燃烧合成氮化硅粉体的性能一致性评价方法和应用

doi:10.15541/jim20230058

无机材料学报 ›› 2023, Vol. 38 ›› Issue (10): 1169-1175.DOI: 10.15541/jim20230058 CSTR: 32189.14.10.15541/jim20230058

所属专题：【结构材料】超高温结构陶瓷(202409)

燃烧合成氮化硅粉体的性能一致性评价方法和应用

李宏华¹(), 东婉茹²(), 王良¹, 杨增朝¹, 李江涛¹()

1.中国科学院理化技术研究所, 低温重点实验室, 北京 100190
2.齐鲁中科光物理与工程技术研究院, 济南 250000

收稿日期:2023-02-06 修回日期:2023-03-08 出版日期:2023-10-20 网络出版日期:2023-03-24
通讯作者: 李江涛, 研究员. E-mail: lijiangtao@mail.ipc.ac.cn;
东婉茹, 助理工程师, E-mail: gntcdongwr@casiop.ac.cn
作者简介:李宏华(1994-), 女, 助理研究员. E-mail: lihonghua@mail.ipc.ac.cn
基金资助:
国家重点研发计划(2022YFE0201200);国家重点研发计划(2017YFB0310303)

Consistency of Silicon Nitride Powders Produced by Combustion Synthesis: Evaluation and Application

LI Honghua¹(), DONG Wanru²(), WANG Liang¹, YANG Zengchao¹, LI Jiangtao¹()

1. Key Laboratory of Cryogenics, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing 100190, China
2. Institute of Optical Physics and Engineering Technology, Qilu Zhongke, Jinan 250000, China

Received:2023-02-06 Revised:2023-03-08 Published:2023-10-20 Online:2023-03-24
Contact: LI Jiangtao, professor. E-mail: lijiangtao@mail.ipc.ac.cn;
DONG Wanru, junior engineer. E-mail: gntcdongwr@casiop.ac.cn
About author:LI Honghua (1994-), female, lecturer. E-mail: lihonghua@mail.ipc.ac.cn
Supported by:
National Key R&D Program of China(2022YFE0201200);National Key R&D Program of China(2017YFB0310303)

摘要/Abstract

摘要：

陶瓷粉体的批次稳定性是陶瓷制品生产商最关心的核心指标, 却又长期无据可依。本研究以燃烧合成的氮化硅粉体为样本, 量化评价不同批次生产的氮化硅粉体的相似程度。首先构建了涵盖静态理化指标、动态流动性指标的粉体性能评价参数体系, 进而测试得到在该参数体系中氮化硅粉体的全部性能数据, 随后对所得性能数据分别采用余弦相似度法和欧氏距离法进行计算, 得到了粉体性能一致性评价数据。结果表明, 基于该参数体系的余弦相似度和欧氏距离均能反映批次粉体间的相似程度, 量化显示出不同批次粉体的差异, 两种方法的计算结果相互验证。对判定为不相似的粉体, 追溯工艺流程中的差异找到了控制氮化硅粉体一致性的关键环节—原料硅粉; 对判定为高度相似的粉体划分为同类, 为不同批次氮化硅粉体的类别划分提供了量化依据。该工作建立的“粉体性能一致性评价体系”为氮化硅粉体产品质量的批次稳定性(性能一致性)提供了有效的评价手段和量化依据。

关键词: 一致性评价, 氮化硅粉体, 余弦相似度, 欧氏距离

Abstract:

The batch stability of ceramic powders is a core indicator that manufacturers of ceramic products are most concerned about, yet has long been undocumented. In this study, the similarity of Si₃N₄ powders produced in different batches was quantitatively evaluated by taking combustion-synthesized Si₃N₄ powders as the sample. A system of powder performance evaluation parameters covering static physicochemical and dynamic flowability indices was firstly constructed. Then, all performance data of Si₃N₄ powders in this parameter system were retested. Subsequently, the consistency evaluation data of Si₃N₄ powders were obtained using the cosine similarity method and the Euclidean distance method. The results show that both methods based on this parameter system can reflect the similarity between batches of powders and quantitatively show the differences between them. Calculation results of the two methods are mutually verified. For powders judged to be dissimilar, differences in the process were traced to find the key link in the consistency between the Si₃N₄powders and the raw silicon powders. For powders judged to be highly similar, they were classified as the same class. These study provides a quantitative basis for the classification of different batches of silicon nitride powders. The “Powder Consistency Evaluation System” established in this work presents an effective evaluation tool and quantitative basis for batch stability (performance consistency) of silicon nitride powder.

Key words: consistency evaluation, silicon nitride powders, cosine similarity, Euclidean distance

中图分类号:

TQ174

李宏华, 东婉茹, 王良, 杨增朝, 李江涛. 燃烧合成氮化硅粉体的性能一致性评价方法和应用[J]. 无机材料学报, 2023, 38(10): 1169-1175.

LI Honghua, DONG Wanru, WANG Liang, YANG Zengchao, LI Jiangtao. Consistency of Silicon Nitride Powders Produced by Combustion Synthesis: Evaluation and Application[J]. Journal of Inorganic Materials, 2023, 38(10): 1169-1175.

图/表 8

参考文献 17

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General indicator	Secondary indicator	Symbol	Unit	Method	Test equipment
Physical property	Particle size	D₁₀	μm	Laser diffraction method	Particle diameter sizer (Dandong Bettersize Instruments, Bettersiza 2600)
		D₅₀	μm
		D₉₀	μm
	Bulk density	ρ_B	kg/m³	Weight-volume method	Intelligent integrated powder characterizer (Dandong Bettersize Instruments, BT-1001)
	Specific surface area	S	m²/g	Gas adsorption method	Gas absorption powder specific surface tester (MicrotracBEL, Belsorp maxⅡ)
Component property	α phase content	A	% (in mass)	Mean-normalised- intensity method	X-ray diffractometers (Rigaku Corporation, MiniFlex600)
	O content	O	% (in mass)	Infrared detection method (CO/CO₂)	Nitrogen/oxygen analyz (HORIBA, EMGA- 820)
	Moisture content	H₂O	% (in mass)	Gravimetric method	Rapid moisture tester (Shenzhen Guanya, SZ-GY820FT)

General indicator	Secondary indicator	Symbol	Unit	Method	Test equipment
Physical property	Particle size	D₁₀	μm	Laser diffraction method	Particle diameter sizer (Dandong Bettersize Instruments, Bettersiza 2600)
		D₅₀	μm
		D₉₀	μm
	Bulk density	ρ_B	kg/m³	Weight-volume method	Intelligent integrated powder characterizer (Dandong Bettersize Instruments, BT-1001)
	Specific surface area	S	m²/g	Gas adsorption method	Gas absorption powder specific surface tester (MicrotracBEL, Belsorp maxⅡ)
Component property	α phase content	A	% (in mass)	Mean-normalised- intensity method	X-ray diffractometers (Rigaku Corporation, MiniFlex600)
	O content	O	% (in mass)	Infrared detection method (CO/CO₂)	Nitrogen/oxygen analyz (HORIBA, EMGA- 820)
	Moisture content	H₂O	% (in mass)	Gravimetric method	Rapid moisture tester (Shenzhen Guanya, SZ-GY820FT)

General indicator	Secondary indicator	Symbol	Unit	Definition
Stability and variable flow rate	Basic flowability energy	BFE	mJ	The energy required for the rotor to overcome the resistance of the powder to rotate
	Stability index	SI	—	Repeated measurements of powder flow energy to characterise its stability
	Flow rate index	FRI	—	Measurement of flow energy at different speeds
	Specific energy	SE	mJ/g	Data measured during the upward movement of the blade through the powder sample
Compressibility	Conditioned bulk density	CBD	g/mL	Loose packing density of pre-treated powders
Compressibility	Compressibility	CPS_m	%	Compressibility at positive stress m kPa
Shear test	Cohesion	C_m	kPa	Shear strength at zero positive stress for a pre-consolidated positive stress of m kPa
	Unconfined yield strength	UYS_m	kPa	The maximum principal stress corresponding to a molar circle tangent to the yield trajectory at a pre- consolidation stress of m kPa and a minimum principal stress of 0
	Maximum principal stress	MPS_m	kPa	Maximum compressive stress calculated from the molar circle at steady state flow under a pre-consolidated positive stress of m kPa
	Flow function	FF_m	—	Ratio of the above maximum principal stress to the unconfined yield strength
	Angle of internal friction	AIF	°	The angle between the shear linear yield trajectory and the x-axis, characterizing the ease with which the powder particles can slide against each other
Aeration test	Aerated energy	AE_n	—	The energy required to move the powder sample when filling the gas at a rate of n mm/s
	Aeration ratio	AR	—	Ratio of the base flow energy to the filling energy after the powder having reached stability in the filling test
	Normalized aeration sensitivity	NAS	s/mm	Sensitivity to the effect of air introduced by the powder, normalized BFE to air velocity ratio
Permeability	Pressure drop	PD_m	100 Pa	Pressure reduction after passing air through a powder sample when a positive stress of m kPa is applied and the air velocity is maintained at 0.5 mm/s

General indicator	Secondary indicator	Symbol	Unit	Definition
Stability and variable flow rate	Basic flowability energy	BFE	mJ	The energy required for the rotor to overcome the resistance of the powder to rotate
	Stability index	SI	—	Repeated measurements of powder flow energy to characterise its stability
	Flow rate index	FRI	—	Measurement of flow energy at different speeds
	Specific energy	SE	mJ/g	Data measured during the upward movement of the blade through the powder sample
Compressibility	Conditioned bulk density	CBD	g/mL	Loose packing density of pre-treated powders
Compressibility	Compressibility	CPS_m	%	Compressibility at positive stress m kPa
Shear test	Cohesion	C_m	kPa	Shear strength at zero positive stress for a pre-consolidated positive stress of m kPa
	Unconfined yield strength	UYS_m	kPa	The maximum principal stress corresponding to a molar circle tangent to the yield trajectory at a pre- consolidation stress of m kPa and a minimum principal stress of 0
	Maximum principal stress	MPS_m	kPa	Maximum compressive stress calculated from the molar circle at steady state flow under a pre-consolidated positive stress of m kPa
	Flow function	FF_m	—	Ratio of the above maximum principal stress to the unconfined yield strength
	Angle of internal friction	AIF	°	The angle between the shear linear yield trajectory and the x-axis, characterizing the ease with which the powder particles can slide against each other
Aeration test	Aerated energy	AE_n	—	The energy required to move the powder sample when filling the gas at a rate of n mm/s
	Aeration ratio	AR	—	Ratio of the base flow energy to the filling energy after the powder having reached stability in the filling test
	Normalized aeration sensitivity	NAS	s/mm	Sensitivity to the effect of air introduced by the powder, normalized BFE to air velocity ratio
Permeability	Pressure drop	PD_m	100 Pa	Pressure reduction after passing air through a powder sample when a positive stress of m kPa is applied and the air velocity is maintained at 0.5 mm/s

	General indicator	Secondary indicator	Symbol	Unit	Class ①	Class ②	Class ③
Physical/ chemical indicator	Physical property	Size	D₁₀	μm	1.870	1.854	2.275
			D₅₀	μm	6.439	6.158	7.798
			D₉₀	μm	16.819	16.038	19.092
		Bulk density	ρ_B	kg/m³	0.229	0.211	0.261
		Specific surface area	S	m²/g	2.599	2.480	1.892
	Component property	α phase content	A	% (in mass)	92.625	94.350	92.231
		O content	O	% (in mass)	1.368	0.940	0.800
		Moisture content	H₂O	% (in mass)	1.086	1.206	1.654
Liquidity indicator	Stability and variable flow rate	Basic flowability energy	BFE	mJ	412.750	458.000	510.500
		Stability index	SI	—	1.058	1.009	1.033
		Flow rate index	FRI	—	1.840	1.659	1.731
		Specific energy	SE	mJ/g	9.283	8.986	9.423
	Compressibility	Conditioned bulk density	CBD	g/mL	0.295	0.287	0.403
	Compressibility	Compressibility	CPS_m	%	32.463	37.462	33.388
	Shear test	Cohesion	C_m	kPa	1.609	1.949	1.711
		Unconfined yield strength	UYS_m	kPa	6.540	7.874	6.989
		Maximum principal stress	MPS_m	kPa	28.175	28.337	28.281
		Flow function	FF_m	—	4.341	3.619	4.055
		Angle of internal friction	AIF	°	37.612	37.325	37.800
	Aeration Test	Aerated energy	AE_n	—	100.200	140.750	104.262
		Aeration ratio	AR	—	4.053	3.975	6.719
		Normalized aeration sensitivity	NAS	s/mm	0.119	0.089	0.119
	Permeability	Pressure drop	PD_m	mbar	20.025	12.492	5.169

燃烧合成氮化硅粉体的性能一致性评价方法和应用

Consistency of Silicon Nitride Powders Produced by Combustion Synthesis: Evaluation and Application

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参考文献 17

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	批号	测试时间	相含量 /%	粒度/µm			氧含量/%	水分 /%	松堆密度 /(g·cm^-3)	比表面 /(m²·g^-1)	稳定性和变流速					压缩性	剪切性能					充气性			透气性 PD(压降)
	批号	测试时间	相含量 /%	D₁₀	D₅₀	D₉₀	氧含量/%	水分 /%	松堆密度 /(g·cm^-3)	比表面 /(m²·g^-1)	BFE	SI	FRI	SE	CBD	CPS	Cohesion	UYS	MPS	FF	AIF	AE	AR	NAS	透气性 PD(压降)
0	Y220317	2022.3	93.9	1.864	6.57	17.1	1.362	1.46	0.24	2.590	413	1.07	1.82	9.25	0.291	33.1	1.64	6.63	28.1	4.24	37.2	105	3.98	0.119	22.7
1	Y220321	2022.3	93.3	1.865	6.798	17.88	1.414	0.98	0.24	2.770	450	1.09	1.78	9.62	0.310	33.4	1.61	6.48	27.9	4.31	37.2	97.9	4.35	0.117	11.5
2	Y2203172	2022.3	95.0	2.02	6.518	16.52	1.124	0.77	0.208	2.210	382	1.04	1.8	8.85	0.272	32.8	1.48	6.13	28.4	4.63	38.6	94.5	3.86	0.105	19.7
3	Y2201141	2022.3	90.8	1.868	6.317	16.75	1.699	1.24	0.22	2.790	407	1.06	1.81	9.46	0.294	32.1	1.57	6.39	28	4.39	37.6	106	3.7	0.118	23.9
4	Y2201142	2022/4/19	90.7	1.933	6.531	17.14	1.538	0.71	0.213	2.610	418	1.02	1.92	9.5	0.289	31	1.58	6.34	27.9	4.4	37.1	95.9	4.41	0.137	13.9
5	Y2204022	2022/4/15	93.0	1.796	6.376	16.65	1.375	0.94	0.23	2.790	375	1.03	1.86	9.03	0.28	32.7	1.71	6.97	28.8	4.12	37.8	95.3	3.82	0.111	23.2
6	Y2204021	2022/4/15	93.4	1.707	6.019	15.94	1.336	1.07	0.24	2.510	365	1.1	1.93	9.04	0.292	31	1.37	5.58	27.8	4.99	37.7	76	4.8	0.144	21.1
7	Y220415	2022/4/15	90.9	1.907	6.387	16.57	1.098	1.52	0.24	2.520	492	1.05	1.8	9.51	0.336	33.6	1.91	7.8	28.5	3.65	37.7	131	3.5	0.103	24.2
8	Y220503	2022/5/4	88.0	2.496	7.73	18.58	0.678	1.65	0.268	1.720	474	1.11	1.83	9.26	0.355	32.6	1.68	6.71	27.7	4.13	36.7	99.6	5.04	0.0736	2.45
9	Y220513	2022/5/19	88.0	2.239	7.127	17.5	0.865	1.14	0.246	2.040	482	1.07	1.86	9.7	0.337	30.2	1.59	6.41	28.1	4.23	37.3	111	4.5	0.0743	1.19
10	Y220602	2022/6/2	89.6	2.378	7.522	17.68	0.683	0.84	0.266	1.620	495	1.06	1.85	9.64	0.355	29.1	1.55	6.28	28	4.45	37.4	81.4	7.09	0.0955	4.1
11	Y220606	2022/6/6	89.6	2.58	7.97	18.31	0.695	1.03	0.254	1.750	531	1	1.68	9.03	0.351	31.5	1.61	6.55	27.7	4.22	37.6	95.7	5.82	0.0896	5.87
12	Y220629	2022/6/29	93.7	1.793	6.212	16.48	1.089	1.15	0.20	2.540	508	1	1.67	9.31	0.294	37.9	2.02	8.17	28.5	3.48	37.5	152	3.76	0.0965	11.7
13	Y220630	20220/6/30	94.1	1.836	6.294	16.55	0.972	0.89	0.204	2.470	440	1.01	1.62	8.69	0.284	37.5	1.95	7.99	28.6	3.58	37.9	130	3.56	0.0634	14.7
14	Y220715	2022/7/15	93.0	1.779	5.617	15.42	0.841	0.84	0.228	2.720	451	1	1.76	9.12	0.298	38.1	1.86	7.56	28.3	3.75	37.6	135	3.87	0.0963	11.9
15	Y220726	2022/7/28	94.2	1.831	5.906	15.59	0.971	1.07	0.213	2.36	453	1.03	1.64	8.82	0.285	35.7	1.84	7.46	28	3.76	37.4	115	4.25	0.0881	14.5
16	Y220727	2022/7/28	95.5	1.873	6.131	16.00	0.867	1.19	0.214	2.44	424	1.02	1.73	8.88	0.291	37.3	1.78	7.17	28.1	3.91	37.2	132	4.21	0.103	14.8
17	Y220808	2022/8/10	94.3	1.946	6.571	16.5	0.931	1.13	0.196	2.71	424	0.987	1.64	8.75	0.272	37.1	2.05	8.26	28.6	3.47	37.1	133	3.96	0.0814	9.44
18	Y220816	2022/8/16	95	1.952	6.444	16.12	0.948	1.71	0.216	2.53	484	0.995	1.58	8.97	0.282	38.7	2.3	9.16	28.6	3.12	36.7	187	3.82	0.0844	11.7
19	Y220830	2022/8/30	95	1.819	6.091	15.64	0.902	1.67	0.219	2.07	480	1.03	1.63	9.35	0.291	37.4	1.79	7.22	28	3.88	37.2	142	4.37	0.102	11.2
20	Y220907	2022/9/7	94.2	2.175	7.215	17.71	0.780	1.17	0.229	1.880	471	0.968	1.8	9.54	0.308	33.8	1.75	7.09	28.4	4	37.5	110	6.74	0.0579	0.735
21	Y220921	2022/9/21	94.4	2.264	7.661	18.58	0.830	1.29	0.274	1.75	517	1.05	1.75	9.54	0.346	40	1.67	6.89	28.4	4.12	38.2	161	4.44	0.0827	1.19
22	Y220923	2022/9/26	92.6	2.416	8.054	19	0.760	2.69	0.256	1.96	509	0.995	1.74	9.59	0.341	29.7	1.53	6.34	28.3	4.46	38.6	48.5	14.9	0.0839	2.95
23	Y220927	2022/9/27	92.6	2.383	8.046	19.29	0.720	2.57	0.256	1.77	531	0.986	1.68	9.75	0.343	34.7	1.92	7.77	28.4	3.65	37.3	94.7	5.34	0.0873	3.81
24	Y220928	2022/9/28	92.8	2.468	8.37	19.82	0.700	1.69	0.259	1.87	562	0.944	1.67	9.74	0.351	31.5	2	8.23	29.6	3.59	38	122	5.45	0.114	7.1
25	Y220930	2022/9/30	94	2.308	7.787	18.68	0.760	2.61	0.246	1.81	600	1.07	1.74	10	0.351	34.8	1.82	7.66	29.4	3.84	39.1	139	4.83	0.105	5.5
26	Y221026	2022/10/26	92.5	2.25	7.838	19.33	0.750	1.73	0.263	1.73	497	1.03	1.7	9.13	0.332	36.2	1.72	7.02	28	3.99	37.8	76.3	8.57	0.151	6.42
27	Y221027	2022/10/28	93.4	2.071	7.371	18.62	0.830	1.97	0.26	1.97	534	1.05	1.51	9.57	0.345	35.5	1.81	7.39	28	3.78	37.7	40.3	15.8	0.14	8.3
28	Y221103	2022/11/2	93.6	2.127	7.65	19.24	0.810	1.86	0.288	1.86	435	1.02	1.75	8.92	0.315	33.9	1.62	6.51	27.7	4.25	37.2	109	5.01	0.182	6.73
29	Y221104	2022/11/4	93.9	2.26	8.356	21.13	0.89	1.01	0.281	2.16	471	1.04	1.75	9.13	0.321	32.3	1.56	6.47	28.2	4.35	38.4	109	5.3	0.173	6.6
30	Y221107	2022/11/9	92.3	2.05	7.604	18.95	0.94	1.21	0.257	1.94	490	1.04	1.74	9.13	1.335	35.1	1.68	6.9	28.3	4.1	38.1	97.1	6.53	0.161	7.18
31	Y221109	2022/11/9	94.6	2.082	7.814	19.86	0.9	1.05	0.258	2.13	547	1.05	1.73	9.44	0.34	33.9	1.77	7.16	28.3	3.95	37.3	184	3.31	0.134	7.59
32	Y221114	2022/11/15	93.8	2.021	7.874	20.9	0.99	2.13	0.245	2.19	493	1.02	1.72	9.2	0.328	33.2	1.84	7.54	28.4	3.77	38.1	99.6	5.57	0.159	5.73

	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30	31	32
0	1	0.957	0.9	0.96	0.922	0.957	0.93	0.927	0.677	0.749	0.695	0.651	0.827	0.81	0.853	0.892	0.904	0.786	0.736	0.86	0.741	0.747	0.654	0.683	0.65	0.728	0.758	0.716	0.798	0.796	0.768	0.832	0.814
1	0.957	1	0.843	0.937	0.938	0.9	0.89	0.883	0.718	0.822	0.75	0.686	0.82	0.765	0.835	0.847	0.854	0.758	0.697	0.836	0.774	0.786	0.676	0.699	0.66	0.742	0.769	0.746	0.788	0.827	0.788	0.865	0.824
2	0.9	0.843	1	0.864	0.834	0.915	0.9	0.81	0.569	0.665	0.664	0.648	0.75	0.812	0.795	0.847	0.865	0.735	0.62	0.781	0.739	0.739	0.648	0.582	0.619	0.711	0.716	0.624	0.722	0.792	0.742	0.758	0.748
3	0.96	0.937	0.864	1	0.955	0.943	0.916	0.9	0.6	0.732	0.637	0.585	0.778	0.742	0.8	0.816	0.809	0.708	0.639	0.765	0.643	0.644	0.586	0.576	0.563	0.648	0.648	0.621	0.676	0.713	0.695	0.737	0.725
4	0.922	0.938	0.834	0.955	1	0.906	0.897	0.848	0.641	0.791	0.716	0.636	0.752	0.676	0.778	0.758	0.78	0.684	0.596	0.724	0.709	0.662	0.606	0.595	0.599	0.637	0.678	0.61	0.715	0.758	0.722	0.771	0.744
5	0.957	0.9	0.915	0.943	0.906	1	0.898	0.914	0.554	0.677	0.607	0.567	0.83	0.849	0.875	0.874	0.881	0.816	0.722	0.783	0.702	0.674	0.582	0.59	0.635	0.675	0.669	0.618	0.694	0.741	0.718	0.757	0.759
6	0.93	0.89	0.9	0.916	0.897	0.898	1	0.785	0.581	0.681	0.657	0.542	0.636	0.641	0.733	0.763	0.787	0.587	0.489	0.712	0.592	0.613	0.571	0.47	0.442	0.571	0.643	0.582	0.723	0.726	0.688	0.682	0.67
7	0.927	0.883	0.81	0.9	0.848	0.914	0.785	1	0.695	0.785	0.703	0.684	0.902	0.858	0.898	0.896	0.876	0.826	0.826	0.874	0.768	0.773	0.653	0.758	0.763	0.818	0.758	0.732	0.73	0.747	0.767	0.844	0.817
8	0.677	0.718	0.569	0.6	0.641	0.554	0.581	0.695	1	0.926	0.922	0.897	0.546	0.503	0.547	0.568	0.587	0.514	0.532	0.634	0.769	0.827	0.772	0.832	0.73	0.778	0.846	0.723	0.811	0.796	0.754	0.804	0.76
9	0.749	0.822	0.665	0.732	0.791	0.677	0.681	0.785	0.926	1	0.947	0.856	0.643	0.557	0.651	0.614	0.629	0.558	0.543	0.674	0.829	0.835	0.786	0.801	0.764	0.827	0.791	0.694	0.754	0.808	0.766	0.837	0.77
10	0.695	0.75	0.664	0.637	0.716	0.607	0.657	0.703	0.922	0.947	1	0.914	0.538	0.476	0.556	0.553	0.576	0.46	0.447	0.622	0.827	0.831	0.835	0.802	0.783	0.806	0.848	0.749	0.806	0.853	0.792	0.822	0.762
11	0.651	0.686	0.648	0.585	0.636	0.567	0.542	0.684	0.897	0.856	0.914	1	0.588	0.567	0.567	0.6	0.609	0.559	0.551	0.638	0.824	0.855	0.841	0.856	0.841	0.81	0.897	0.772	0.834	0.881	0.807	0.846	0.81
12	0.827	0.82	0.75	0.778	0.752	0.83	0.636	0.902	0.546	0.643	0.538	0.588	1	0.949	0.949	0.946	0.929	0.951	0.947	0.932	0.8	0.786	0.556	0.733	0.742	0.787	0.71	0.704	0.654	0.675	0.717	0.838	0.796
13	0.81	0.765	0.812	0.742	0.676	0.849	0.641	0.858	0.503	0.557	0.476	0.567	0.949	1	0.929	0.959	0.935	0.964	0.921	0.878	0.752	0.757	0.519	0.657	0.687	0.729	0.676	0.648	0.62	0.665	0.685	0.779	0.751
14	0.853	0.835	0.795	0.8	0.778	0.875	0.733	0.898	0.547	0.651	0.556	0.567	0.949	0.929	1	0.948	0.951	0.917	0.882	0.903	0.766	0.77	0.526	0.647	0.654	0.714	0.684	0.652	0.67	0.678	0.707	0.794	0.735
15	0.892	0.847	0.847	0.816	0.758	0.874	0.763	0.896	0.568	0.614	0.553	0.6	0.946	0.959	0.948	1	0.979	0.931	0.907	0.945	0.755	0.769	0.558	0.67	0.65	0.731	0.724	0.714	0.705	0.698	0.722	0.814	0.77
16	0.904	0.854	0.865	0.809	0.78	0.881	0.787	0.876	0.587	0.629	0.576	0.609	0.929	0.935	0.951	0.979	1	0.929	0.89	0.948	0.791	0.794	0.578	0.687	0.659	0.731	0.748	0.699	0.757	0.732	0.74	0.835	0.787
17	0.786	0.758	0.735	0.708	0.684	0.816	0.587	0.826	0.514	0.558	0.46	0.559	0.951	0.964	0.917	0.931	0.929	1	0.959	0.866	0.767	0.725	0.519	0.69	0.706	0.702	0.672	0.645	0.635	0.65	0.663	0.781	0.764
18	0.736	0.697	0.62	0.639	0.596	0.722	0.489	0.826	0.532	0.543	0.447	0.551	0.947	0.921	0.882	0.907	0.89	0.959	1	0.897	0.747	0.734	0.495	0.739	0.726	0.726	0.671	0.667	0.634	0.596	0.637	0.788	0.746
19	0.86	0.836	0.781	0.765	0.724	0.783	0.712	0.874	0.634	0.674	0.622	0.638	0.932	0.878	0.903	0.945	0.948	0.866	0.897	1	0.822	0.852	0.638	0.781	0.714	0.825	0.788	0.781	0.767	0.718	0.753	0.864	0.808
20	0.741	0.774	0.739	0.643	0.709	0.702	0.592	0.768	0.769	0.829	0.827	0.824	0.8	0.752	0.766	0.755	0.791	0.767	0.747	0.822	1	0.925	0.838	0.901	0.888	0.893	0.852	0.781	0.782	0.824	0.789	0.887	0.852
21	0.747	0.786	0.739	0.644	0.662	0.674	0.613	0.773	0.827	0.835	0.831	0.855	0.786	0.757	0.77	0.769	0.794	0.725	0.734	0.852	0.925	1	0.785	0.885	0.845	0.912	0.906	0.801	0.85	0.875	0.847	0.927	0.862
22	0.654	0.676	0.648	0.586	0.606	0.582	0.571	0.653	0.772	0.786	0.835	0.841	0.556	0.519	0.526	0.558	0.578	0.519	0.495	0.638	0.838	0.785	1	0.869	0.824	0.857	0.871	0.869	0.782	0.82	0.763	0.739	0.84
23	0.683	0.699	0.582	0.576	0.595	0.59	0.47	0.758	0.832	0.801	0.802	0.856	0.733	0.657	0.647	0.67	0.687	0.69	0.739	0.781	0.901	0.885	0.869	1	0.936	0.928	0.909	0.857	0.83	0.814	0.792	0.865	0.901
24	0.65	0.66	0.619	0.563	0.599	0.635	0.442	0.763	0.73	0.764	0.783	0.841	0.742	0.687	0.654	0.65	0.659	0.706	0.726	0.714	0.888	0.845	0.824	0.936	1	0.92	0.86	0.796	0.774	0.834	0.792	0.869	0.887
25	0.728	0.742	0.711	0.648	0.637	0.675	0.571	0.818	0.778	0.827	0.806	0.81	0.787	0.729	0.714	0.731	0.731	0.702	0.726	0.825	0.893	0.912	0.857	0.928	0.92	1	0.88	0.832	0.782	0.828	0.82	0.879	0.9
26	0.758	0.769	0.716	0.648	0.678	0.669	0.643	0.758	0.846	0.791	0.848	0.897	0.71	0.676	0.684	0.724	0.748	0.672	0.671	0.788	0.852	0.906	0.871	0.909	0.86	0.88	1	0.922	0.945	0.936	0.899	0.896	0.941
27	0.716	0.746	0.624	0.621	0.61	0.618	0.582	0.732	0.723	0.694	0.749	0.772	0.704	0.648	0.652	0.714	0.699	0.645	0.667	0.781	0.781	0.801	0.869	0.857	0.796	0.832	0.922	1	0.819	0.814	0.815	0.8	0.872
28	0.798	0.788	0.722	0.676	0.715	0.694	0.723	0.73	0.811	0.754	0.806	0.834	0.654	0.62	0.67	0.705	0.757	0.635	0.634	0.767	0.782	0.85	0.782	0.83	0.774	0.782	0.945	0.819	1	0.941	0.867	0.893	0.913
29	0.796	0.827	0.792	0.713	0.758	0.741	0.726	0.747	0.796	0.808	0.853	0.881	0.675	0.665	0.678	0.698	0.732	0.65	0.596	0.718	0.824	0.875	0.82	0.814	0.834	0.828	0.936	0.814	0.941	1	0.893	0.923	0.934
30	0.768	0.788	0.742	0.695	0.722	0.718	0.688	0.767	0.754	0.766	0.792	0.807	0.717	0.685	0.707	0.722	0.74	0.663	0.637	0.753	0.789	0.847	0.763	0.792	0.792	0.82	0.899	0.815	0.867	0.893	1	0.867	0.883
31	0.832	0.865	0.758	0.737	0.771	0.757	0.682	0.844	0.804	0.837	0.822	0.846	0.838	0.779	0.794	0.814	0.835	0.781	0.788	0.864	0.887	0.927	0.739	0.865	0.869	0.879	0.896	0.8	0.893	0.923	0.867	1	0.922
32	0.814	0.824	0.748	0.725	0.744	0.759	0.67	0.817	0.76	0.77	0.762	0.81	0.796	0.751	0.735	0.77	0.787	0.764	0.746	0.808	0.852	0.862	0.84	0.901	0.887	0.9	0.941	0.872	0.913	0.934	0.883	0.922	1

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