2.8
47
(a)
(b)
(Å)
2.7
46
45
<yAI-O >
<A I-O>
AIz=0
AIz=0
(°)
2.6
2.5
44
2.4
43
2.3
0.66
28
0.68
0.70
0.72
0.74
0.76
0.66
(c)
0.68
0.70
0.72
0.74
0.76
(d)
-16
26
-18
-20
aAI
dAI
(°)
(°)
24
22
-22
20
-24
18
0.66
1.75
0.68
0.70
0.72
0.74
0.76
0.66
(e)
0.68
0.70
0.72
0.74
0.76
(f)
114
1.70
113
< tO-B -O > (°)
<B -O> (Å)
1.65
1.60
112
111
1.55
110
1.50
0.66
0.68
0.70
0.72
c/a obs
0.74
0.76
0.66
0.68
0.70
0.72
0.74
c/a obs
F igure 8
Correlations of observed c/a ratios with the following crystal-chemical parameters: <AI-O>AIz=0 (a),
<yAI-O > AIz=0 (b), dAI (c), a AI (d), <B-O> (e), and <t O-B-O > (f). Legend for synbols as in Figure 3.
0.76
10.4
±0.5%
10.2
a (Å)
10.0
9.8
9.6
9.4
(a)
9.2
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
8.0
Ab initio :
7.6
CO
CC
C O, energy-prohibited
C C , energy-prohibited
c (Å)
7.4
7.2
7.0
C ompos ition Label No.:
6.8
(b)
6.6
6.4
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
2.80
±0.5%
2.75
2.70
2.65
(A I-O1) (Å)
2.60
2.55
2.50
2.45
2.40
2.35
2.30
(c)
2.25
2.20
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
2.80
±0.5%
2.75
2.70
2.60
AIz=0
2.55
(A I-O1)
(Å)
2.65
2.40
s ingle-crys tal, R <= 4.0%
s ingle-crys tal, R > 4.0%
R ietveld
±0.5%
7.8
2.50
E xperimental:
2.45
2.35
2.30
(d)
2.25
2.20
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
C ompos ition Label No.
F igure 9
C omparis on of experimental data with ab initio res ults .
15
16
17
0 = C d 10 (P O 4 ) 6 C l 2
1 = C a 10 (P O 4 ) 6 F 2
2 = C a 10 (P O 4 ) 6 B r 2
3 = P b 10 (P O 4 ) 6 F 2
4 = P b 10 (P O 4 ) 6 C l 2
5 = P b 10 (P O 4 ) 6 B r 2
6 = P b 10 (V O 4 ) 6 C l 2
7 = P b 10 (As O 4 ) 6 C l 2
8 = C a 4 P b 6 (As O 4 ) 6 C l 2
9 = S r 10 (P O 4 ) 6 F 2
10 = S r 10 (P O 4 ) 6 C l 2
11 = S r 10 (P O 4 ) 6 B r 2
12 = S r 10 (V O 4 ) 6 F 2
13 = S r 10 (V O 4 ) 6 C u 2 O 2
14 = B a 10 (P O 4 ) 6 F 2
15 = B a 10 (P O 4 ) 6 C l 2
16 = B a 10 (P O 4 ) 6 B r 2
17 = B a 10 (MnO 4 ) 6 F 2
0.30
(e)
±2%
0.25
0.20
(Å)
0.15
AI-O
0.10
D
0.05
0.00
-0.05
E xperimental:
-0.10
0
1
0.25
2
3
4
5
6
7
8
9
10
11
12
13
14
15
±2%
16
17
(f)
s ingle-crys tal, R <= 4.0%
s ingle-crys tal, R > 4.0%
R ietveld
0.20
Ab initio :
(Å)
0.15
CO
CC
C O, energy-prohibited
C C , energy-prohibited
AIz=0
0.10
AI-O
0.05
D
0.00
C ompos ition Label No.:
-0.05
-0.10
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
48
±0.5%
(g)
47
y
AI-O1
(°)
46
45
44
43
42
41
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
48
(h)
±0.5%
47
0 = C d 10 (P O 4 ) 6 C l 2
1 = C a 10 (P O 4 ) 6 F 2
2 = C a 10 (P O 4 ) 6 B r 2
3 = P b 10 (P O 4 ) 6 F 2
4 = P b 10 (P O 4 ) 6 C l 2
5 = P b 10 (P O 4 ) 6 B r 2
6 = P b 10 (V O 4 ) 6 C l 2
7 = P b 10 (As O 4 ) 6 C l 2
8 = C a 4 P b 6 (As O 4 ) 6 C l 2
9 = S r 10 (P O 4 ) 6 F 2
10 = S r 10 (P O 4 ) 6 C l 2
11 = S r 10 (P O 4 ) 6 B r 2
12 = S r 10 (V O 4 ) 6 F 2
13 = S r 10 (V O 4 ) 6 C u 2 O 2
14 = B a 10 (P O 4 ) 6 F 2
15 = B a 10 (P O 4 ) 6 C l 2
16 = B a 10 (P O 4 ) 6 B r 2
17 = B a 10 (MnO 4 ) 6 F 2
(°)
46
AI-O1
y
AIz=0
45
44
43
F igure 9
C ontinued.
42
0
1
2
3
4
5
6
7
8
9
10
11
C ompos ition Label No.
12
13
14
15
16
17
28
(i)
±1.0%
26
dAI
(°)
24
22
20
E xperimental:
18
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
-8
16
17
(j)
-10
s ingle-crys tal, R <= 4.0%
s ingle-crys tal, R > 4.0%
R ietveld
Ab initio :
-12
CO
CC
C O, energy-prohibited
C C , energy-prohibited
a
AI
(°)
-14
-16
-18
C ompos ition Label No.:
-20
-22
±2.0%
-24
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
1.76
±0.5%
1.72
<B -O> (Å)
1.68
1.64
1.60
1.56
1.52
(k)
1.48
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
118
(l)
117
(°)
116
0 = C d 10 (P O 4 ) 6 C l 2
1 = C a 10 (P O 4 ) 6 F 2
2 = C a 10 (P O 4 ) 6 B r 2
3 = P b 10 (P O 4 ) 6 F 2
4 = P b 10 (P O 4 ) 6 C l 2
5 = P b 10 (P O 4 ) 6 B r 2
6 = P b 10 (V O 4 ) 6 C l 2
7 = P b 10 (As O 4 ) 6 C l 2
8 = C a 4 P b 6 (As O 4 ) 6 C l 2
9 = S r 10 (P O 4 ) 6 F 2
10 = S r 10 (P O 4 ) 6 C l 2
11 = S r 10 (P O 4 ) 6 B r 2
12 = S r 10 (V O 4 ) 6 F 2
13 = S r 10 (V O 4 ) 6 C u 2 O 2
14 = B a 10 (P O 4 ) 6 F 2
15 = B a 10 (P O 4 ) 6 C l 2
16 = B a 10 (P O 4 ) 6 B r 2
17 = B a 10 (MnO 4 ) 6 F 2
±0.5%
115
<tO-B -O >
114
113
112
F igure 9
C ontinued.
111
110
0
1
2
3
4
5
6
7
8
9
10
11
C ompos ition Label No.
12
13
14
15
16
17
4.7
±0.5%
4.6
4.5
rAII
(Å)
4.4
4.3
4.2
4.1
4.0
(m)
3.9
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
3.4
±1.0%
3.2
(Å)
CO
CC
C O, energy-prohibited
C C , energy-prohibited
(A II-X)
2.8
2.6
C ompos ition Label No.:
2.4
(n)
2.2
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
124
16
17
(o)
123
122
(°)
121
AII
s ingle-crys tal, R <= 4.0%
s ingle-crys tal, R > 4.0%
R ietveld
Ab initio :
3.0
a
E xperimental:
120
±0.5%
119
118
117
116
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
150
16
17
(p)
0 = C d 10 (P O 4 ) 6 C l 2
1 = C a 10 (P O 4 ) 6 F 2
2 = C a 10 (P O 4 ) 6 B r 2
3 = P b 10 (P O 4 ) 6 F 2
4 = P b 10 (P O 4 ) 6 C l 2
5 = P b 10 (P O 4 ) 6 B r 2
6 = P b 10 (V O 4 ) 6 C l 2
7 = P b 10 (As O 4 ) 6 C l 2
8 = C a 4 P b 6 (As O 4 ) 6 C l 2
9 = S r 10 (P O 4 ) 6 F 2
10 = S r 10 (P O 4 ) 6 C l 2
11 = S r 10 (P O 4 ) 6 B r 2
12 = S r 10 (V O 4 ) 6 F 2
13 = S r 10 (V O 4 ) 6 C u 2 O 2
14 = B a 10 (P O 4 ) 6 F 2
15 = B a 10 (P O 4 ) 6 C l 2
16 = B a 10 (P O 4 ) 6 B r 2
17 = B a 10 (MnO 4 ) 6 F 2
±0.5%
145
(°)
140
fO3-A II -O3
135
130
F igure 9
C ontinued.
125
120
0
1
2
3
4
5
6
7
8
9
10
11
C ompos ition Label No.
12
13
14
15
16
17
2.8
±1.0%
2.7
(Å)
2.6
(A II-O3)
2.5
2.4
2.3
2.2
(q)
2.1
0
1
2.9
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
±1.0%
(Å)
(A II-O3')
CO
CC
C O, energy-prohibited
C C , energy-prohibited
2.7
2.6
C ompos ition Label No.:
2.5
(r)
2.4
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
2.7
±1.0%
2.6
(Å)
s ingle-crys tal, R <= 4.0%
s ingle-crys tal, R > 4.0%
R ietveld
Ab initio :
2.8
(A II-O2)
E xperimental:
2.5
2.4
2.3
(s )
2.2
0
1
3.6
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
(t)
±1.0%
0 = C d 10 (P O 4 ) 6 C l 2
1 = C a 10 (P O 4 ) 6 F 2
2 = C a 10 (P O 4 ) 6 B r 2
3 = P b 10 (P O 4 ) 6 F 2
4 = P b 10 (P O 4 ) 6 C l 2
5 = P b 10 (P O 4 ) 6 B r 2
6 = P b 10 (V O 4 ) 6 C l 2
7 = P b 10 (As O 4 ) 6 C l 2
8 = C a 4 P b 6 (As O 4 ) 6 C l 2
9 = S r 10 (P O 4 ) 6 F 2
10 = S r 10 (P O 4 ) 6 C l 2
11 = S r 10 (P O 4 ) 6 B r 2
12 = S r 10 (V O 4 ) 6 F 2
13 = S r 10 (V O 4 ) 6 C u 2 O 2
14 = B a 10 (P O 4 ) 6 F 2
15 = B a 10 (P O 4 ) 6 C l 2
16 = B a 10 (P O 4 ) 6 B r 2
17 = B a 10 (MnO 4 ) 6 F 2
(A II-O1)
(Å)
3.4
3.2
3.0
F igure 9
C ontinued.
2.8
2.6
0
1
2
3
4
5
6
7
8
9
10
11
C ompos ition Label No.
12
13
14
15
16
17