An exact analytical formula for the line tension of screw dislocations in bcc metals

The temperature dependence of the flow stress of bcc metals is controlled by the line tension of screw dislocations. In this paper, the line tension of a screw dislocation with Burgers vector in the direction is derived in analytical closed form in terms of the cubic elastic constants. The new formula assumes the form of a polynomial of order 16 divided by the square root of a polynomial of order 30 in the elastic constants. It is used to prove that the line tension of a screw dislocation is the same in every plane passing through the direction.