Examples

Janssen, T.; Janner, A.; Looijenga-Vos, A.; Wolff, P. M. de

doi:10.1107/97809553602060000624

International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

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International Tables for Crystallography (2006). Vol. C. ch. 9.8, p. 936

Section 9.8.3.5. Examples

T. Janssen,^a A. Janner,^a A. Looijenga-Vos^b and P. M. de Wolff^c ^‡

^a Institute for Theoretical Physics, University of Nijmegen, Toernooiveld, NL-6525 ED Nijmegen, The Netherlands,^bRoland Holstlaan 908, NL-2624 JK Delft, The Netherlands, and ^cMeermanstraat 126, 2614 AM, Delft, The Netherlands

9.8.3.5. Examples

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(A) Na₂CO₃

Na₂CO₃ has a phase transition at about 753 K from the hexagonal to the monoclinic phase. At about 633 K, one vibration mode becomes unstable and below the transition temperature T_i = 633 K there is a modulated γ-phase (de Wolff & Tuinstra, 1986). At low temperature (128 K), a transition to a commensurate phase has been reported.

The main reflections in the modulated phase belong to a monoclinic lattice, and the satellites to a modulation with wavevector q = αa* + γc*, b axis unique. The dimension of the modulation is one. The main reflections satisfy the condition $[hkl0, h+k={\rm even}.]$ Therefore, the lattice of the average structure is C-centred monoclinic. For the satellites, the same general condition holds (hklm, h + k = even). From Table 9.8.3.6, one sees after a change of axes that the Bravais class of the modulated structure is $[\hbox{No. 4: }2/mC(\alpha0\gamma).]$ Table 9.8.3.2(a) shows that the point group of the vector module is $[2/m(\bar11)]$ . The point group of the modulated structure is equal to or a subgroup of this one.

The space group of the average structure determined from the main reflections is C2/m (No. 12 in International Tables for Crystallography, Volume A). The superspace group may then be determined from the special reflection condition $[h0lm, m={\rm even}]$ using Table 9.8.3.5. There are five superspace groups with basic group No. 12. Among them there are two in Bravais class 4. The reflection condition mentioned leads to the group $[\hbox{No. }12.2=C2/m(\alpha0\gamma)0s = P{^{C2/m}_{\kern5pt{\bar1} \kern5pt s}}]$ In principle, the superspace group could be a subgroup of this, but, since the transition normal–incommensurate is of second order, Landau theory predicts that the basic space group is the symmetry group of the unmodulated monoclinic phase, which is [C2/m] .

Table 9.8.3.5| top | pdf | superspace group finder
(3 + 1)-Dimensional superspace groups

The number labelling the superspace group is denoted by n.m, where n is the number attached to the three-dimensional basic space group and m numbers the various superspace groups having the same basic space group. The symbol of the basic space group, the symbol for the four-dimensional point group K_s, the number of the four-dimensional Bravais class to which the superspace group belongs (Table 9.8.3.2a), and the superspace-group symbol are also given. The superspace-group symbol is indicated in the short notation, i.e. for the basic group one uses the short symbol from International Tables for Crystallography, Volume A, and then the values of τ are given for each of the generators in this symbol, unless all these values are zero. Then, instead of writing a number of zeros, one omits them all. Finally, the special reflection conditions due to non-primitive translations are given, for hklm if q^r = 0 and for HKLm otherwise. Recall the HKLm are the indices with respect to a conventional basis $[{\bf a}_c^*, {\bf b}_c^*, {\bf c}_c^*, {\bf q}^i]$ as in Table 9.8.3.2(a). The reflection conditions due to centring translations are given in Table 9.8.3.6.

No.	Basic space group	Point group K_s	Bravais class No.	Group symbol	Special reflection conditions
1.1	P1	(1, 1)	1	P1(αβγ)
2.1	$[P{\bar 1}]$	( $[{\bar 1}]$ , $[{\bar 1}]$ )	1	P $[{\bar 1}]$ (αβγ)
3.1	P2	(2, $[{\bar 1}]$ )	2	P2(αβ0)
3.2		(2, $[{\bar 1}]$ )	3	P2(αβ $[{{1}\over{2}}]$ )
3.3		(2, 1)	5	P2(00γ)
3.4		(2, 1)	5	P2(00γ)s	00lm: m = 2n
3.5		(2, 1)	6	P2( $[{{1}\over{2}}]$ 0γ)
4.1	P2₁	(2, $[{\bar 1}]$ )	2	P2₁(αβ0)	00l0: l = 2n
4.2		(2, 1)	5	P2₁(00γ)	00lm: l = 2n
4.3		(2, 1)	6	P2₁( $[{{1}\over{2}}]$ 0γ)	00Lm: L = 2n
5.1	B2	(2, $[{\bar 1}]$ )	4	B2(αβ0)
5.2		(2, 1)	7	B2(00γ)
5.3		(2, 1)	7	B2(00γ)s	00lm: m = 2n
5.4		(2, 1)	8	B2(0 $[{{1}\over{2}}]$ γ)
6.1	Pm	(m, 1)	2	Pm(αβ0)
6.2		(m, 1)	2	Pm(αβ0)s	hk0m: m = 2n
6.3		(m, 1)	3	Pm(αβ $[{{1}\over{2}}]$ )
6.4		(m, $[{\bar 1}]$ )	5	Pm(00γ)
6.5		(m, $[{\bar 1}]$ )	6	Pm( $[{{1}\over{2}}]$ 0γ)
7.1	Pb	(m, 1)	2	Pb(αβ0)	hk0m: k = 2n
7.2		(m, 1)	3	Pb(αβ $[{{1}\over{2}}]$ )	HK0m: K = 2n
7.3		(m, $[{\bar 1}]$ )	5	Pb(00γ)	hk00: k = 2n
7.4		(m, $[{\bar 1}]$ )	6	Pb( $[{{1}\over{2}}]$ 0γ)	HK00: K = 2n
8.1	Bm	(m, 1)	4	Bm(αβ0)
8.2		(m, 1)	4	Bm(αβ0)s	hk0m: m = 2n
8.3		(m, $[{\bar 1}]$ )	7	Bm(00γ)
8.4		(m, $[{\bar 1}]$ )	8	Bm(0 $[{{1}\over{2}}]$ γ)
9.1	Bb	(m, 1)	4	Bb(αβ0)	hk0m: k = 2n
9.2		(m, $[{\bar 1}]$ )	7	Bb(00γ)	hk00: k = 2n
10.1	P2/m	(2/m, $[{\bar 1}1]$ )	2	P2/m(αβ0)
10.2		(2/m, $[{\bar 1}1]$ )	2	P2/m(αβ0)0s	hk0m: m = 2n
10.3		(2/m, $[{\bar 1}1]$ )	3	P2/m(αβ $[{{1}\over{2}}]$ )
10.4		(2/m, $[1{\bar 1}]$ )	5	P2/m(00γ)
10.5		(2/m, $[1{\bar 1}]$ )	5	P2/m(00γ)s0	00lm: m = 2n
10.6		(2/m, $[1{\bar 1}]$ )	6	P2/m( $[{{1}\over{2}}]$ 0γ)
11.1	P2₁/m	(2/m, $[{\bar 1}1]$ )	2	P2₁/m(αβ0)	00l0: l = 2n
11.2		(2/m, $[{\bar 1}1]$ )	2	P2₁/m(αβ0)0s	00l0: l = 2n; hk0m: m = 2n
11.3		(2/m, $[1{\bar 1}]$ )	5	P2₁/m(00γ)	00lm: l = 2n
11.4		(2/m, $[1{\bar 1}]$ )	6	P2₁/m( $[{{1}\over{2}}]$ 0γ)	00Lm: L = 2n
12.1	B2/m	(2/m, $[{\bar 1}1]$ )	4	B2/m(αβ0)
12.2		(2/m, $[{\bar 1}1]$ )	4	B2/m(αβ0)0s	hk0m: m = 2n
12.3		(2/m, $[1{\bar 1}]$ )	7	B2/m(00γ)
12.4		(2/m, $[1{\bar 1}]$ )	7	B2/m(00γ)s0	00lm: m = 2n
12.5		(2/m, $[1{\bar 1}]$ )	8	B2/m( $[{{1}\over{2}}]$ 0γ)
13.1	P2/b	(2/m, $[{\bar 1}1]$ )	2	P2/b(αβ0)	hk0m: k = 2n
13.2		(2/m, $[{\bar 1}1]$ )	3	P2/b(αβ $[{{1}\over{2}}]$ )	HK0m: m = 2n
13.3		(2/m, $[1{\bar 1}]$ )	5	P2/b(00γ)	hk00: k = 2n
13.4		(2/m, $[1{\bar 1}]$ )	5	P2/b(00γ)s0	00lm: m = 2n; hk00: k = 2n
13.5		(2/m, $[1{\bar 1}]$ )	6	P2/b( $[{{1}\over{2}}]$ 0γ)	HK00: K = 2n
14.1	P2₁/b	(2/m, $[{\bar 1}1]$ )	2	P2₁/b(αβ0)	00l0: l = 2n; hk0m: k = 2n
14.2		(2/m, $[1{\bar 1}]$ )	5	P2₁/b(00γ)	00lm: l = 2n; hk00: k = 2n
14.3		(2/m, $[1{\bar 1}]$ )	6	P2₁/b( $[{{1}\over{2}}]$ 0γ)	00Lm: L = 2n; HK00: K = 2n
15.1	B2/b	(2/m, $[{\bar 1}1]$ )	4	B2/b(αβ0)	hk0m: k = 2n
15.2		(2/m, $[1{\bar 1}]$ )	7	B2/b(00γ)	hk00: k = 2n
15.3		(2/m, $[1{\bar 1}]$ )	7	B2/b(00γ)s0	00lm: m = 2n; hk00: k = 2n
16.1	P222	(222, $[{\bar 1}{\bar 1}1]$ )	9	P222(00γ)
16.2			9	P222(00γ)00s	00lm: m = 2n
16.3			10	P222(0 $[{{1}\over{2}}]$ γ)
16.4			11	P222( $[{{1}\over{2}}{{1}\over{2}}]$ γ)
17.1	P222₁	(222, $[{\bar 1}{\bar 1}1]$ )	9	P222₁(00γ)	00lm: l = 2n
17.2			10	P222₁(0 $[{{1}\over{2}}]$ γ)	00Lm: L = 2n
17.3			11	P222₁( $[{{1}\over{2}}{{1}\over{2}}]$ γ)	00Lm: L = 2n
17.4			9	P2₁22(00γ)	h000: h = 2n
17.5			9	P2₁22(00γ)00s	h000: h = 2n; 00lm: m = 2n
17.6			10	P2₁22(0 $[{{1}\over{2}}]$ γ)	H000: H = 2n
18.1	P2₁2₁2	(222, $[{\bar 1}{\bar 1}1]$ )	9	P2₁2₁2(00γ)	h000: h = 2n; 0k00: k = 2n
18.2			9	P2₁2₁2(00γ)00s	h000: h = 2n; 0k00: k = 2n; 00lm: m = 2n
18.3			9	P2₁22₁(00γ)	h000: h = 2n; 00lm: l = 2n
18.4			10	P2₁22₁(0 $[{{1}\over{2}}]$ γ)	H000: H = 2n; 00Lm: L = 2n
19.1	P2₁2₁2₁	(222, $[{\bar 1}{\bar 1}1]$ )	9	P2₁2₁2₁(00γ)	h000: h = 2n; 0k00: k = 2n; 00lm: l = 2n
20.1	C222₁	(222, $[{\bar 1}{\bar 1}1]$ )	13	C222₁(00γ)	00lm: l = 2n
20.2			14	C222₁(10γ)	00Lm: L = 2n
20.3			15	A2₁22(00γ)	h000: h = 2n
20.4			15	A2₁22(00γ)00s	h000: h = 2n; 00lm: m = 2n
21.1	C222	(222, $[{\bar 1}{\bar 1}1]$ )	13	C222(00γ)
21.2			13	C222(00γ)00s	00lm: m = 2n
21.3			14	C222(10γ)
21.4			14	C222(10γ)00s	00Lm: m = 2n
21.5			15	A222(00γ)
21.6			15	A222(00γ)00s	00lm: m = 2n
21.7			16	A222( $[{{1}\over{2}}]$ 0γ)
22.1	F222	(222, $[{\bar 1}{\bar 1}1]$ )	17	F222(00γ)
22.2			17	F222(00γ)00s	00lm: m = 2n
22.3			18	F222(10γ)
23.1	I222	(222, $[{\bar 1}{\bar 1}1]$ )	12	I222(00γ)
23.2			12	I222(00γ)00s	00lm: m = 2n
24.1	I2₁2₁2₁	(222, $[{\bar 1}{\bar 1}1]$ )	12	I2₁2₁2₁(00γ)	h000: h = 2n; 0k00: k = 2n; 00lm: l = 2n
24.2			12	I2₁2₁2₁(00γ)00s	h000: h = 2n; 0k00: k = 2n; 00lm: l + m = 2n
25.1	Pmm2	(mm2, 111)	9	Pmm2(00γ)
25.2			9	Pmm2(00γ)s0s	0klm: m = 2n
25.3			9	Pmm2(00γ)ss0	0klm: m = 2n; h0lm: m = 2n
25.4			10	Pmm2(0 $[{{1}\over{2}}]$ γ)
25.5			10	Pmm2(0 $[{{1}\over{2}}]$ γ)s0s	0KLm: m = 2n
25.6			11	Pmm2( $[{{1}\over{2}}{{1}\over{2}}]$ γ)
25.7		(m2m, $[1{\bar 1}{\bar 1}]$ )	10	Pm2m(0 $[{{1}\over{2}}]$ γ)
25.8			10	Pm2m(0 $[{{1}\over{2}}]$ γ)s00	0KLm: m = 2n
25.9		(2mm, $[{\bar 1}1{\bar 1}]$ )	9	P2mm(00γ)
25.10			9	P2mm(00γ)0s0	h0lm: m = 2n
25.11			10	P2mm(0 $[{{1}\over{2}}]$ γ)
25.12			11	P2mm( $[{{1}\over{2}}{{1}\over{2}}]$ γ)
26.1	Pmc2₁	(mm2, 111)	9	Pmc2₁(00γ)	h0lm: l = 2n
26.2			9	Pmc2₁(00γ)s0s	0klm: m = 2n; h0lm: l = 2n
26.3			10	Pmc2₁(0 $[{{1}\over{2}}]$ γ)	H0Lm: L = 2n
26.4			10	Pmc2₁(0 $[{{1}\over{2}}]$ γ)s0s	0KLm: m = 2n; H0Lm: L = 2n
26.5			10	Pcm2₁(0 $[{{1}\over{2}}]$ γ)	0KLm: L = 2n
26.6			11	Pmc2₁( $[{{1}\over{2}}{{1}\over{2}}]$ γ)	H0Lm: L = 2n
26.7		(2mm, $[{\bar 1}1{\bar 1}]$ )	9	P2₁am(00γ)	h0lm: h = 2n
26.8			9	P2₁am(00γ)0s0	h0lm: h + m = 2n
26.9			9	P2₁ma(00γ)	hk00: h = 2n
26.10			9	P2₁ma(00γ)0s0	h0lm: m = 2n; hk00: h = 2n
26.11			10	P2₁am(0 $[{{1}\over{2}}]$ γ)	H0Lm: H = 2n
26.12			10	P2₁ma(0 $[{{1}\over{2}}]$ γ)	HK00: H = 2n
27.1	Pcc2	(mm2, 111)	9	Pcc2(00γ)	0klm: l = 2n; h0lm: l = 2n
27.2			9	Pcc2(00γ)s0s	0klm: l + m = 2n; h0lm: l = 2n
27.3			10	Pcc2(0 $[{{1}\over{2}}]$ γ)	0KLm: L = 2n; H0Lm: L = 2n
27.4			11	Pcc2( $[{{1}\over{2}}{{1}\over{2}}]$ γ)	0KLm: L = 2n; H0Lm: L = 2n
27.5		(2mm, $[{\bar 1}1{\bar 1}]$ )	9	P2aa(00γ)	h0lm: h = 2n; hk00: h = 2n
27.6			9	P2aa(00γ)0s0	h0lm: h + m = 2n; hk00: h = 2n
27.7			10	P2aa(0 $[{{1}\over{2}}]$ γ)	H0Lm: H = 2n; HK00: H = 2n
28.1	Pma2	(mm2, 111)	9	Pma2(00γ)	h0lm: h = 2n
28.2			9	Pma2(00γ)s0s	0klm: m = 2n; h0lm: h = 2n
28.3			9	Pma2(00γ)ss0	0klm: m = 2n; h0lm: h + m = 2n
28.4			9	Pma2(00γ)0ss	h0lm: h + m = 2n
28.5			10	Pma2(0 $[{{1}\over{2}}]$ γ)	H0Lm: H = 2n
28.6			10	Pma2(0 $[{{1}\over{2}}]$ γ)s0s	0KLm: m = 2n; H0Lm: H = 2n
28.7		(m2m, $[1{\bar 1}{\bar 1}]$ )	10	Pm2a(0 $[{{1}\over{2}}]$ γ)	HK00: H = 2n
28.8			10	Pm2a(0 $[{{1}\over{2}}]$ γ)s00	0KLm: m = 2n; HK00: H = 2n
28.9			10	Pc2m(0 $[{{1}\over{2}}]$ γ)	0KLm: L = 2n
28.10		(2mm, $[{\bar 1}1{\bar 1}]$ )	9	P2cm(00γ)	h0lm: l = 2n
28.11			9	P2mb(00γ)	hk00: k = 2n
28.12			9	P2mb(00γ)0s0	h0lm: m = 2n; hk00: k = 2n
28.13			10	P2cm(0 $[{{1}\over{2}}]$ γ)	H0Lm: L = 2n
28.14			11	P2cm( $[{{1}\over{2}}{{1}\over{2}}]$ γ)	H0Lm: L = 2n
29.1	Pca2₁	(mm2, 111)	9	Pca2₁(00γ)	0klm: l = 2n; h0lm: h = 2n
29.2			9	Pca2₁(00γ)0ss	0klm: l = 2n; h0lm: h + m = 2n
29.3			10	Pca2₁(0 $[{{1}\over{2}}]$ γ)	0KLm: L = 2n; H0Lm: H = 2n
29.4		(2mm, $[{\bar 1}1{\bar 1}]$ )	9	P2₁ca(00γ)	hk00: h = 2n; h0lm: l = 2n
29.5			9	P2₁ab(00γ)	h0lm: h = 2n; hk00: k = 2n
29.6			9	P2₁ab(00γ)0s0	h0lm: h + m = 2n; hk00: k = 2n
29.7			10	P2₁ca(0 $[{{1}\over{2}}]$ γ)	H0Lm: L = 2n; HK00: H = 2n
30.1	Pcn2	(mm2, 111)	9	Pcn2(00γ)	0klm: l = 2n; h0lm: h + l = 2n
30.2			9	Pcn2(00γ)s0s	0klm: l + m = 2n; h0lm: h + l = 2n
30.3			10	Pcn2(0 $[{{1}\over{2}}]$ γ)	0KLm: L = 2n; H0Lm: H + L = 2n
30.4		(2mm, $[{\bar 1}1{\bar 1}]$ )	9	P2na(00γ)	h0lm: h + 1 = 2n; hk00: h = 2n
30.5			9	P2an(00γ)	h0lm: h = 2n; hk00: h + k = 2n
30.6			9	P2an(00γ)0s0	h0lm: h + m = 2n; hk00: h + k = 2n
30.7			10	P2na(0 $[{{1}\over{2}}]$ γ)	H0Lm: H + L = 2n; HK00: H = 2n
30.8			11	P2an( $[{{1}\over{2}}{{1}\over{2}}]$ γ)0q0	H0Lm: 2H + m = 4n; HK00: H + K = 2n
31.1	Pmn2₁	(mm2, 111)	9	Pmn2₁(00γ)	h0lm: h + l = 2n
31.2			9	Pmn2₁(00γ)s0s	0klm: m = 2n; h0lm: h + l = 2n
31.3			10	Pmn2₁(0 $[{{1}\over{2}}]$ γ)	H0Lm: H + L = 2n
31.4			10	Pmn2₁(0 $[{{1}\over{2}}]$ γ)s0s	0KLm: m = 2n; H0Lm: H + L = 2n
31.5		(2mm, $[{\bar 1}1{\bar 1}]$ )	9	P2₁nm(00γ)	h0lm: h + l = 2n
31.6			9	P2₁mn(00γ)	hk00: h + k = 2n
31.7			9	P2₁mn(00γ)0s0	hk00: h + k = 2n; h0lm: m = 2n
31.8			10	P2₁nm(0 $[{{1}\over{2}}]$ γ)	H0Lm: H + L = 2n
32.1	Pba2	(mm2, 111)	9	Pba2(00γ)	0klm: k = 2n; h0lm: h = 2n
32.2			9	Pba2(00γ)s0s	0klm: k + m = 2n; h0lm: h = 2n
32.3			9	Pba2(00γ)ss0	0klm: k + m = 2n; h0lm: h + m = 2n
32.4			11	Pba2( $[{{1}\over{2}}{{1}\over{2}}]$ γ)qq0	0KLm: 2K + m = 4n; H0Lm: 2H + m = 4n
32.5		(m2m, $[1{\bar 1}{\bar 1}]$ )	10	Pc2a(0 $[{{1}\over{2}}]$ γ)	0KLm: L = 2n; HK00: H = 2n
32.6		(2mm, $[{\bar 1}1{\bar 1}]$ )	9	P2cb(00γ)	h0lm: l = 2n; hk00: k = 2n
33.1	Pbn2₁	(mm2, 111)	9	Pbn2₁(00γ)	0klm: k = 2n; h0lm: h + l = 2n
33.2			9	Pbn2₁(00γ)s0s	0klm: k + m = 2n; h0lm: h + l = 2n
33.3			11	Pbn2₁( $[{{1}\over{2}}{{1}\over{2}}]$ γ)qq0	0KLm: 2K + m = 4n; H0Lm: 2H + 2L + m = 4n
33.4		(2mm, $[{\bar 1}1{\bar 1}]$ )	9	P2₁nb(00γ)	h0lm: h + l = 2n; hk00: k = 2n
33.5			9	P2₁cn(00γ)	h0lm: l = 2n; hk00: h + k = 2n
34.1	Pnn2	(mm2, 111)	9	Pnn2(00γ)	0klm: k + l = 2n; h0lm: h + l = 2n
34.2			9	Pnn2(00γ)s0s	0klm: k + l + m = 2n; h0lm: h + l = 2n
34.3			11	Pnn2( $[{{1}\over{2}}{{1}\over{2}}]$ γ)qq0	0KLm: 2K + 2L + m = 4n; H0Lm: 2H + 2L + m = 4n
34.4		(2mm, $[{\bar 1}1{\bar 1}]$ )	9	P2nn(00γ)	h0lm: h + l = 2n; hk00: h + k = 2n
34.5			11	P2nn( $[{{1}\over{2}}{{1}\over{2}}]$ γ)0q0	H0Lm: 2H + 2L + m = 4n; HK00: H + K = 2n
35.1	Cmm2	(mm2, 111)	13	Cmm2(00γ)
35.2			13	Cmm2(00γ)s0s	0klm: m = 2n
35.3			13	Cmm2(00γ)ss0	0klm: m = 2n; h0lm: m = 2n
35.4			14	Cmm2(10γ)
35.5			14	Cmm2(10γ)s0s	0KLm: m = 2n
35.6			14	Cmm2(10γ)ss0	0KLm: m = 2n; H0Lm: m = 2n
35.7		(2mm, $[{\bar 1}1{\bar 1}]$ )	15	A2mm(00γ)
35.8			15	A2mm(00γ)0s0	h0lm: m = 2n
35.9			16	A2mm( $[{{1}\over{2}}]$ 0γ)
35.10			16	A2mm( $[{{1}\over{2}}]$ 0γ)0s0	H0Lm: m = 2n
36.1	Cmc2₁	(mm2, 111)	13	Cmc2₁(00γ)
36.2			13	Cmc2₁(00γ)s0s	0klm: m = 2n; h0lm: l = 2n
36.3			14	Cmc2₁(10γ)	H0Lm: L = 2n
36.4			14	Cmc2₁(10γ)s0s	0KLm: m = 2n; H0Lm: L = 2n
36.5		(2mm, $[{\bar 1}1{\bar 1}]$ )	15	A2₁am(00γ)	h0lm: h = 2n
36.6			15	A2₁am(00γ)0s0	h0lm: h + m = 2n
36.7			15	A2₁ma(00γ)	hk00: h = 2n
36.8			15	A2₁ma(00γ)0s0	h0lm: m = 2n; hk00: h = 2n
37.1	Ccc2	(mm2, 111)	13	Ccc2(00γ)	0klm: l = 2n; h0lm: l = 2n
37.2			13	Ccc2(00γ)s0s	0klm: l + m = 2n; h0lm: l = 2n
37.3			14	Ccc2(10γ)	0KLm: L = 2n; H0Lm: L = 2n
37.4			14	Ccc2(10γ)s0s	0KLm: L + m = 2n; H0Lm: L = 2n
37.5		(2mm, $[{\bar 1}1{\bar 1}]$ )	15	A2aa(00γ)	h0lm: h = 2n; hk00: h = 2n
37.6			15	A2aa(00γ)0s0	h0lm: h + m = 2n; hk00: h = 2n
38.1	C2mm	(2mm, $[{\bar 1}1{\bar 1}]$ )	13	C2mm(00γ)
38.2			13	C2mm(00γ)0s0	h0lm: m = 2n
38.3			14	C2mm(10γ)
38.4			14	C2mm(10γ)0s0	H0Lm: m = 2n
38.5		(mm2, 111)	15	Amm2(00γ)
38.6			15	Amm2(00γ)s0s	0klm: m = 2n
38.7			15	Amm2(00γ)ss0	0klm: m = 2n; h0lm: m = 2n
38.8			15	Amm2(00γ)0ss	h0lm: m = 2n
38.9			16	Amm2( $[{{1}\over{2}}]$ 0γ)
38.10			16	Amm2( $[{{1}\over{2}}]$ 0γ)0ss	H0Lm: m = 2n
38.11		(m2m, $[1{\bar 1}{\bar 1}]$ )	15	Am2m(00γ)
38.12			15	Am2m(00γ)s00	0klm: m = 2n
38.13			16	Am2m( $[{{1}\over{2}}]$ 0γ)
39.1	C2mb	(2mm, $[{\bar 1}1{\bar 1}]$ )	13	C2mb(00γ)	hk00: k = 2n
39.2			13	C2mb(00γ)0s0	h0lm: m = 2n; hk00: k = 2n
39.3			14	C2mb(10γ)	HK00: K = 2n
39.4			14	C2mb(10γ)0s0	H0Lm: m = 2n; HK00: K = 2n
39.5		(mm2, 111)	15	Abm2(00γ)	0klm: k = 2n
39.6			15	Abm2(00γ)s0s	0klm: k + m = 2n
39.7			15	Abm2(00γ)ss0	0klm: k + m = 2n; h0lm: m = 2n
39.8			15	Abm2(00γ)0ss	0klm: k = 2n; h0lm: m = 2n
39.9			16	Abm2( $[{{1}\over{2}}]$ 0γ)	0KLm: K = 2n
39.10			16	Abm2( $[{{1}\over{2}}]$ 0γ)0ss	0KLm: K + m = 2n
39.11		(m2m, $[1{\bar 1}{\bar 1}]$ )	15	Ac2m(00γ)	0klm: l = 2n
39.12			15	Ac2m(00γ)s00	0klm: l + m = 2n
39.13			16	Ac2m( $[{{1}\over{2}}]$ 0γ)	0KLm: L = 2n
40.1	C2cm	(2mm, $[{\bar 1}1{\bar 1}]$ )	13	C2cm(00γ)	h0lm: l = 2n
40.2			14	C2cm(10γ)	H0Lm: L = 2n
40.3		(mm2, 111)	15	Ama2(00γ)	h0lm: h = 2n
40.4			15	Ama2(00γ)s0s	0klm: m = 2n; h0lm: h = 2n
40.5			15	Ama2(00γ)ss0	0klm: m = 2n; h0lm: h + m = 2n
40.6			15	Ama2(00γ)0ss	h0lm: h + m = 2n
40.7		(m2m, $[1{\bar 1}{\bar 1}]$ )	15	Am2a(00γ)	hk00: h = 2n
40.8			15	Am2a(00γ)s00	0klm: m = 2n; hk00: h = 2n
41.1	C2cb	(2mm, $[{\bar 1}1{\bar 1}]$ )	13	C2cb(00γ)	h0lm: l = 2n; hk00: k = 2n
41.2			14	C2cb(10γ)	H0Lm: L = 2n; HK00: K = 2n
41.3		(mm2, 111)	15	Aba2(00γ)	0klm: k = 2n; h0lm: h = 2n
41.4			15	Aba2(00γ)s0s	0klm: k + m = 2n; h0lm: h = 2n
41.5			15	Aba2(00γ)ss0	0klm: k + m = 2n; h0lm: h + m = 2n
41.6			15	Aba2(00γ)0ss	0klm: k = 2n; h0lm: h + m = 2n
41.7		(m2m, $[1{\bar 1}{\bar 1}]$ )	15	Ac2a(00γ)	0klm: l = 2n; hk00: h = 2n
41.8			15	Ac2a(00γ)s00	0klm: l + m = 2n; hk00: h = 2n
42.1	Fmm2	(mm2, 111)	17	Fmm2(00γ)
42.2			17	Fmm2(00γ)s0s	0klm: m = 2n
42.3			17	Fmm2(00γ)ss0	0klm: m = 2n; h0lm: m = 2n
42.4			18	Fmm2(10γ)
42.5			18	Fmm2(10γ)s0s	0KLm: m = 2n
42.6			18	Fmm2(10γ)ss0	0KLm: m = 2n; H0Lm: m = 2n
42.7		(2mm, $[{\bar 1}1{\bar 1}]$ )	17	F2mm(00γ)
42.8			17	F2mm(00γ)0s0	h0lm: m = 2n
42.9			18	F2mm(10γ)
42.10			18	F2mm(10γ)0s0	H0Lm: m = 2n
43.1	Fdd2	(mm2, 111)	17	Fdd2(00γ)	0klm: k + l = 4n
43.2			17	Fdd2(00γ)s0s	0klm: k + l + 2m = 4n; h0lm: h + l = 4n
43.3		(2mm, $[{\bar 1}1{\bar 1}]$ )	17	F2dd(00γ)	h0lm: h + l = 4n
44.1	Imm2	(mm2, 111)	12	Imm2(00γ)
44.2			12	Imm2(00γ)s0s	0klm: m = 2n
44.3			12	Imm2(00γ)ss0	0klm: m = 2n; h0lm: m = 2n
44.4		(2mm, $[{\bar 1}1{\bar 1}]$ )	12	I2mm(00γ)
44.5			12	I2mm(00γ)0s0	h0lm: m = 2n
45.1	Iba2	(mm2, 111)	12	Iba2(00γ)	0klm: k = 2n; h0lm: h = 2n
45.2			12	Iba2(00γ)s0s	0klm: k + m = 2n; h0lm: h = 2n
45.3			12	Iba2(00γ)ss0	0klm: k + m = 2n; h0lm: h + m = 2n
45.4		(2mm, $[{\bar 1}1{\bar 1}]$ )	12	I2cb(00γ)	h0lm: l = 2n; hk00: k = 2n
45.5			12	I2cb(00γ)0s0	h0lm: l + m = 2n; hk00: k = 2n
46.1	Ima2	(mm2, 111)	12	Ima2(00γ)	h0lm: h = 2n
46.2			12	Ima2(00γ)s0s	0klm: m = 2n; h0lm: h = 2n
46.3			12	Ima2(00γ)ss0	0klm: m = 2n; h0lm: h + m = 2n
46.4			12	Ima2(00γ)0ss	h0lm: h + m = 2n
46.5		(2mm, $[{\bar 1}1{\bar 1}]$ )	12	I2mb(00γ)	hk00: k = 2n
46.6			12	I2mb(00γ)0s0	h0lm: m = 2n; hk00: k = 2n
46.7			12	I2cm(00γ)	h0lm: l = 2n
46.8			12	I2cm(00γ)0s0	h0lm: l + m = 2n
47.1	Pmmm	(mmm, $[11{\bar 1}]$ )	9	Pmmm(00γ)
47.2			9	Pmmm(00γ)s00	0klm: m = 2n
47.3			9	Pmmm(00γ)ss0	0klm: m = 2n; h0lm: m = 2n
47.4			10	Pmmm(0 $[{{1}\over{2}}]$ γ)
47.5			10	Pmmm(0 $[{{1}\over{2}}]$ γ)s00	0KLm: m = 2n
47.6			11	Pmmm( $[{{1}\over{2}}{{1}\over{2}}]$ γ)
48.1	Pnnn	(mmm, $[11{\bar 1}]$ )	9	Pnnn(00γ)	0klm: k + l = 2n; h0lm: h + l = 2n; hk00: h + k = 2n
48.2			9	Pnnn(00γ)s00	0klm: k + l + m = 2n; h0lm: h + l = 2n; hk00: h + k = 2n
48.3			11	Pnnn( $[{{1}\over{2}}{{1}\over{2}}]$ γ)qq0	0KLm: 2K + 2L + m = 4n; H0Lm: 2H + 2L + m = 2n; HK00: H + K = 2n
49.1	Pccm	(mmm, $[11{\bar 1}]$ )	9	Pccm(00γ)	0klm: l = 2n; h0lm: l = 2n
49.2			9	Pccm(00γ)s00	0klm: l + m = 2n; h0lm: l = 2n
49.3			9	Pmaa(00γ)	h0lm: h = 2n; hk00: h = 2n
49.4			9	Pmaa(00γ)s00	0klm: m = 2n; h0lm: h = 2n; hk00: h = 2n
49.5			9	Pmaa(00γ)ss0	0klm: m = 2n; h0lm: h + m = 2n; hk00: h = 2n
49.6			9	Pmaa(00γ)0s0	h0lm: h + m = 2n; hk00: h = 2n
49.7			10	Pccm(0 $[{{1}\over{2}}]$ γ)	0KLm: L = 2n; H0Lm: L = 2n
49.8			10	Pmaa(0 $[{{1}\over{2}}]$ γ)	H0Lm: H = 2n; HK00: H = 2n
49.9			10	Pmaa(0 $[{{1}\over{2}}]$ γ)s00	0KLm: m = 2n; H0Lm: H = 2n; HK00: H = 2n
49.10			11	Pccm ( $[{{1}\over{2}}{{1}\over{2}}]$ γ)	0KLm: L = 2n; H0Lm: L = 2n
50.1	Pban	(mmm, $[11{\bar 1}]$ )	9	Pban(00γ)	0klm: k = 2n; h0lm: h = 2n
50.2			9	Pban(00γ)s00	0klm: k + m = 2n; h0lm: h = 2n
50.3			9	Pban(00γ)ss0	0klm: k + m = 2n; h0lm: h + m = 2n
50.4			9	Pcna(00γ)	0klm: l = 2n; h0lm: h + l = 2n; hk00: h = 2n
50.5			9	Pcna(00γ)s00	0klm: l + m = 2n; h0lm: h + l = 2n; hk00: h = 2n
50.6			10	Pcna(0 $[{{1}\over{2}}]$ γ)	0KLm: L = 2n; H0Lm: H + L = 2n; HK00: H = 2n
50.7			11	Pban( $[{{1}\over{2}}{{1}\over{2}}]$ γ)qq0	0KLm: 2K + m = 4n; H0Lm: 2H + m = 4n; HK00: H + K = 2n
51.1	Pmma	(mmm, $[11{\bar 1}]$ )	9	Pmma(00γ)	hk00: h = 2n
51.2			9	Pmma(00γ)s00	0klm: m = 2n; hk00: h = 2n
51.3			9	Pmma(00γ)ss0	0klm: m = 2n; h0lm: m = 2n; hk00: h = 2n
51.4			9	Pmma(00γ)0s0	h0lm: m = 2n; hk00: h = 2n
51.5			9	Pmam(00γ)	h0lm: h = 2n
51.6			9	Pmam(00γ)s00	0klm: m = 2n; h0lm: h = 2n
51.7			9	Pmam(00γ)ss0	0klm: m = 2n; h0lm: h + m = 2n
51.8			9	Pmam(00γ)0s0	h0lm: h + m = 2n
51.9			9	Pmcm(00γ)	h0lm: l = 2n
51.10			9	Pmcm(00γ)s00	0klm: m = 2n; h0lm: l = 2n
51.11			10	Pmma(0 $[{{1}\over{2}}]$ γ)	HK00: H = 2n
51.12			10	Pmma(0 $[{{1}\over{2}}]$ γ)s00	0KLm: m = 2n; HK00: H = 2n
51.13			10	Pmam(0 $[{{1}\over{2}}]$ γ)	H0Lm: H = 2n
51.14			10	Pmam(0 $[{{1}\over{2}}]$ γ)s00	0KLm: m = 2n; H0Lm: H = 2n
51.15			10	Pmcm(0 $[{{1}\over{2}}]$ γ)	H0Lm: L = 2n
51.16			10	Pmcm(0 $[{{1}\over{2}}]$ γ)s00	0KLm: m = 2n; H0Lm: L = 2n
51.17			10	Pcmm(0 $[{{1}\over{2}}]$ γ)	0KLm: L = 2n
51.18			11	Pcmm( $[{{1}\over{2}}{{1}\over{2}}]$ γ)	0KLm: L = 2n
52.1	Pnna	(mmm, $[11{\bar 1}]$ )	9	Pnna(00γ)	0klm: k + l = 2n; h0lm: h + l = 2n; hk00: h = 2n
52.2			9	Pnna(00γ)s00	0klm: k + l + m = 2n; h0lm: h + l = 2n; hk00: h = 2n
52.3			9	Pbnn(00γ)	0klm: k = 2n; h0lm: h + l = 2n; hk00: h + k = 2n
52.4			9	Pbnn(00γ)s00	0klm: k + m = 2n; h0lm: h + l = 2n; hk00: h + k = 2n
52.5			9	Pcnn(00γ)	0klm: l = 2n; h0lm: h + l = 2n; hk00: h + k = 2n
52.6			9	Pcnn(00γ)s00	0klm: l + m = 2n; h0lm: h + l = 2n; hk00: h + k = 2n
52.7			11	Pbnn( $[{{1}\over{2}}{{1}\over{2}}]$ γ)qq0	0KLm: 2K + m = 4n; H0Lm: 2H + 2L + m = 4n; HK00: H + K = 2n
53.1	Pmna	(mmm, $[11{\bar 1}]$ )	9	Pmna(00γ)	h0lm: h + l = 2n; hk00: h = 2n
53.2			9	Pmna(00γ)s00	0klm: m = 2n; h0lm: h + l = 2n; hk00: h = 2n
53.3			9	Pcnm(00γ)	0klm: l = 2n; h0lm: h + l = 2n
53.4			9	Pcnm(00γ)s00	0klm: l + m = 2n; h0lm: h + l = 2n
53.5			9	Pbmn(00γ)	0klm: k = 2n; hk00: h + k = 2n
53.6			9	Pbmn(00γ)s00	0klm: k + m = 2n; hk00: h + k = 2n
53.7			9	Pbmn(00γ)ss0	0klm: k + m = 2n; h0lm: m = 2n; hk00: h + k = 2n
53.8			9	Pbmn(00γ)0s0	0klm: k = 2m; h0lm: m = 2n; hk00: h + k = 2n
53.9			10	Pmna(0 $[{{1}\over{2}}]$ γ)	H0Lm: H + L = 2n; HK00: H = 2n
53.10			10	Pmna(0 $[{{1}\over{2}}]$ γ)s00	0KLm: m = 2n; H0Lm: H + L = 2n; HK00: H = 2n
53.11			10	Pcnm(0 $[{{1}\over{2}}]$ γ)	0KLm: L = 2n; H0Lm: H + L = 2n
54.1	Pcca	(mmm, $[11{\bar 1}]$ )	9	Pcca(00γ)	0klm: l = 2n; h0lm: l = 2n; hk00: h = 2n
54.2			9	Pcca(00γ)s00	0klm: l + m = 2n; h0lm: l = 2n; hk00: h = 2n
54.3			9	Pcaa(00γ)	0klm: l = 2n; h0lm: h = 2n; hk00: h = 2n
54.4			9	Pcaa(00γ)0s0	0klm: l = 2n; h0lm: h + m = 2n; hk00: h = 2n
54.5			9	Pbab(00γ)	0klm: k = 2n; h0lm: h = 2n; hk00: k = 2n
54.6			9	Pbab(00γ)s00	0klm: k + m = 2n; h0lm: h = 2n; hk00: k = 2n
54.7			9	Pbab(00γ)ss0	0klm: k + m = 2n; h0lm: h + m = 2n; hk00: k = 2n
54.8			9	Pbab(00γ)0s0	0klm: k = 2n; h0lm: h + m = 2n; hk00: k = 2n
54.9			10	Pcca(0 $[{{1}\over{2}}]$ γ)	0KLm: L = 2n; H0Lm: L = 2n; HK00: H = 2n
54.10			10	Pcaa(0 $[{{1}\over{2}}]$ γ)	0KLm: L = 2n; H0Lm: H = 2n; HK00: H = 2n
55.1	Pbam	(mmm, $[11{\bar 1}]$ )	9	Pbam(00γ)	0klm: k = 2n; h0lm: h = 2n
55.2			9	Pbam(00γ)s00	0klm: k + m = 2n; h0lm: h = 2n
55.3			9	Pbam(00γ)ss0	0klm: k + m = 2n; h0lm: h + m = 2n
55.4			9	Pcma(00γ)	0klm: l = 2n; hk00: h = 2n
55.5			9	Pcma(00γ)0s0	0klm: l = 2n; h0lm: m = 2n; hk00: h = 2n
55.6			10	Pcma(0 $[{{1}\over{2}}]$ γ)	0KLm: L = 2n; HK00: H = 2n
56.1	Pccn	(mmm, $[11{\bar 1}]$ )	9	Pccn(00γ)	0klm: l = 2n; h0lm: l = 2n; hk00: h + k = 2n
56.2			9	Pccn(00γ)s00	0klm: l + m = 2n; h0lm: l = 2n; hk00: h + k = 2n
56.3			9	Pbnb(00γ)	0klm: k = 2n; h0lm: h + l = 2n; hk00: k = 2n
56.4			9	Pbnb(00γ)s00	0klm: k + m = 2n; h0lm: h + l = 2n; hk00: k = 2n
57.1	Pcam	(mmm, $[11{\bar 1}]$ )	9	Pcam(00γ)	0klm: l = 2n; h0lm: h = 2n
57.2			9	Pcam(00γ)0s0	0klm: l = 2n; h0lm: h + m = 2n
57.3			9	Pmca(00γ)	h0lm: l = 2n; hk00: h = 2n
57.4			9	Pmca(00γ)s00	0klm: m = 2n; h0lm: l = 2n; hk00: h = 2n
57.5			9	Pbma(00γ)	0klm: k = 2n; hk00: h = 2n
57.6			9	Pbma(00γ)s00	0klm: k + m = 2n; hk00: h = 2n
57.7			9	Pbma(00γ)ss0	0klm: k + m = 2n; h0lm: m = 2n; hk00: h = 2n
57.8			9	Pbma(00γ)0s0	0klm: k = 2n; h0lm: m = 2n; hk00: h = 2n
57.9			10	Pcam(0 $[{{1}\over{2}}]$ γ)	0KLm: L = 2n; H0Lm: H = 2n
57.10			10	Pmca(0 $[{{1}\over{2}}]$ γ)	H0Lm: L = 2n; HK00: H = 2n
57.11			10	Pmca(0 $[{{1}\over{2}}]$ γ)s00	0KLm: m = 2n; H0Lm: L = 2n; HK00: H = 2n
58.1	Pnnm	(mmm, $[11{\bar 1}]$ )	9	Pnnm(00γ)	0klm: k + l = 2n; h0lm: h + l = 2n
58.2			9	Pnnm(00γ)s00	0klm: k + l + m = 2n; h0lm: h + l = 2n
58.3			9	Pmnn(00γ)	h0lm: h + l = 2n; hk00: h + k = 2n
58.4			9	Pmnn(00γ)s00	0klm: m = 2n; h0lm: h + l = 2n; hk00: h + k = 2n
59.1	Pmmn	(mmm, $[11{\bar 1}]$ )	9	Pmmn(00γ)	hk00: h + k = 2n
59.2			9	Pmmn(00γ)s00	0klm: m = 2n; hk00: h + k = 2n
59.3			9	Pmmn(00γ)ss0	0klm: m = 2n; h0lm: m = 2n; hk00: h + k = 2n
59.4			9	Pmnm(00γ)	h0lm: h + l = 2n
59.5			9	Pmnm(00γ)s00	0klm: m = 2n; h0lm: h + l = 2n
59.6			10	Pmnm(0 $[{{1}\over{2}}]$ γ)	H0Lm: H + L = 2n
59.7			10	Pmnm(0 $[{{1}\over{2}}]$ γ)s00	0KLm: m = 2n; H0Lm: H + L = 2n
60.1	Pbcn	(mmm, $[11{\bar 1}]$ )	9	Pbcn(00γ)	0klm: k = 2n; h0lm: l = 2n; hk00: h + k = 2n
60.2			9	Pbcn(00γ)s00	0klm: k + m = 2n; h0lm: l = 2n; hk00: h + k = 2n
60.3			9	Pnca(00γ)	0klm: k + l = 2n; h0lm: l = 2n; hk00: h = 2n
60.4			9	Pnca(00γ)s00	0klm: k + l + m = 2n; h0lm: l = 2n; hk00: h = 2n
60.5			9	Pbna(00γ)	0klm: k = 2n; h0lm: h + l = 2n; hk00: h = 2n
60.6			9	Pbna(00γ)s00	0klm: k + m = 2n; h0lm: h + l = 2n; hk00: h = 2n
61.1	Pbca	(mmm, $[11{\bar 1}]$ )	9	Pbca(00γ)	0klm: k = 2n; h0lm: l = 2n; hk00: h = 2n
61.2			9	Pbca(00γ)s00	0klm: k + m = 2n; h0lm: l = 2n; hk00: h = 2n
62.1	Pnma	(mmm, $[11{\bar 1}]$ )	9	Pnma(00γ)	0klm: k + l = 2n; hk00: h = 2n
62.2			9	Pnma(00γ)0s0	0klm: k + l = 2n; h0lm: m = 2n; hk00: h = 2n
62.3			9	Pbnm(00γ)	0klm: k = 2n; h0lm: h + l = 2n
62.4			9	Pbnm(00γ)s00	0klm: k + m = 2n; h0lm: h + l = 2n
62.5			9	Pmcn(00γ)	h0lm: l = 2n; hk00: h + k = 2n
62.6			9	Pmcn(00γ)s00	0klm: m = 2n; h0lm: l = 2n; hk00: h + k = 2n
63.1	Cmcm	(mmm, $[11{\bar 1}]$ )	13	Cmcm(00γ)	h0lm: l = 2n
63.2			13	Cmcm(00γ)s00	0klm: m = 2n; h0lm: l = 2n
63.3			14	Cmcm(10γ)	H0Lm: L = 2n
63.4			14	Cmcm(10γ)s00	0KLm: m = 2n; H0Lm: L = 2n
63.5			15	Amam(00γ)	h0lm: h = 2n
63.6			15	Amam(00γ)s00	0klm: m = 2n; h0lm: h = 2n
63.7			15	Amam(00γ)ss0	0klm: m = 2n; h0lm: h + m = 2n
63.8			15	Amam(00γ)0s0	h0lm: h + m = 2n
63.9			15	Amma(00γ)	hk00: h = 2n
63.10			15	Amma(00γ)s00	0klm: m = 2n; hk00: h = 2n
63.11			15	Amma(00γ)ss0	0klm: m = 2n; h0lm: m = 2n; hk00: h = 2n
63.12			15	Amma(00γ)0s0	h0lm: m = 2n; hk00: h = 2n
64.1	Cmca	(mmm, $[11{\bar 1}]$ )	13	Cmca(00γ)	h0lm: l = 2n; hk00: h = 2n
64.2			13	Cmca(00γ)s00	0klm: m = 2n; h0lm: l = 2n; hk00: h = 2n
64.3			14	Cmca(10γ)	H0Lm: L = 2n; HK00: H = 2n
64.4			14	Cmca(10γ)s00	0KLm: m = 2n; H0Lm: L = 2n; HK00: H = 2n
64.5			15	Abma(00γ)	0klm: k = 2n; hk00: h = 2n
64.6			15	Abma(00γ)s00	0klm: k + m = 2n; hk00: h = 2n
64.7			15	Abma(00γ)ss0	0klm: k + m = 2n; h0lm: m = 2n; hk00: h = 2n
64.8			15	Abma(00γ)0s0	0klm: k = 2n; h0lm: m = 2n; hk00: h = 2n
64.9			15	Acam(00γ)	0klm: l = 2n; h0lm: h = 2n
64.10			15	Acam(00γ)s00	0klm: l + m = 2n; h0lm: h = 2n
64.11			15	Acam(00γ)ss0	0klm: l + m = 2n; h0lm: h + m = 2n
64.12			15	Acam(00γ)0s0	0klm: l = 2n; h0lm: h + m = 2n
65.1	Cmmm	(mmm, $[11{\bar 1}]$ )	13	Cmmm(00γ)
65.2			13	Cmmm(00γ)s00	0klm: m = 2n
65.3			13	Cmmm(00γ)ss0	0klm: m = 2n; h0lm: m = 2n
65.4			14	Cmmm(10γ)
65.5			14	Cmmm(10γ)s00	0KLm: m = 2n
65.6			14	Cmmm(10γ)ss0	0KLm: m = 2n; H0Lm: m = 2n
65.7			15	Ammm(00γ)
65.8			15	Ammm(00γ)s00	0klm: m = 2n
65.9			15	Ammm(00γ)ss0	0klm: m = 2n; h0lm: m = 2n
65.10			15	Ammm(00γ)0s0	h0lm: m = 2n
65.11			16	Ammm( $[{{1}\over{2}}]$ 0γ)
65.12			16	Ammm( $[{{1}\over{2}}]$ 0γ)0s0	H0Lm: m = 2n
66.1	Cccm	(mmm, $[11{\bar 1}]$ )	13	Cccm(00γ)	0klm: l = 2n; h0lm: l = 2n
66.2			13	Cccm(00γ)s00	0klm: l + m = 2n; h0lm: l = 2n
66.3			14	Cccm(10γ)	0KLm: L = 2n; H0Lm: L = 2n
66.4			14	Cccm(10γ)s00	0KLm: L + m = 2n; H0Lm: L = 2n
66.5			15	Amaa(00γ)	h0lm: h = 2n; hk00: h = 2n
66.6			15	Amaa(00γ)s00	0klm: m = 2n; h0lm: h = 2n; hk00: h = 2n
66.7			15	Amaa(00γ)ss0	0klm: m = 2n; h0lm: h + m = 2n; hk00: h = 2n
66.8			15	Amaa(00γ)0s0	h0lm: h + m = 2n; hk00: h = 2n
67.1	Cmma	(mmm, $[11{\bar 1}]$ )	13	Cmma(00γ)	hk00: h = 2n
67.2			13	Cmma(00γ)s00	0klm: m = 2n; hk00: h = 2n
67.3			13	Cmma(00γ)ss0	0klm: m = 2n; h0lm: m = 2n; hk00: h = 2n
67.4			14	Cmma(10γ)	HK00: H = 2n
67.5			14	Cmma(10γ)s00	0KLm: m = 2n; HK00: H = 2n
67.6			14	Cmma(10γ)ss0	0KLm: m = 2n; H0Lm: m = 2n; HK00: H = 2n
67.7			15	Acmm(00γ)	0klm: l = 2n
67.8			15	Acmm(00γ)s00	0klm: l + m = 2n
67.9			15	Acmm(00γ)ss0	0klm: l + m = 2n; h0lm: m = 2n
67.10			15	Acmm(00γ)0s0	0klm: l = 2n; h0lm: m = 2n
67.11			16	Acmm( $[{{1}\over{2}}]$ 0γ)	0KLm: L = 2n
67.12			16	Acmm( $[{{1}\over{2}}]$ 0γ)0s0	0KLm: L = 2n; H0Lm: m = 2n
68.1	Ccca	(mmm, $[11{\bar 1}]$ )	13	Ccca(00γ)	0klm: l = 2n; h0lm: l = 2n; hk00: h = 2n
68.2			13	Ccca(00γ)s00	0klm: l + m = 2n; h0lm: l = 2n; hk00: h = 2n
68.3			14	Ccca(10γ)	0KLm: L = 2n; H0Lm: L = 2n; HK00: H = 2n
68.4			14	Ccca(10γ)s00	0KLm: L + m = 2n; H0Lm: L = 2n; HK00: H = 2n
68.5			15	Acaa(00γ)	0klm: l = 2n; h0lm: h = 2n; hk00: h = 2n
68.6			15	Acaa(00γ)s00	0klm: l + m = 2n; h0lm: h = 2n; hk00: h = 2n
68.7			15	Acaa(00γ)ss0	0klm: l + m = 2n; h0lm: h + m = 2n; hk00: h = 2n
68.8			15	Acaa(00γ)0s0	0klm: l = 2n; h0lm: h + m = 2n; hk00: h = 2n
69.1	Fmmm	(mmm, $[11{\bar 1}]$ )	17	Fmmm(00γ)
69.2			17	Fmmm(00γ)s00	0klm: m = 2n
69.3			17	Fmmm(00γ)ss0	0klm: m = 2n; h0lm: m = 2n
69.4			18	Fmmm(10γ)
69.5			18	Fmmm(10γ)s00	0KLm: m = 2n
69.6			18	Fmmm(10γ)ss0	0KLm: m = 2n; H0Lm: m = 2n
70.1	Fddd	(mmm, $[11{\bar 1}]$ )	17	Fddd(00γ)	0klm: k + l = 4n; h0lm: h + l = 4n; hk00: h + k = 4n
70.2			17	Fddd(00γ)s00	0klm: k + l + 2m = 4n; h0lm: h + l = 4n; hk00: h + k = 4n
71.1	Immm	(mmm, $[11{\bar 1}]$ )	12	Immm(00γ)
71.2			12	Immm(00γ)s00	0klm: m = 2n
71.3			12	Immm(00γ)ss0	0klm: m = 2n; h0lm: m = 2n
72.1	Ibam	(mmm, $[11{\bar 1}]$ )	12	Ibam(00γ)	0klm: k = 2n; h0lm: h = 2n
72.2			12	Ibam(00γ)s00	0klm: k + m = 2n; h0lm: h = 2n
72.3			12	Ibam(00γ)ss0	0klm: k + m = 2n; h0lm: h + m = 2n
72.4			12	Imcb(00γ)	h0lm: l = 2n; hk00: k = 2n
72.5			12	Imcb(00γ)s00	0klm: m = 2n; h0lm: l = 2n; hk00: k = 2n
72.6			12	Imcb(00γ)ss0	0klm: m = 2n; h0lm: l + m = 2n; hk00: k = 2n
72.7			12	Imcb(00γ)0s0	h0lm: l + m = 2n; hk00: k = 2n
73.1	Ibca	(mmm, $[11{\bar 1}]$ )	12	Ibca(00γ)	0klm: k = 2n; h0lm: l = 2n; hk00: h = 2n
73.2			12	Ibca(00γ)s00	0klm: k + m = 2n; h0lm: l = 2n; hk00: h = 2n
73.3			12	Ibca(00γ)ss0	0klm: k + m = 2n; h0lm: l + m = 2n; hk00: h = 2n
74.1	Imma	(mmm, $[11{\bar 1}]$ )	12	Imma(00γ)	hk00: h = 2n
74.2			12	Imma(00γ)s00	0klm: m = 2n; hk00: h = 2n
74.3			12	Imma(00γ)ss0	0klm: m = 2n; h0lm: m = 2n; hk00: h = 2n
74.4			12	Icmm(00γ)	0klm: l = 2n
74.5			12	Icmm(00γ)s00	0klm: l + m = 2n
74.6			12	Icmm(00γ)ss0	0klm: l + m = 2n; h0lm: m = 2n
74.7			12	Icmm(00γ)0s0	0klm: l = 2n; h0lm: m = 2n
75.1	P4	(4, 1)	19	P4(00γ)
75.2			19	P4(00γ)q	00lm: m = 4n
75.3			19	P4(00γ)s	00lm: m = 2n
75.4			20	P4( $[{{1}\over{2}}{{1}\over{2}}]$ γ)
75.5			20	P4( $[{{1}\over{2}}{{1}\over{2}}]$ γ)q	00Lm: m = 4n
76.1	P4₁	(4, 1)	19	P4₁(00γ)	00lm: l = 4n
76.2			20	P4₁( $[{{1}\over{2}}{{1}\over{2}}]$ γ)	00Lm: L = 4n
77.1	P4₂	(4, 1)	19	P4₂(00γ)	00lm: l = 2n
77.2			19	P4₂(00γ)q	00lm: 2l + m = 4n
77.3			20	P4₂( $[{{1}\over{2}}{{1}\over{2}}]$ γ)	00Lm: L = 2n
77.4			20	P4₂( $[{{1}\over{2}}{{1}\over{2}}]$ γ)q	00Lm: 2L + m = 4n
78.1	P4₃	(4, 1)	19	P4₃(00γ)	00lm: l = 4n
78.2			20	P4₃( $[{{1}\over{2}}{{1}\over{2}}]$ γ)	00Lm: L = 4n
79.1	I4	(4, 1)	21	I4(00γ)
79.2			21	I4(00γ)q	00lm: m = 4n
79.3			21	I4(00γ)s	00lm: m = 2n
80.1	I4₁	(4, 1)	21	I4₁(00γ)	00lm: l = 4n
80.2			21	I4₁(00γ)q	00lm: l + m = 4n
81.1	$[P{\bar 4}]$	( $[{\bar 4}]$ , $[{\bar 1}]$ )	19	P $[{\bar 4}]$ (00γ)
81.2			20	P $[{\bar 4}]$ ( $[{{1}\over{2}}{{1}\over{2}}]$ γ)
82.1	$[I{\bar 4}]$	( $[{\bar 4}]$ , $[{\bar 1}]$ )	21	I $[{\bar 4}]$ (00γ)
83.1	P4/m	(4/m, $[1{\bar 1}]$ )	19	P4/m(00γ)
83.2			19	P4/m(00γ)s0	00lm: m = 2n
83.3			20	P4/m( $[{{1}\over{2}}{{1}\over{2}}]$ γ)
84.1	P4₂/m	(4/m, $[1{\bar 1}]$ )	19	P4₂/m(00γ)	00lm: l = 2n
84.2			20	P4₂/m( $[{{1}\over{2}}{{1}\over{2}}]$ γ)	00Lm: L = 2n
85.1	P4/n	(4/m, $[1{\bar 1}]$ )	19	P4/n(00γ)	hk00: h + k = 2n
85.2			19	P4/n(00γ)s0	00lm: m = 2n; hk00: h + k = 2n
85.3			20	P4/n( $[{{1}\over{2}}{{1}\over{2}}]$ γ)q0	00Lm: m = 4n; HK00: H = 2n, K = 2n
86.1	P4₂/n	(4/m, $[1{\bar 1}]$ )	19	P4₂/n(00γ)	00lm: l = 2n; hk00: h + k = 2n
86.2			20	P4₂/n( $[{{1}\over{2}}{{1}\over{2}}]$ γ)q0	00Lm: 2L + m = 4n; HK00: H = 2n, K = 2n
87.1	I4/m	(4/m, $[1{\bar 1}]$ )	21	I4/m(00γ)
87.2			21	I4/m(00γ)s0	00lm: m = 2n
88.1	I4₁/a	(4/m, $[1{\bar 1}]$ )	21	I4₁/a(00γ)	00lm: l = 4n; hk00: h = 2n
89.1	P422	(422, $[1{\bar 1}{\bar 1}]$ )	19	P422(00γ)
89.2			19	P422(00γ)q00	00lm: m = 4n
89.3			19	P422(00γ)s00	00lm: m = 2n
89.4			20	P422( $[{{1}\over{2}}{{1}\over{2}}]$ γ)
89.5			20	P422( $[{{1}\over{2}}{{1}\over{2}}]$ γ)q00	00Lm: m = 4n
90.1	P42₁2	(422, $[1{\bar 1}{\bar 1}]$ )	19	P42₁2(00γ)	h000: h = 2n
90.2			19	P42₁2(00γ)q00	00lm: m = 4n; h000: h = 2n
90.3			19	P42₁2(00γ)s00	00lm: m = 2n; h000: h = 2n
91.1	P4₁22	(422, $[1{\bar 1}{\bar 1}]$ )	19	P4₁22(00γ)	00lm: l = 4n
91.2			20	P4₁22( $[{{1}\over{2}}{{1}\over{2}}]$ γ)	00Lm: L = 4n
92.1	P4₁2₁2	(422, $[1{\bar 1}{\bar 1}]$ )	19	P4₁2₁2(00γ)	00lm: l = 4n; h000: h = 2n
93.1	P4₂22	(422, $[1{\bar 1}{\bar 1}]$ )	19	P4₂22(00γ)	00lm: l = 2n
93.2			19	P4₂22(00γ)q00	00lm: 2l + m = 4n
93.3			20	P4₂22( $[{{1}\over{2}}{{1}\over{2}}]$ γ)	00Lm: L = 2n
93.4			20	P4₂22( $[{{1}\over{2}}{{1}\over{2}}]$ γ)q00	00Lm: 2L + m = 4n
94.1	P4₂2₁2	(422, $[1{\bar 1}{\bar 1}]$ )	19	P4₂2₁2(00γ)	00lm: l = 2n; h000: h = 2n
94.2			19	P4₂2₁2(00γ)q00	00lm: 2l + m = 4n; h000: h = 2n
95.1	P4₃22	(422, $[1{\bar 1}{\bar 1}]$ )	19	P4₃22(00γ)	00lm: l = 4n
95.2			20	P4₃22( $[{{1}\over{2}}{{1}\over{2}}]$ γ)	00Lm: L = 4n
96.1	P4₃2₁2	(422, $[1{\bar 1}{\bar 1}]$ )	19	P4₃2₁2(00γ)	00lm: l = 4n; h000: h = 2n
97.1	I422	(422, $[1{\bar 1}{\bar 1}]$ )	21	I422(00γ)
97.2			21	I422(00γ)q00	00lm: m = 4n
97.3			21	I422(00γ)s00	00lm: m = 2n
98.1	I4₁22	(422, $[1{\bar 1}{\bar 1}]$ )	21	I4₁22(00γ)	00lm: l = 4n
98.2			21	I4₁22(00γ)q00	00lm: l + m = 4n
99.1	P4mm	(4mm, 111)	19	P4mm(00γ)
99.2			19	P4mm(00γ)ss0	00lm: m = 2n; 0klm: m = 2n
99.3			19	P4mm(00γ)0ss	0klm: m = 2n; hhlm: m = 2n
99.4			19	P4mm(00γ)s0s	00lm: m = 2n; hhlm: m = 2n
99.5			20	P4mm( $[{{1}\over{2}}{{1}\over{2}}]$ γ)
99.6			20	P4mm( $[{{1}\over{2}}{{1}\over{2}}]$ γ)0ss	0KLm: m = 2n; HHLm: m = 2n
100.1	P4bm	(4mm, 111)	19	P4bm(00γ)	0klm: k = 2n
100.2			19	P4bm(00γ)ss0	00lm: m = 2n; 0klm: m = 2n
100.3			19	P4bm(00γ)0ss	0klm: k + m = 2n; hhlm: m = 2n
100.4			19	P4bm(00γ)s0s	00lm: m = 2n; 0klm: k = 2n; hhlm: m = 2n
100.5			20	P4bm( $[{{1}\over{2}}{{1}\over{2}}]$ γ)qq0	00Lm: m = 4n; KKLm: 2K + m = 4n
100.6			20	P4bm( $[{{1}\over{2}}{{1}\over{2}}]$ γ)qqs	00Lm: m = 4n; KKLm: 2K + m = 4n; H0Lm: m = 2n
101.1	P4₂cm	(4mm, 111)	19	P4₂cm(00γ)	00lm: l = 2n; 0klm: l = 2n
101.2			19	P4₂cm(00γ)0ss	00lm: l = 2n; 0klm: l + m = 2n; hhlm: m = 2n
101.3			20	P4₂cm( $[{{1}\over{2}}{{1}\over{2}}]$ γ)	00Lm: L = 2n; HHLm: L = 2n
101.4			20	P4₂cm( $[{{1}\over{2}}{{1}\over{2}}]$ γ)0ss	00Lm: L = 2n; HHLm: L + m = 2n; H0Lm: m = 2n
102.1	P4₂nm	(4mm, 111)	19	P4₂nm(00γ)	00lm: l = 2n; 0klm: k + l = 2n
102.2			19	P4₂nm(00γ)0ss	00lm: l = 2n; 0klm: k + l + m = 2n; hhlm: m = 2n
102.3			20	P4₂nm( $[{{1}\over{2}}{{1}\over{2}}]$ γ)qq0	00Lm: 2L + m = 4n; HHLm: 2H + 2L + m = 4n
102.4			20	P4₂nm( $[{{1}\over{2}}{{1}\over{2}}]$ γ)qqs	00Lm: 2L + m = 4n; HHLm: 2H + 2L + m = 4n; H0Lm: m = 2n
103.1	P4cc	(4mm, 111)	19	P4cc(00γ)	0klm: l = 2n; hhlm: l = 2n
103.2			19	P4cc(00γ)ss0	00lm: m = 2n; 0klm: l + m = 2n; hhlm: l = 2n
103.3			20	P4cc( $[{{1}\over{2}}{{1}\over{2}}]$ γ)	HHLm: L = 2n; H0Lm: L = 2n
104.1	P4nc	(4mm, 111)	19	P4nc(00γ)	0klm: k + l = 2n; hhlm: l = 2n
104.2			19	P4nc(00γ)ss0	00lm: m = 2n; 0klm: k + l + m = 2n; hhlm: l = 2n
104.3			20	P4nc( $[{{1}\over{2}}{{1}\over{2}}]$ γ)qq0	00Lm: m = 4n; HHLm: 2H + 2L + m = 4n; H0Lm: L = 2n
105.1	P4₂mc	(4mm, 111)	19	P4₂mc(00γ)	00lm: l = 2n; hhlm: l = 2n
105.2			19	P4₂mc(00γ)ss0	00lm: l + m = 2n; 0klm: m = 2n; hhlm: l = 2n
105.3			20	P4₂mc( $[{{1}\over{2}}{{1}\over{2}}]$ γ)	00Lm: L = 2n; H0Lm: L = 2n
106.1	P4₂bc	(4mm, 111)	19	P4₂bc(00γ)	00lm: l = 2n; 0klm: k = 2n; hhlm: l = 2n
106.2			19	P4₂bc(00γ)ss0	00lm: l + m = 2n; 0klm: k + m = 2n; hhlm: l = 2n
106.3			20	P4₂bc( $[{{1}\over{2}}{{1}\over{2}}]$ γ)qq0	00Lm: 2L + m = 4n; HHLm: 2H + m = 4n; H0Lm: L = 2n
107.1	I4mm	(4mm, 111)	21	I4mm(00γ)
107.2			21	I4mm(00γ)ss0	00lm: m = 2n; 0klm: m = 2n
107.3			21	I4mm(00γ)0ss	0klm: m = 2n; hhlm: m = 2n
107.4			21	I4mm(00γ)s0s	00lm: m = 2n; hhlm: m = 2n
108.1	I4cm	(4mm, 111)	21	I4cm(00γ)	0klm: l = 2n
108.2			21	I4cm(00γ)ss0	00lm: m = 2n; 0klm: l + m = 2n
108.3			21	I4cm(00γ)0ss	0klm: l + m = 2n; hhlm: m = 2n
108.4			21	I4cm(00γ)s0s	00lm: m = 2n; 0klm: l = 2n; hhlm: m = 2n
109.1	I4₁md	(4mm, 111)	21	I4₁md(00γ)	00lm: l = 4n; hhlm: 2h + l = 4n
109.2			21	I4₁md(00γ)ss0	00lm: l + 2m = 4n; 0klm: m = 2n; hhlm: 2h + l = 4n
110.1	I4₁cd	(4mm, 111)	21	I4₁cd(00γ)	00lm: l = 4n; 0klm: l = 2n; hhlm: 2h + l = 4n
110.2			21	I4₁cd(00γ)ss0	00lm: l + 2m = 4n; 0klm: l + m = 2n; hhlm: 2h + l = 4n
111.1	$[P{\bar 4}2m]$	( $[{\bar 4}2m]$ , $[{\bar 1}{\bar 1}1]$ )	19	P $[{\bar 4}]$ 2m(00γ)
111.2			19	P $[{\bar 4}]$ 2m(00γ)00s	hhlm: m = 2n
111.3			20	P $[{\bar 4}]$ 2m( $[{{1}\over{2}}{{1}\over{2}}]$ γ)
111.4			20	P $[{\bar 4}]$ 2m( $[{{1}\over{2}}{{1}\over{2}}]$ γ)00s	H0Lm: m = 2n
112.1	$[P{\bar 4}2c]$	( $[{\bar 4}2m]$ , $[{\bar 1}{\bar 1}1]$ )	19	P $[{\bar 4}]$ 2c(00γ)	hhlm: l = 2n
112.2			20	P $[{\bar 4}]$ 2c( $[{{1}\over{2}}{{1}\over{2}}]$ γ)	H0Lm: L = 2n
113.1	$[P{\bar 4}2_1m]$	( $[{\bar 4}2m]$ , $[{\bar 1}{\bar 1}1]$ )	19	P $[{\bar 4}]$ 2₁m(00γ)	h000: h = 2n
113.2			19	P $[{\bar 4}]$ 2₁m(00γ)00s	h000: h = 2n; hhlm: m = 2n
114.1	$[P{\bar 4}2_1c]$	( $[{\bar 4}2m]$ , $[{\bar 1}{\bar 1}1]$ )	19	P $[{\bar 4}]$ 2₁c(00γ)	h000: h = 2n; hhlm: l = 2n
115.1	$[P{\bar 4}m2]$	( $[{\bar 4}m2]$ , $[{\bar 1}1{\bar 1}]$ )	19	P $[{\bar 4}]$ m2(00γ)
115.2			19	P $[{\bar 4}]$ m2(00γ)0s0	0klm: m = 2n
115.3			20	P $[{\bar 4}]$ m2( $[{{1}\over{2}}{{1}\over{2}}]$ γ)
116.1	$[P{\bar 4}c2]$	( $[{\bar 4}m2]$ , $[{\bar 1}1{\bar 1}]$ )	19	P $[{\bar 4}]$ c2(00γ)	0klm: l = 2n
116.2			20	P $[{\bar 4}]$ c2( $[{{1}\over{2}}{{1}\over{2}}]$ γ)	HHLm: L = 2n
117.1	$[P{\bar 4}b2]$	( $[{\bar 4}m2]$ , $[{\bar 1}1{\bar 1}]$ )	19	P $[{\bar 4}]$ b2(00γ)	0klm: k = 2n
117.2			19	P $[{\bar 4}]$ b2(00γ)0s0	0klm: k + m = 2n
117.3			20	P $[{\bar 4}]$ b2( $[{{1}\over{2}}{{1}\over{2}}]$ γ)0q0	HHLm: 2H + m = 4n
118.1	$[P{\bar 4}n2]$	( $[{\bar 4}m2]$ , $[{\bar 1}1{\bar 1}]$ )	19	P $[{\bar 4}]$ n2(00γ)	0klm: k + l = 2n
118.2			20	P $[{\bar 4}]$ n2( $[{{1}\over{2}}{{1}\over{2}}]$ γ)0q0	HHLm: 2H + 2L + m = 4n
119.1	$[I{\bar 4}m2]$	( $[{\bar 4}m2]$ , $[{\bar 1}1{\bar 1}]$ )	21	I $[{\bar 4}]$ m2(00γ)
119.2			21	I $[{\bar 4}]$ m2(00γ)0s0	0klm: m = 2n
120.1	$[I{\bar 4}c2]$	( $[{\bar 4}m2]$ , $[{\bar 1}1{\bar 1}]$ )	21	I $[{\bar 4}]$ c2(00γ)	0klm: l = 2n
120.2			21	I $[{\bar 4}]$ c2(00γ)0s0	0klm: l + m = 2n
121.1	$[I{\bar 4}2m]$	( $[{\bar 4}2m]$ , $[{\bar 1}{\bar 1}1]$ )	21	I $[{\bar 4}]$ 2m(00γ)
121.2			21	I $[{\bar 4}]$ 2m(00γ)00s	hhlm: m = 2n
122.1	$[I{\bar 4}2d]$	( $[{\bar 4}2m]$ , $[{\bar 1}{\bar 1}1]$ )	21	I $[{\bar 4}]$ 2d(00γ)	hhlm: 2h + l = 4n
123.1	P4/mmm	(4/mmm, $[1{\bar 1}11]$ )	19	P4/mmm(00γ)
123.2			19	P4/mmm(00γ)s0s0	00lm: m = 2n; 0klm: m = 2n
123.3			19	P4/mmm(00γ)00ss	0klm: m = 2n; hhlm: m = 2n
123.4			19	P4/mmm(00γ)s00s	00lm: m = 2n; hhlm: m = 2n
123.5			20	P4/mmm( $[{{1}\over{2}}{{1}\over{2}}]$ γ)
123.6			20	P4/mmm( $[{{1}\over{2}}{{1}\over{2}}]$ γ)00ss	HHLm: m = 2n; H0Lm: m = 2n
124.1	P4/mcc	(4/mmm, $[1{\bar 1}11]$ )	19	P4/mcc(00γ)	0klm: l = 2n; hhlm: l = 2n
124.2			19	P4/mcc(00γ)s0s0	00lm: m = 2n; 0klm: l + m = 2n; hhlm: l = 2n
124.3			20	P4/mcc( $[{{1}\over{2}}{{1}\over{2}}]$ γ)	HHLm: L = 2n; H0Lm: L = 2n
125.1	P4/nbm	(4/mmm, $[1{\bar 1}11]$ )	19	P4/nbm(00γ)	hk00: h + k = 2n; 0klm: k = 2n
125.2			19	P4/nbm(00γ)s0s0	00lm: m = 2n; hk00: h + k = 2n; 0klm: k + m = 2n
125.3			19	P4/nbm(00γ)00ss	hk00: h + k = 2n; 0klm: k + m = 2n; hhlm: m = 2n
125.4			19	P4/nbm(00γ)s00s	00lm: m = 2n; hk00: h + k = 2n; 0klm: k = 2n; hhlm: m = 2n
125.5			20	P4/nbm( $[{{1}\over{2}}{{1}\over{2}}]$ γ)q0q0	00Lm: m = 4n; HK00: H = 2n, K = 2n; HHLm: 2H + m = 4n
125.6			20	P4/nbm( $[{{1}\over{2}}{{1}\over{2}}]$ γ)q0qs	00Lm: m = 4n; HK00: H = 2n, K = 2n; HHLm: 2H + m = 4n; H0Lm: m = 2n
126.1	P4/nnc	(4/mmm, $[1{\bar 1}11]$ )	19	P4/nnc(00γ)	hk00: h + k = 2n; h0lm: h + l = 2n; hhlm: l = 2n
126.2			19	P4/nnc(00γ)s0s0	00lm: m = 2n; hk00: h + k = 2n; h0lm: h + l + m = 2n; hhlm: l = 2n
126.3			20	P4/nnc( $[{{1}\over{2}}{{1}\over{2}}]$ γ)q0q0	00Lm: m = 4n; HK00: H = 2n, K = 2n; HHLm: 2H + 2L + m = 4n; H0Lm: L = 2n
127.1	P4/mbm	(4/mmm, $[1{\bar 1}11]$ )	19	P4/mbm(00γ)	0klm: k = 2n
127.2			19	P4/mbm(00γ)s0s0	00lm: m = 2n; 0klm: k + m = 2n
127.3			19	P4/mbm(00γ)00ss	0klm: k + m = 2n; hhlm: m = 2n
127.4			19	P4/mbm(00γ)s00s	00lm: m = 2n; 0klm: k = 2n; hhlm: m = 2n
128.1	P4/mnc	(4/mmm, $[1{\bar 1}11]$ )	19	P4/mnc(00γ)	0klm: k + l = 2n; hhlm: l = 2n
128.2			19	P4/mnc(00γ)s0s0	00lm: m = 2n; 0klm: k + l + m = 2n; hhlm: l = 2n
129.1	P4/nmm	(4/mmm, $[1{\bar 1}11]$ )	19	P4/nmm(00γ)	hk00: h + k = 2n
129.2			19	P4/nmm(00γ)s0s0	00lm: m = 2n; hk00: h + k = 2n; 0klm: m = 2n
129.3			19	P4/nmm(00γ)00ss	hk00: h + k = 2n; 0klm: m = 2n; hhlm: m = 2n
129.4			19	P4/nmm(00γ)s00s	00lm: m = 2n; hk00: h + k = 2n; hhlm: m = 2n
130.1	P4/ncc	(4/mmm, $[1{\bar 1}11]$ )	19	P4/ncc(00γ)	hk00: h + k = 2n; 0klm: l = 2n; hhlm: l = 2n
130.2			19	P4/ncc(00γ)s0s0	00lm: m = 2n; hk00: h + k = 2n; 0klm: l + m = 2n; hhlm: l = 2n
131.1	P4₂/mmc	(4/mmm, $[1{\bar 1}11]$ )	19	P4₂/mmc(00γ)	00lm: l = 2n; hhlm: l = 2n
131.2			19	P4₂/mmc(00γ)s0s0	00lm: l + m = 2n; 0klm: m = 2n; hhlm: l = 2n
131.3			20	P4₂/mmc( $[{{1}\over{2}}{{1}\over{2}}]$ γ)	00Lm: L = 2n; H0Lm: L = 2n
132.1	P4₂/mcm	(4/mmm, $[1{\bar 1}11]$ )	19	P4₂/mcm(00γ)	00lm: l = 2n; 0klm: l = 2n
132.2			19	P4₂/mcm(00γ)00ss	00lm: l = 2n; 0klm: l + m = 2n; hhlm: m = 2n
132.3			20	P4₂/mcm( $[{{1}\over{2}}{{1}\over{2}}]$ γ)	00Lm: L = 2n; HHLm: L = 2n
132.4			20	P4₂/mcm( $[{{1}\over{2}}{{1}\over{2}}]$ γ)00ss	00Lm: L = 2n; HHLm: L + m = 2n; H0Lm: m = 2n
133.1	P4₂/nbc	(4/mmm, $[1{\bar 1}11]$ )	19	P4₂/nbc(00γ)	00lm: l = 2n; hk00: h + k = 2n; 0klm: k = 2n; hhlm: l = 2n
133.2			19	P4₂/nbc(00γ)s0s0	00lm: l + m = 2n; hk00: h + k = 2n; 0klm: k + m = 2n; hhlm: l = 2n
133.3			20	P4₂/nbc( $[{{1}\over{2}}{{1}\over{2}}]$ γ)q0q0	00Lm: 2L + m = 4n; HK00: H = 2n, K = 2n; HHLm: 2H + m = 4n; H0Lm: L = 2n
134.1	P4₂/nnm	(4/mmm, $[1{\bar 1}11]$ )	19	P4₂/nnm(00γ)	00lm: l = 2n; hk00: h + k = 2n; 0klm: k + l = 2n
134.2			19	P4₂/nnm(00γ)00ss	00lm: l = 2n; hk00: h + k = 2n; 0klm: k + l + m = 2n; hhlm: m = 2n
134.3			20	P4₂/nnm( $[{{1}\over{2}}{{1}\over{2}}]$ γ)q0q0	00Lm: 2L + m = 4n; HK00: H = 2n, K = 2n; HHLm: 2H + 2L + m = 4n
134.4			20	P4₂/nnm( $[{{1}\over{2}}{{1}\over{2}}]$ γ)q0qs	00Lm: 2L + m = 4n; HK00: H + K = 2n; HHLm: 2H + 2L + m = 4n; H0Lm: m = 2n
135.1	P4₂/mbc	(4/mmm, $[1{\bar 1}11]$ )	19	P4₂/mbc(00γ)	00lm: l = 2n; 0klm: k = 2n; hhlm: l = 2n
135.2			19	P4₂/mbc(00γ)s0s0	00lm: l + m = 2n; 0klm: k + m = 2n; hhlm: l = 2n
136.1	P4₂/mnm	(4/mmm, $[1{\bar 1}11]$ )	19	P4₂/mnm(00γ)	00lm: l = 2n; 0klm: k + l = 2n
136.2			19	P4₂/mnm(00γ)00ss	00lm: l = 2n; 0klm: k + l + m = 2n; hhlm: m = 2n
137.1	P4₂/nmc	(4/mmm, $[1{\bar 1}11]$ )	19	P4₂/nmc(00γ)	00lm: l = 2n; hk00: h + k = 2n; hhlm: l = 2n
137.2			19	P4₂/nmc(00γ)s0s0	00lm: l + m = 2n; hk00: h + k = 2n; 0klm: m = 2n; hhlm: l = 2n
138.1	P4₂/ncm	(4/mmm, $[1{\bar 1}11]$ )	19	P4₂/ncm(00γ)	00lm: l = 2n; hk00: h + k = 2n; 0klm: l = 2n
138.2			19	P4₂/ncm(00γ)00ss	00lm: l = 2n; hk00: h + k = 2n; 0klm: l + m = 2n; hhlm: m = 2n
139.1	I4/mmm	(4/mmm, $[1{\bar 1}11]$ )	21	I4/mmm(00γ)
139.2			21	I4/mmm(00γ)s0s0	00lm: m = 2n; 0klm: m = 2n
139.3			21	I4/mmm(00γ)00ss	0klm: m = 2n; hhlm: m = 2n
139.4			21	I4/mmm(00γ)s00s	00lm: m = 2n; hhlm: m = 2n
140.1	I4/mcm	(4/mmm, $[1{\bar 1}11]$ )	21	I4/mcm(00γ)	0klm: l = 2n
140.2			21	I4/mcm(00γ)s0s0	00lm: m = 2n; 0klm: l + m = 2n
140.3			21	I4/mcm(00γ)00ss	0klm: l + m = 2n; hhlm: m = 2n
140.4			21	I4/mcm(00γ)s00s	00lm: m = 2n; 0klm: l = 2n; hhlm: m = 2n
141.1	I4₁/amd	(4/mmm, $[1{\bar 1}11]$ )	21	I4₁/amd(00γ)	00lm: l = 4n; hk00: h = 2n; hhlm: 2h + l = 4n
141.2			21	I4₁/amd(00γ)s0s0	00lm: l + 2m = 4n; hk00: h = 2n; 0klm: m = 2n; hhlm: 2h + l = 4n
142.1	I4₁/acd	(4/mmm, $[1{\bar 1}11]$ )	21	I4₁/acd(00γ)	00lm: l = 4n; hk00: h = 2n; 0klm: l = 2n; hhlm: 2h + l = 4n
142.2			21	I4₁/acd(00γ)s0s0	00lm: l + 2m = 4n; hk00: h = 2n; 0klm: l + m = 2n; hhlm: 2h + l = 4n
143.1	P3	(3, 1)	23	P3( $[{{1}\over{3}}{{1}\over{3}}]$ γ)
143.2			24	P3(00γ)
143.3			24	P3(00γ)t	00lm: m = 3n
144.1	P3₁	(3, 1)	23	P3₁( $[{{1}\over{3}}{{1}\over{3}}]$ γ)	00Lm: L = 3n
144.2			24	P3₁(00γ)	00lm: l = 3n
145.1	P3₂	(3, 1)	23	P3₂( $[{{1}\over{3}}{{1}\over{3}}]$ γ)	00Lm: L = 3n
145.2			24	P3₂(00γ)	00lm: l = 3n
146.1	R3	(3, 1)	22	R3(00γ)
146.2			22	R3(00γ)t	00lm: m = 3n
147.1	$[P{\bar 3}]$	( $[{\bar 3}]$ , $[{\bar 1}]$ )	23	P $[{\bar 3}]$ ( $[{{1}\over{3}}{{1}\over{3}}]$ γ)
147.2			24	P $[{\bar 3}]$ (00γ)
148.1	$[R{\bar 3}]$	( $[{\bar 3}]$ , $[{\bar 1}]$ )	22	R $[{\bar 3}]$ (00γ)
149.1	P312	(312, $[11{\bar 1}]$ )	23	P312( $[{{1}\over{3}}{{1}\over{3}}]$ γ)
149.2			24	P312(00γ)
149.3			24	P312(00γ)t00	00lm: m = 3n
150.1	P321	(321, $[1{\bar 1}1]$ )	24	P321(00γ)
150.2			24	P321(00γ)t00	00lm: m = 3n
151.1	P3₁12	(312, $[11{\bar 1}]$ )	23	P3₁12( $[{{1}\over{3}}{{1}\over{3}}]$ γ)	00Lm: L = 3n
151.2			24	P3₁12(00γ)	00lm: l = 3n
152.1	P3₁21	(321, $[1{\bar 1}1]$ )	24	P3₁21(00γ)	00lm: l = 3n
153.1	P3₂12	(312, $[11{\bar 1}]$ )	23	P3₂12( $[{{1}\over{3}}{{1}\over{3}}]$ γ)
153.2			24	P3₂12(00γ)	00lm: l = 3n
154.1	P3₂21	(321, $[1{\bar 1}1]$ )	24	P3₂21(00γ)	00lm: l = 3n
155.1	R32	(32, $[1{\bar 1}]$ )	22	R32(00γ)
155.2			22	R32(00γ)t0	00lm: m = 3n
156.1	P3m1	(3m1, 111)	24	P3m1(00γ)
156.2			24	P3m1(00γ)0s0	0klm: m = 2n
157.1	P31m	(31m, 111)	23	P31m( $[{{1}\over{3}}{{1}\over{3}}]$ γ)
157.2			23	P31m( $[{{1}\over{3}}{{1}\over{3}}]$ γ)00s	$[H{\bar H}Lm]$ : m = 2n
157.3			24	P31m(00γ)
157.4			24	P31m(00γ)00s	hhlm: m = 2n
158.1	P3c1	(3m1, 111)	24	P3c1(00γ)	0klm: l = 2n
159.1	P31c	(31m, 111)	23	P31c( $[{{1}\over{3}}{{1}\over{3}}]$ γ)	$[H{\bar H}Lm]$ : L = 2n
159.2			24	P31c(00γ)	hhlm: l = 2n
160.1	R3m	(3m, 11)	22	R3m(00γ)
160.2			22	R3m(00γ)0s	hhlm: m = 2n
161.1	R3c	(3m, 11)	22	R3c(00γ)	hhlm: l = 2n
162.1	$[P{\bar 3}1m]$	( $[{\bar 3}1m]$ , $[{\bar 1}11]$ )	23	P $[{\bar 3}]$ 1m( $[{{1}\over{3}}{{1}\over{3}}]$ γ)
162.2			23	P $[{\bar 3}]$ 1m( $[{{1}\over{3}}{{1}\over{3}}]$ γ)00s	$[H{\bar H}Lm]$ : m = 2n
162.3			24	P $[{\bar 3}]$ 1m(00γ)
162.4			24	P $[{\bar 3}]$ 1m(00γ)00s	hhlm: m = 2n
163.1	$[P{\bar 3}1c]$	( $[{\bar 3}1m]$ , $[{\bar 1}11]$ )	23	P $[{\bar 3}]$ 1c( $[{{1}\over{3}}{{1}\over{3}}]$ γ)	$[H{\bar H}Lm]$ : L = 2n
163.2			24	P $[{\bar 3}]$ 1c(00γ)	hhlm: l = 2n
164.1	$[P{\bar 3}m1]$	( $[{\bar 3}m1]$ , $[{\bar 1}11]$ )	24	P $[{\bar 3}]$ m1(00γ)
164.2			24	P $[{\bar 3}]$ m1(00γ)0s0	0klm: m = 2n
165.1	$[P{\bar 3}c1]$	( $[{\bar 3}m1]$ , $[{\bar 1}11]$ )	24	P $[{\bar 3}]$ c1(00γ)	0klm: l = 2n
166.1	$[R{\bar 3}m]$	( $[{\bar 3}m]$ , $[{\bar 1}1]$ )	22	R $[{\bar 3}]$ m(00γ)
166.2			22	R $[{\bar 3}]$ m(00γ)0s	hhlm: m = 2n
167.1	$[R{\bar 3}c]$	( $[{\bar 3}m]$ , $[{\bar 1}1]$ )	22	R $[{\bar 3}]$ c(00γ)	hhlm: l = 2n
168.1	P6	(6, 1)	24	P6(00γ)
168.2			24	P6(00γ)h	00lm: m = 6n
168.3			24	P6(00γ)t	00lm: m = 3n
168.4			24	P6(00γ)s	00lm: m = 2n
169.1	P6₁	(6, 1)	24	P6₁(00γ)	00lm: l = 6n
170.1	P6₅	(6, 1)	24	P6₅(00γ)	00lm: l = 6n
171.1	P6₂	(6, 1)	24	P6₂(00γ)	00lm: l = 3n
171.2			24	P6₂(00γ)h	00lm: 2l + m = 6n
172.1	P6₄	(6, 1)	24	P6₄(00γ)	00lm: l = 3n
172.2			24	P6₄(00γ)h	00lm: 2l + m = 6n
173.1	P6₃	(6, 1)	24	P6₃(00γ)	00lm: l = 2n
173.2			24	P6₃(00γ)h	00lm: 3l + m = 6n
174.1	$[P{\bar 6}]$	( $[{\bar 6}]$ , $[{\bar 1}]$ )	24	P $[{\bar 6}]$ (00γ)
175.1	P6/m	(6/m, $[1{\bar 1}]$ )	24	P6/m(00γ)
175.2			24	P6/m(00γ)s0	00lm: m = 2n
176.1	P6₃/m	(6/m, $[1{\bar 1}]$ )	24	P6₃/m(00γ)	00lm: l = 2n
177.1	P622	(622, $[1{\bar 1}{\bar 1}]$ )	24	P622(00γ)
177.2			24	P622(00γ)h00	00lm: m = 6n
177.3			24	P622(00γ)t00	00lm: m = 3n
177.4			24	P622(00γ)s00	00lm: m = 2n
178.1	P6₁22	(622, $[1{\bar 1}{\bar 1}]$ )	24	P6₁22(00γ)	00lm: l = 6n
179.1	P6₅22	(622, $[1{\bar 1}{\bar 1}]$ )	24	P6₅22(00γ)	00lm: l = 6n
180.1	P6₂22	(622, $[1{\bar 1}{\bar 1}]$ )	24	P6₂22(00γ)	00lm: l = 3n
180.2			24	P6₂22(00γ)h00	00lm: 2l + m = 6n
181.1	P6₄22	(622, $[1{\bar 1}{\bar 1}]$ )	24	P6₄22(00γ)	00lm: l = 3n
181.2			24	P6₄22(00γ)h00	00lm: 2l + m = 6n
182.1	P6₃22	(622, $[1{\bar 1}{\bar 1}]$ )	24	P6₃22(00γ)
182.2			24	P6₃22(00γ)h00	00lm: 3l + m = 6n
183.1	P6mm	(6mm, 111)	24	P6mm(00γ)
183.2			24	P6mm(00γ)ss0	00lm: m = 2n; 0klm: m = 2n
183.3			24	P6mm(00γ)0ss	0klm: m = 2n; hhlm: m = 2n
183.4			24	P6mm(00γ)s0s	00lm: m = 2n; hhlm: m = 2n
184.1	P6cc	(6mm, 111)	24	P6cc(00γ)	0klm: l = 2n; hhlm: l = 2n
184.2			24	P6cc(00γ)s0s	00lm: m = 2n; 0klm: l = 2n; hhlm: l + m = 2n
185.1	P6₃cm	(6mm, 111)	24	P6₃cm(00γ)	00lm: l = 2n; 0klm: l = 2n
185.2			24	P6₃cm(00γ)0ss	00lm: l = 2n; 0klm: l + m = 2n; hhlm: m = 2n
186.1	P6₃mc	(6mm, 111)	24	P6₃mc(00γ)	00lm: l = 2n; hhlm: l = 2n
186.2			24	P6₃mc(00γ)0ss	00lm: l = 2n; 0klm: m = 2n; hhlm: l + m = 2n
187.1	$[P{\bar 6}m2]$	( $[{\bar 6}m2]$ , $[{\bar 1}1{\bar 1}]$ )	24	P $[{\bar 6}]$ m2(00γ)
187.2			24	P $[{\bar 6}]$ m2(00γ)0s0	0klm: m = 2n
188.1	$[P{\bar 6}c2]$	( $[{\bar 6}m2]$ , $[{\bar 1}1{\bar 1}]$ )	24	P $[{\bar 6}]$ c2(00γ)	0klm: l = 2n
189.1	$[P{\bar 6}2m]$	( $[{\bar 6}2m]$ , $[{\bar 1}{\bar 1}1]$ )	24	P $[{\bar 6}]$ 2m(00γ)
189.2			24	P $[{\bar 6}]$ 2m(00γ)00s	hhlm: m = 2n
190.1	$[P{\bar 6}2c]$	( $[{\bar 6}2m]$ , $[{\bar 1}{\bar 1}1]$ )	24	P $[{\bar 6}]$ 2c(00γ)	hhlm: l = 2n
191.1	P6/mmm	(6/mmm, $[1{\bar 1}11]$ )	24	P6/mmm(00γ)
191.2			24	P6/mmm(00γ)s0s0	00lm: m = 2n; 0klm: m = 2n
191.3			24	P6/mmm(00γ)00ss	0klm: m = 2n; hhlm: m = 2n
191.4			24	P6/mmm(00γ)s00s	00lm: m = 2n; hhlm: m = 2n
192.1	P6/mcc	(6/mmm, $[1{\bar 1}11]$ )	24	P6/mcc(00γ)	0klm: l = 2n; hhlm: l = 2n
192.2			24	P6/mcc(00γ)s00s	00lm: m = 2n; 0klm: l = 2n; hhlm: l + m = 2n
193.1	P6₃/mcm	(6/mmm, $[1{\bar 1}11]$ )	24	P6₃/mcm(00γ)	00lm: l = 2n; 0klm: l = 2n
193.2			24	P6₃/mcm(00γ)00ss	00lm: l = 2n; 0klm: l + m = 2n; hhlm: m = 2n
194.1	P6₃/mmc	(6/mmm, $[1{\bar 1}11]$ )	24	P6₃/mmc(00γ)	00lm: l = 2n; hhlm: l = 2n
194.2			24	P6₃/mmc(00γ)00ss	00lm: l = 2n; 0klm: m = 2n; hhlm: l + m = 2n

Table 9.8.3.6| top | pdf |
Centring reflection conditions for (3 + 1)-dimensional Bravais classes

The centring reflection conditions are given for the 24 Bravais classes, belonging to six systems (with number and symbol according to Table 9.8.3.2a). If qⁱ = q these are the usual conditions for hklm, the indices of the reflections expressed with respect to a*, b*, c*, q. Otherwise the conditions are for indices HKLm with respect to a conventional basis $[{\bf a}_c^*, {\bf b}_c^*, {\bf c}_c^*, {\bf q}^i]$ of the vector module M*. The relation between indices HKLm and hklm is given in the fourth column. Planar monoclinic and axial monoclinic mean a monoclinic lattice of main reflections and with the (irrational part of the) modulation wavevector in the mirror plane, or along the unique axis, respectively.

System	qⁱ vector	Reflection conditions	Relation of indices	Bravais class
System	qⁱ vector	Reflection conditions	Relation of indices	No.	Symbol
Triclinic	(αβγ)			1	$[{\bar 1}]$ P(αβγ)
Planar monoclinic	(αβ0)			2	2/mP(αβ0)
				3	2/mP(αβ $[{{1}\over{2}}]$ )
				4	2/mB(αβ0)
Axial monoclinic	(00γ)			5	2/mP(00γ)
				6	2/mP( $[{{1}\over{2}}]$ 0γ)
				7	2/mB(00γ)
				8	2/mB(0 $[{{1}\over{2}}]$ γ)
Orthorhombic	(00γ)			9	mmmP(00γ)
				10	mmmP(0 $[{{1}\over{2}}]$ γ)
				11	mmmP( $[{{1}\over{2}}{{1}\over{2}}]$ γ)
				12	mmmI(00γ)
				13	mmmC(00γ)
				14	mmmC(10γ)
				15	mmmA(00γ)
				16	mmmA( $[{{1}\over{2}}]$ 0γ)
				17	mmmF(00γ)
				18	mmmF(10γ)
Tetragonal	(00γ)			19	4/mmmP(00γ)
				20	4/mmmP( $[{{1}\over{2}}{{1}\over{2}}]$ γ)
				21	4/mmmI(00γ)
Hexagonal/Trigonal	(00γ)			22	$[{\bar 3}]$ mR(00γ)
				23	$[{\bar 3}]$ 1mP( $[{{1}\over{3}}{{1}\over{3}}]$ γ)
				24	6/mmmP(00γ)

(B) ThBr₄

Thorium tetrabromide has an incommensurately modulated phase below [T_i] = 95 K (Currat, Bernard & Delamoye, 1986). Above that temperature, the structure has space group [I4_1/amd] (No. 141 in International Tables for Crystallography, Volume A). At [T_i] , a mode becomes unstable and a modulated β-phase sets in with modulation wavevector γc*. The dimension of the modulation is one, consequently.

The main reflections belong to a tetragonal lattice. The general reflection condition is $[hklm, h+k+l \hbox{ even}.]$ Looking at Table 9.8.3.6, one finds the Bravais class to be No. 21 = I4/mmm(00γ). Table 9.8.3.2(a) gives $[4/mmm(1\bar111)]$ for the point group of the vector module.

For the determination of the symmetry group of the modulated structure, one has the special reflection conditions $[hk00, h\hbox{ even}; \quad hhl0, 2h+l=4n; \quad (00l0, l=4n) \atop 0klm\hbox{ (and $h0lm$) absent for {\it m}} =1.]$ Higher-order satellites have not been observed. The main reflections lead to the basic group [I4_1/amd] . If one generalizes the reflection condition observed for 0klm to 0klm, m = even, the superspace group is found from Table 9.8.3.5 under the groups 141.x as $[\hbox{No. }141.2=I4_1/amd(00\gamma)s0s0 = P^{I4_1/amd}_{\kern5pt s\kern5pt \bar1 \,s\,1}.]$

Bis(n-propylammonium) tetrachloromanganate (PAMC) has several phase transitions. Above about 395 K, it is orthorhombic with space group Abma. At [T_i] , this β-phase goes over into the incommensurately modulated γ-phase (Depmeier, 1986; Kind & Muralt, 1986). The wavevector of the modulation is $[\alpha{\bf a}^*+{\bf c}^*]$ . Therefore, the dimension of the modulation is one. Interchanging the a and c axes, one sees from Table 9.8.3.2(a) that the Bravais class is No. 14 = mmmC(10γ). In this new setting, the conventional basis of the vector module is a*, b*, c*, and γc* and the general reflection condition becomes $[HKLm, H+K+m={\rm even}.]$ Therefore, if one considers the vector module as the projection of a four-dimensional lattice, the reflection condition corresponds to a $[({1\over2}{1\over2}0{1\over2})]$ centring in four dimensions.

The point group of the vector module is $[mmm(11\bar1)]$ . The basic space group being Abma (or Ccmb in the new setting), the superspace group follows from Table 9.8.3.5 as $[\hbox{No. }64.3=Ccmb(10\gamma)=L^{Ccmb}_{\kern 5pt 1\kern0.5pt1\kern0.5pt\bar1}]$ or, in the original setting $[\hbox{No. }64.3=Abma(\alpha01)=N^{Abma}_{\kern 5pt\bar1\kern.5pt1\kern.5pt1} \, .]$ No. 64.4 can be excluded because the reflections do not show the special reflection condition 0KLm, m = even.

References

Currat, R., Bernard, L. & Delamoye, P. (1986). Incommensurate phase in β-ThBr₄. Incommensurate phases in dielectrics, edited by R. Blinc & A. P. Levanyuk, pp. 161–203. Amsterdam: North-Holland.Google Scholar

Depmeier, W. (1986). Incommensurate phases in PAMC: where are we now? Ferroelectrics, 66, 109–123.Google Scholar

International Tables for Crystallography (2005). Vol. A, edited by Th. Hahn, fifth ed. Heidelberg: Springer.Google Scholar

Kind, R. & Muralt, P. (1986). Unique incommensurate–commensurate phase transitions in a layer structure perovskite. Incommensurate phases in dielectrics, edited by R. Blinc & A. P. Levanyuk, pp. 301–317. Amsterdam: North-Holland.Google Scholar

Wolff, P. M. de & Tuinstra, F. (1986). The incommensurate phase of Na₂CO₃. Incommensurate phases in dielectrics, edited by R. Blinc & A. P. Levanyuk, pp. 253–281. Amsterdam: North-Holland.Google Scholar

International Tables for Crystallography (2006). Vol. C. ch. 9.8, p. 936