Implanted π+ mesons as novel probes in monocrystalline solids

Volume 83A, number 7 IMPLANTED PHYSICS LETTERS ir~MESONS 15 June 1981 AS NOVEL PROBES IN MONOCRYSTALLINE SOLIDS K. MAIER, G. FLIK, D. HERLACH, G. JUNEMANN, H. REMPP and A. SEEGER Institut für Theoretische und Angewandte Physik, Universität Stuttgart, Fed. Rep. Germany and Institut fur Physik, Max-Planck.Institut für Metallforschung, D- 7000 Stuttgart 80, Fed. Rep. Germany and H.-D. CARSTANJEN Sektion Physik, Universitdt Munchen, D-8000 Munich, Fed. Rep. Germany Received 13 April 1981 We report on the first observation of the lattice steering (“channeling”) of 4.12 MeV positive muons (iii), resulting from the decay of thermalized positive pions (ir~)implanted in Ta single crystals. The steering effect manifests itself as a peak in the ~ intensity (relative height 1.25, FWHM 0.3°)in a (100) crystal direction. Conclusions on the behaviour of ~ in Ta as well as potential future applications of the technique are discussed. The present note reports on the first application of positive ir-mesons (pions) outside of nuclear and elementary particle physics. Like positrons (e+) and positive muons (p+), positive pions (ir~)injected into condensed matter thermalize in times short compared with their mean lifetimes r~± = 2.6 X 10—8 s. After thermalization, the electrostatic repulsion by the fluclei tends to localize the ir~in the interstices of crystals. In addition, they may be trapped by crystal imperfections, say, vacancies in metals, in much the same way as e~or ~ [1,2]. Positive pions decay almost exclusively according to /2 ‘ (fl‘ ‘~ into monoenergetic positive muons (of kinetic energy E/2 = 4.12 MeV and momentum = 29.73 MeV/c) and muon neutrinos Pions have no magnetic moment. Hence the only possibility to obtain information on implanted ir~in crystals appears to be through lattice steering (“channeling”) of the decay ~ emitted from the 7T~.In nearly perfect crystals axial, lattice steering effects are expected for those ~ whose trajectories deviate from densely packed lattice rows by angles ~i that are smaller than about Lindhard’s [3,4] critical angle ~cr = 2(Ze2/4irc0p,2v/2d)112 (2) (Z = atomic number of the host nuclei, e = elementary charge, d = interatomic distance in the channeling direction, V/2 = muon velocity = 0.27c, 0 8.85 X 10—12 As V—1 m~.) The channeling resulting from the lattice steering of positively charged particles injected into crystals is well known [5,6]. Here we are dealing with the inverse situation, namely, the effects of lattice steering on the directional distribution of swift particles corning from an internal source. The observable effects may be due either to flux-enhancement [71(if the source is located in an interstice) or to blocking [4 8 9] (e.g., if the source is located on a lattice site because it has been trapped by a vacancy). For such experiments positive pions constitute ideal sources: They may be implanted into any materials, there is no interaction between the pions (there is rarely more than one pion in the sample at a time), the radiation damage accumulated in a typical experiment is negligible. The experiments were performed at the irEl channel of SIN * 1 using ~ of momentum 150 MeV/c. *1 Schweizerisches Institut für Nuklearforschung, CH-5 234 Villigen, Switzerland. 0 031—9163/81/0000—0000/$ 02.50 © North-Holland Publishing Company 341 Volume 83A, number 7 PHYSICS LETTERS The intensity of the beam was 2 X 108 7T~/5.After passing a beryllium degrader about 1.5 X 106 7r~/s were stopped in our samples within the range of the 4.1 MeV muons. Specific difficulties to cope with were: (i) the high e~background (to a large extent unavoidable due to scattering of beam positrons and to decay positrons from stopped muons), (ii) the smallness of the critical angle (for a (100) direction in Ta [Z = 73, d = 3.3 X 10~0m,bce] eq. (1) gives ~cr = 43’), (iii) because of the small.angle scattering by phonons and electrons only muons that have lost less than about 0.5 MeV (coming from a depth of less than 1 0—20gm) are expected to show the lattice-steering effects; hence the entire information is carried by the fraction (0.5/4.1) X (7~~r/47T) = X 10 6 of the p~ coming from pions stopped within the range of 4.1 MeV muons from the surface. The angular distribution of the ji~intensity was measured by a windowless position-sensitive plastic scintillation detector (NEI 10, active area 250 mm diameter, thickness 1.5 mm, 360°radial light output guided to 4 photomultiplier tubes collecting the light of 90° sectors each) placed in vacuum at a distance of 6 m from the sample. The resolutions are: position better than 2 cm in either direction, energy 0.3 MeV FWHM for 4 MeV ,u~.Intensity profiles are measured for four independent E/2+ windows simultaneously. The positron. background is reduced by (i) energy discrimination for positrons coming from the sample and (ii) 300 mm diameter anticoincidence scintillation countertubes on both sides of the detector for prompt decay positrons coming from muons stopped in the detector. A more detailed description of the experimental set-up has been given elsewhere [101. The sample consisted of two X-ray aligned halfcylinders obtained by slicing a Ta single crystal along its axis. It offered a cross section of 2 X 3 cm2 to the ~ beam. The mosaic spread as determined with 411 keV y-rays was 4’, the main impurities were (in at.ppm) Nb: 50, Mo: 20, W: 15, O+N: 30. Counter characteristics were eliminated by taking the ratios (normalized to equal number of total counts in the detector) of muon intensity profiles for two different orientations of the crystal with respect to the detector, As an example, fig. 1 shows the histogram obtained 342 15 June 1981 - —~ A — —~ z w l~2 w —‘ Ui 0.1° (y) ANGLE Fig. 1. Normalized intensity of decay muons from positive pions stopped in a Ta single crystal at 200 K. The [100] direction was aligned to positions A or of measuring the two-dimensional position-sensitive detector for haif ofBthe time each. The distance of the two maxima corre~ondsto the tilt of 0.45° performed on the crystal. by plotting the absolute deviation of a ratio profile from unity taken with a Ta crystal at 200 K near a (100) direction. The separation of the two maxima corresponds to a tilt by 0.45°and agrees within experimental error with the rotation performed on the crystal. This provides strong evidence that the maxima in the intensity profiles in (100) are due to lattice steering in the crystal and not to a feature of the detecting equipment. The observed maxima are rather high and narrow (relative peak height 1.25, FWHM Li = O.4Si~1cr)as may be seen by comparing with the height 1.3 and the width ~ = 0~4~Pcr observed for the (100) channeling of 750 key3 He~ions [11] in a study of deuterium in tetrahedral interstices in Ta*2. The following conclusions may be drawn: (i) The majority of the pions occupy interstitial sites of fairly high symmetry (e.g. tetrahedral and/or octahedral interstices). Occupation of low-symmetry sites (off-centre positions in the (100) channels) would be incompatible with the height and narrowness of the observed flux-enhancement peak. (ii) The majority of pions have not been trapped by impurities, since trapping would result in such offcentre positions, too. *2 This is based on Lindhard’s rule of reversibility [3,12], which should hold to quite a good approximation in the present comparison. Volume 83A, number 7 PHYSICS LETTERS (iii) By analogous arguments the probability distributions of the ir+ are rather strongly localized. Quantitative estimates for the ~ vibration amplitudes or the extension of the pion wave-function are difficult to make; for reference purposes we state that the abovementioned observations on deuterium correspond to a vibration amplitude of about 0.1 A. The muon intensity maxima observed in (100) and (in a preliminary experiment [10]) in (111) are compatible with both octahedral or tetrahedral occupancy [13]. Which of the two sites are preferentially occupied may be decided by a quantitative compari. son of these maxima (see, e.g., the cases of deuterium hi Ta [11] and 180 in Nb [14], but this will have to await measurements in both directions on the same crystal. In the judgment of the writers, the results presen. ted have opened up a new field, namely the use of ir+ as probes in crystals of suffient size and perfection. The determination of the ir~location provides us with information on the interaction of positive point charges with the host crystal and possibly also on the formation of pionium atoms, Pi = (ir~e).It may contribute in an important way to the understanding of the behaviour of hydrogen in crystalline material. On account of their shorter lifetime therinalized ir~are much less likely to be trapped by impurities than ~ Nevertheless, the trapping at imperfections present in sufficient concentration may be used to monitor such imperfections and to determine the diffusion coefficient of thermalized ~ [1,2]. Finally we add some remarks on the extension of the present technique to the lattice steering of relativistic e~emitted by thermalized ~ [15]. For a given material this implies a decrease of ~cr by about a factor 0.4, which in many cases should not be too serious from the point of view of crystal perfection. The substantial reduction of the fraction of useful counts will require an increase of the counting times by about one order of magnitude. The most critical problem appears to be that the present technique will not be available for selecting e~with small energy ldsses since 15 June 1981 positrons from the p~decay have a continuous energy spectiiim. The authors would like to acknowledge the excellent experimental conditions at SIN and many stimulating discussions with Drs. R. Frosch and C. Petitjean. They are further indebted to G. Wiederoder and M. Krenke (University of Stuttgart) for their technical assistance, to R. Henes, P. Keppler, and W. Maisch (Max-Planck-Institut für Metallforschung) for growing and preparing the single crystals, to the Kristalllabor of KFA Jülich, in particular to M. Fattah, for their collaboration and, last but not least, to K..P. Doring (University of Stuttgart) for his help in the data handling. References [1] K. Maier, D. Herlach, A. Seeger and H.-D. Carstanjen, Proposal for an experimentat SIN, RA79-02 (1979). [2] A. in: Positron annihilation, R.R. Hasiguti andSeeger, K. Fujiwara (The Japan Instituteeds. of Metals, Sendai 1980) ~. 771. [3] J. Lindhard, K. Dan. Vidensk. Selsk. Mat. Fys. Medd. 34 (1965) No. 4. [4] E. llggerhØj, Phys. Lett. 22 (1966) 382. [5] Gemmell, Mod. Phys. 46 (1974) 129. [6] D.S. R. Sizmann andRev. C. Varelas, in: Festkorperprobleme XVII, ed. J. Treusch (Vieweg, Braunschweig, 1977) ~,. 261. [71 D.V. Morgan and D. van Vliet, Radiat. Eff. 12(1972)203. [8] B. Domeij and K. Bjorkquist, Phys. Lett. 14 (1965) 127. [9] A.F. V.S. Kulikauskas and M.M. Melov, Phys. Lett. Tulinov, 18 (1965) 304. [10] K. Maier, in: Nuclear physics: Methods in materials search, eds. K. Bethge, H. Baumann, H. Jex and F. Rauch, (Vieweg, Braunschweig, 1980) p. 264. [11] M. Antoniniand H.-D. Carstanjen, Phys. Stat. Sol. (a) K153. [12] 34 B.D.(1976) Patterson, Am. J. Phys. 48 (1980) 995. [13] H.-D. Carstanjen, Phys. Stat. Sol. (a) 59 (1980) 11. [14] P.P. Matyash, N.A. Skakun and N.P. Dikii, JETP Lett. 19 (1974) 19. [15] B.D. Patterson, AS. Arrott and Th. Wichert, 8th Conf. on High energy physics and nuclear structure (Vancouver, 197?), unpublished. 343