1Dependence of Raman spectra on hydrostatic pressure

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