Statistical Structure Gene Modeling of Alkali to Spectroscopic Properties of Nd<bold>∶</bold>Phosphate Glass

Yuechun Hou; Chen Dai; Liyan Zhang

doi:10.3788/CJL230530

Chinese Journal of Lasers, Volume. 50, Issue 22, 2211002(2023)

Statistical Structure Gene Modeling of Alkali to Spectroscopic Properties of Nd∶Phosphate Glass

Yuechun Hou^1,2, Chen Dai³, and Liyan Zhang^1、*

¹Key Laboratory of Materials for High Power Laser, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China

²Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China

³College of Materials Science and Engineering, Hunan University, Changsha 410082, Hunan, China

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Abstract Get PDF(in Chinese)

Figures & Tables(13)

Fig. 1. BL,PL,PN glass properties response as a function of the addition of Li₂O,Na₂O

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Fig. 2. IR spectra and residual between the simulated and measured spectra. (a) Measured (black symbols) and curve-fitting derived (green lines) IR spectra of BL, PL2, and PN2 glasses (spectra are shifted vertically for clarity),and individual bands (orange lines) of BL glass; (b) residual (ΔI) between the simulated and measured spectra of BL glass

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Fig. 3. IR difference spectrs of PL2 (black line) and PN2 (red dot) to BL glass

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Fig. 4. S-P models. (a) σ_emi; (b) τ_f; (c) Δλ_eff; (d) Ω₂; (e) Ω₄; (f) Ω₆ (* denotes BL, ▷ denotes PL1‒4, and ● denotes PN1‒4)

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Fig. 5. S-P models. (a) σ_emi(without PL2); (b) τ_f(without PN2); (c) Δλ_eff; (d) Ω₂(without PL2); (e) Ω₄(without PN2); (f) Ω₆(without PN3)

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Fig. 6. C-S models. (* denotes BL, ▷ denotes PL1‒4, ● denotes PN1‒4). (a) Li₂O; (b) Na₂O

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Fig. 7. Illustration of C-S-P model based glass property design for achieving specific composition

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Table 1. Composition of the glass samples (normalized)

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Table 1. Composition of the glass samples (normalized)

No.	Mole fraction /%
No.	Li₂O	Na₂O	K₂O	P₂O₅	MgO	Al₂O₃	R₂O₃	Nd₂O₃
BL	0	0	23.76	59.41	8.91	4.95	1.99	0.99
PL1	1.94	0	23.30	58.25	8.74	4.85	1.95	0.97
PL2	3.81	0	22.86	57.14	8.57	4.76	1.91	0.95
PL3	5.61	0	22.43	56.07	8.41	4.67	1.88	0.93
PL4	7.34	0	22.02	55.05	8.26	4.59	1.82	0.92
PN1	0	1.94	23.30	58.25	8.74	4.85	1.95	0.97
PN2	0	3.81	22.86	57.14	8.57	4.76	1.91	0.95
PN3	0	5.61	22.43	56.07	8.41	4.67	1.88	0.93
PN4	0	7.34	22.02	55.05	8.26	4.59	1.82	0.92
PLN	2.00	3.04	22.56	56.41	8.46	4.70	1.88	0.94

Table 2. Properties of the glass samples

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Table 2. Properties of the glass samples

No.	σ_emi /pm²	Ω₂ /pm²	Ω₄ /pm²	Ω₆ /pm²	τ_f /μs	Δλ_eff /nm	n_d
BL	4.37	4.68	5.20	6.17	337	24.69	1.5083
PL1	4.26	4.74	4.82	5.85	326	24.41	1.5108
PL2	4.31	4.50	4.93	5.84	330	24.39	1.5107
PL3	4.23	4.54	4.78	5.77	334	24.71	1.5114
PL4	4.34	4.46	5.07	5.87	327	24.66	1.5128
PN1	4.28	4.50	4.77	5.83	330	24.56	1.5088
PN2	4.30	4.50	4.87	5.84	336	24.45	1.5088
PN3	4.45	4.53	4.99	5.99	341	24.29	1.5083
PN4	4.10	4.84	4.55	5.46	354	24.20	1.5088
PLN	4.13	4.62	4.84	5.73	331	24.49	1.5119

Table 3. Integral area of IR bands derived from IR curve fitting

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Table 3. Integral area of IR bands derived from IR curve fitting

No.	Integral area
No.	A₁	A₂	A₃	A₄	A₅	A₆	A₇	A₈	A₉	A₁₀	A₁₁	A₁₂	A₁₃	A₁₄	A₁₅
BL	21.9	3.1	0.9	2.7	1.2	4.3	6.9	9.2	8.5	12.0	3.7	1.1	7.2	8.6	8.8
PL1	22.2	5.2	0.8	2.4	2.0	4.7	7.2	9.0	7.8	10.7	4.3	1.0	6.0	7.4	9.1
PL2	21.0	6.1	0.6	2.3	2.5	5.0	7.3	9.0	7.6	9.6	5.3	0.5	5.7	7.1	10.3
PL3	23.5	3.7	0.9	3.0	1.6	4.7	7.2	9.1	8.2	11.7	3.1	1.2	6.2	7.6	8.5
PL4	23.1	3.6	0.8	2.6	2.2	5.1	7.4	9.0	7.8	10.6	4.2	0.9	6.2	7.5	8.9
PN1	21.9	4.7	0.7	2.4	2.5	5.4	7.8	9.1	7.6	8.9	5.8	0.6	5.5	6.7	10.4
PN2	21.7	2.5	1.0	2.8	0.9	4.1	7.1	9.9	8.8	12.1	3.5	1.2	7.3	8.5	8.4
PN3	22.3	4.2	0.8	2.4	2.2	5.1	7.7	9.3	7.9	9.7	5.2	1.2	6.1	7.1	8.7
PN4	20.4	7.1	0.7	2.3	2.5	5.2	7.6	9.1	7.5	8.6	5.9	0.7	5.6	6.7	10.0
PLN	21.4	5.8	0.7	2.4	2.3	4.9	7.4	9.1	7.7	10.4	4.7	0.8	5.7	7.1	9.6

Table 4. IR band positions identified from this study and band assignments taken from literatures

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Table 4. IR band positions identified from this study and band assignments taken from literatures

A_i（structural unit）	Bands observed in this work /cm^-1	Band assignments based on phosphates vibrational spectra taken from literatures
A₁	477‒491	458‒680 cm^-1，bending vibrations of bridging phosphorus：δ（O—P—O）；a fundamental frequency of PO $_{4}^{3 -}$ or harmonics of P=O bending vibrations
A₂	569‒582
A₃	716‒720	684‒830 cm^-1，symmetric stretching vibration of P—O—P bridges bonded to a phosphorus atom in P^（2） unit：ν_s（P—O—P）
A₄	762‒762
A₅	863‒877	860‒1002 cm^-1，asymmetric stretching vibration of P—O—P bridges：ν_as（P—O—P）of P^（2） unit
A₆	900‒919
A₇	1006‒1016	1000‒1100 cm^-1，symmetric vibration of P—O^-groups of chain terminator：ν_s（P—O^-）of chain terminator；asymmetric stretching vibration of PO $_{2}^{-}$ groups：ν_as（PO $_{2}^{-}$ ）of P^（2） unit
A₈	1108‒1118	1108‒1118 cm^-1，stretching vibration of PO $_{2}^{-}$ terminal groups：ν_s（PO $_{2}^{-}$ ）
A₉	1162‒1170	1148‒1280 cm^-1，asymmetric stretching vibration of PO $_{2}^{-}$ groups：ν_as（PO $_{2}^{-}$ ）of P^（2） unit
A₁₀	1263‒1273
A₁₁	1304‒1327	1250‒1420cm^-1，asymmetric stretching vibration of the two nonbridging oxygen atoms bonded to phosphorus atoms：ν_as（O—P—O）or ν_as（PO $_{2}^{-}$ ）；harmonics of ν（P—O）from two bridging oxygen bonds and two non-bridging bonds，（P—O）and（P—O^-）
A₁₂	1376‒1420
A₁₃	1485‒1575	bonding vibration of P—OH：ν_as（O—H）
A₁₄	1632‒1638
A₁₅	1835‒1909

Table 5. Analysis of variance of statistical S-P models

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Table 5. Analysis of variance of statistical S-P models

Item	σ_emi	τ_f	Δλ_eff	Ω₂	Ω₄	Ω₆
Analysis of variance
Root mean square error	0.0196	2.1109	0.0327	0.0356	0.0417	0.0292
Corrected total degree of freedom	7	7	8	7	7	7
F-ratio	47.47	32.30	60.65	25.18	40.4746	74.87
Prob>F	<0.0048	<0.0084	<0.0054	<0.0121	<0.0061	<0.0025
Parameter estimation
Intercept（t-ratio）	5.94（36.52）	459.06（19.01）	26.41（40.34）	9.78（7.16）	6.84（8.93）	-28.86（-7.95）
A₁（t-ratio）	Insignificant	-16.57（-10.81）	Insignificant	-0.13（-4.60）	Insignificant	Insignificant
A₂（t-ratio）	-0.11（-11.25）	Insignificant	-0.12（-7.92）	0.07（3.13）	-0.12（-6.07）	0.20（6.80）
A₃（t-ratio）	-1.02（-5.13）	Insignificant	Insignificant	1.60（5.84）	-2.79（-6.72）	Insignificant
A₄（t-ratio）	-0.27（-4.99）	36.94（5.75）	0.47（5.81）	Insignificant	Insignificant	Insignificant
A₆（t-ratio）	Insignificant	23.09（3.42）	Insignificant	Insignificant	Insignificant	Insignificant
A₇（t-ratio）	Insignificant	Insignificant	Insignificant	Insignificant	Insignificant	2.73（9.25）
A₈（t-ratio）	Insignificant	Insignificant	-0.41（-8.25）	-0.44（-4.65）	Insignificant	Insignificant
A₁₂（t-ratio）	0.36（6.18）	Insignificant	Insignificant	Insignificant	Insignificant	Insignificant
A₁₃（t-ratio）	Insignificant	38.02（7.90）	Insignificant	Insignificant	0.34（6.86）	Insignificant
A₁₄（t-ratio）	Insignificant	Insignificant	Insignificant	Insignificant	Insignificant	4.34（11.08）
A₁₅（t-ratio）	Insignificant	Insignificant	0.13（5.17）	Insignificant	-0.14（-2.92）	Insignificant

Table 6. Model validation results and relative error
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Table 6. Model validation results and relative error
Parameter Measured value Predicted value
Relative error /
%
σ_emi /pm² 4.13 4.14 0.24
τ_f /μs 331 333 0.60
Δλ_eff /nm 24.49 24.5 0.04
Ω₂ /pm² 4.62 4.62 0.01
Ω₄ /pm² 4.84 4.83 0.21
Ω₆ /pm² 5.73 5.72 0.17

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Yuechun Hou, Chen Dai, Liyan Zhang. Statistical Structure Gene Modeling of Alkali to Spectroscopic Properties of Nd∶Phosphate Glass[J]. Chinese Journal of Lasers, 2023, 50(22): 2211002

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