Dia-electrics

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.