Scattering curve lignite

Figure 2. Scattering curves for PSOC 93 lignite (circles) and PSOC 248 subbituminous coal (squares). The points show the corrected scattering data, and the curves were obtained from least-square fits of Equation 3 with n=l.

Beulah lignite on both the Beeman and Kratky systems at the University of Missouri, using the same sample that was studied at the University of North Dakota. As before, all scattering curves were nearly identical except at the largest scattering angles, where the Kratky system showed a higher intensity than the Beeman systems,... 

Figure 3. The corrected scattering curve for PSOC 86 lignite (squares) and the fit of Equation 6 (line).

The total x-ray specific surfaces of Beulah lignite determined at the University of North Dakota and the University of Missouri agree within the estimated uncertainty. For the specific surfaces of the macropores and the transitional pores, the agreement, though still within the estimate uncertainty, is not so close. This greater difference may be a result of the fact that the scattering curves from the Universities of North Dakota and Missouri were determined by fits of Equation (3) with n = 2 and n = 1,... 

The transitional-pore specific surfaces listed in Table 1 for all of the subbltumlnous coals except PSOC 138 are about 3 to 8 times as large as the corresponding macropore specific surfaces. The ratio of the area associated with the transitional pores to that for the macropores is large enough in these subbltumlnous coals that at least a trace of an Inflection can be seen on careful examination of the scattering curves. On the other hand, for the subbltumlnous Coal 138 and for the lignites, the specific surfaces of the macropores and the transitional pores are more nearly equal, and no inflection is evident in the scattering curves. 

A different type of analysis has now provided this information (20) The dimension distributions p(a) of independent spherical scatterers with uniform density and diameter a which produces each of the terms in the sum in Equation (3) can be calculated (19) After obtaining the constants in the sum in Equation (3) by least-squares fits of this equation to the scattering curve measured for Beulah lignite at the University of North Dakota, we used these constants to evaluate the sum of the pore-dimension distribution functions for uniform spheres that are obtained (19) from the terms in the sum in Equation (3) The sum of these pore-dimension distributions was very similar to the power-law distribution given by Equation (4) The fact that we could obtain almost the same power-law dimension distribution by two independent methods suggests that such a distribution may be a good approximation to the pore-... 

By modifying and extending the results presented in Reference (19), we have developed a technique to calculate pore-dimension distributions from the scattering curves for lignites. Equation (5) was obtained under the assumption that the dimension distribution was given by Equation (4) for all values of the dimension a Calculations (20) show that if, on the other hand, the scattered intensity can be approximated by Equation (5) for < h < ho, and if the entire measured curve can be represented by the expression... 

Quantities calculated in our fits of Equation (6) to the scattering curves for lignites are listed in Table 3. The curves in Figures 3 and 4 were determined from the fits of Equation (6) ... 

The expoaents 7-y in Table 3 fall into two groups, with values less and greater than 3. The difference in exponents is compensated for by a change in the value of the constant D2, so that the resulting fitted curves are nearly the same for all of the lignite samples, just as the measured scattering curves are almost... 

We have found that scattering patterns like Curve 1 in Fig. 2 are typical of lignites and of some sub-bituminous and high-volatile bituminous coals. 

Although we were able to obtain satisfactory fits of (3) with n 1 for all of the low-rank PSOC coals discussed below, the scattering data for Beulah lignite obtained with the Bonse-Hart and Beeman systems extended over such a wide Interval of scattering angles that we found that n had to be Increased to 2 in order to obtain a good fit for this curve. 

Figure 4, The scattered intensity for Beulah lignite as measured with the Bonse-Hart and Beeman collimation systems (squares) at the University of North Dakota. The curve was drawn from a least-squares fit of Equation 6, and the points are the corrected scattered intensities.

As can be seen from the curve for PSOC coal 93 in Figure 2, the scattering data from lignites can also be fitted quite well with Equation (3) The quality of the fits of the two equations is nearly the same The fact that both equations can be employed in the fits is a result, we believe, of the fact that both Equations (3) and (6) correspond in this case to similar pore-dimension distributions ... 

---