I sometimes think Tatiana looks so determined in her photos because one had to stay very still so the photo would not blur.
By the turn of the century, photo technology had improved enough that this was no longer the case. The informal photos taken by the IF are pretty much equivalent to our modern snapshots -- a click and the image was captured.
Yes. At the early XX Century, yu wouldn't need to be quiet as a statue just to get a photo. Yo may notice it for the great amount of casual pics of the IF in which they are playing, dancing, moving and so on. Besides, if Tatiana would look determined for a long exposition before the ohto camera, her sisters and brother would must appear as determined too.

I think it was just her personnality showing at the pics. Anastasia's spunky moods also showed in the pics we have of her, as well as Maria's sweetness and inocence and Olga's complicated character...
RealAnastasia.