Geometrical parameterization of the crystal chemistry of P63/m apatites: comparison with experimental data and ab initio results

0.66 0.68 0.70 0.72 0.74 0.76 2.3 2.4 2.5 2.6 2.7 2.8

(a)

<

A

I-O

>

A Iz = 0

(

Å

)

0.66 0.68 0.70 0.72 0.74 0.76 43 44 45 46 47

(b)

<

A I-O

>

A Iz = 0

(

°)

0.66 0.68 0.70 0.72 0.74 0.76 18 20 22 24 26 28

(c)

A I

(

°)

0.66 0.68 0.70 0.72 0.74 0.76 -24 -22 -20 -18 -16

(d)

A I

(

°)

0.66 0.68 0.70 0.72 0.74 0.76 1.50 1.55 1.60 1.65 1.70 1.75

c/a

_obs

(e)

<

B

-O

>

(Å

)

0.66 0.68 0.70 0.72 0.74 0.76 110 111 112 113 114

<

O -B -O

>

(°

)

F igure 8

Correlations of observed c/a ratios with the following crystal-chemical parameters: <AI-O> (a),

<y > (b), d (c), a (d), <B-O> (e), and <t > (f). Legend for synbols as in Figure 3.

c/a

_obs

(f)

d

a

y

t

AIz=0

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 9.2 9.4 9.6 9.8 10.0 10.2 10.4

±0.5%

(a)

a ( Å ) E xperimental: single-crystal, R <= 4.0% single-crystal, R > 4.0% R ietveld Ab initio : C O C C C O, energy-prohibited C C , energy-prohibited C omposition Label No.:

0 = C d₁₀ (P O₄)₆ C l₂ 1 = C a₁₀ (P O₄)₆ F₂ 2 = C a₁₀ (P O₄)₆ B r₂ 3 = P b₁₀ (P O₄)₆ F₂ 4 = P b₁₀ (P O₄)₆ C l₂ 5 = P b₁₀ (P O₄)₆ B r₂ 6 = P b₁₀ (V O₄)₆ C l₂ 7 = P b₁₀ (AsO₄)₆ C l₂ 8 = C a₄P b₆ (AsO₄)₆ C l₂ 9 = S r₁₀ (P O₄)₆ F₂ 10 = S r₁₀ (P O₄)₆ C l₂ 11 = S r₁₀ (P O₄)₆ B r₂ 12 = S r₁₀ (V O₄)₆ F₂ 13 = S r₁₀ (V O₄)₆ C u₂O₂ 14 = B a₁₀ (P O₄)₆ F₂ 15 = B a₁₀ (P O₄)₆ C l₂ 16 = B a₁₀ (P O₄)₆ B r₂ 17 = B a₁₀ (MnO₄)₆ F₂ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 6.4 6.6 6.8 7.0 7.2 7.4 7.6 7.8 8.0

±0.5%

(b)

c (Å ) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 2.20 2.25 2.30 2.35 2.40 2.45 2.50 2.55 2.60 2.65 2.70 2.75 2.80

±0.5%

(c)

(A I-O 1 ) ( Å ) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 2.20 2.25 2.30 2.35 2.40 2.45 2.50 2.55 2.60 2.65 2.70 2.75 2.80

±0.5%

(d)

C omposition Label No.

( A I-O 1 ) A Iz = 0 ( Å )

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25 0.30 ±2%

(e)

E xperimental: single-crystal, R <= 4.0% single-crystal, R > 4.0% R ietveld Ab initio : C O C C C O, energy-prohibited C C , energy-prohibited C omposition Label No.:

0 = C d₁₀ (P O₄)₆ C l₂ 1 = C a₁₀ (P O₄)₆ F₂ 2 = C a₁₀ (P O₄)₆ B r₂ 3 = P b₁₀ (P O₄)₆ F₂ 4 = P b₁₀ (P O₄)₆ C l₂ 5 = P b₁₀ (P O₄)₆ B r₂ 6 = P b₁₀ (V O₄)₆ C l₂ 7 = P b₁₀ (AsO₄)₆ C l₂ 8 = C a₄P b₆ (AsO₄)₆ C l₂ 9 = S r₁₀ (P O₄)₆ F₂ 10 = S r10 (P O4)6 C l2 11 = S r₁₀ (P O₄)₆ B r₂ 12 = S r₁₀ (V O₄)₆ F₂ 13 = S r₁₀ (V O₄)₆ C u₂O₂ 14 = B a₁₀ (P O₄)₆ F₂ 15 = B a₁₀ (P O₄)₆ C l₂ 16 = B a₁₀ (P O₄)₆ B r₂ 17 = B a₁₀ (MnO₄)₆ F₂ A I-O

(Å

)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25 _±2%

(f)

A I-O A Iz = 0

(

Å

)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 41 42 43 44 45 46 47 48 ±0.5%

_(g)

A I-O 1

(

°)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 42 43 44 45 46 47 48 ±0.5%

F igure 9

C ontinued.

C omposition Label No.

(h)

A I-O 1 A Iz = 0

(

°)

D

D

y

y

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 20 22 24 26 28

±1.0%

(i)

A I ( °) E xperimental: single-crystal, R <= 4.0% single-crystal, R > 4.0% R ietveld Ab initio : C O C C C O, energy-prohibited C C , energy-prohibited C omposition Label No.:

0 = C d₁₀ (P O₄)₆ C l₂ 1 = C a₁₀ (P O₄)₆ F₂ 2 = C a₁₀ (P O₄)₆ B r₂ 3 = P b₁₀ (P O₄)₆ F₂ 4 = P b₁₀ (P O₄)₆ C l₂ 5 = P b₁₀ (P O₄)₆ B r₂ 6 = P b₁₀ (V O₄)₆ C l₂ 7 = P b₁₀ (AsO₄)₆ C l₂ 8 = C a₄P b₆ (AsO₄)₆ C l₂ 9 = S r₁₀ (P O₄)₆ F₂ 10 = S r₁₀ (P O₄)₆ C l₂ 11 = S r₁₀ (P O₄)₆ B r₂ 12 = S r₁₀ (V O₄)₆ F₂ 13 = S r₁₀ (V O₄)₆ C u₂O₂ 14 = B a₁₀ (P O₄)₆ F₂ 15 = B a₁₀ (P O₄)₆ C l₂ 16 = B a₁₀ (P O₄)₆ B r₂ 17 = B a₁₀ (MnO₄)₆ F₂ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 -24 -22 -20 -18 -16 -14 -12 -10 -8

±2.0%

(j)

A I ( °) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1.48 1.52 1.56 1.60 1.64 1.68 1.72 1.76

±0.5%

(k)

< B -O > ( Å ) 110 111 112 113 114 115 116 117 118

F igure 9

C ontinued.

±0.5%

(l)

< O -B -O > (° )

a

d

t

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 ±0.5%

(m)

A II ( Å ) E xperimental: single-crystal, R <= 4.0% single-crystal, R > 4.0% R ietveld Ab initio : C O C C C O, energy-prohibited C C , energy-prohibited C omposition Label No.:

0 = C d₁₀ (P O₄)₆ C l₂ 1 = C a₁₀ (P O₄)₆ F₂ 2 = C a₁₀ (P O₄)₆ B r₂ 3 = P b₁₀ (P O₄)₆ F₂ 4 = P b₁₀ (P O₄)₆ C l₂ 5 = P b₁₀ (P O₄)₆ B r₂ 6 = P b₁₀ (V O₄)₆ C l₂ 7 = P b₁₀ (AsO₄)₆ C l₂ 8 = C a₄P b₆ (AsO₄)₆ C l₂ 9 = S r₁₀ (P O₄)₆ F₂ 10 = S r₁₀ (P O₄)₆ C l₂ 11 = S r₁₀ (P O₄)₆ B r₂ 12 = S r₁₀ (V O₄)₆ F₂ 13 = S r₁₀ (V O₄)₆ C u₂O₂ 14 = B a₁₀ (P O₄)₆ F₂ 15 = B a₁₀ (P O₄)₆ C l₂ 16 = B a₁₀ (P O₄)₆ B r₂ 17 = B a₁₀ (MnO₄)₆ F₂ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 2.2 2.4 2.6 2.8 3.0 3.2 3.4 ±1.0%

(n)

(A II -X ) (Å ) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 116 117 118 119 120 121 122 123 124 ±0.5%

(o)

A II ( °) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 120 125 130 135 140 145 150

F igure 9

C ontinued.

±0.5%

(p)

C omposition Label No.

O 3 -A II -O 3 ( °)

r

a

f

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 ±1.0%

(q)

(A II -O 3 ) (Å ) E xperimental: single-crystal, R <= 4.0% single-crystal, R > 4.0% R ietveld Ab initio : C O C C C O, energy-prohibited C C , energy-prohibited C omposition Label No.:

0 = C d₁₀ (P O₄)₆ C l₂ 1 = C a₁₀ (P O₄)₆ F₂ 2 = C a₁₀ (P O₄)₆ B r₂ 3 = P b₁₀ (P O₄)₆ F₂ 4 = P b₁₀ (P O₄)₆ C l₂ 5 = P b₁₀ (P O₄)₆ B r₂ 6 = P b₁₀ (V O₄)₆ C l₂ 7 = P b₁₀ (AsO₄)₆ C l₂ 8 = C a₄P b₆ (AsO₄)₆ C l₂ 9 = S r₁₀ (P O₄)₆ F₂ 10 = S r₁₀ (P O₄)₆ C l₂ 11 = S r₁₀ (P O₄)₆ B r₂ 12 = S r₁₀ (V O₄)₆ F₂ 13 = S r₁₀ (V O₄)₆ C u₂O₂ 14 = B a₁₀ (P O₄)₆ F₂ 15 = B a₁₀ (P O₄)₆ C l₂ 16 = B a₁₀ (P O₄)₆ B r₂ 17 = B a₁₀ (MnO₄)₆ F₂ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 2.4 2.5 2.6 2.7 2.8 2.9 _±1.0%

(r)

(A II -O 3 ') (Å ) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 2.2 2.3 2.4 2.5 2.6 2.7 ±1.0%

(s )

(A II -O 2 ) (Å ) 2.6 2.8 3.0 3.2 3.4 3.6

F igure 9

C ontinued.

±1.0%

_(t)

(A II -O 1 ) (Å )