 Solution

The trivalent dopant is comparable in radius to Na${}^{+}$ and is naturally accommodated on a sodium site rather than a chloride site. One charge-balanced incorporation reaction isThree cation sites are filled by one Y ion and two vacancies; the three chloride ions occupy the corresponding anion sites. The effective $+2$ substitutional charge is balanced by two singly negative sodium vacancies.

YCl${}_3$ doping primarily increases sodium-vacancy-mediated ionic conductivity, provided the vacancies remain mobile rather than strongly bound to the dopant. In contrast, sodium-rich doping introduces electrons and anion vacancies or interstitial-related defects. Neither mechanism requires holes as its compensating carrier, and an increase in vacancy number need not translate proportionally into conductivity if defect association reduces mobility.