Effect of tin diffusion on the optical behavior of float glass in the soft-x-ray region

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The optical responses of two sides of float glass in the soft-x-ray region were studied at the Indus-1 synchrotron facility. To the best of our knowledge these are the first experimentally obtained optical data for both sides of float glass in the
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  Effect of tin diffusion on the optical behavior offloat glass in the soft-x-ray region Mohammed H. Modi, Gyanendra S. Lodha, Kawal Jeet S. Sawhney, andRajendra V. Nandedkar The optical responses of two sides of float glass in the soft-x-ray region were studied at the Indus-1synchrotron facility. To the best of our knowledge these are the first experimentally obtained opticaldata for both sides of float glass in the soft-x-ray region. Optical constants    and    were determined byuse of angle-dependent reflectance techniques in the wavelength range 80–200 Å. On the side of theglass that was tin indiffused, a significant difference in    value from that of the non-tin-side surface wasobserved. The measured data were compared with Henke’s tabulated value of SiO 2 . The surfaceroughness of float glass was separately determined by hard-x-ray reflectivity to minimize the number of fitting variables. The effect of a contamination layer on the determination of optical constants wasavoided by an appropriate sample-cleaning method. © 2003 Optical Society of America OCIS codes:  120.4530, 340.7470, 240.6700, 230.4170. 1. Introduction Float glass finds wide applications as a low-cost sub-strate in x-ray optics. Casting soda lime glass ontomolten tin produces float glass. The process of fab-ricationleadstotindiffusionontothefaceoftheglassthat is in contact with molten tin. The other faceremains in contact with an inert atmosphere. Thetwo surfaces are thus different and are identified asthe tin-side surface and the non-tin-side surface, re-spectively. Because of its low rms roughness andcosteffectiveness,floatglassisusedasasubstrateforx-ray and neutron optics applications. 1 For x-rayoptics applications, detailed characterization of thetwo surfaces is essential. In particular, the opticalparameters that may get modified by the presence of any impurities need to be studied in detail. Themajor ingredients of float glass are SiO 2   70 wt. %  ,Na 2 O   14 wt. %  , MgO, and CaO. Many studies of the optical properties of SiO 2  in the soft-x-ray regionhavebeenreported. 2–5 Discrepanciesinopticaldatain the close vicinity of absorption edges have beenreported. Even for single elements new studieshave been carried out to generate more-reliable datasets experimentally. 6 Nevertheless, in the soft-x-ray region the overlap of electron wave functions of the constituents of float glass may significantly mod-ify the optical constants. The penetration depth of soft x ray is small, so the presence of any impuritiesnear the surface may significantly affect the opticalresponse. The optical constants of the two sides of float glass are expected to be different.Because of the technological importance of floatglass, various aspects of its surface morphology havebeen studied extensively. 7  A large range of surface-sensitive techniques has been employed to explorethe two distinct surfaces of the glass. Tin diffusionwas analyzed by grazing-incidence reflectivity. 8 Hayashi  et al . 9,10 used secondary ion mass spec-trometry and photoelectron spectroscopy techniquesas an aid in understanding the diffusion mechanism. As the appearance of wrinkling on surfaces of floatglass that has been reheated at   600 °C is a majorproblem, they correlated the tin concentration nearthe surface with the thermal stability of the floatglass. They have generated a profile of tin concen-tration as a function of temperature. They foundthat the tin migrates toward the surface when theglass is reheated. Changing the tin concentrationnear the surface will lead to a change in optical con-stants.The effect of tin diffusion on density, especiallynear the surface, of float glass was investigated byuse of x-ray reflection and fluorescence techniques, 7 The authors are with the Synchrotron Utilization Division, Cen-treforAdvancedTechnology,Indore452013,India. G.S.Lodha’se-mail address is lodha@cat.ernet.in.Received 18 June 2003; revised manuscript received 2 Septem-ber 2003.0003-6935  03  346939-06$15.00  0 © 2003 Optical Society of America 1 December 2003    Vol. 42, No. 34    APPLIED OPTICS 6939  and higher density for the tin-side surface   2.56g   cm 3   than for the non-tin-side surface   2.45 g   cm 3  was reported. This difference is attributed to diffu-sion of tin from the bath into the glass. Townsend  etal . 11 discussed the effect of tin diffusion on therefractive-indexpro fi leinvisibleregion. Diel  etal . 12 investigated the optical response of the non-tin-sidesurface in the soft-x-ray region. They reported onthe optical constants in the 2 – 250-  Å   region   1  Å     0.1nm  , using angle-dependent re fl ectivity measure-ments. Nevertheless, to the best of our knowledge,no study has been reported of a comparison of opticalconstants in the soft-x-ray region on the tin and thenon-tin sides of   fl oat glass.We have derived the optical constants of the twosides of   fl oat glass in the wavelength region 80 – 200  Å  , using angle-dependent re fl ectivity measurements.The soft-x-ray re fl ectivity experiments were carriedout by use of a re fl ectivity beam line at the Indus-1synchrotron source. 13 The optical data for the tin-side surface of   fl oat glass were generated experi-mentally for the  fi rst time to our knowledge in thesoft-x-ray region. 2. Experiment  A. Instruments  Angle-dependent re fl ectivity measurements werecarried out at the Indus-1 synchrotron facility   450-MeV electron storage ring    with a bending magnetextreme-ultraviolet  soft-x-ray re fl ectometry beamline. The re fl ectometry beam line employed a toroi-dal grating monochromator for high  fl ux and mod-erate spectral resolution. Three gratings withdifferent groove densities were used to delivermonochromatic radiation in range 40 – 1000  Å  . Thewavelength resolution      of the beam line was200 – 300. Harmonic suppression  fi lters were in-stalled after the monochromator to eliminate higher-order contamination. The beam line produced a1-mm 2 focused beam with a vertical divergence of 5 mrad. A beam line operating in an ultrahigh- vacuum environment was connected to a high- vacuum re fl ectometer   5    10  6 Pa   through adifferential pumping system. The re fl ectometer vacuum was limited by the presence of stepping mo-tors, connecting wires, etc. inside the main chamber.Two coaxially aligned rotary stages of 160-mm di-ameter were used to accomplish the   – 2   rotary mo-tion of sample and detector. To bring the sample inandoutofthedirectbeamwemountedalineartrans-lationstageonasamplerotationstage. Thisfeatureallowed the direct beam intensity required for nor-malizing the re fl ectivity data to be monitored. Anextreme-ultraviolet-soft-x-ray silicon photodiode de-tector   International Radiation Detectors, Inc.   with100% internal quantum ef  fi ciency was used. 14 Thedetector signal was measured with a Keithley-6514electrometer. Control and re fl ectivity data were ac-quired with software written in Microsoft VC  .We reduced the scattered component in the directbeam by placing a 1.5-mm pinhole immediately infront of the sample.Pink  fl uorescence under ultraviolet illuminationidenti fi es the tin side of   fl oat glass. The surfaceroughness of the two sides of the  fl oat glass was mea-sured by use of hard-x-ray re fl ectivity. These mea-surements were carried out on a Siemens D5000diffractometer with a grazing-incidence attachmentand a sealed tube with a copper target     1.54  Å   .The incident beam was collimated by a 0.05-mm slitat the source, and a razor blade was kept close to thesample surface, yielding a beam divergence of 0.02 ° .The razor blade generated a micrometer-sized slit atthe sample, thereby reducing the divergence of thebeam and the sample area. 15 The roughness valuesderived for tin-side and the non-tin-side surfaceswere 13 and 6  Å  , respectively.The soft-x-ray re fl ectivity measurements for deter-mination of optical constants were carried out in s -polarization geometry   electric  fi eld component per-pendicular to the plane of incidence  , where the   – 2  angular scans were performed in the 0 – 45 °  range.The optical constants of the two sides of   fl oat glasswere determined in the 80 – 200-  Å   range by measure-ments of angle versus re fl ectivity. B. Sample Preparation In  fl oat glass samples the presence of a contamina-tionlayerisamajorproblem. Ionexchangebetweenalkali ions such as sodium and water molecules leadsto the formation of low-density contamination lay-ers. 16 It is dif  fi cult to quantify the structure of thislayer, and thus the number of   fi tting variables in-creases. Any uncertainty in parameters of the con-tamination layer will affect the derived values of optical constants. To remove the low-density – organic contamination from the  fl oat glass surface,we cleaned the sample ultrasonically in methanol. After that we heated sample for 8 h at   140  ° C in anoxygen environment under ultraviolet illumination.Immediately after cleaning, the sample was loadedinto a re fl ectometer ’ s vacuum chamber. Details of thecleaningprocesshavebeenreportedbySou fl iandGullikson. 17 C. Procedure for Data Analysis To  fi t the experimental curves we used Fresnel ’ s re- fl ectivity formula 18 to carry out nonlinear least-squares  fi tting. The re fl ected  fi eld intensity for s -polarized light was determined from the relation  R s   sin     n     2  cos 2  1  2  2  sin     n     2  cos 2  1  2  2 , (1)where  R s isthere fl ectivityof  s -polarizedlight,  isthegrazing-incidenceanglemeasuredfromthesurfaceof the sample, and  n      1      i   is the refractiveindex. In a least-squares re fi nement procedure the 6940 APPLIED OPTICS    Vol. 42, No. 34    1 December 2003   valuesof   and  wereoptimizedbyaminimumvalueof    2 , where  2    j   R o   j    R m   j  2 w  j 2  , (2)where  R o    j   and  R m    j   are the observed and modelre fl ectivities, respectively, at an angle     j ;  w   j  is aweightingfactorforGaussiannoiseintheexperimen-tal data.In general the re fl ectivity model depends on thestructural parameters in addition to the optical con-stants. The structural parameters involved are sur-face and interface roughness and layer thickness.For optical-constant-related experiments, particu-larly in soft-x-ray region, it is desirable to freezestructural parameters by using some independenttechniques. Variation of the structural parametersleads to signi fi cant errors in derived optical con-stants, as was discussed by Windt  et al . 19 Theyshowed the effect of variation in surface roughnessover the derived optical constants. The numbers of  fi tting variables of re fl ectivity formalism were re-duced to    and    only. The tabulated values of Henke  et al . 20 for SiO 2  optical constants were takenas the starting guess for the  fi tting. We took theroughness effect into account by multiplying theFresnel re fl ection coef  fi cient by the Debye – Wallerfactor. 21 The  fi t was made over an angular range of 0 – 45 ° . In the  fi nal stage of   fi tting, the roughnessparameter was allowed to change over a limitedrange, to improve the  fi tting quality. 3. Results and Discussion  A. Non-Tin-Side Surface Figure 1 shows the soft-x-ray re fl ectivity curves fortwo sides of a  fl oat glass sample measured at     190  Å  , along with the best- fi t pro fi les. Because of thedifference in density between the two sides of the fl oatglass,there fl ectivitycurveshowsadifferenceinthecriticalangleregion. Wepresenttheopticalcon-stants obtained by the data reduction technique de-scribed in Subsection 2.C in both tabular and graphicform. The graphic form is Fig. 2, where the data of thenon-tin-sidesurfaceareplottedasdiscretepoints.Error bars show the uncertainties in the data points.For comparison, Henke ’ s data for SiO 2  are shown bythe dotted curve. The measured values of the opti-cal constants are listed in Table 1, along with theuncertainties, which are given in parentheses.Because SiO 2  is one of the major constituents of  fl oat glass, for the non-tin-side surface we observedthat both    and    follow the trend of Henke ’ s data of SiO 2  with an upward shift in    value. Away fromthe silicon-  L  edge   124  Å    the upward shift was in therange 5 – 15%; near the edge it increased to 30 – 80%.The upward shift in the    value may be attributed tochanges in  fl oat-glass composition and to the higherdensity of the glass compared with that of pure SiO 2 .Earlier, the non-tin-side surface of   fl oat glass wasinvestigated by Diel  et al . 12 by angle-dependent re- fl ectivity techniques in the 2 – 250-  Å   range. In theirstudy the results obtained were compared with SiO 2 optical data tabulated by Phillipp. 4 The data of Diel  etal . also showed an upward shift in    values   Fig. 2  .However, near the carbon-  K   edge   44  Å    and thesilicon-  L  edge they were not able to generate a good Fig.1. Re fl ectivitypro fi lesofthetwosidesof  fl oatglassmeasuredat     190  Å  . The tin-side surface exhibits a larger critical anglebecause of its larger surface density contributed by diffused tin.Measured data, open circles; best  fi t to the measured data, solidcurves.Fig. 2. Optical constants    and    measured for the non-tin-sidesurface, shown with corresponding error bars. Optical constants   and    measured by Diel  et al . 12 are also shown. The tabulateddata for SiO 2  given in Ref. 20 are shown by the continuous curve. 1 December 2003    Vol. 42, No. 34    APPLIED OPTICS 6941  qualityof  fi tbecauseofthepresenceofcontaminationlayers. This contamination led to signi fi cant errorsin calculations of     and   . In our study the effects of contamination were prevented by proper cleaning and handling of the sample. This is evident fromFig.3,inwhichthe fi ttedre fl ectivitycurveofthe fl oatglass sample measured at     120  Å   is shown. Weobtained the good quality of the  fi t by taking     and   of the sample as  fi tting variables. This result sug-gests that, if a sample is properly cleaned, it is notnecessary to assume the presence of a contaminationlayer during the  fi tting. A similar result of remov-ing the contamination layer was reported by Grimal  et al . 22 They cleaned the samples with deionizedwater followed by drying in a pure-nitrogen atmo-sphere. The effectiveness of the cleaning waschecked by photoelectron spectroscopy and hard-x-ray re fl ectivity. However, they found that the con-tamination layer reappeared within 48 h on exposureto ambient. Because the presence of a contamina-tion layer makes it extremely dif  fi cult to determine   and    accurately, one must be cautious about imme-diateloadingofthesampleinavacuumenvironment. B. Tin-Side Surface  Angle-dependent re fl ectivity measurements of thetin-side surface of   fl oat glass were carried out in therange 80 – 200  Å  . We made a detailed  fi t of the re- fl ectivity data, assuming a homogeneous surface thatwas enriched with tin and other composites diffusedfrom the tin bath during fabrication. The diffusionof tin inside the  fl oat glass was studied extensivelywith the various depth-sensitive techniques de-scribed above. Tin diffusion to a depth of 500  Å   ormore was reported. 9,10 The diffused tin, which ar-ranged itself inside the  fl oat glass with the glass ’ sbasicconstituents,modi fi edthesurfacedensity. Be-cause the penetration depth of a soft x ray is small  Fig. 4 for SiO 2  at     80  Å   , instead of modeling thetin-side surface into different layers we found thatthe optical parameters of a single surface with mod-i fi ed surface density are suf  fi cient to describe theoptical behavior of the surface. For detailed  fi tting of the re fl ectivity data, optical parameters    and   along with surface roughness are considered  fi tting  variables. In Fig. 5 the optical constants for thetin-side surface of   fl oat glass are plotted. For com-parison with those of pure SiO 2 , Henke ’ s tabulated Table 1. Optical Constants of Non-Tin-Side Surfaces of Float GlassObtained from Angle-Dependent Reflectivity Measurements    Å   Measurement a Henke ’ s Data b     75 0.0119  2   0.0072  6   0.0103 0.00759125 0.0223  4   0.008  1   0.0118 0.00883130 0.0251  4   0.009  1   0.0189 0.00978135 0.0282  5   0.010  1   0.0218 0.0107190 0.0505  9   0.022  2   0.0469 0.0274200 0.054  1   0.024  2   0.0514 0.0313 a For the experimental    and    values the uncertainties in thelast signi fi cant digit are given in parentheses. b Ref. 20.Fig. 3. Re fl ectivity pro fi le at     120  Å  , along with the best- fi tcurve. We obtained the  fi tted curve by re fi ning the    and    valuesof a single surface; the effect of a contamination layer was pre- vented by use of an appropriate cleaning method as discussed inSubsection 2.B. The plot labeled  “ residue ”  shows the quality of   fi tover the full angular range.Fig. 4. Penetration depth of soft x radiation in SiO 2  calculated at    80  Å  . 6942 APPLIED OPTICS    Vol. 42, No. 34    1 December 2003  dataarealsoshown. Measuredvaluesof   and  arelisted in Table 2. The optical constants of the tin-side surface are higher than those of the non-tin-sidesurface. A shift in delta value of 10 – 50% with re-spect to non-tin-side data was observed. The pres-ence of diffused tin is responsible for changes in theoptical parameters.In the visible region the change in the refractive-index pro fi le across the depth of the  fl oat glass on thetin-side face was investigated by Townsend  et al . 11 The observed change in refractive index was de-scribed in connection with the tin penetration depthstudied by Rutherford backscattering and particle-inducedx-rayemissiontechniques. Theyfoundthatthe increase in refractive index at 4880  Å   was due tothe presence of Sn 2  and Sn 4  . Because  fl oat glassis a widely used substrate material in x-ray optics,the optical constants generated for both its surfacesare indispensable. The difference in the refractiveindicesofthetwofacesofthe fl oatglasssuggeststhatone has to be aware of which surface of the  fl oat glassis being used for coating of x-ray mirrors. It wouldbe interesting to further investigate the optical be-havior of tin-side surfaces in different spectral re-gions. 4. Conclusions The optical responses of two sides of   fl oat glass in thesoft-x-ray region were investigated. To the best of our knowledge the optical data for the tin-side sur-faceofthe fl oatglassweregeneratedforthe fi rsttimeexperimentally in the soft-x-ray region. We appliedthe angle-dependent re fl ectivity technique to deter-mine the optical parameters of the two sides in thewavelength range 80 – 200  Å  . Measurements of re- fl ectivity at various wavelengths were carried out byuse of the re fl ectivity beam line at the Indus-1 syn-chrotron radiation facility. We found that for a non-tin-side surface the optical constants follow the trendof Henke ’ s tabulated data of SiO 2  with an upwardshift in    value. The    value measured for the tin-side surface was high compared with the    values of the non-tin-side surface. We attribute this differ-ence to a change in surface density that is due to thepresence of diffused tin. The effect on the determi-nation of optical parameters caused by contamina-tion on top of either surface can be prevented by useof an appropriate cleaning method.We acknowledge the technical help of A. K. Sinhaduring measurements. Thanks are also due to R.Dhawan, R. K. Gupta, and M. Singh for their help inbeam line operation and re fl ectivity measurements. References 1. Z. Yin, L. Berman, S. Dierker, E. Defresne, and D. P. Siddons, “  A simple x-ray focusing mirror using   fl oat glass, ”  in  Optics for High Brightness Synchrotron Radiation Beamlines II  , L. E.Berman and J. Arthur, eds., Proc. SPIE  2856,  307 – 313   1996  .2. E. Filatova, V. Lukyanov, R. Barchewitz, J. M. Andre, M. Idir,and Ph. Stemmler,  “ Optical constants of amorphous SiO 2  fromphotonsintherangeof60 – 3000eV, ” J.Phys.Condens.Matter 11,  3355 – 3370   1999  .3. E. O. Filatova, A. I. Stepanov, and V. A. Luk ’ yanov,  “ Disper-sion of optical constants of amorphous SiO 2  in the energyregion between 50 and 900 eV, ”  Opt. Spectrosc.  81,  416 – 420  1996  .4. H. R. Phillipp,  “ Silicon dioxide   SiO 2   glass  , ”  in  Handbook of Optical Constants of Solids , E. D. Palik, ed.    Academic, Or-lando, Fla., 1998  , pp. 749 – 763.5. P. Tripathi, G. S. Lodha, M. H. Modi, A. K. Sinha, K. J. S.Sawhney, and R. V. Nandedkar,  “ Optical constants of siliconandsilicondioxideusingsoftx-rayre fl ectancemeasurements, ” Opt. Commun.  211,  215 – 223   2002  .6. B.Sae-laoandR.Sou fl i, “ Measurementsoftherefractiveindexof yttrium in the 50 – 1300-eV energy region, ”  Appl. Opt.  41, 7309 – 7316   2002  .Fig. 5. Optical constants    and    measured for the tin-side sur-faceshownwithcorrespondingerrorbars. ThetabulateddataforSiO 2  obtained from Ref. 20 are shown by the continuous curve. Table 2. Optical Constants of Tin-Side Surfaces of Float GlassObtained from Angle-Dependent Re fl ectivity Measurements    Å   Measurement a   80 0.0160  3   0.0072  7  85 0.0181  3   0.0081  7  90 0.0206  3   0.0106  9  100 0.0194  8   0.0095  3  105 0.0246  4   0.011  1  110 0.0261  4   0.013  1  115 0.0308  6   0.018  1  120 0.0277  5   0.012  1  130 0.0335  7   0.019  2  135 0.0328  5   0.011  1  140 0.0340  5   0.013  1  190 0.057  1   0.043  4  200 0.060  1   0.048  4  a For the experimental    and    values the uncertainties in thelast signi fi cant digit are given in parentheses. 1 December 2003    Vol. 42, No. 34    APPLIED OPTICS 6943
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