  An accurate description of atomic interactions, such as that provided by
first principles quantum mechanics, is fundamental to realistic prediction of
the properties that govern plasticity, fracture or crack propagation in metals.
However, the computational complexity associated with modern schemes explicitly
based on quantum mechanics limits their applications to systems of a few
hundreds of atoms at most.
  This thesis investigates the application of the Gaussian Approximation
Potential (GAP) scheme to atomistic modelling of tungsten - a bcc transition
metal which exhibits a brittle-to-ductile transition and whose plasticity
behaviour is controlled by the properties of $\frac{1}{2} \langle 111 \rangle$
screw dislocations. We apply Gaussian process regression to interpolate the
quantum-mechanical (QM) potential energy surface from a set of points in atomic
configuration space. Our training data is based on QM information that is
computed directly using density functional theory (DFT). To perform the
fitting, we represent atomic environments using a set of rotationally,
permutationally and reflection invariant parameters which act as the
independent variables in our equations of non-parametric, non-linear
regression.
  We develop a protocol for generating GAP models capable of describing lattice
defects in metals by building a series of interatomic potentials for tungsten.
We then demonstrate that a GAP potential based on a Smooth Overlap of Atomic
Positions (SOAP) covariance function provides a description of the $\frac{1}{2}
\langle 111 \rangle$ screw dislocation that is in agreement with the DFT model.
We use this potential to simulate the mobility of $\frac{1}{2} \langle 111
\rangle$ screw dislocations by computing the Peierls barrier and model
dislocation-vacancy interactions to QM accuracy in a system containing more
than 100,000 atoms.
