eter J. M. Morthoven, Margaret A. Wechter, and Adolf F. Voigt Institute for Atomic Research and Depamnenl of Chemistry, Iowa State Unioersity, Ames, Iowa 50010 ethod of nondestruct~veactivation analysis has been applied to the determination of gadolinium and europium in their tungsten bronzes. Synchrotron ~ r ~ ~ s s t r a was ~ l ~ used n g to produce the reactions leoGd (y, n) la9Gd, 1 a 3 E (y, ~ n) lZzEu, lssW ( 7 , p) l*jTa IsBW(yl pn) ls4Ta9 and the ratio of rare earth to tungsten acthities was compared to that found in samples of known composition. A linear least-squares fitting program was used for analysis of the gammaray scintillation spectra. This program requires information about all components present in the spectrum after irradiation. A component need not be , but may be a mixture of several, so and standard are counted at exactly the same time after irradiation and identical irradiation and countin times are used. The sample spectrum is assume to be a linear combination of the component spectra. The program allows coarse and dine gain adjustments to be made, the latter by an iterative procedure in which a direct search method Is applied.
THETUNGSTEN BRONZES, first reported by Wohler (1, Z), are nonstoichiometric compounds which may be represented by the formula M,WQ3, where 0 < x < 1, and M is any one of a number of elements. For the present investigation M represents gadolinium or europium. Analysis of the bronzes by wet chemical methods is quite difficult and slow because of the inertness of these substances to chemical attack (3-6). Activation analysis has been shown to be a useful method for determining compositions in the sodium ( 7 ) , potassium, rubidium, and barium (8) tungsten bronzes as well as in the similar sodium vanadium bronzes (9). A useful secondary analytical method has been observed in the case of those bronzes which crystallize in cubic symmetry. In these cases, illustrated particularly by the sodium bronzes (7, IO), the lattice parameter is a h e a r function ofthe value of x . Once this function has been determined from samples of known composition, a precise determination of the composition can be made from x-ray diffraction measurements. However, many of the tungsten bronzes have no cubic ranges or crystallize in other symmetries in addition to cubic. Activation analysis is quite successful in many of these cases and is being applied routinely to several of the bronzes in this laboratory. (1) I?. Wohler, Ann. Chim. Phys. Ser. 2,29,43 (1823). (2) F. Wohler, Pogg. Ann., 2, 350 (1824). (3) V. Spitzin and L. Kaschtanoff, 2. Anorg. Allgem. Chem., 157, 141 (1926). (4) V. Spitzin and L. Kaschtanoff,Z . Anal. Chem, 15,440 (1928). (5) B. A. Raby and C. V. Banks, ANAL.C m x : 36, 1106 (1964). (6) M. J. Sienko and S. M. Morehouse, Inorg. Chem., 2,485 (1963). ( 7 ) R. J. Reuland and A. F. Voigt, ANAL. CHEhf., 35,1263 (1963). (8) M. A. Wechter and A. F. Voigt, Ibid., 38, 1681 (1966). (9) M. N. Soltys and G. H. Morrison, Ibid., 36,293 (1964). (10) B. W. Brown and E. Banks, J . Am. Chem. SOC.,76,963 (1954).
1594
e
ANALYTICAL CHEMISTRY
In the present investigation, a method was developed for the nondestructive quantitative determination of gadolinium and europium in their tungsten bronzes by activation with synchrotron bremsstrahlung. This procedure utilizes the electron synchrotron as the irradiation source and relies on a linear least-squares fitting program for data analysis. The program was written in Fortran IV for use with the IBM 36050 computer. Linear Least Squares Analysis. The analysis of radioactive samples by a computer method is relatively easy, once the components of the mixture are identified. Usually it is not difficult to obtain this information from the history of the sample and the characteristic peaks in the spectrum, or from a decay study. The sample spectrum will then be a linear combination of the spectra of the pure components, measured in the same geometry and with the same gain. The procedure used is not essentially different from those used in other progams of this kind (11-15). The basic equation for the spectrum which represents the sum of the individual spectra of N components is: N
4
=
c xi + R,
t=1
(1)
si1
in which A, = count rate of sample in channel j S f , = count rate of component i in channel j Xi = contribution-factor of component i Rj = difference between calculated and experimental rate. In a least-squares analysis the sum R, of the weighted squares of the deviations, R,,has to be minimized, or Y
in which W, = weight factor = 1/uj2 uj = standard deviation of count rate NC = number of channels in the fit In order to find the minimum, Equation 2 has to be differentiated partially with respect to X I , X2, - - - -XA,..This yields a set of N normal equations, which can be presented in matrix notation as : I
(11) E. Schonfeld. A. H. Kibbev, _ .and W. Davis, Jr., Nucl. Imtr.
. kethods, 45, l(1966). 1121 E. Schonfeld. AEC Reot. ORNL-3975 (1966).
