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K. Srinivasan, George Thomas C, P. Padaikathan, N.V.Ashoka / International Journal of
       Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
                      Vol. 3, Issue 1, January -February 2013, pp.927-930

 Synthesis and Characterization of Fluorinated Superconducting
                   Y3Ba5Cu8Oy Compound
  K. Srinivasan*, George Thomas C **, P. Padaikathan***, N.V.Ashoka**
        *Department of Physics, Govt. First Grade College, K. R. Puram, Bangalore – 560 036, India
                 **Department of Physics, Christ University, Bangalore – 560 029, India
       ***Department of Materials Engineering, Indian Institute of Science, Bangalore – 560 012, India


Abstract:
         The effect of fluorine addition on              fluorine substitution at the oxygen site. More
morphological, structural and electrical                 recently Aliabadi et al., [9] and Tavana et al., [10]
properties of superconducting samples of                 have reported a new yttrium based high Tc
composition Y3Ba5Cu8Oy-xFx (x = 0.0, 0.2, 0.4            superconductor Y3Ba5Cu8O15 (Y-358) with a Tc
& 0.6) were investigated by X-ray diffraction            above 100 K. This prompted us to investigate the
(XRD), scanning electron microscopy (SEM)                new superconductor for further enhancement of Tc
and       transition     temperature       (Tc)          by substituting fluorine for oxygen. In this paper, we
measurements. The samples were synthesized               report the results of our attempts to synthesize and
by solid state reaction method. The XRD of               characterize the pure and the fluorinated Y-358
the samples revealed a structure similar to              superconductors.
that of Y-123 compound with about three time
larger ‘c’ axis. The grain size calculated was               II. Experimental
found to increase with fluorine doping as                          Samples of the nominal composition
indicated by SEM micrograph. As the fluorine             Y3Ba5Cu8Oy-xFx (x = 0.0, 0.2, 0.4 & 0.6), designated
amount increased, the Tc onset of the                    as Y0, Y2, Y4 and Y6 were prepared by standard
superconducting phase was found to be                    solid-state    reaction     technique.   Appropriate
increased. Over all, the fluorine addition had           stoichiometric ratios of high purity powders of Y2O3,
improved the superconducting property of the             BaCO3, CuO and CuF2 were mixed thoroughly and
samples considerably.                                    finely ground. The samples were taken in ceramic
Keywords: High Tc superconductor, solid state            crucibles and calcined in open atmosphere at 810°C
reaction, XRD, SEM, Tc measurements, fluorine            for 21 hours using a tubular furnace. The powders
doping.                                                  were re-ground and pressed in the form of pellets of
                                                         10 mm diameter and about 2 mm thickness under a
    I. Introduction                                      pressure of 5000 kg/cm2. The samples Y0 and Y2
          The discovery of superconductivity in La-      were then sintered at 950°C for 20 hours and furnace
Ba-Cu-O system with a critical temperature (Tc) of       cooled to room temperature. A slight melting was
30 K by Bednorz and Müller [1] in the year 1986 led      noticed on the surface of the sample Y2 and
to a tremendous amount of research activity in the       therefore all further sintering was carried out at
field of high temperature superconductors. Basically     lower temperatures. The pellets of all the samples
this was to understand the mechanism as well as to       were then sintered at 940°C for 24 hours and again at
initiate search for new superconducting materials at     930ºC for 24 hours with one intermediate grinding
still higher temperatures. The Tc of around 92 K was     and pelletisation. The XRD data was recorded using
reported by Chu et al., [2] in a well known              a compact PHILIPS Pro analytical automated
compound Y1Ba2Cu3O7 (Y-123) in 1987. The                 diffractometer with copper Kα source ( = 1.5405 Å)
research in oxide superconductors was continued to       in the two theta ranges from 10º to 100º. The grain
bring out new aspects arising out of their structure     morphology of the fractured surface of the samples
and synthesis process. These ideas were soon             was analyzed using scanning electron microscope
adopted by many researchers to find out higher Tc        (Quanta ASM 840A). The Tc of the samples was
materials in Y-Ba-Cu-O family. In the year 1988,         determined by self inductance method using a
Marsh et al., [3] reported that Y1Ba2Cu4O16 (Y-124)      Colpitt’s oscillator and a frequency counter. The
superconducts at 80 K. Bordet et al., [4] reported       temperature of the sample was recorded using a
superconductivity in Y2Ba4Cu7O15 (Y-247) with Tc         calibrated chromel – alumel thermocouple with an
of 40 K. Fisk et al., [5] and Hor et al., [6] have       accuracy of ±1ºC.
shown that in Y-123 system superconductors, the
substitution at rare earth site or alkaline-earth site       III. Results and discussion
will not change Tc considerably. But Ovshinsky et              The X-ray diffractograms of the samples Y0
al., and Gupta et al., [7, 8] have reported that a       and Y2 along with that of standard Y-123 are shown
substantial increase of Tc in Y-123 system by            in Fig.1, and that of the samples Y4 and Y6 are

                                                                                               927 | P a g e
K. Srinivasan, George Thomas C, P. Padaikathan, N.V.Ashoka / International Journal of
       Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
                      Vol. 3, Issue 1, January -February 2013, pp.927-930

shown in Fig. 2. As seen from the figure, most of the       composition graph is shown in Fig.5. The plots of
peaks of Y0, Y2, Y4 and Y6 are identical with that          frequency versus temperature of the samples are
of Y-123. This observation is similar to that of            shown in Fig.6. As seen, the Tc onset of the samples
Udomsamuthirun et al., [11]. The prominent peaks            have increased with increase in fluorine amount and
of the samples were indexed in an orthorhombic              a saturation value is reached at about x = 0.6 (Fig. 7).
system. The ‘c’ value of our samples is almost 3            This can be explained as due to optimization of the
times the ‘c’ value of Y-123 sample [Table-1]. This         oxygen content in the sample by fluorine
result is similar to the one reported by Aliabadi et al.,   substitution. The Tc of Y-Ba-Cu-O superconductor is
[9]. But we observed a prominent peak at 2θ ≈ 15º           known to vary with oxygen stoichiometry and is
which was not accounted by Aliabadi et al. The              found to be a maximum for a particular value of
scanning electron microscope (SEM) images of the            oxygen content (Rao et al., [12] Namgung et al., [13]
samples are projected in Fig. 3. The surface images         and Narottam P.Bansal et al., [14]). The Tc value
of the samples by SEM revealed the presence of              decreases, for oxygen content above or below this
pores. Also it is observed that the average grain size,     optimum value. By the fluorine substitution, the
calculated from XRD data using Scherrer formula:            optimum value of oxygen content is attained at
t=0.89*/B*cos θB (where t is the grain size,  is          which Tc onset is maximum. Increase in fluorine
the wavelength of the X-ray, θB is the Bragg angle          amount beyond x = 0.6 may not further increase the
and B is the FWHM), increases as the fluorine               Tc onset value since that will disturb the optimum
content increases and reaches a saturation value at x       oxygen stoichiometry.
= 0.2 (Fig.4). Lattice parameter ‘b’ versus fluorine




                                  Fig. 1, XRD spectra of samples Y-123, Y2 and Y0




                                     Fig. 2, XRD spectra of samples Y4 and Y6



                                                                                                   928 | P a g e
K. Srinivasan, George Thomas C, P. Padaikathan, N.V.Ashoka / International Journal of
   Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
                  Vol. 3, Issue 1, January -February 2013, pp.927-930




                                            Y0                                                                                          Y2




                                   Y4                                                              Y6
                    Fig. 3, SEM micrographs of the samples (Magnification of 5000 and marker length 10, 5 µm)

                                                                                                  3.88

                  125
                                                                                                  3.86

                  120
                                                                                                  3.84
                                                                        Lattice parameter b [Å]




                  115
                                                                                                  3.82
                  110
Grain size [nm]




                                                                                                  3.80
                  105
                                                                                                  3.78
                  100
                                                                                                  3.76
                  95
                                                                                                  3.74
                  90
                                                                                                  3.72
                  85
                                                                                                  3.70
                  80                                                                                     0.0   0.1   0.2        0.3      0.4      0.5   0.6
                        0.0   0.1    0.2     0.3     0.4   0.5   0.6
                                       Composition [x]                                                                     Composition [x]
                        Fig. 4, Grain size versus composition          Fig. 5, Lattice parameter versus composition




                                                                                                                                               929 | P a g e
K. Srinivasan, George Thomas C, P. Padaikathan, N.V.Ashoka / International Journal of
         Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
                        Vol. 3, Issue 1, January -February 2013, pp.927-930


                                                                                                                 108

                         60.5
                                                                                                                 106
                                                                         x=0.0 (Y0)
                                                                         x=0.2 (Y2)                              104
                         60.0
                                                                         x=0.4 (Y4)
                                                                         x=0.6 (Y6)                              102
       Frequency (kHz)




                         59.5




                                                                                                  Tc onset [K]
                                                                                                                 100

                         59.0                                                                                    98

                                                                                                                 96
                         58.5
                                                                                                                 94

                         58.0
                                                                                                                 92


                         57.5                                                                                    90
                                 80   90    100    110       120   130     140    150                                    0.0   0.1      0.2      0.3    0.4   0.5      0.6

                                                         Tc (K)                                                                           Composition [x]

                                Fig. 6, Tc curves of samples Y0, Y2, Y4 and Y6                      Fig. 7, Tc onset versus composition

                                                  Table.1, Tc and Lattice parameters details of the samples
                                           Compounds               Y0     (x            Y2 (x                     Y4     (x          Y6     (x
                                                                    = 0.0)               = 0.2)                    = 0.4)             = 0.6)
                                           Tc onset (K)               92                  98                        105                 106
                                              a (Å)                      3.902           3.942                         3.863           3.871
                                              b (Å)                      3.824           3.863                         3.802           3.721
                                              c (Å)                  30.690             31.382                     31.330            32.499
                                           Cell volume               457.933            477.956                    460.188           468.115
                                               (Å)3


      IV. Conclusions                                                                               J. Karpinski, E. Kaldis, Nature 336, 596
          This study confirms the formation of Y-358                                                (1988).
superconducting phase. The crystalline structures of                                       [5]      Z. Fisk, J. O. Thomson, E. Zirngiebl, J. L.
all the samples are similar to that of Y-123 but for                                                Smith, S. W. Cheong, Solid State Commun.,
the ‘c’ axis which is almost three times the ‘c’ axis of                                            62, 743(1987).
Y-123. Fluorine Doping can be used to optimize the                                         [6]      P. H. Hor, R. L. Meng, Y. A. Wang, L. Gao, Z.
oxygen stoichiometry and thereby enhancing the Tc                                                   J. Huang, J. Bechtold, K. Forster, C.W.Chu,
onset value. It is noteworthy that the fluorine doping                                              Phys. Rev. Lett. 58, 1891 (1987).
not only improved superconducting behavior of the                                          [7]      S. R. Ovshinsky, R. T. Young, D. D. Allred, G.
Y-358 phase but also decreased the melting point of                                                 DeMaggio, G. A. Vander Leeden, Phys. Rev.
the sample.                                                                                         Lett. 58, 2579 (1987).
                                                                                           [8]      A. Gupta, R. Jagannathan, E. I. Cooper, J.A.
      V. Acknowledgements                                                                           Giess, Ilndman, B. Whussey, Appl. Phys.
One of the authors (KS) is thankful to the University                                               Lett. 52, 2077 (1988).
Grants Commission, New Delhi, India for their                                              [9]      A. Aliabadi, Y. A. Farshchi, M. Akhavan, ,
research support under FIP-XI plan period.                                                          Physica C 469, 2012 (2009).
                                                                                           [10]     A. Tavana, M. Akhavan, Eur. Phys. J. B 73,
References                                                                                          79 (2009).
[1]    J. G. Bednorz, K. A. Müller, Z. Phys. B 64,                                         [11]     P. Udomsamuthirun, T. Kruaehong, T.
       189 (1986).                                                                                  Nilkamjon, S. Ratreng, J. Supercond. Nov.
[2]    K. Wu, J. R. Ashburn, C. J. Torng, P. H. Hor,                                                Magn. 23, 1377 (2010).
       R. L. Meng, L. Gao, Z. J. Huang, Y. Q. Wang,                                        [12]     C. N. R. Rao, B. Raveau, Accounts of chemical
       C.W. Chu, Phys. Rev. Lett. 58, 908 (1987).                                                   research,Vol.22,106,(1989).
[3]    P. Marsh, R. M. Fleming, M. L. Mandich, A.                                          [13]     C. I. Namgung, J. T. S.Irving, J. H. Binks, E. E.
       M. DeSantolo, J. Kwo, M. Hong, L. J.                                                         Lachowski, A. R. West, Supercond. Sci.
       Martinez-Miranda, Nature 334, 660 (1988).                                                    Technol.2,181 (1989).
[4]    P. Bordet, C. Chaillout, J. Chenavas, J. L.                                         [14]     P. Narottam, Bansal, L.Sandkuhi, Ann,
       Hodeau, M. Marezio,                                                                          American Institute of Physics, 52, 838, (1988).


                                                                                                                                                       930 | P a g e

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  • 1. K. Srinivasan, George Thomas C, P. Padaikathan, N.V.Ashoka / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 1, January -February 2013, pp.927-930 Synthesis and Characterization of Fluorinated Superconducting Y3Ba5Cu8Oy Compound K. Srinivasan*, George Thomas C **, P. Padaikathan***, N.V.Ashoka** *Department of Physics, Govt. First Grade College, K. R. Puram, Bangalore – 560 036, India **Department of Physics, Christ University, Bangalore – 560 029, India ***Department of Materials Engineering, Indian Institute of Science, Bangalore – 560 012, India Abstract: The effect of fluorine addition on fluorine substitution at the oxygen site. More morphological, structural and electrical recently Aliabadi et al., [9] and Tavana et al., [10] properties of superconducting samples of have reported a new yttrium based high Tc composition Y3Ba5Cu8Oy-xFx (x = 0.0, 0.2, 0.4 superconductor Y3Ba5Cu8O15 (Y-358) with a Tc & 0.6) were investigated by X-ray diffraction above 100 K. This prompted us to investigate the (XRD), scanning electron microscopy (SEM) new superconductor for further enhancement of Tc and transition temperature (Tc) by substituting fluorine for oxygen. In this paper, we measurements. The samples were synthesized report the results of our attempts to synthesize and by solid state reaction method. The XRD of characterize the pure and the fluorinated Y-358 the samples revealed a structure similar to superconductors. that of Y-123 compound with about three time larger ‘c’ axis. The grain size calculated was II. Experimental found to increase with fluorine doping as Samples of the nominal composition indicated by SEM micrograph. As the fluorine Y3Ba5Cu8Oy-xFx (x = 0.0, 0.2, 0.4 & 0.6), designated amount increased, the Tc onset of the as Y0, Y2, Y4 and Y6 were prepared by standard superconducting phase was found to be solid-state reaction technique. Appropriate increased. Over all, the fluorine addition had stoichiometric ratios of high purity powders of Y2O3, improved the superconducting property of the BaCO3, CuO and CuF2 were mixed thoroughly and samples considerably. finely ground. The samples were taken in ceramic Keywords: High Tc superconductor, solid state crucibles and calcined in open atmosphere at 810°C reaction, XRD, SEM, Tc measurements, fluorine for 21 hours using a tubular furnace. The powders doping. were re-ground and pressed in the form of pellets of 10 mm diameter and about 2 mm thickness under a I. Introduction pressure of 5000 kg/cm2. The samples Y0 and Y2 The discovery of superconductivity in La- were then sintered at 950°C for 20 hours and furnace Ba-Cu-O system with a critical temperature (Tc) of cooled to room temperature. A slight melting was 30 K by Bednorz and Müller [1] in the year 1986 led noticed on the surface of the sample Y2 and to a tremendous amount of research activity in the therefore all further sintering was carried out at field of high temperature superconductors. Basically lower temperatures. The pellets of all the samples this was to understand the mechanism as well as to were then sintered at 940°C for 24 hours and again at initiate search for new superconducting materials at 930ºC for 24 hours with one intermediate grinding still higher temperatures. The Tc of around 92 K was and pelletisation. The XRD data was recorded using reported by Chu et al., [2] in a well known a compact PHILIPS Pro analytical automated compound Y1Ba2Cu3O7 (Y-123) in 1987. The diffractometer with copper Kα source ( = 1.5405 Å) research in oxide superconductors was continued to in the two theta ranges from 10º to 100º. The grain bring out new aspects arising out of their structure morphology of the fractured surface of the samples and synthesis process. These ideas were soon was analyzed using scanning electron microscope adopted by many researchers to find out higher Tc (Quanta ASM 840A). The Tc of the samples was materials in Y-Ba-Cu-O family. In the year 1988, determined by self inductance method using a Marsh et al., [3] reported that Y1Ba2Cu4O16 (Y-124) Colpitt’s oscillator and a frequency counter. The superconducts at 80 K. Bordet et al., [4] reported temperature of the sample was recorded using a superconductivity in Y2Ba4Cu7O15 (Y-247) with Tc calibrated chromel – alumel thermocouple with an of 40 K. Fisk et al., [5] and Hor et al., [6] have accuracy of ±1ºC. shown that in Y-123 system superconductors, the substitution at rare earth site or alkaline-earth site III. Results and discussion will not change Tc considerably. But Ovshinsky et The X-ray diffractograms of the samples Y0 al., and Gupta et al., [7, 8] have reported that a and Y2 along with that of standard Y-123 are shown substantial increase of Tc in Y-123 system by in Fig.1, and that of the samples Y4 and Y6 are 927 | P a g e
  • 2. K. Srinivasan, George Thomas C, P. Padaikathan, N.V.Ashoka / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 1, January -February 2013, pp.927-930 shown in Fig. 2. As seen from the figure, most of the composition graph is shown in Fig.5. The plots of peaks of Y0, Y2, Y4 and Y6 are identical with that frequency versus temperature of the samples are of Y-123. This observation is similar to that of shown in Fig.6. As seen, the Tc onset of the samples Udomsamuthirun et al., [11]. The prominent peaks have increased with increase in fluorine amount and of the samples were indexed in an orthorhombic a saturation value is reached at about x = 0.6 (Fig. 7). system. The ‘c’ value of our samples is almost 3 This can be explained as due to optimization of the times the ‘c’ value of Y-123 sample [Table-1]. This oxygen content in the sample by fluorine result is similar to the one reported by Aliabadi et al., substitution. The Tc of Y-Ba-Cu-O superconductor is [9]. But we observed a prominent peak at 2θ ≈ 15º known to vary with oxygen stoichiometry and is which was not accounted by Aliabadi et al. The found to be a maximum for a particular value of scanning electron microscope (SEM) images of the oxygen content (Rao et al., [12] Namgung et al., [13] samples are projected in Fig. 3. The surface images and Narottam P.Bansal et al., [14]). The Tc value of the samples by SEM revealed the presence of decreases, for oxygen content above or below this pores. Also it is observed that the average grain size, optimum value. By the fluorine substitution, the calculated from XRD data using Scherrer formula: optimum value of oxygen content is attained at t=0.89*/B*cos θB (where t is the grain size,  is which Tc onset is maximum. Increase in fluorine the wavelength of the X-ray, θB is the Bragg angle amount beyond x = 0.6 may not further increase the and B is the FWHM), increases as the fluorine Tc onset value since that will disturb the optimum content increases and reaches a saturation value at x oxygen stoichiometry. = 0.2 (Fig.4). Lattice parameter ‘b’ versus fluorine Fig. 1, XRD spectra of samples Y-123, Y2 and Y0 Fig. 2, XRD spectra of samples Y4 and Y6 928 | P a g e
  • 3. K. Srinivasan, George Thomas C, P. Padaikathan, N.V.Ashoka / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 1, January -February 2013, pp.927-930 Y0 Y2 Y4 Y6 Fig. 3, SEM micrographs of the samples (Magnification of 5000 and marker length 10, 5 µm) 3.88 125 3.86 120 3.84 Lattice parameter b [Å] 115 3.82 110 Grain size [nm] 3.80 105 3.78 100 3.76 95 3.74 90 3.72 85 3.70 80 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Composition [x] Composition [x] Fig. 4, Grain size versus composition Fig. 5, Lattice parameter versus composition 929 | P a g e
  • 4. K. Srinivasan, George Thomas C, P. Padaikathan, N.V.Ashoka / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 1, January -February 2013, pp.927-930 108 60.5 106 x=0.0 (Y0) x=0.2 (Y2) 104 60.0 x=0.4 (Y4) x=0.6 (Y6) 102 Frequency (kHz) 59.5 Tc onset [K] 100 59.0 98 96 58.5 94 58.0 92 57.5 90 80 90 100 110 120 130 140 150 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Tc (K) Composition [x] Fig. 6, Tc curves of samples Y0, Y2, Y4 and Y6 Fig. 7, Tc onset versus composition Table.1, Tc and Lattice parameters details of the samples Compounds Y0 (x Y2 (x Y4 (x Y6 (x = 0.0) = 0.2) = 0.4) = 0.6) Tc onset (K) 92 98 105 106 a (Å) 3.902 3.942 3.863 3.871 b (Å) 3.824 3.863 3.802 3.721 c (Å) 30.690 31.382 31.330 32.499 Cell volume 457.933 477.956 460.188 468.115 (Å)3 IV. Conclusions J. Karpinski, E. Kaldis, Nature 336, 596 This study confirms the formation of Y-358 (1988). superconducting phase. The crystalline structures of [5] Z. Fisk, J. O. Thomson, E. Zirngiebl, J. L. all the samples are similar to that of Y-123 but for Smith, S. W. Cheong, Solid State Commun., the ‘c’ axis which is almost three times the ‘c’ axis of 62, 743(1987). Y-123. Fluorine Doping can be used to optimize the [6] P. H. Hor, R. L. Meng, Y. A. Wang, L. Gao, Z. oxygen stoichiometry and thereby enhancing the Tc J. Huang, J. Bechtold, K. Forster, C.W.Chu, onset value. It is noteworthy that the fluorine doping Phys. Rev. Lett. 58, 1891 (1987). not only improved superconducting behavior of the [7] S. R. Ovshinsky, R. T. Young, D. D. Allred, G. Y-358 phase but also decreased the melting point of DeMaggio, G. A. Vander Leeden, Phys. Rev. the sample. Lett. 58, 2579 (1987). [8] A. Gupta, R. Jagannathan, E. I. Cooper, J.A. V. Acknowledgements Giess, Ilndman, B. Whussey, Appl. Phys. One of the authors (KS) is thankful to the University Lett. 52, 2077 (1988). Grants Commission, New Delhi, India for their [9] A. Aliabadi, Y. A. Farshchi, M. Akhavan, , research support under FIP-XI plan period. Physica C 469, 2012 (2009). [10] A. Tavana, M. Akhavan, Eur. Phys. J. B 73, References 79 (2009). [1] J. G. Bednorz, K. A. Müller, Z. Phys. B 64, [11] P. Udomsamuthirun, T. Kruaehong, T. 189 (1986). Nilkamjon, S. Ratreng, J. Supercond. Nov. [2] K. Wu, J. R. Ashburn, C. J. Torng, P. H. Hor, Magn. 23, 1377 (2010). R. L. Meng, L. Gao, Z. J. Huang, Y. Q. Wang, [12] C. N. R. Rao, B. Raveau, Accounts of chemical C.W. Chu, Phys. Rev. Lett. 58, 908 (1987). research,Vol.22,106,(1989). [3] P. Marsh, R. M. Fleming, M. L. Mandich, A. [13] C. I. Namgung, J. T. S.Irving, J. H. Binks, E. E. M. DeSantolo, J. Kwo, M. Hong, L. J. Lachowski, A. R. West, Supercond. Sci. Martinez-Miranda, Nature 334, 660 (1988). Technol.2,181 (1989). [4] P. Bordet, C. Chaillout, J. Chenavas, J. L. [14] P. Narottam, Bansal, L.Sandkuhi, Ann, Hodeau, M. Marezio, American Institute of Physics, 52, 838, (1988). 930 | P a g e