Multiple scaling power in liquid gallium under pressure conditions

Abstract

Generally, a single scaling exponent, ${D}_{f}$, can characterize the fractal structures of metallic glasses according to the scaling power law. However, when the scaling power law is applied to liquid gallium upon compression, the results show multiple scaling exponents and the values are beyond 3 within the first four coordination spheres in real space, indicating that the power law fails to describe the fractal feature in liquid gallium. The increase in the first coordination number with pressure leads to the fact that first coordination spheres at different pressures are not similar to each other in a geometrical sense. This multiple scaling power behavior is confined within a correlation length of \ensuremath{\xi} \ensuremath{\approx} 14--15 \AA{} at applied pressure according to decay of $G$($r$) in liquid gallium. Beyond this length the liquid gallium system could roughly be viewed as homogeneous, as indicated by the scaling exponent, ${D}_{s}$, which is close to 3 beyond the first four coordination spheres.