CdSxSe1-x nanocrystals in a silicate glass

A dilute system of CdS,Sel-, nanocrystals with low anisotropy and low size dispersion has been studied by SAXS. The presence of angularities at the surface of the nanoparticles is evidenced from the limit at zero of the chord distribution function. Moreover in a model of spherical particles the size given by the average chord does not agree with that given by the integral parameters. A cubic particle shape has been used to evaluation of the size distribution. This distribution agrees with the expected one, and allows to confirm the validity of a polyedral model for the treatment of the SAXS data. Structural information on the particle surface can be deduced from the presence of the angularities. Introduction In CdS,Sel-, doped glasses the crystal sizes are of the same order of magnitude than the radius of the exciton. Quantum confinment effects are then expected and observed-The influence of the size on the excitonic, optic and electronic properties of the material has given rise to a large number of studies. It has been observed that other structural parameters (as the surface and the structural defects) may affect the optical response of the nanoparticles. Since a few years many groups have dealed with a better structural knowledge of the nanoparticles. The kinetic of the growth has been studied by TEM, HRTEM and SAXS. HRTEM studies have been used to get information on the structure of the nanocrystals. For nanoparticles with size of the order of 50A it has been observed that the shape is nearly isotropic and that the size distribution is low [I]. The results given by different methods have also been compared. It has been observed that the sizes measured by HRTEM are significantly lower than those measured by SAXS. Moreover domains of absorption contrast extending outside the lattice images in HRTEM studies have been observed-This suggest the presence of a domain of "intermediate" order at the surface of the nanoparticles, ie amorphous or misoriented with respect to the monocrystalline kern. It it then of a great interest to get futher information about the surface of the particles. The use of SAXS data to get information about nanostructures is well developped-The theoretical methods for the evaluation of structural parameters in a dilute system containing identical monodisperse particles are well known, however the problem of the SAXS study of non monodisperse dilute systems has been often attacked and is still open. The great deal is how to get separatly information about the shape and the polydispersion of the particles. It has been shown by Mering and Tchoubar [2] that a cleat distinction between smooth and angular particles can be made from the study of the asymptotic behaviour of the scattering curve in range of high q. Several studies have been devoted to the determination of the size distribution for polydispersed systems of spherical particles. The particles angularities are not taken into account in these descriptions. In most case one must count oneself lucky to have a general characterization of size polydispersity and shape. The main reason is the great loss of information due to averaging a polydisperse system of non isotropic particles. In the system studied here the CdS,Sel, nanocrystals embeded in a the glass matrix are known to be nearly isotropic and to have a narrow size distribution. It can therefore be expected that some information about the particle shape can be separated from the information about size dispersion. The present study is an attempt to get this information. Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jp4:1993878 378 JOURNAL DE PHYSIQUE IV Chord distribution and particle angularities The chord distribution is an useful description of a multiphase medium. It has been shown [3] that this description can be used to detect angularities at the surface of particles. If straight lines are assumed to pass through a volume containing particles, in every direction and everywhere, one defines the chord distribution function G(x) by the probability G(x)dx for one line to intersect a particle by a segment of length x. G(x) satisfy the normalisation condition: loWG(x)dx =l. The chord distribution function is related to the correlation function y(r): y"(r) =-(2/rd)6(0) + (l/rd)G(r) rd is the first moment of the chord distribution rd= xG(x)dx. The evaluation of the limit of G(r) for r->O is especially useful. This limit is related to the angularities on particles surfaces 13.41. If the particles are round shaped G(O)=O, if the particles present some angularities G(O)#O. An experimental determination of this limit is obtained from the difference of areas above and below the asymptote in a Porod plot q4I(q)= f(q).This experimental determination is limited by the range of validity of the asymptotic behaviour (q/; s1=/; sf2 =/; sg2=/; sv3= / with = ISnF(S)dS. An information about the size dispersion can then be obtained by comparing the sizes Si deduced from the different characteristic parameters: af.Sf= rf; al.S1=lc; avSv=rv ; adSd= rd; agSg= rg Samples and data treatment The glass studied was prepared by the Schott Glaswerke and has a composition close to that of the commercial filters RG630 (around SiO2 46%, K20 20%, ZnO 21%, Ti02 6%, B2O3 4%, in weight % of each oxide). The total amount of the colouring elements Cd, S and Se does not exceed 1% in weight. The nanocrystals are obtained by an heat treatment of 2 hours at T = 590°C. The thickness of the sample is 120pm. The sample was carefully polished with 0.5mm diamond paste to avoid any superimposed scattering due to surface effects. The SAXS measurements have been performed using a RIGAKU rotating anode working with a powder of 5kW. The X-ray beam of wavenlength 1.5405A (CuKaI) was focused in the detector plane by a curved Ge l 11 monochromator. Point-like slit conditions with an irradiated cross section of about 0.4Xlmm2 were used. The intensity for each value of q is proportional to the counting rates of a gas detector. In order to to get a statistic error of less than 5% even in the high q domain the acquisition time is 60 hours. The scattering curve were obtained in the range of scattering vector amplitude (q4nsinOlh) q ~ n = 0 . 5 10-3A-1 to qmax=O.S A-1,with ~ q = 10-3A-1. The first step in data treatment consist in a smoothing of the curve and a substraction of the background due to the glass (figure 1). The smoothing is performed using spline row data functions. The contribution of the glass consist in shortafter glass range electron density fluctuations and can be taken on the substractian form Ig(q)=cte. At large values of q the asymptotic intensity is then I(q) = A/q4+B. The Porod law is fulfilled for the nanocrystals. A is proportionnal to the internal surface of the cystals and the term B is the background term due to the glass. This background is substracted from the data to get the intensity scattered by the figure I : different steps for the data treatment. The second step is to obtain normalized data. A plot ln(I)=f(q2) is performed. A linear regression between q2=510-5 and q2=5 10-3 gives a radius of gyration Rg=24A with a correlation coefficient of 0.95. The data are extrapolated at high q from the constant asymptotic limit of the curve q41(q) and at low q from the Guinier plot. For a dilute system, the intensity can be then normalised in the usual way: IN(q)=I(q)/P, with P total scattering power of the nanocrystals in the sample P=(1/2n) IOmq21(q)dq. A Lognormal size distribution is used: F(r)= (r In s d(2n.)) -1 exp -{ln2(r/p)/21n2s}, @is the algebric mean of the distribution and s the geometric standart deviation). For this distribution the nth moments of S are related to s and p in a very simple way: < Sn >= p e x p {k21h2(s/2) 1. Consequently, the linear size Si are [lo] : Si=exp (lnp+kiln2s), with ki= 5/2,7/2,4,9/2 and 7 for i=d,l,f,v and g, respectively. For a given shape defined by the coefficients a i , the linear sizes Si are obtained from the characteristic parameters. When the values of Log(Si) are plotted versus k , if a straight line is obtained it indicates that a lognormal distribution conveniently approximate the real size distribution (figure 3). The geometric mean and the standard deviation for the lognormal distribution are obtained from the slope and the origin of the straitgh line. Moreover if the approximation made for the particle shape is consistent, the size obtained from the differential parameter is coherent with those obtained from the integral parameters. figure 2: Porod plot for the normalized scattered intensity. figure 3 : Logarithmic plot of the size parameters Si for a lognormale size dismibution (spherical and cubic particles) The characteristic parameters are obtained from the normalized intensity: =32.5+2A, <1>=46.f3A, =2430f120A2, <~>=13600&7000A3, =23.5f 1.5A. Results and Discussion The plot q41N(q) =f(q) is given in figure 2. One finds G ( 0 ) = 0 . 0 2 ~ . 0 0 3 ~ l . ~ h i s non-zero value shows that there are angularities at the surface of the particles. This value has been compared to the theoretical values of G(0) obtained for different models of shape with similar radius of gyration ~ ~ = 2 4 A . For a cylindrical shape with the height equal to the diameter 2A, G(O)=(8/3n)/(A+H)= 0.015. For polyedral shapes with low anisotropy (hexagonal shape with H=2A, cubic shape, parallelepipedon with A=B=0.8C etc ...) G(0) is about 0.015 6 0.020. This allows to reveal the polyedric shape for the nanocrystals.