How to recognize motivated applicants in PhD interview?
I really don't think there is a tried and true solution to this problem, but in the end it boils down to asking:


Why does the student want to do a PhD? 


Most students that apply with us don't have a very good sense of what a PhD is, so there really is no "wrong" answer here. However, I consider it a red flag if I get the impression that the student really arrived at the decision to do a PhD via exclusion (don't want to do or is scared of "real" work, need some money to pay rent). I also am very sceptical of students that do a PhD because they hope for better career opportunities afterwards - my experience is that those students too often end up putting in the minimal hours needed to get the degree.


Is the student interested in staying in research, or do they know right from the start that they will go back to industry after finishing? 


Similar to before, students that foresee at least the possibility of staying in research tend to be more motivated to go beyond what they perceive as the minimum requirements for getting a PhD. What you don't want is a student that constantly talks about that one guy many years back that graduated with two weak conference papers, and asks why (s)he should be investing all this weekend work into A+ papers if that's apparently not strictly required to graduate.


What do they expect from doing research? 


Again, most applicants have no very clear idea about research at this point, but the answer to this question can tell you something about what the student values in a job / career. This will allow you to judge how likely it is that they find what they want in your lab, and hence be motivated. For instance, I have found that "I really like to travel to exotic places" is a surprisingly good motivator for students to put in work for this paper to a conference in Hawaii. "I like flexibility" or "I like to work on my own ideas and projects" is also a good motivator for academia, up to a point. However, I tend to remind people that present-day academia, at least in science and engineering, is no ivory tower where people are completely protected from outside pressure and forces. What's not great is if the student apparently values job security or high salary, because both is typically not available in academia for a long time from the moment you start your PhD.

A tricky but important point is also judging how well the student will "fit in" with the current team. It is important here to not end up discriminating based on nationality, age, gender, or marital status, but there is no arguing that being the "odd person out" in an otherwise tightly knitted team will not be great for the motivation of the student. Of course it is your task to manage your team in a way that they will integrate whoever you end up hiring, but at the end of the day you cannot force your team to like somebody and/or invite them to private outings etc.