  The size and shape of the primary dendrite tips determine the principal
length scale of the microstructure evolving during solidification of alloys.
In-situ X-ray measurements of the tip shape in metals have been unsuccessful so
far due to insufficient spatial resolution or high image noise. To overcome
these limitations, high-resolution synchrotron radiography and advanced image
processing techniques are applied to a thin sample of a solidifying Ga-35wt.%In
alloy. Quantitative in-situ measurements are performed of the growth of
dendrite tips during the fast initial transient and the subsequent steady
growth period, with tip velocities ranging over almost two orders of magnitude.
The value of the dendrite tip shape selection parameter is found to be
$\sigma^* = 0.0768$, which suggests an interface energy anisotropy of
$\varepsilon_4 = 0.015$ for the present Ga-In alloy. The non-axisymmetric
dendrite tip shape amplitude coefficient is measured to be $A_4 \approx 0.004$,
which is in excellent agreement with the universal value previously established
for dendrites.
