Table 2: Diagnostic spectral parameters of the 10 and 20 $\mu$ m bands of amorphous magnesium silicates based on calculations of the absorption cross section per unit volume $C/\langle{V}\rangle$ (in cm^-1) for small spheres (Sph.) and a continuous distribution of ellipsoids (CDE) for particles in the Rayleigh limit. $\lambda$ and A represent the peak position in $\mu$ m and the absorption cross section per unit volume $C/\langle{V}\rangle$ in cm^-1, respectively. W stands for the FWHM of the bands. The band ratio has been calculated by dividing the intensity of the 20 $\mu$ m band by the intensity of the 10 $\mu$ m band.
10 $\mu$ m 20 $\mu$ m band ratio

Comp. $\lambda_{10}$ [ $\mu$ m] A₁₀[cm^-1] W₁₀ [ $\mu$ m] $\lambda_{20}$ [ $\mu$ m] A₂₀[cm^-1] W₂₀ [ $\mu$ m] A₂₀/A₁₀

Sph. CDE Sph. CDE Sph. CDE Sph. CDE Sph. CDE Sph. CDE Sph. CDE

Mg_0.7SiO_2.7 9.15 9.20 6945 7043 1.41 1.56 20.21 20.86 3413 3825 5.61 5.68 0.49 0.54

MgSiO₃ 9.26 9.37 6165 6642 1.88 2.10 19.41 20.22 2520 3023 8.53 10.0 0.41 0.46

Mg_1.5SiO_3.5 9.62 9.74 6725 6992 1.99 2.41 18.11 18.70 3533 4020 9.91 13.3 0.52 0.57

Mg₂SiO₄ 9.80 9.91 6923 7395 2.05 2.43 17.42 17.90 3165 3698 10.0 13.0 0.47 0.50

Mg_2.4SiO_4.4 10.07 10.2 4778 5198 2.66 2.80 17.11 17.76 3925 4395 9.83 13.1 0.82 0.84

**Table 2:** Diagnostic spectral parameters of the 10 and 20 $\mu$ m bands of amorphous magnesium silicates based on calculations of the absorption cross section per unit volume $C/\langle{V}\rangle$ (in cm^-1) for small spheres (Sph.) and a continuous distribution of ellipsoids (CDE) for particles in the Rayleigh limit. $\lambda$ and A represent the peak position in $\mu$ m and the absorption cross section per unit volume $C/\langle{V}\rangle$ in cm^-1, respectively. W stands for the FWHM of the bands. The band ratio has been calculated by dividing the intensity of the 20 $\mu$ m band by the intensity of the 10 $\mu$ m band.
	10 $\mu$ m	20 $\mu$ m	band ratio
Comp.	$\lambda_{10}$ [ $\mu$ m]	A₁₀[cm^-1]	W₁₀ [ $\mu$ m]	$\lambda_{20}$ [ $\mu$ m]	A₂₀[cm^-1]	W₂₀ [ $\mu$ m]	A₂₀/A₁₀
	Sph.	CDE	Sph.	CDE	Sph.	CDE	Sph.	CDE	Sph.	CDE	Sph.	CDE	Sph.	CDE
Mg_0.7SiO_2.7	9.15	9.20	6945	7043	1.41	1.56	20.21	20.86	3413	3825	5.61	5.68	0.49	0.54
MgSiO₃	9.26	9.37	6165	6642	1.88	2.10	19.41	20.22	2520	3023	8.53	10.0	0.41	0.46
Mg_1.5SiO_3.5	9.62	9.74	6725	6992	1.99	2.41	18.11	18.70	3533	4020	9.91	13.3	0.52	0.57
Mg₂SiO₄	9.80	9.91	6923	7395	2.05	2.43	17.42	17.90	3165	3698	10.0	13.0	0.47	0.50
Mg_2.4SiO_4.4	10.07	10.2	4778	5198	2.66	2.80	17.11	17.76	3925	4395	9.83	13.1	0.82	0.84

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