Optimization of Immobilization of Strontium and Uranium by the Solid Matrix
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ABSTRACT One of the basic physical parameters which defines: (1) the capacity of the solid matrix for the incorporation (sorption) of the impurity and (2) the stability of the solid matrix - impurity system, is the ion-ion interaction potential, representing the main term of the cohesive energy. Using this parameter determined in the frame of the pseudopotential theory and pseudoatomic approximation we have investigated the systems HAP-Sr and HAP-UO 2 . In analysis, the hydroxyapatite (HAP, Calo(PO 4)6(OH) 2) was selected as a model solid matrix since insoluble phosphates, phosphate ceramic and apatite-like materials are candidates for the immobilization of radionuclides. The substitution of calcium atoms by different impurities in 2 HAP can be presented by the formula: Cal 0-,M(PO 4)6(OH) 2, where 0 < x _ where Z* is the valence number for the given metal, Kf= (37t 2Z*/Q)I/3 is the Fermi wave number, 0 is the atomic volume, EF = K)2 is the Fermi energy and V(2Kf) is the formfactor of the electron-ion interaction potential corresponding to the wave number 2Kf. Starting from the general model pseudopotential [12, 13], the values V(2Kf) can be given in the following form: V(2Kf)=-
Za sin(21ra 2 Z*) 2
(4)
where the coefficients cc and at 2 are: -0.2500 Ry a1
0.520
for short and the first half of long periods
0.048
for the second half of long periods.
(X2 -0.0625 Ry
Previously, it has been demonstrated that the value of ion-ion interaction potential V(r) for the polycomponent system can be satisfactory determined in the frame of the pseudoatomic approximation [6], where solid solutions are treated as if they were composed of identical pseudoatoms having average properties (Z*, Q, ac1 and a 2) [14]. 137
RESULTS AND DISCUSSION The present study was carried out in order to determine the relationship between stability of the HAP and concentration of the incorporated impurities. In this analysis as a measure of stability of the solid matrix the V(r) was used, representing the structurally dependent component of the cohesive energy [15]. The ion-ion potential for HAP determined according to equation (3) is presented in Fig. 1.The average values for the parameters Z*, fl, cc and ct2 for HAP are given in Table I (for x=0). The values V(r0) represents the dominant term of the ion-ion interaction corresponding to the structurally dependent component of the cohesive energy. This value will be further used as a measure of stability of the HAP - impurity system. Table I The values of ion-ion interaction potential V(r) and position of the first deep
minimum (ro) for HAP-Sr and HAP-U0 2 system, calculated from equation (3), for c(X 0.25 Ry, (X2 = 0.52 Ry and Z*HAj.Sr = 4.727.
0 (HAP) 0.2 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0
HAP-U0
HAP-Sr
x
2
(2 [a.u.]
ro [a.u.]
V(r) 10-1 [Ry]
Q [a.u.3]
Z
ro [a.u.]
257.837 258.427 259.312 260.794 262.281 263.773 265.271 266.775 268.284 269.799 271.320 272.846 274.378 275.916 277.459 279.009 280.564 282.125 283.691 285.264 286.842 288.
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