Being a granddaughter of Queen Victoria, Alix was taught from a young age to look somber in photographs. However, if you look around the the Alexandra Picture threads, you will find pictures of her smiling and occasionally showing her teeth. Also, she rarely smiled in public because she was very shy and probably suffered from some sort of social anxiety disorder and therefore felt uneasy when around people who were not her family or friends. This situation mainly applies to court functions, as Alexandra seemed to have had no problem running her charity bazaars or nursing the wounded soldiers in the hospitals. Oh, and she was also in near constant pain due to her sciatica, which doesn't really make a person feel cheerful when it feels like your back is broken and the skin has been ripped off the backs of your legs.
I did read that Alix was very shy in public and was very awkward during formal galas. She would have an outbreak of small red patches on her hands and cheeks and such. Maybe it was because she knew not many people in Russia, including Maria of Dagmar, liked her.
Sorry if my information is wrong, I'm new to Alix and the Romanovs!