Ron Guth: After a hiatus of 13 years, the Mint began producing quarter eagles again in 1821, albeit in limited quantities. The head of Liberty on the new design is of roughly the same size as on the 1808 issue, but much of the bust was removed, thus centering the head and allowing stars to appear in a perfect semi-circle. The reversxe design was modified, but only slightly, mostly to improve the appearance of the eagle. Though known as the Capped Bust, Large Diameter, there is little size difference between this and the Capped Bust, Reduced Diameter (struck from 1829-1834). The actual difference between the two is the result of the introduction of the collar die (or "close" collar) in 1829. The collar die standardized the diameter of the coin, thus the variation one sees on the 1821-1827 issues disappears on all later types.
As was typical of the period, mintages were based on demand for particular denominations. In the case of the quarter eagles, demand was low, thus mintages are miniscule for all dates of this type, ranging from a mere 760 pieces in 1826 to a "whopping" 4,434 coins in 1825. As if that was not low enough, many of the surviving examples were destroyed when their metal value exceeded their face value whenever the value of gold rose to a certain point.
All examples of this type are scarce. Problem-free examples are the exception and nice, Mint State examples are exceedingly rare. The finest example of this type certified by PCGS is an amazing 1825 in MS-67.