Data in Brief
Elsevier
image
Data on the theoretical X-Ray attenuation and transmissions for lithium-ion battery cathodes
Volume: 30
DOI 10.1016/j.dib.2020.105539
  • PDF   
  • XML   
  •       
Abstract

This article reports the data required for planning attenuation-based X-ray characterisation e.g. X-ray computed tomography (CT), of lithium-ion (Li-ion) battery cathodes. The data reported here is to accompany a co-submitted manuscript (10.1016/j.matdes.2020.108585 [1]) which compares two well-known X-ray attenuation data sources: Henke et al. and Hubbell et al., and applies methodology reported by Reiter et al. to extend this data towards the practical characterisation of prominent cathode materials. This data may be used to extend beyond the analysis reported in the accompanying manuscript, and may aid in the applications for other materials, not limited to Li-ion batteries.

Keywords
Heenan, Tan, Wade, Jervis, Brett, and Shearing: Data on the theoretical X-Ray attenuation and transmissions for lithium-ion battery cathodes

Specifications table

SubjectMaterials Science
Specific subject areaX-ray properties of prominent Li-ion battery cathode materials, for optimising X-ray computed tomography characterisation.
Type of data38 Tables
How data were acquiredNo experimental data was collected for this work, all data reported is calculated using spreadsheets generated in Excel 2016 software from spectroscopy and modelling data from published sources [2] and [3].
Data formatComputed from analysed from raw reference data.
Parameters for data collectionAll parameters and equations used for the calculations that generated this data are in Section 2.1.
Description for data collectionThe methodology for the calculations that were employed in order to obtain this data is outlined within the complimentary article and within Section 2 of this article.
Data source locationCity: London
Country: England
GPS: N/A
Data accessibilityWithin the article
Related research articleHeenan, T.M.M.
Theoretical transmissions for X-ray computed tomography studies of lithium-ion battery cathodes.
Materials & Design
10.1016/j.matdes.2020.108585

Value of the Data

    • This data allows for the optimisation of X-ray CT imaging for Li-ion cathodes
    • These tables will benefit all who investigate structures using attenuation-based X-ray imaging
    • This may also be used to calculated X-ray properties for analogous chemistries

Data description

Table 1 displays literature references for the crystallographic densities and chemical compositions for NMC111, 532, 622 and 811. Table 2, Table 3, Table 4, Table 5, Table 6, Table 7, Table 8, Table 9 report the first set of data calculated from the information published by Hubbell and Seltzer [2], followed by Table 10, Table 11, Table 12, Table 13, Table 14, Table 15, Table 16, Table 17, Table 18, Table 19 using information published by Henke et al. [3]. It should be noted that, for direct comparison, the same literature references for the crystallographic densities of the various NMC chemistries were used for both sets of calculations [4], [5], [6], [7]. Table 20, Table 21, Table 22, Table 23, Table 24, Table 25, Table 26, Table 27, Table 28, Table 29, Table 30, Table 31, Table 32, Table 33, Table 34, Table 35 report the theoretical X-ray transmissions for the various cathode materials for numerous experimental scenarios, e.g. incident beam energies and sample thickness. Using derivations outlined by Reiter et al. [8], the optimal thicknesses for NMC for beam energies from 1 – 100 keV are reported in Tables 36 and 37. And finally, the applicability of these values for operational experiments is considered by examining the influence of lithiaiton upon the aforementioned metrics in Table 38. For a full analysis and discussion see the related research article [1].

Table 1
Referenced crystallographic densities, in g cm−3 for four NMC chemistries (to 2 d.p) [47].
NMC111NMC532NMC622NMC811
ChemistryLiNi0.1Mn0.1Co0.1O2LiNi0.5Mn0.3Co0.2O2LiNi0.6Mn0.2Co0.2O2LiNi0.8Mn0.1Co0.1O2
ρ4.744.724.754.80
Table 2
X-ray mass attenuation coefficients for the constituent elements within NMC for incident beam energies of 1 – 10 keV, produced from work by Hubbell and Seltzer [2] and presented in cm2 g−1 to 2 d.p.
1 keV2 keV3 keV4 keV5 keV6 keV8 keV10 keV
Li233.9027.077.553.111.620.990.510.34
Ni9855.002049.00709.40328.20179.30109.0049.52209.00
Mn8093.001421.00485.10222.90121.2073.50273.40151.40
Co9796.001779.00612.90283.00154.3093.70324.80184.10
O4590.00694.90217.1093.1547.9027.7011.635.95
Table 3
X-ray mass attenuation coefficients for the constituent elements within NMC for incident beam energies of 10 – 100 keV, produced from work by Hubbell and Seltzer [2] and presented in cm2 g−1 to 2 d.p.
10 keV20 keV30 keV40 keV50 keV60 keV80 keV100 keV
Li0.340.190.160.160.150.140.140.13
Ni209.0032.2010.344.602.471.510.730.44
Mn151.4022.537.143.171.711.060.530.34
Co184.1028.038.963.982.141.310.640.39
O5.950.870.380.260.210.190.170.16
Table 4
X-ray mass attenuation coefficients for various NMC chemistries for incident beam energies of 1 – 10 keV, produced from work by Hubbell and Seltzer [2] and presented in cm2 g−1 to 2 d.p.
1 keV2 keV3 keV4 keV5 keV6 keV8 keV10 keV
NMC 1117056.501277.27432.33197.15106.5364.24131.49110.20
NMC 5327110.631314.75445.73203.44110.0166.37105.26113.84
NMC 6227221.131353.19459.47209.90113.5768.5492.36117.47
NMC 8117333.731407.53478.88219.01118.6171.6262.88122.56
Table 5
X-ray mass attenuation coefficients for various NMC chemistries for incident beam energies of 10 – 100 keV, produced from work by Hubbell et al. [1] and presented in cm2 g−1 to 2 d.p.
10 keV20 keV30 keV40 keV50 keV60 keV80 keV100 keV
NMC 111110.2016.755.392.431.340.850.440.29
NMC 532113.8417.355.592.521.390.870.460.30
NMC 622117.4717.965.792.611.430.900.470.31
NMC 811122.5618.816.072.741.500.940.490.32
Table 6
X-ray linear attenuation coefficients for various NMC chemistries for incident beam energies of 1 – 10 keV, produced from work by Hubbell and Seltzer [2] and presented in cm−1 to 2 d.p.
1 keV2 keV3 keV4 keV5 keV6 keV8 keV10 keV
NMC 11133,447.826054.242049.24934.51504.97304.48623.28522.33
NMC 53233,562.196205.632103.86960.26519.26313.25496.83537.32
NMC 62234,300.386427.662182.47997.01539.48325.58438.69557.99
NMC 81135,201.916756.142298.651051.24569.31343.78301.83588.31
Table 7
X-ray linear attenuation coefficients for various NMC chemistries for incident beam energies of 10 – 100 keV, produced from work by Hubbell and Seltzer [2] and presented in cm−1 to 2 d.p.
10 keV20 keV30 keV40 keV50 keV60 keV80 keV100 keV
NMC 111522.3379.4025.5711.536.354.012.101.40
NMC 532537.3281.9126.4011.906.554.132.151.42
NMC 622557.9985.3127.5112.406.824.292.231.46
NMC 811588.3190.2929.1513.147.214.522.331.52
Table 8
X-ray attenuation length for various NMC chemistries for incident beam energies of 1 – 10 keV, produced from work by Hubbell and Seltzer [2] and presented in µm to 2 d.p.
1 keV2 keV3 keV4 keV5 keV6 keV8 keV10 keV
NMC 1110.301.654.8810.7019.8032.8416.0419.15
NMC 5320.301.614.7510.4119.2631.9220.1318.61
NMC 6220.291.564.5810.0318.5430.7122.8017.92
NMC 8110.281.484.359.5117.5629.0933.1317.00
Table 9
X-ray attenuation length for various NMC chemistries for incident beam energies of 10 – 100 keV, produced from work by Hubbell and Seltzer [2] and presented in µm to 2 d.p.
10 keV20 keV30 keV40 keV50 keV60 keV80 keV100 keV
NMC 11119.15125.94391.07867.001573.692492.534753.607162.80
NMC 53218.61122.08378.81840.111526.832422.854643.217031.71
NMC 62217.92117.22363.44806.291467.192332.624491.836836.76
NMC 81117.00110.75343.04761.301387.442211.004283.766562.53
Table 10
X-ray attenuation lengths for the light elements within NMC for incident beam energies of 1 – 8 keV, produced from work by Henke et al. [3] and presented in cm to 2 d.p.
1 keV2 keV3 keV4 keV5 keV6 keV8 keV
Li0.010.070.280.711.442.475.03
O0.151.003.207.4414.6725.7262.10
Table 11
X-ray attenuation lengths for the light elements within NMC for incident beam energies of 10 – 30 keV, produced from work by Henke et al. [3] and presented in cm to 2 d.p.
10 keV20 keV30 keV
Li7.5011.7412.32
O124.57949.882188.29
Table 12
X-ray attenuation lengths for the heavy elements within NMC for incident beam energies of 1 – 8 keV, produced from work by Henke et al. [3] and presented in µm to 2 d.p.
1 keV2 keV3 keV4 keV5 keV6 keV8 keV
Ni0.110.561.643.526.4510.6623.76
Mn0.170.982.946.4511.9119.535.03
Co0.120.641.914.187.7612.853.52
Table 13
X-ray attenuation lengths for the heavy elements within NMC for incident beam energies of 10 – 30 keV, produced from work by Henke et al. [3] and presented in µm to 2 d.p.
10 keV20 keV30 keV
Ni5.4336.04113.42
Mn9.1063.52202.47
Co6.2542.24133.55
Table 14
X-ray linear attenuation coefficients for the constituent elements within NMC for incident beam energies of 1 – 8 keV, produced from work by Henke et al. [3] and presented in cm−1 to 2 d.p.
1 keV2 keV3 keV4 keV5 keV6 keV8 keV
Li118.9913.423.591.400.690.410.20
Ni92,912.6317,818.176093.962842.151550.51938.30420.95
Mn58,254.0110,241.163398.571550.98839.83512.051988.30
Co86,464.8015,618.925236.072391.961288.96778.432840.83
O6.601.000.310.130.070.040.02
Table 15
X-ray linear attenuation coefficients for the constituent elements within NMC for incident beam energies of 10 – 30 keV, produced from work by Henke et al. [3] and presented in cm−1 to 2 d.p.
10 keV20 keV30 keV
Li0.130.090.08
Ni1842.54277.5088.17
Mn1098.94157.4349.39
Co1601.10236.7274.88
O0.010.000.00
Table 16
X-ray mass attenuation coefficients for the constituent elements within NMC for incident beam energies of 1 – 8 keV, produced from work by Henke et al. [3] and presented in cm−2 g−1 to 2 d.p.
1 keV2 keV3 keV4 keV5 keV6 keV8 keV
Li222.8025.106.702.601.300.800.40
Ni10,437.302001.60684.60319.30174.20105.4047.30
Mn7980.001402.90465.60212.50115.0070.10272.40
Co9715.101754.90588.30268.80144.8087.50319.20
O4615.50699.20218.4094.1047.7027.2011.30
Table 17
X-ray mass attenuation coefficients for the constituent elements within NMC for incident beam energies of 10 – 30 keV, produced from work by Henke et al. [3] and presented in cm−2 g−1 to 2 d.p.
10 keV20 keV30 keV
Li0.200.200.20
Ni207.0031.209.90
Mn150.5021.606.80
Co179.9026.608.40
O5.600.700.30
Table 18
X-ray mass attenuation coefficients for the various NMC chemistries for incident beam energies of 1 – 8 keV, produced from work by Henke et al. [3] and presented in cm−2 g−1 to 2 d.p.
1 keV2 keV3 keV4 keV5 keV6 keV8 keV
NMC 1117144.061260.68419.02190.76102.3261.43129.58
NMC 5327266.101295.60432.23197.48106.1663.76103.59
NMC 6227417.661332.26445.63204.01109.7765.9290.62
NMC 8117611.091383.44464.69213.52115.1269.1461.28
Table 19
X-ray mass attenuation coefficients for the various NMC chemistries for incident beam energies of 10 – 30 keV, produced from work by Henke et al. [3] and presented in cm−2 g−1 to 2 d.p.
10 keV20 keV30 keV
NMC 111108.6516.035.10
NMC 532112.4516.665.31
NMC 622116.0117.265.50
NMC 811121.1718.135.79
Table 20
Theoretical X-ray transmission for NMC 111 for thicknesses of 1 – 10 µm and incident beam energies of 1 – 10 keV, presented as a percentage to 2 d.p.
1 keV2 keV3 keV4 keV5 keV6 keV8 keV10 keV
1 µm3.53%54.58%81.47%91.08%95.08%97.00%93.96%94.91%
2 µm0.12%29.79%66.38%82.95%90.39%94.09%88.28%90.08%
3 µm0.00%16.26%54.08%75.55%85.94%91.27%82.95%85.50%
4 µm0.00%8.88%44.06%68.81%81.71%88.53%77.93%81.15%
5 µm0.00%4.85%35.89%62.67%77.69%85.88%73.22%77.02%
6 µm0.00%2.64%29.24%57.08%73.86%83.30%68.80%73.10%
7 µm0.00%1.44%23.82%51.99%70.22%80.80%64.64%69.38%
8 µm0.00%0.79%19.41%47.35%66.77%78.38%60.74%65.85%
9 µm0.00%0.43%15.81%43.13%63.48%76.03%57.07%62.49%
10 µm0.00%0.23%12.88%39.28%60.35%73.75%53.62%59.31%
Table 21
Theoretical X-ray transmission for NMC 111 for thicknesses of 1 – 10 µm and incident beam energies of 10 – 100 keV, presented as a percentage to 2 d.p.
10 keV20 keV30 keV40 keV50 keV60 keV80 keV100 keV
1 µm94.91%99.21%99.74%99.88%99.94%99.96%99.98%99.99%
2 µm90.08%98.42%99.49%99.77%99.87%99.92%99.96%99.97%
3 µm85.50%97.65%99.24%99.65%99.81%99.88%99.94%99.96%
4 µm81.15%96.87%98.98%99.54%99.75%99.84%99.92%99.94%
5 µm77.02%96.11%98.73%99.42%99.68%99.80%99.89%99.93%
6 µm73.10%95.35%98.48%99.31%99.62%99.76%99.87%99.92%
7 µm69.38%94.59%98.23%99.20%99.56%99.72%99.85%99.90%
8 µm65.85%93.85%97.98%99.08%99.49%99.68%99.83%99.89%
9 µm62.49%93.10%97.72%98.97%99.43%99.64%99.81%99.87%
10 µm59.31%92.37%97.48%98.85%99.37%99.60%99.79%99.86%
Table 22
Theoretical X-ray transmission for NMC 111 for thicknesses of 10 – 100 µm and incident beam energies of 1 – 10 keV, presented as a percentage to 2 dp.
1 keV2 keV3 keV4 keV5 keV6 keV8 keV10 keV
10 µm0.00%0.23%12.88%39.28%60.35%73.75%53.62%59.31%
20 µm0.00%0.00%1.66%15.43%36.42%54.39%28.75%35.18%
30 µm0.00%0.00%0.21%6.06%21.98%40.11%15.42%20.87%
40 µm0.00%0.00%0.03%2.38%13.27%29.58%8.27%12.38%
50 µm0.00%0.00%0.00%0.93%8.01%21.82%4.43%7.34%
60 µm0.00%0.00%0.00%0.37%4.83%16.09%2.38%4.35%
70 µm0.00%0.00%0.00%0.14%2.92%11.87%1.27%2.58%
80 µm0.00%0.00%0.00%0.06%1.76%8.75%0.68%1.53%
90 µm0.00%0.00%0.00%0.02%1.06%6.46%0.37%0.91%
100 µm0.00%0.00%0.00%0.01%0.64%4.76%0.20%0.54%
Table 23
Theoretical X-ray transmission for NMC 111 for thicknesses of 10 – 100 µm and incident beam energies of 10 – 100 keV, presented as a percentage to 2 d.p.
10 keV20 keV30 keV40 keV50 keV60 keV80 keV100 keV
10 µm59.31%92.37%97.48%98.85%99.37%99.60%99.79%99.86%
20 µm35.18%85.32%95.01%97.72%98.74%99.20%99.58%99.72%
30 µm20.87%78.80%92.62%96.60%98.11%98.80%99.37%99.58%
40 µm12.38%72.79%90.28%95.49%97.49%98.41%99.16%99.44%
50 µm7.34%67.23%88.00%94.40%96.87%98.01%98.95%99.30%
60 µm4.35%62.10%85.78%93.31%96.26%97.62%98.75%99.17%
70 µm2.58%57.36%83.61%92.24%95.65%97.23%98.54%99.03%
80 µm1.53%52.98%81.50%91.19%95.04%96.84%98.33%98.89%
90 µm0.91%48.94%79.44%90.14%94.44%96.45%98.12%98.75%
100 µm0.54%45.20%77.44%89.11%93.84%96.07%97.92%98.61%
Table 24
Theoretical X-ray transmission for NMC 532 for thicknesses of 1 – 10 µm and incident beam energies of 1 – 10 keV, presented as a percentage to 2 d.p.
1 keV2 keV3 keV4 keV5 keV6 keV8 keV10 keV
1 µm3.49%53.76%81.03%90.84%94.94%96.92%95.15%94.77%
2 µm0.12%28.91%65.65%82.53%90.14%93.93%90.54%89.81%
3 µm0.00%15.54%53.20%74.97%85.57%91.03%86.15%85.11%
4 µm0.00%8.36%43.10%68.11%81.24%88.22%81.98%80.66%
5 µm0.00%4.49%34.93%61.87%77.13%85.50%78.00%76.44%
6 µm0.00%2.42%28.30%56.21%73.23%82.87%74.22%72.44%
7 µm0.00%1.30%22.93%51.06%69.53%80.31%70.63%68.65%
8 µm0.00%0.70%18.58%46.38%66.01%77.83%67.20%65.06%
9 µm0.00%0.38%15.05%42.14%62.67%75.43%63.94%61.66%
10 µm0.00%0.20%12.20%38.28%59.50%73.11%60.85%58.43%
Table 25
Theoretical X-ray transmission for NMC 532 for thicknesses of 1 – 10 µm and incident beam energies of 10 – 100 keV, presented as a percentage to 2 d.p.
10 keV20 keV30 keV40 keV50 keV60 keV80 keV100 keV
1 µm94.77%99.18%99.74%99.88%99.93%99.96%99.98%99.99%
2 µm89.81%98.38%99.47%99.76%99.87%99.92%99.96%99.97%
3 µm85.11%97.57%99.21%99.64%99.80%99.88%99.94%99.96%
4 µm80.66%96.78%98.95%99.53%99.74%99.84%99.91%99.94%
5 µm76.44%95.99%98.69%99.41%99.67%99.79%99.89%99.93%
6 µm72.44%95.20%98.43%99.29%99.61%99.75%99.87%99.91%
7 µm68.65%94.43%98.17%99.17%99.54%99.71%99.85%99.90%
8 µm65.06%93.66%97.91%99.05%99.48%99.67%99.83%99.89%
9 µm61.66%92.89%97.65%98.93%99.41%99.63%99.81%99.87%
10 µm58.43%92.14%97.39%98.82%99.35%99.59%99.78%99.86%
Table 26
Theoretical X-ray transmission for NMC 532 for thicknesses of 10 – 100 µm and incident beam energies of 1 – 10 keV, presented as a percentage to 2 d.p.
1 keV2 keV3 keV4 keV5 keV6 keV8 keV10 keV
10 µm0.00%0.20%12.20%38.28%59.50%73.11%60.85%58.43%
20 µm0.00%0.00%1.49%14.65%35.40%53.45%37.02%34.14%
30 µm0.00%0.00%0.18%5.61%21.06%39.07%22.53%19.95%
40 µm0.00%0.00%0.02%2.15%12.53%28.57%13.71%11.66%
50 µm0.00%0.00%0.00%0.82%7.45%20.88%8.34%6.81%
60 µm0.00%0.00%0.00%0.31%4.44%15.27%5.07%3.98%
70 µm0.00%0.00%0.00%0.12%2.64%11.16%3.09%2.33%
80 µm0.00%0.00%0.00%0.05%1.57%8.16%1.88%1.36%
90 µm0.00%0.00%0.00%0.02%0.93%5.97%1.14%0.79%
100 µm0.00%0.00%0.00%0.01%0.56%4.36%0.70%0.46%
Table 27
Theoretical X-ray transmission for NMC 532 for thicknesses of 10 – 100 µm and incident beam energies of 10 – 100 keV, presented as a percentage to 2 d.p.
10 keV20 keV30 keV40 keV50 keV60 keV80 keV100 keV
10 µm58.43%92.14%97.39%98.82%99.35%99.59%99.78%99.86%
20 µm34.14%84.89%94.86%97.65%98.70%99.18%99.57%99.72%
30 µm19.95%78.21%92.39%96.49%98.05%98.77%99.36%99.57%
40 µm11.66%72.06%89.98%95.35%97.41%98.36%99.14%99.43%
50 µm6.81%66.39%87.63%94.22%96.78%97.96%98.93%99.29%
60 µm3.98%61.17%85.35%93.11%96.15%97.55%98.72%99.15%
70 µm2.33%56.36%83.13%92.01%95.52%97.15%98.50%99.01%
80 µm1.36%51.93%80.96%90.92%94.90%96.75%98.29%98.87%
90 µm0.79%47.84%78.85%89.84%94.28%96.35%98.08%98.73%
100 µm0.46%44.08%76.80%88.78%93.66%95.96%97.87%98.59%
Table 28
Theoretical X-ray transmission for NMC 622 for thicknesses of 1 – 10 µm and incident beam energies of 1 – 10 keV, presented as a percentage to 2 d.p.
1 keV2 keV3 keV4 keV5 keV6 keV8 keV10 keV
1 µm3.24%52.58%80.39%90.51%94.75%96.80%95.71%94.57%
2 µm0.10%27.65%64.63%81.92%89.77%93.70%91.60%89.44%
3 µm0.00%14.54%51.96%74.15%85.06%90.69%87.67%84.59%
4 µm0.00%7.65%41.77%67.11%80.59%87.79%83.91%80.00%
5 µm0.00%4.02%33.58%60.74%76.36%84.98%80.30%75.65%
6 µm0.00%2.11%27.00%54.98%72.35%82.25%76.86%71.55%
7 µm0.00%1.11%21.70%49.76%68.55%79.62%73.56%67.67%
8 µm0.00%0.58%17.45%45.04%64.95%77.07%70.40%63.99%
9 µm0.00%0.31%14.03%40.77%61.54%74.60%67.38%60.52%
10 µm0.00%0.16%11.28%36.90%58.31%72.21%64.49%57.24%
Table 29
Theoretical X-ray transmission for NMC 622 for thicknesses of 1 – 10 µm and incident beam energies of 10 – 100 keV, presented as a percentage to 2 d.p.
10 keV20 keV30 keV40 keV50 keV60 keV80 keV100 keV
1 µm94.57%99.15%99.73%99.88%99.93%99.96%99.98%99.99%
2 µm89.44%98.31%99.45%99.75%99.86%99.91%99.96%99.97%
3 µm84.59%97.47%99.18%99.63%99.80%99.87%99.93%99.96%
4 µm80.00%96.65%98.91%99.51%99.73%99.83%99.91%99.94%
5 µm75.65%95.82%98.63%99.38%99.66%99.79%99.89%99.93%
6 µm71.55%95.01%98.36%99.26%99.59%99.74%99.87%99.91%
7 µm67.67%94.20%98.09%99.14%99.52%99.70%99.84%99.90%
8 µm63.99%93.40%97.82%99.01%99.46%99.66%99.82%99.88%
9 µm60.52%92.61%97.55%98.89%99.39%99.61%99.80%99.87%
10 µm57.24%91.82%97.29%98.77%99.32%99.57%99.78%99.85%
Table 30
Theoretical X-ray transmission for NMC 622 for thicknesses of 10 – 100 µm and incident beam energies of 1 – 10 keV, presented as a percentage to 2 d.p.
1 keV2 keV3 keV4 keV5 keV6 keV8 keV10 keV
10 µm0.00%0.16%11.28%36.90%58.31%72.21%64.49%57.24%
20 µm0.00%0.00%1.27%13.61%34.00%52.14%41.59%32.76%
30 µm0.00%0.00%0.14%5.02%19.82%37.65%26.82%18.75%
40 µm0.00%0.00%0.02%1.85%11.56%27.19%17.29%10.73%
50 µm0.00%0.00%0.00%0.68%6.74%19.63%11.15%6.14%
60 µm0.00%0.00%0.00%0.25%3.93%14.18%7.19%3.52%
70 µm0.00%0.00%0.00%0.09%2.29%10.24%4.64%2.01%
80 µm0.00%0.00%0.00%0.03%1.34%7.39%2.99%1.15%
90 µm0.00%0.00%0.00%0.01%0.78%5.34%1.93%0.66%
100 µm0.00%0.00%0.00%0.00%0.45%3.86%1.24%0.38%
Table 31
Theoretical X-ray transmission for NMC 622 for thicknesses of 10 – 100 µm and incident beam energies of 10 – 100 keV, presented as a percentage to 2 d.p.
10 keV20 keV30 keV40 keV50 keV60 keV80 keV100 keV
10 µm57.24%91.82%97.29%98.77%99.32%99.57%99.78%99.85%
20 µm32.76%84.31%94.65%97.55%98.65%99.15%99.56%99.71%
30 µm18.75%77.42%92.08%96.35%97.98%98.72%99.33%99.56%
40 µm10.73%71.09%89.58%95.16%97.31%98.30%99.11%99.42%
50 µm6.14%65.28%87.15%93.99%96.65%97.88%98.89%99.27%
60 µm3.52%59.94%84.78%92.83%95.99%97.46%98.67%99.13%
70 µm2.01%55.04%82.48%91.68%95.34%97.04%98.45%98.98%
80 µm1.15%50.54%80.24%90.55%94.69%96.63%98.23%98.84%
90 µm0.66%46.40%78.06%89.44%94.05%96.22%98.02%98.69%
100 µm0.38%42.61%75.95%88.34%93.41%95.80%97.80%98.55%
Table 32
Theoretical X-ray transmission for NMC 811 for thicknesses of 1 – 10 µm and incident beam energies of 1 – 10 keV, presented as a percentage to 2 d.p.
1 keV2 keV3 keV4 keV5 keV6 keV8 keV10 keV
1 µm2.96%50.88%79.46%90.02%94.47%96.62%97.03%94.29%
2 µm0.09%25.89%63.15%81.04%89.24%93.36%94.14%88.90%
3 µm0.00%13.18%50.18%72.95%84.30%90.20%91.34%83.82%
4 µm0.00%6.70%39.87%65.67%79.63%87.15%88.63%79.03%
5 µm0.00%3.41%31.69%59.12%75.23%84.21%85.99%74.52%
6 µm0.00%1.74%25.18%53.22%71.06%81.36%83.44%70.26%
7 µm0.00%0.88%20.01%47.91%67.13%78.61%80.95%66.24%
8 µm0.00%0.45%15.90%43.13%63.42%75.96%78.55%62.46%
9 µm0.00%0.23%12.63%38.82%59.91%73.39%76.21%58.89%
10 µm0.00%0.12%10.04%34.95%56.59%70.91%73.95%55.53%
Table 33
Theoretical X-ray transmission for NMC 811 for thicknesses of 1 – 10 µm and incident beam energies of 10 – 100 keV, presented as a percentage to 2 d.p.
10 keV20 keV30 keV40 keV50 keV60 keV80 keV100 keV
1 µm94.29%99.10%99.71%99.87%99.93%99.95%99.98%99.98%
2 µm88.90%98.21%99.42%99.74%99.86%99.91%99.95%99.97%
3 µm83.82%97.33%99.13%99.61%99.78%99.86%99.93%99.95%
4 µm79.03%96.45%98.84%99.48%99.71%99.82%99.91%99.94%
5 µm74.52%95.59%98.55%99.35%99.64%99.77%99.88%99.92%
6 µm70.26%94.73%98.27%99.21%99.57%99.73%99.86%99.91%
7 µm66.24%93.88%97.98%99.08%99.50%99.68%99.84%99.89%
8 µm62.46%93.03%97.69%98.95%99.43%99.64%99.81%99.88%
9 µm58.89%92.20%97.41%98.82%99.35%99.59%99.79%99.86%
10 µm55.53%91.37%97.13%98.70%99.28%99.55%99.77%99.85%
Table 34
Theoretical X-ray transmission for NMC 811 for thicknesses of 10 – 100 µm and incident beam energies of 1 – 10 keV, presented as a percentage to 2 d.p.
1 keV2 keV3 keV4 keV5 keV6 keV8 keV10 keV
10 µm0.00%0.12%10.04%34.95%56.59%70.91%73.95%55.53%
20 µm0.00%0.00%1.01%12.22%32.03%50.28%54.68%30.83%
30 µm0.00%0.00%0.10%4.27%18.12%35.65%40.43%17.12%
40 µm0.00%0.00%0.01%1.49%10.26%25.28%29.90%9.51%
50 µm0.00%0.00%0.00%0.52%5.80%17.93%22.11%5.28%
60 µm0.00%0.00%0.00%0.18%3.28%12.71%16.35%2.93%
70 µm0.00%0.00%0.00%0.06%1.86%9.01%12.09%1.63%
80 µm0.00%0.00%0.00%0.02%1.05%6.39%8.94%0.90%
90 µm0.00%0.00%0.00%0.01%0.60%4.53%6.61%0.50%
100 µm0.00%0.00%0.00%0.00%0.34%3.21%4.89%0.28%
Table 35
Theoretical X-ray transmission for NMC 811 for thicknesses of 10 – 100 µm and incident beam energies of 10 – 100 keV, presented as a percentage to 2 d.p.
10 keV20 keV30 keV40 keV50 keV60 keV80 keV100 keV
10 µm55.53%91.37%97.13%98.70%99.28%99.55%99.77%99.85%
20 µm30.83%83.48%94.34%97.41%98.57%99.10%99.53%99.70%
30 µm17.12%76.27%91.63%96.14%97.86%98.65%99.30%99.54%
40 µm9.51%69.69%88.99%94.88%97.16%98.21%99.07%99.39%
50 µm5.28%63.67%86.44%93.64%96.46%97.76%98.84%99.24%
60 µm2.93%58.17%83.95%92.42%95.77%97.32%98.61%99.09%
70 µm1.63%53.15%81.54%91.22%95.08%96.88%98.38%98.94%
80 µm0.90%48.56%79.20%90.02%94.40%96.45%98.15%98.79%
90 µm0.50%44.37%76.92%88.85%93.72%96.01%97.92%98.64%
100 µm0.28%40.54%74.71%87.69%93.05%95.58%97.69%98.49%
Table 36
Theoretical thicknesses for optimal contrast-to-noise ratio for various NMC chemistries and incident beam energies of 1 – 10 keV, presented in µm to 2 d.p.
1 keV2 keV3 keV4 keV5 keV6 keV8 keV10 keV
NMC 1110.603.309.7621.4039.6065.6832.0838.30
NMC 5320.603.229.5020.8238.5263.8440.2637.22
NMC 6220.583.129.1620.0637.0861.4245.6035.84
NMC 8110.562.968.7019.0235.1258.1866.2634.00
Table 37
Theoretical thicknesses for optimal contrast-to-noise ratio for various NMC chemistries and incident beam energies of 10 – 100 keV, presented in µm to 2 d.p.
10 keV20 keV30 keV40 keV50 keV60 keV80 keV100 keV
NMC 11138.30251.88782.141734.003147.384985.069507.2014,325.60
NMC 53237.22244.16757.621680.223053.664845.709286.4214,063.42
NMC 62235.84234.44726.881612.582934.384665.248983.6613,673.52
NMC 81134.00221.50686.081522.602774.884422.008567.5213,125.06
Table 38
The influence of lithiation state upon the X-ray attenuation properties of NMC811 for three incident beam energies: 1, 10 and 100 keV, presented are X-ray mass attenuation coefficients in cm2 g−1 (to 2 d.p.).
Lithiation state, xState of Charge (SoC)Incident Beam Energy
1 keV10 keV100 keV
0.0Li1.0Ni0.8Mn0.1Co0.1O27333.73122.560.32
0.2Li0.8Ni0.8Mn0.1Co0.1O27436.50124.330.32
0.4Li0.6Ni0.8Mn0.1Co0.1O27542.29126.150.32
0.6Li0.4Ni0.8Mn0.1Co0.1O27651.23128.030.33
0.8Li0.2Ni0.8Mn0.1Co0.1O27763.46129.960.33
1.0Li0.0Ni0.8Mn0.1Co0.1O27879.15131.950.33

Experimental design, materials and methods

Essential X-ray equations

No raw data was acquired for this work. All data was calculated from the references. The following set of equations describe all calculations within this work.

X-ray mass attenuation coefficient for a material, from its constituent elements (Eq. (1)).

μm(E0)=i[wi.μm(i,E0)]
Converting X-ray mass attenuation coefficient to the X-ray linear attenuation coefficient (Eq. (2)).
μ(E0)=μm(E0).ρ
Converting X-ray linear attenuation coefficient to the X-ray attenuation length (Eq. (3)).
λ(E0)=μ(E0)1
Calculating X-ray transmission from the X-ray linear attenuation coefficient or the X-ray attenuation length (Eq. (4)).
T=et.μ(E0)=etλ(E0)
Material thickness for optimum image contrast (Eq. (5)).
t.μ(Eo)=2
TTransmission%
ITransmitted X-ray intensityenergy per area per time
I0Incident X-ray intensityenergy per area per time
E0Incident X-ray energyenergy
tThickness of the samplelength
iConstituent elementno-units
wiWeight fraction of element i%
μm(E0)X-ray mass attenuation coefficientarea per weight
μ(E0)X-ray linear attenuation coefficientinverse length
λ(E0)X-ray attenuation lengthlength

X-Ray attenuation data calculated from Hubbell

These tables report data produced from work by Hubbell and Seltzer [2].

X-Ray attenuation data calculated from Henke

These tables report data produced from work by Henke et al. [3].

The same literature references for the crystallographic densities of the various NMC chemistries were used for both the attenuation calculations based upon Hubbell and Henke [4], [5], [6], [7].

X-Ray transmissions for NMC111

Firstly transmission values for small samples.

Secondly transmission values for large samples.

X-Ray transmissions for NMC532

Firstly transmission values for small samples.

Secondly transmission values for large samples.

X-Ray transmissions for NMC622

Firstly transmission values for small samples.

Secondly transmission values for large samples.

X-Ray transmissions for NMC811

Firstly transmission values for small samples.

Secondly transmission values for large samples.

Theoretical NMC thickness for optimum image contrast

Using derivations outlined by Reiter et al. [8], the theoretical thickness for optimum image contrast can be calculated using Eq. (5): firstly, for low energies (Table 36), and secondly, for high energies (Table 37).

Theoretical influence of electrode lithiation

All calculations thus far have reported results based upon fully lithiated material, because the influence of lithiation is assumed negligible with comparison to variations in the incident beam energy or chemical composition. In order to demonstrate the validity of this assumption, Table 38 reports the theoretical variation in X-ray mass attenuation coefficient with state of charge (quantified by the value of x within Li1-xNi0.8Mn0.1Co0.1O2) for three incident beam energies: 1, 10, 100 keV.

References

1 

    Heenan T.M.M., Tan C., Wade A.J., Jervis R., Brett D.J.L., Shearing P.R.. Theoretical transmissions for X-ray computed tomography studies of lithium-ion battery cathodes. Mater. Des. 2020. 108585

2 

Hubbell, J.H. and Seltzer, S.M., 1995. Tables of X-ray Mass Attenuation Coefficients and Mass Energy-Absorption Coefficients 1keV to 20 MeV for Elements Z= 1 to 92 and 48 Additional Substances of Dosimetric Interest (No. PB-95-220539/XAB; NISTIR-5632).

3 

    Henke B.L., Gullikson E.M., Davis J.C.. X-ray interactions: photoabsorption, scattering, transmission, and reflection at E= 50-30,000eV, Z= 1-92. Atom. Data Nucl. Data Tables 54: 2 1993. , pp.181-342

4 

    Fujii Y., Miura H., Suzuki N., Shoji T., Nakayama N.. Structural and electrochemical properties of LiNi1/3Co1/3Mn1/3O2–LiMg1/3Co1/3Mn1/3O2 solid solutions. Solid State Ionics 178: 11–12 2007. , pp.849-857

5 

    Gu Y.J., Zhang Q.G., Chen Y.B., Liu H.Q., Ding J.X., Wang Y.M., Wang H.F., Chen L., Wang M., Fan S.W., Zang Q.F.. Reduction of the lithium and nickel site substitution in Li1+ xNi0. 5Co0. 2Mn0. 3O2 with Li excess as a cathode electrode material for Li-ion batteries. J. Alloys Compd. 630: 2015. , pp.316-322

6 

    Zheng X., Li X., Huang Z., Zhang B., Wang Z., Guo H., Yang Z.. Enhanced electrochemical performance of LiNi0. 6Co0. 2Mn0. 2O2 cathode materials by ultrasonic-assisted co-precipitation method. J. Alloys Compd. 644: 2015. , pp.607-614

7 

    Jung R., Morasch R., Karayaylali P., Phillips K., Maglia F., Stinner C., Shao-Horn Y., Gasteiger H.A.. Effect of ambient storage on the degradation of Ni-rich positive electrode materials (NMC811) for Li-ion batteries. J. Electrochem. Soc. 165: 2 2018. , pp.A132-A141

8 

    Reiter M., Krumm M., Kasperl S., Kuhn C., Erler M., Weiß D., Heinzl C., Gusenbauer C., Kastner J.Evaluation of transmission based image quality optimisation for X-ray computed tomographyProceedings of the Conference on Industrial Computed Tomography (ICT) 2012, September. , pp.241-250

Acknowledgments

The authors would like to acknowledge the EPSRC (EP/M014045/1), the Royal Academy of Engineering (CiET1718\59). This work was carried out with funding from the Faraday Institution (faraday.ac.uk; EP/S003053/1), grant number FIRG001.

Conflict of Interest

The authors declare that they have no known conflicts of interest to declare.