Why is there a large increase in volume when an alkali metal is dissolved in liquid ammonia?

My teacher said unexplainedly that when alkali metals dissolves in liquid ammonia, there is a large increase in the volume. I found a paper that confirms this fact [[1](https://doi.org/10.1021/ja01624a022)]:



> 
> In the course of recent research it was necessary to obtain the volume change associated with the solution of lithium, sodium and potassium in liquid ammonia.
> That the solution of these metals in liquid ammonia is accompanied by a relatively large increase in volume has long been known.
> From the densities of sodium and potassium solutions it has been shown that these volume changes pass through a maximum at about $3N.$
> 
> 
> 


I am still unaware of the reason for the increase of final volume $V\_\mathrm{f}$ after reaction between metal $\ce{M}$ and liquid ammonia $\ce{NH3}$:


$$V\_\mathrm{f} \gg V\_0(\ce{M}) + V\_0(\ce{NH3})$$


### Reference


1. Marshall, P.; Hunt, H. Volume Changes for Metal Solutions in Liquid Ammonia. *J. Am. Chem. Soc.* **1955**, 77 (19), 5016–5016. DOI: [10.1021/ja01624a022](https://doi.org/10.1021/ja01624a022).


