovazzo ABOUT SOME PRATICAL ASPECTS OF X-RAY DIFFRACTION: FROM SINGLE CRYSTAL TO POWDERS :.. 15 V. Valvoda ABOUT SOME PRATICAL ASPECTS OF X-RAY DIFFRACTION: FROM POWDER TO THIN FILM 33 G. Berti PRECISION AND ACCURACY, TWO STEPS TOWARDS THE STANDARDIZATION OF XRPD MEASUREMENTS 51 V. Valvoda POLYCRYSTALLINE THIN FILM: A REVIEW 67 P.Scardi SIZE / STREAIN ANALYSIS AND WHOLE PATTERN FITTING 85 M.Leoni and P.Scardi RESIDUAL STRESS AND TEXTURE ANALYSIS 113 A. Balerna, C. Meneghini, S. Bordoni, and S. Mobilio X-RAY DIFFRACTION USING SYNCHROTRON RADIATION ON THE GILDA BEAMLINE AT THE E.S.R.F 155 B. Gilles GRAZING INCIDENCE DIFFRACTION: A REVIEW 177 R. J. Cernik GLANCING ANGLE SYNCHROTRON X-RAY DIFFRACTION 205 G. A. Battiston and R. Garbasi FILM THICKNESS DETERMINATION BY GRAZING INCIDENCE DIFFRACTION 225 P. Imperatori THIN FILM SURFACE RECONSTRUCTION ANALYSIS 245 G. Cappuccio, M. L. Terranova and V. Sessa CVD DIAMOND COATINGS ON TITANIUM: CHARACTERIZATION BY XRD TECHNIQUES 259 A. Morone PULSED LASER DEPOSITION AND CHARACTERIZATION OF THIN SUPERCONDUCTING FILMS 273 S. I. Zheludeva and M. V. Kovalchuk XRSW METHOD, ITS APPLICATION AND DEVELOPMENT 289 S. Lagomarsino THIN FILMS AND BURIED CHARACTERIZATION WITH X-RAY STANDING WAVES 321 S. Di Fonzo THIN FILMS CHARACTERIZATION BY RESONANTLY EXCITED INTERNAL STANDING WAVES 335 C. Veroli TRICKS & TIPS IN HANDLING A POWDER DIFFRACTOMETER 357 A. Haase X-RAY DIFFRACTOMETER CONFIGURATIONS FOR THIN FILM ANALYSIS 371 A. Haase ADVANCES IN THIN FILM DIFFRACTION INSTRUMENTATION BY X-RAY OPTICS 379 BASIC OF X-RAY DIFFRACTION Carmelo Giacovazzo Universita' di Bari, Dipartimento Geomineralogico Via Orabona, 4-70125 Bari, Italy The pages which follow are extracted from the book FUNDAMENTALS OF CRYSTALLOGRAPHY by C. Giacovazzo, H. L. Monaco, D. Viterbo, F. Scordari, G. Gilli, G. Zanotti & M. Citti. Ed. by C. Giacovazzo. By courtesy of Oxford Science Publications — 1 — Introduction The basic concepts of X-ray diffraction may be more easily understood if it is made preliminary use of a mathematical background. In these pages we will first define the delta function and its use for the representation of a lattice. Then the concepts of Fourier transform and convolution are given. At the end of this talk one should realize that a crystal is the convolution of the lattice with a function representing the content of the unit cell. The Dirac delta function In a three-dimensional space the Dirac delta function <5(r-r0) has the following properties 6 = 0 for r^r0, 6 = 00 for r = r0, I 6(r-ro)dr=l (3.A.I) Js where S indicates the integration space. Thus the delta function corresponds to an infinitely sharp line of unit weight located at r0. It is easily seen that, if r0 = xoa + yob + zoc, then d(r- r0) = 6{x - x0) 6(y - y0) d(z - *). (3.A.2) d(x—x0) may be considered as the limit of different analytical functions. For example, as the limit for a —> 0 of the Gaussian function Of particular usefulness will be the relation <5(JC - JC0) » f exp [2n\x*{x - *<>)] &* (3.A.4) J — 00 where x* is a real variable. It easily seen that (3.A.4) satisfies the properties — 2 — 174 I Carmelo Giacovazzo 2- 9-1 Y3- 1- Fig. 3.A.I. The function Y = (sin 2itgx\l(itx) is 2 0 plotted for g= 1,3. Clearly Y{~x) = Y(x). (3.A.I): indeed its right-hand side may be written as $ lim f -*„)] dx* = lim The function sin[2jzg(x—xo)]/[n(x—xo)] takes the maximum value 2g at jc=;to (see Fig. 3.A.I), oscillates with period l/g, and has decreasing subsidiary maxima with increasing x: the value of its integral from — «> to +0° is unitary for any value of g. Therefore the limit for g—*•<» of sin [2ng{x — xo)]/[n:(x — x0)] satisfies all the properties of a delta function. Consequently we can also write: v u/ (3.A.5) ~ ~ ~ ;™; 7t(x-x0) In a three-dimensional space (3.A.4) becomes <5(r-ro) = J exp[2mr*'(r-ro)]dr* (3.A.6) where 5* indicates the r* space. Two important properties of the delta function are: ( /(r)6(r-ro)-/(ro)5(r-ro). ' ' Indeed, for r¥=r0, left- and right-hand members of (3.A.7) are both vanishing, for r = r0 both are infinite. From (3.A.7) 1/(r)6(r-ro)dr=/(ro) (3.A.8) is derived. Consequently 1<5(r - r2) 6(r - rx) dr = d(r2 - r,). (3.A.9) The lattice function L Delta functions can be used to represent lattice functions. For example, in a one-dimensional space a lattice with period a may be represented by L(x)= § *(*-*») (3-A.10) « = — oo where xn = na and n is an integer value. L(x) vanishes everywhere except at 3 — The diffraction of X-rays by crystals | 175 the points na. Analogously a three-dimensional lattice defined by unit vectors a, b, c may be represented by L{r)= § 8(r-rUtV.w) (3.A.11) U,V,W=— oo where rUiV%w = ua + vb + wc and u, u, W are integer values. Accordingly, in a three-dimensional space: (1) a periodic array of points along the z axis with positions zn = nc may be represented as Py(r) = 6(x) 6(y) 2_ «(z - *„); (3.A.12) (2) a series of lines in the (x, z) plane, parallel to x and separated by c may be represented by P2(r) = <5( v) 2 ^(2 ~ ^n); (3.A. 13) rt = —oo (3) a series of planes parallel to the (x, y) plane and separated by c is represented by ft(r)= 2 <5(z-zn). (3.A.14) The Fourier transform The Fourier transform of the function p(r) is given (for practical reasons we follow the convention of including 2n in the exponent) by F{r*) = f p(r) exp (2*rir* • r) dr. (3. A. 15) The vector r* may be considered as a vector in 'Fourier transform space', while we could conventionally say that r is a vector in 'direct space'. We show now that p(r)=[ F(r*) exp (-2jzir* • r) dr*. (3.A.16) Because of (3. A. 15) the right-hand side of (3. A. 16) becomes | p(r')(/_ exp [2mr* • (r' - r)] dr*) dr', which, in turn, because of (3.A.6), reduces to f p(r')5(r'-r)dr'=p(r).

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