Table 3. Parameters from Fitting the Si–O, S–O, and (O–O)_S Peaks in T(r) and ΔT(r)^a.

parameters		LiSi and LiSiS	NaSi and NaSiS	NaCaSi and NaCaSiS	NaBaSi and NaBaSiS
fit to the first peak of T(r) for the undoped sample	rSiO (Å)	1.6222(2)	1.62491(6)	1.6251(2)	1.62584(5)
	uSiO (Å)	0.0511(3)	0.05844(8)	0.0548(3)	0.05703(6)
	nSiO	4.10(2)	4.016(3)	3.92(1)	3.908(2)
fit to the first peak of T(r) for the doped sample	rSiO (Å)	1.6219(2)	1.6231(2)		1.6262(2)
	nSiO	4.129(6)	4.006(8)		3.91(4)
	rSO (Å)	1.478(3)	1.475(2)		1.54(1)
	uSO (Å)	0.044b	0.044(2)		0.08(1)
	nSO	3.7(1)	3.1(1)		4.7(6)
fit to peaks in the doped–undoped difference	rSO (Å)	1.4686(4)	1.4755(3)	1.522(1)	1.5136(5)
	uSO (Å)	0.0443(6)	0.0313(6)	0.024(2)	0.0556(9)
	nSO	3.74(2)	3.07(1)	3.57(4)	3.02(2)
	rOO(S) (Å)	2.4091(4)	2.4038(4)	2.386(1)	2.4151(7)
	uOO(S) (Å)	0.0626(6)	0.0734(6)	0.081(2)	0.065(1)
	nOO(S)	0.358(2)	0.514(2)	0.130(2)	0.309(3)
	O–Ŝ–O	110.2	109.1	103.2	105.8
predictions
undoped sample	rOO(Si) (Å)	2.6490	2.6535	2.6538	2.6550
	nOO(Si)	4.38	4.38	4.38	4.38
	nOSi	1.46	1.46	1.46	1.46
doped sample	rOO(Si) (Å)	2.6486	2.6505		2.6556
	nOO(Si)	3.98	3.87	4.22	3.98
	nOO(S)	0.364	0.468	0.150	0.364
	nOSi	1.33	1.29	1.41	1.33

^aSee text for details. The SO₃ doping of NaCaSiS is too small to allow a meaningful fitting of two peaks to the first peak in T(r).

^bFor LiSiS, the S–O peak width was fixed at a value taken from NaSiS in order to obtain a meaningful fit. Statistical errors from the fits are given in parentheses. (The parameter r_jk represents the interatomic distance between atoms j and k, while u_jk (written as in eq 5) represents the root mean square variation in r_jk, and n_jk represents the coordination number. For O–O distances, an additional bracket is used to differentiate oxygen pairs in the sulfur (r_OO(S)) and silicon (r_OO(Si)) coordination shells. O–Ŝ–O is the bond angle at the sulfur atom.)