1dependence of raman spectra on hydrostatic pressure
TRANSCRIPT
Electronic supplementary information (ESI): Density functionalstudy of phase stabilities and Raman spectra of Yb2O3, Yb2SiO5and Yb2Si2O7 under pressure
Takafumi Ogawa,∗a Noriko Otani,a Taishi Yokoi,b Craig A. J. Fisher,a Akihide Kuwabara,a,c HirokiMoriwake,a,c Masato Yoshiya,a,d Satoshi Kitaoka,b and Masasuke Takataa,b
1 Dependence of Raman spectra on hydrostatic pressure
100 200 300 400 500 600 700
Frequency [cm−1]
−4
−2
0
2
4
6
8
10
12
Intensity
[arb
.units]
-4 GPa
-2 GPa
0 GPa
2 GPa
4 GPa
6 GPa
8 GPa
P=10 GPa
(a)
−4 −2 0 2 4 6 8 10Pressure [GPa]
100
200
300
400
500
600
700
Frequency
[cm−1]
(b)
Fig. S1 Dependence of (a) Raman spectra and (b) peak positions of C-type Yb2O3 on hydrostatic pressure.
a Nanostructures Research Laboratory, Japan Fine Ceramics Center, Nagoya 456-8587, Japan. E-mail: [email protected] Materials Research and Development Laboratory, Japan Fine Ceramics Center, Nagoya 456-8587, Japan.c Center for Materials Research by Information Integration, National Institute for Materials Science, Tsukuba 305-0047, Japand Department of Adaptive Machine Systems, Osaka University, Osaka 565-0871, Japan
1
Electronic Supplementary Material (ESI) for Physical Chemistry Chemical Physics.This journal is © the Owner Societies 2018
200 400 600 800 1000
Frequency [cm−1]
−3
0
1
2
Intensity
[arb
.units]
(a)
-1. 6 GPa
-1. 2 GPa
-0. 8 GPa
-0. 4 GPa
0 GPa
0. 4 GPa
0. 8 GPa
1. 2 GPa
1. 6 GPa
−2 −1 0 1 2Pressure [GPa]
200
400
600
800
1000
Frequen
cy[cm−1]
(b)
Fig. S2 Dependence of (a) Raman spectra and (b) peak positions of X2-Yb2SiO5 on hydrostatic pressure.
200 400 600 800 1000
Frequency [cm−1]
−2
0
2
Intensity
[arb
.units]
-1. 6 GPa
-1. 2 GPa
-0. 8 GPa
-0. 4 GPa
0 GPa
0. 4 GPa
0. 8 GPa
1. 2 GPa
1. 6 GPa(a)
−2 −1 0 1 2Pressure [GPa]
0
200
400
600
800
1000
Frequen
cy[cm−1]
(b)
Fig. S3 Dependence of (a) Raman spectra and (b) peak positions of β -Yb2Si2O7 on hydrostatic pressure.
2
2 Vibrations of SixOy tetrahedral units in Yb2SiO5 and Yb2Si2O7The parameter used to measure maximum deviation in a bond length during vibration is defined in the manuscript as
∆li j =rrri j
2− rrr0i j
2
r0i jA
. (1)
Since expressing the interatomic vector by the atomic positions and vibrational displacement vectors leads to
rrri j = (rrr0j +uuu j)− (rrr0
i +uuui) = rrr0i j +uuu j−uuui, (2)
the parameter, ∆li j, can be rewritten as
∆li j = 2rrr0
i j · (uuu j−uuui)
r0i jA
+(uuu j−uuui)
2
r0i jA
. (3)
The second term on the right hand side of this equation vanishes when A is sufficiently smaller than r0i j (A/r0
i j → 0), leading to aconverged value of ∆li j in the limit of small A. To confirm this behaviour, the dependence of ∆li j on A is examined for a mode ofX2-Yb2SiO5 as shown in Fig. S4. From the figure, we can see that the ∆li j changes slightly for A < 10−2. In this study, we used A = 10−3
to calculate ∆li j. The bond lengths between Si and O atoms and vibrational amplitudes, u2i /A2 and ∆li j, for characteristic modes with
frequencies above 600 cm−1 are shown in Figs. S5 – S10, where the structural pictures of SixOy were drawn using VESTA1 and Ramanspectra which were broadened by 7.0 and 0.05 cm−1 wide Lorentzians are shown by blue and red lines, respectively. The bond lengthsin Si3O10 and SiO4 units in α-Yb2Si2O7 are summarised in Table S1.
10-4 10-3 10-2 10-1
A [Å]
8
9
10
11
12
13
14
15
16
∆l ij
Fig. S4 Dependence of maximum deviations in a bond length, ∆li j, on an amplitude, A, for the Si-O4 bond in X2-Yb2SiO5 for the 853 cm-1 peak,shown in Fig. S5 (f).
References1 K. Momma, F. Izumi, J. Appl. Crystallogr., 2011, 44, 1272–1276.
3
(c) 964 cm-1
(a)
(d) 919 cm-1
(e) 878 cm-1 (f) 853 cm-1
(b)
O1
O2 O3
O4Si
1.65
1.63
1.64
1.64
964919
878853
Fig. S5 (a) Structure of the SiO4 unit in X2-Yb2SiO5, (b) high frequency range of the calculated Raman spectrum of X2-Yb2SiO5, and (c-f) vibrationalamplitudes and ∆li j for the normal modes at 964, 919, 878, and 853 cm−1, respectively.
4
(c) 931 cm-1
(a)
(d) 928 cm-1
(e) 880 cm-1 (f) 829 cm-1
(b)
O1
O2 O3
O4Si
1.68
1.63
1.64
1.68
928+931
880
829
Fig. S6 (a) Structure of the SiO4 unit in X1-Yb2SiO5, (b) high frequency range of the calculated Raman spectrum of X1-Yb2SiO5, and (c-f) vibrationalamplitudes and ∆li j for the normal modes at 931, 928, 880, and 829 cm−1, respectively.
5
(c) 908 cm-1
(a)
(d) 886 cm-1
(e) 885 cm-1 (f) 643 cm-1
(b)
O1
O2
O3
O5
Si1
1.65
1.64
1.64
908885+886
643O4
O6
O7
Si2
1.65
Fig. S7 (a) Structure of the Si2O7 unit in β -Yb2Si2O7, (b) high frequency range of the calculated Raman spectrum of β -Yb2Si2O7, and (c-f) vibrationalamplitudes and ∆li j for the normal modes at 908, 886, 885, and 643 cm−1, respectively.
6
(c) 906 cm-1
(a)
(d) 870 cm-1
(e) 643 cm-1
(b)
O1
O2
O3
O5
Si1
1.65
1.64
1.64
906
870
643O4
O6
O7
Si2
1.64
Fig. S8 (a) Structure of the Si2O7 unit in γ-Yb2Si2O7, (b) high frequency range of the calculated Raman spectrum of γ-Yb2Si2O7, and (c-e) vibrationalamplitudes and ∆li j for the normal modes at 906, 870, and 643 cm-1, respectively.
7
(c) 957 cm-1
(a)
(d) 953 cm-1
(b)
O2
O1O3
O7
Si1
1.641.66
1.63
957+953
890674
O4O6
O5
Si21.68
(e) 890 cm-1 (f) 674 cm-1
Fig. S9 (a) Structure of the Si2O7 unit in X-Yb2Si2O7, (b) high frequency range of the calculated Raman spectrum of X-Yb2Si2O7, and (c-f) vibrationalamplitudes and ∆li j for the normal modes at 957, 953, 890, and 674 cm-1, respectively.
8
(c) 975 cm-1
(a)
(b)
O1
O3
Si1
975700
Si4
Si2
Si3
O4
O5
O6
O7
O8 O9
O10
O11O12
O13
O14
898
O2
Yb
Fig. S10 (a) Structure of the Si2O7 unit in α-Yb2Si2O7, (b) high frequency range of the calculated Raman spectrum of α-Yb2Si2O7, and (c) vibrationalamplitudes and ∆li j for the normal mode at 975 cm-1.
9
(e) 898 cm-1
(f) 700 cm-1
Fig. S10 (Continued) (d, e) normalized amplitudes and bond deviations for the normal modes at 898, and 700 cm-1, respectively.
10
Table S1 Bond lengths between Si and O atoms in α-Yb2Si2O7.
Bonds Bond length [Å]Si1-O1 1.62Si1-O2 1.64Si1-O3 1.66Si1-O4 1.66Si2-O4 1.66Si2-O5 1.64Si2-O6 1.62Si2-O7 1.68Si3-O7 1.75Si3-O8 1.65Si3-O9 1.63Si3-O10 1.63Si4-O11 1.67Si4-O12 1.64Si4-O13 1.62Si4-O14 1.62
11