We define a dia-electric material by
$$\boxed{-1<\chi_e<0}$$
Since,
$$\mathbf{P}(\mathbf{r}) = \varepsilon_0\frac{N\alpha(\mathbf{r})}{1-\frac{1}{3}N(\mathbf{r})\alpha(\mathbf{r})}\mathbf{E}(\mathbf{r}) = \varepsilon_0\chi_\text{e}(\mathbf{r})\mathbf{E}(\mathbf{r})$$
Since usually \(N\alpha>0\), for a homogenous material to be dia-electric, we must have
$$1-\frac{1}{3}N\alpha<0.$$
Therefore a material with
$$\boxed{\alpha\frac{\rho N_A}{M}> 3}$$
should be a dia-electric.
