Half Moon - The Best Time of its View

According to "The Best Time for Moon Viewing" by science.com, 

...the interval when the Moon is at or just past First Quarter phase, or at or just before Last Quarter phase, is when we get the best views of the lunar landscape right along the sunrise-sunset line or terminator.
The terminator can also be defined as that variable line between the illuminated portion and the part of the Moon in shadow. Along with the fact that a half Moon offers more viewing comfort to the eye as opposed to a full Moon, using a telescope with just small optical power (magnifications of 20 to 40x), or even with good binoculars, we can then see a wealth of detail on its surface.  Around those times when the Moon is half-lit or gibbous phase, those features lying close to the terminator stand out in sharp, clear relief.