A NOVEL 2D ANALYSIS METHOD TO CHARACTERIZE INDIVIDUAL GRAINS USING HIGH-ENERGY X-RAY MICROBEAM DIFFRACTION

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1 69 A OVEL D AALYSS METHOD TO CHARACTERZE DVDUAL GRAS USG HGH-EERGY X-RAY MCROBEAM DFFRACTO E. Jmenez-Melero,. H. van Djk, L. Zhao, J. Setsma, and S. van der Zwaag 3 Fundamental Aspects of Materals and Energy, Faculty of Appled Scences, Delft Unversty of Technology, Mekelweg 5, 69 JB Delft, The etherlands Department of Materals Scence and Engneerng, Delft Unversty of Technology, Mekelweg, 68 CD Delft, The etherlands 3 Faculty of Aerospace Engneerng, Delft Unversty of Technology, Klujverweg, 69 HS Delft, The etherlands ABSTRACT The development of a novel D analyss method for hgh-energy X-ray dffracton measurements usng a synchrotron mcrobeam s reported. ts applcaton to study n stu the martenstc transformaton of small ndvdual austente (fcc) grans embedded n a complex ferrtc/bantc/martenstc (bcc) multphase mcrostructure s also reported. TRODUCTO The desgn and development of new multphase mcrostructures for specfc technologcal applcatons requre not only a characterzaton of the fnal mcrostructure, but also a detaled knowledge at the level of ndvdual grans of the phase transformatons takng place durng the materal processng. The avalablty of ntense hgh-energy X-ray beams (5 to 3 kev) at a number of synchrotron sources has unlocked the door to unprecedented X-ray dffracton studes of a wde scope of processes n the bulk of the materal [ 4]. Furthermore, the recent development of new optcs components to focus the X-ray beam down to mcro-dmensons [5], n combnaton wth algebrac reconstructon technques [6], has substantally ncreased the spatal resoluton attanable n hgh-energy X-ray dffracton experments. The state-of-the-art research n materal scence no longer ams at obtanng nformaton about the average gran behavor, but at gettng detaled nformaton at the level of the ever smaller ndvdual grans present n complex multphase mcrostructures. The determnaton of the characterstcs of ndvdual mcron-szed metastable austente grans n the complex ferrtc/bantc/martenstc matrx of low-alloyed TRP steels s a nce example of ths trend and an example of great scentfc and technologcal relevance [7,8]. Three-dmensonal synchrotron X-ray dffracton (3DXRD) mcroscopy consttutes an deal tool to study mcron-szed austente grans embedded n complex multphase mcrostructures. The mcro-dmensons of the hgh-energy X-ray beam permt to llumnate only a reduced number of grans wthn the bulk materal, so that sngle dffracton spots clearly appear wthn the dffracton rngs []. The ntegrated ntensty of these dffracton spots s drectly proportonal to the volume of the gran from whch t orgnates [9]. However, the dffracton spots from small grans are relatvely weak and normally close to the background ntensty. The exstng analyss procedures consst of reducng the two-dmensonal data nto one dmenson by bnnng the radal angle along a chosen dffracton rng [,3], and then subtractng a constant background for

2 Ths document was presented at the Denver X-ray Conference (DXC) on Applcatons of X-ray Analyss. Sponsored by the nternatonal Centre for Dffracton Data (CDD). Ths document s provded by CDD n cooperaton wth the authors and presenters of the DXC for the express purpose of educatng the scentfc communty. All copyrghts for the document are retaned by CDD. Usage s restrcted for the purposes of educaton and scentfc research. DXC Webste CDD Webste -

3 7 each dffracton spot. Ths sgnfcantly decreases the sgnal-to-nose rato. n the present paper, a new analyss method of the two-dmensonal dffracton data that takes nto account the local structure of the background wll be presented. Ths method s appled to the case of low-alloyed multphase TRP steels, where the martenstc transformaton of metastable austente grans contrbutes substantally to the outstandng combnaton of hgh strength and formablty [7,]. Because of ther relatvely small gran sze, the study of the ndvdual austente grans n TRP steels s extremely dffcult wth the exstng D analyss procedures. The new method presented here substantally ncreases the resoluton and accuracy of the characterzaton of ndvdual grans. EXPERMETAL A cylndrcal TRP steel sample wth a dameter of.5 mm wth the chemcal composton of.8 wt% C,.539 wt% Mn,.67 wt% S,.75 wt% Al,.8 wt% P, and balance Fe was used n ths study. ts complex multphase mcrostructure contaned mcron-szed metastable austente grans embedded n a ferrtc-bantc-martenstc matrx [4,8]. Synchrotron X-ray dffracton experments were performed at the 3DXRD mcroscope avalable at the D beam lne of the European Synchrotron Radaton Faclty (Grenoble, France), n order to characterze the dfferent phases present n the TRP mcrostructure at room temperature. A monochromatc X-ray mcrobeam wth an energy of 8 kev llumnated the cylndrcal sample. The grans that fulflled the Bragg condton generated a dffracton spot on the two-dmensonal detector placed behnd the sample. The sample was rotated around ts vertcal axs over an angle of ω =.5 durng an exposure tme of s. A total ω-range from -3 to +3 was covered n the experments n subsequent exposures. Three dfferent beam szes were employed (7 7 (S), 8 9 (M), and (L) µm ) n order to determne whether the complete volume of the grans of nterest was llumnated by the X-ray beam. The martenstc transformaton of the ndvdual austente grans was montored n stu by coolng the sample from room temperature to K n steps of K []. DATA AALYSS Fgure (a) dsplays a two-dmensonal dffracton pattern of TRP steel at room temperature for a selected ω-angle. The {}, {}, and {3} austente reflectons (fcc structure), as well as the {}, {}, and {} ferrte reflectons (bcc structure), have been analyzed n detal n ths study. Each dffracton rng conssts of a number of sngle spots orgnatng from ndvdual grans n the materal, together wth a powder sgnal stemmng from dffractng grans wth a sze below the expermental detecton lmt for ndvdual grans of 5 µm 3. The evoluton of the ndvdual grans n the mcrostructure can be convenently assessed n stu by montorng the poston and ntensty of the espondng sngle dffracton spots on the detector as a functon of temperature. Fgure (b) shows a dffracton spot from the {} austente rng. The austente gran from whch t orgnated has transformed nto martenste (bcc structure) durng coolng, so that only the powder sgnal remans n the same area of the detector after coolng [see Fgure (c)]. Such a transformaton does not occur for the ferrte grans, whch already have the equlbrum crystal structure.

4 7 a γ 3 γ Before coolng 6 b Y γ Y 35 After coolng X 695 c X Fgure. X-ray dffracton pattern of TRP steel. (a) Complete two-dmensonal dffracton pattern at room temperature. (b) A sngle austente (γ) dffracton peak from the {} rng at room temperature before coolng. (c) The same regon as n (b) after coolng the sample to K and heatng back to room temperature (taken from reference [4]). An adequate background ecton s requred n order to derve accurate nformaton from the sngle dffracton spots. The collected ntenstes ( ) can be characterzed by three coordnates (X, Y, ω ), where X and Y are the coordnates on the two-dmensonal detector, whle ω ndcates the sample rotaton angle. Alternatvely, the polar coordnates (R, η ) can be used nstead of (X, Y ) to specfy the pxel poston on the detector. They are defned as follows: R [( X X ) + ( Y Y ) ] / = () C [( X X ) ( Y Y )] C C Y X 3 68 η = arctan / () where (X C, Y C ) espond to the coordnates of the beam center. Three ntegraton boxes of ncreasng sze can be placed symmetrcally around a selected dffracton spot wth a maxmum ntensty at (X m, Y m, ω m ) (see Table ). The dfference between two consecutve boxes gves rse to two outer shells surroundng the nner ntegraton box (Box ). The characterstcs of these outer shells are dsplayed n Table. We wll dscuss two ways n whch the background ecton can be appled: () assumng the background to be constant and () takng nto account the local structure of the background. The smplest approach for the background ecton assumes the local background to be constant. 6 4 C 8 6

5 7 Ths background contrbuton can be subtracted from the total ntensty of the nner box ( Total ) Box Total Total by makng use of Shell or Shell ( ( k) = Box ( k) *, wth k =, ). These two ected ntenstes can be used to check that the background ecton was performed adequately, and that the sze of the ntegraton box was optmal. Three cases can occur: () < ( ) : not all the Bragg ntensty s ncluded n Box ( () () > ( ) : overlap wth neghborng peaks ( ( ) () ( ) : the sze of Box s optmal ( ( ) ( ) too large) (3) too large) (4) ) (5) When the condton n Eq. (5) occurs, the resultant ntensty can be translated nto the espondng gran volume [9]. Furthermore, the analyss of the same regon at the detector and n ω-range for the three beam szes allows for the determnaton f the studed gran was completely llumnated by the X-ray beam. Table. Descrpton of the three ntegraton boxes. Box Box Box umber of pxels = X Y ω ( X + )( Y + ) ( ) = ω + ( X + )( Y + 4) ( 4) = 4 ω + Total ntensty Total = = Box Total = = Box Total = = Box Table. Characterstcs of the two outer shells. Shell Shell umber of pxels ( Shell) = ( Shell ) = Average background ntensty ( ) = ( ) ( ) Box Box / ( ) = ( ) ( ) Box Box / The constant background ecton procedure can be appled when the selected dffracton spot s much more ntense than the background ntensty, as n the case for ferrte dffracton spots. However, when the dffracton spot to be analyzed s relatvely weak, as n the case for the retaned austente grans, the local background structure can not be neglected. The background s concentrated along the dffracton rng, because of the presence of a sgnfcant amount of small dffractng austente grans and tals from neghborng sngle dffracton spots. The background contrbuton s then assumed to depend only on the dstance to the center of the detector (R),

6 73 based on the occurrence of ths relatvely strong powder sgnal wthout apparent texture along the dffracton rngs. n ths case, a dstrbuton of ntenstes as a functon of the dstance R can be derved for each of the two shells, so that the ntensty of an element j of that dstrbuton at a dstance R results from an average over M pxel ntenstes wth the same R value (bnned n nteger pxel numbers):, j M ( R ) = ( R ) = M (6) Fgure dsplays the ntensty dstrbuton for both shells, together wth an equvalent dstrbuton for Box, n the case of a ferrte and an austente dffracton spot. A relable dstrbuton wthout dscontnutes can only be obtaned when a sgnfcant number of pxel ntenstes (M) s used to obtan each, j ( R ). Typcally the number of pxels nvolved n a sngle dffracton spot s of the order of three hundred pxels or hgher. a (R) (counts) 5 5 Ferrte Fgure. Dstrbuton of ntenstes as a functon of the dstance to the center of the detector (R) for Box, Shell, and Shell, n the case of (a) a ferrte and (b) an austente dffracton spot. Once an equvalent dstrbuton has been obtaned for Shell and, the total ntensty n Box can be obtaned by subtractng from each pxel ntensty ( ) the,j (R ) wth the same R value (rounded to an nteger number), accordng to: peak = [ ( X, Y, ω ) ( R )] = ( X, Y, ω ) = (7) Box Shell Shell R (pxels) (R) (counts) R (pxels), j = The total ntensty peak s drectly proportonal to the volume of the gran from whch the dffracton spot orgnated [9]. n ths way, the volume of the austente grans can be determned at each temperature, so that ts transformaton nto martenste can be montored n stu durng coolng. Fgure 3 dsplays the volume of an ndvdual austente gran as a functon of temperature for the two proposed background ecton procedures. The subtracton of a nonconstant background demonstrates that ths gran was completely llumnated by the medum and large beam szes. Ths gran transforms completely nto martenste at a temperature of 3 K. b Austente Box Shell Shell

7 74 The ected pxel ntenstes [ (X,Y,ω )] can not only be used to determne the ntegrated peak ntensty and hence the espondng gran volume, but also to derve the peak poston and the peak wdth from the weghted averages wth respect to the dfferent coordnates: = ( X, Y, ω )/ ( X, Y, ω ) < z > = z (8) = = ( X, Y, ω )/ ( X, Y, ω ) < z > = z (9) = = z z σ z < > < > () where z = ω, R, η (or X, Y). The peak poston (<R>) can be translated nto the lattce parameter of the espondng gran [], whch n turn contans nformaton about the chemcal content of the gran and local strans, f present. The peak wdths serve to study the gran mosacty and the spread n lattce parameter. t s worth notng that all ths nformaton can be derved from a sngle dffracton spot wthout any assumpton about ts shape. The error n the derved parameters can be consstently evaluated based on Posson statstcs. a Gran Volume ( µm 3 ) beam S beam M beam L COOLG Temperature (K) Gran Volume ( µm 3 ) Temperature (K) Fgure 3. Temperature dependence of the volume of an ndvdual austente gran derved from the collected ntegrated ntensty for the three beam szes, usng (a) constant and (b) non-constant background ecton. The dashed lnes ndcate the detecton lmt for ndvdual grans. The marker sze esponds to the expermental error. Wth the developed method, the stablty of ndvdual austente grans wth respect to the martenstc transformaton can be assessed as a functon of ther mcrostructural parameters such as gran sze, chemcal composton, and local strans. Ths novel analyss method can also be appled for a fast evaluaton of a large number of grans smultaneously. Snce ths method allows the automated analyss of relatvely small grans close to the detecton lmt, new nsghts nto the frst stages of the formaton of new grans wthn the bulk of multphase mcrostructures are envsaged. b beam S beam M beam L COOLG

8 75 REFERECES [] Poulsen, H. F. Three-Dmensonal X-ray Dffracton Mcroscopy: Mappng Polycrystals and ther Dynamcs; Sprnger: Berln, 4. [] Laurdsen, E. M.; Juul Jensen, D.; Poulsen, H. F.; Lenert, U. Scr. Mater., 43, [3] Offerman, S. E.; van Djk,. H.; Setsma, J.; Grgull, S.; Laurdsen, E. M.; Margules, L.; Poulsen, H. F.; Rekveldt, M. Th.; van der Zwaag, S. Scence, 98, 3 5. [4] Jmenez-Melero, E.; van Djk,. H.; Zhao, L.; Setsma, J.; Offerman, S. E.; Wrght, J. P.; van der Zwaag, S. Scr. Mater. 7, 56, [5] Lenert, U.; Schulze, C.; Honkmäk, V.; Tschentscher, Th.; Garbe, S.; Hgnette, O.; Horsewell, A.; Lngham, M.; Poulsen, H. F.; Thomsen,. B.; Zegler, E. J. Synchrotron Radat. 998, 5, 6 3. [6] Poulsen, H. F.; Fu, X. J. Appl. Crystallogr. 3, 36, [7] Mltzer, M. Scence, 98, [8] Zaefferer, S.; Ohlert, J.; Bleck, W. Acta Mater. 4, 5, [9] Warren, B. E. X-ray Dffracton; Dover: ew York, 99. [] van Djk,. H.; Butt, A. M.; Zhao, L.; Setsma, J.; Offerman, S. E.; Wrght, J. P.; van der Zwaag, S. Acta Mater. 5, 53,