Tri-n-butyl phosphate (TBP) is an important extractant for separating hexavalent uranium and tetravalent plutonium from used nuclear fuel by solvent extraction. In such solvent extractions using TBP, the organic phase occasionally separates into two organic phases, namely, light and heavy organic phases. The latter one in particular is called the third phase. The purpose of this work is to elucidate the mechanism whereby the third phase forms in biphasic liquid-liquid solvent extraction of heavy metal ions. Toward this end, small- and wide-angle X-ray and neutron scattering (SWAXS and SWANS) experiments were conducted to examine the microscopic structures of TBP/octane mixtures. These investigations of solute associations in TBP-containing organic phases before extraction of heavy metal ions provide insights into system performance. After the extraction of heavy metal ions, for example, the microscopic structures formed in the organic phase are likely to be correlated with the initial microscopic structures, which are revealed here. SWAXS and SWANS, with accurate estimations of incoherent scattering intensities for all solution samples, revealed the following: (i) TBP self-associates in octane, and the average distance between two TBP molecules in the TBP assemblies is evaluated as 0.9-1.0 nm; (ii) the shape of the TBP assembly is ellipsoidal; and (iii) the attractive interaction among TBP assemblies in octane is miniscule, and thus, they tend to be dispersed homogeneously due to the excluded volume effect.