Each crystal direction has in principle its own threshold displacement energy, so for a full description one should know the full threshold displacement surface T d ( θ θ , ϕ ϕ ) = T d ( [ h k l ] ) for all non-equivalent crystallographic directions [hkl]. Then T d , m i n = min ( T d ( θ θ , ϕ ϕ ) ) and T d , a v e = a v e ( T d ( θ θ , ϕ ϕ ) ) where the minimum and average is with respect to all angles in three dimensions.