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INFN - LABORATORI NAZIONALI Dl FRASCATI ^/sif-ZE R- - °iLp/o4?- LNF - 96/049 OR) 17 Settembre 1996 V School on X-ray Diffraction from Polycrystalline Materials THIN FILM CHARACTERISATION BY ADVANCED X-RAY DIFFRACTION TECHNIQUES Frascati, October 2-5,1996 Editors Giorgio Cappuccio and Maria Letizia Terranova DISTRIBUTION OF THIS DOCUMENT IS UNLIMITED FOREIGN SALES PROHIBITED ^ SIS - Pubblicazioni Laboratori Nazionali di Frascati P. O. Box 13,1-00044 Frascati (Italy) 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 Material! 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 -I) Organising Committee: G. Artioli (Univ. Milano -1) M. Bellotto (CTG - Paris - F) G. Berti (Univ. Pisa -1) 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-I) 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) 1 ' Secretary: V. Sessa (Univ. Tor Vergata - Roma -1) DISCLAIMER Portions of this document may be illegible in electronic image products. Images are produced from the best available original document “ Sine qua (i.e. scientia) mortalium vita non regitur liberaliter ” 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 modem 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 modem 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. Balema, 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. Cemik 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 XT T?00^/7 BASIC OF X-RAY DIFFRACTION Carmelo Giacovazzo Universita’ diBari, 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 4 --- 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 6(r —r0) has the following properties 6 = 0 for r¥=r0, 6=°° for r = r0, f d(r — r0)dr=l (3.A.1) 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 = x 0a + y0b + ZqC, then 6(r -/-<,) = 6(:c - x 0) S(y - yQ) 6(z - zb). (3.A.2) 6(x — x 0) may be considered as the limit of different analytical functions. For example, as the limit for a -* 0 of the Gaussian function w(a'* o>=^exp(~^iii?L)- (3-A-3) Of particular usefulness will be the relation /•+* « 6(x - x 0) = J exp [2xix*(x - * 0)] dr* (3.A.4) where x* is a real variable. It easily seen that (3.A.4) satisfies the properties — 2 — 174 | Carmelo Giacovazzo Fig. 3A1. The function y = (sin 2;rgx)/(jrx) is plotted for g = 1,3. Clearly Y{-x ) = yjx). (3.A.1): indeed its right-hand side may be written as sin [2jzg(x - x0)] lim exp [2?rix*(x — x0)] dx* = lim 8~*' " J-8 5-»oc jt(x-x0) The function sin [2ng{x — x<f)\l[n(x — x<fj\ takes the maximum value 2g at x =x0 (see Fig. 3.A.1), oscillates with period 1/g, and has decreasing subsidiary maxima with increasing x: the value of its integral from —to +oo is unitary for any value of g. Therefore the limit for g—*■» of sin[2jrg(x —x 0)]/[jt(x —x0)] satisfies all the properties of a delta function. Consequently we can also write: sin[2jrg(x-x 0)] <5(x — x0) = lim (3.A.5) ji(x -x0) In a three-dimensional space (3.A.4) becomes <5(r-r0)= [ exp [2mr* • (r - r0)] dr* (3.A.6) JS' where S* indicates the r* space. Two important properties of the delta function are: <5(r-ro) = 5(r0-r) /(r)S(r —r0)=/(r0)<5(r-r0). V ' * 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) f fir) <5(r - r0) dr =/(r„) (3.A.8) Js is derived. Consequently [ d(r — r2) <5(r — rt) dr = d(r2 - rj. (3.A.9) Js 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)= § S(x-x„) (3.A.10) where x„ = 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)= 2 d(r — r„iUiW) (3.A.11) U,V,W = —co where ru v tv= 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 z„ = nc may be represented as Pi(r) = 8(x) d(y) 2 <5(z-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 ■Pz(r) = <5(y) 2 d(z - z„); (3.A.13) (3) a series of planes parallel to the (x, y) plane and separated by c is represented by +eo P%(r)= 2 <5(z - z„). (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 (2jrir* • 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 (—2mr* • r) dr*. (3.A.16) Js* Because of (3.A.15) the right-hand side of (3.A.16) becomes J p(r')^J exp [2rnr* • (r' — r)] dr*j dr', which, in turn, because of (3.A.6), reduces to [ P(r') S(r'- r) dr'= p(r). Js Relations (3.A.15) and (3.A.16) may be written as F(r*) = T[p(r)], (3.A.17) p(r) = T"1[F(r*)] (3.A.18) respectively: we will also say that p is the inverse transform of F.

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