A Comprehensive Monte Carlo-Simulated Dataset of WAXD Patterns of Wood Cellulose Microfibrils
Abstract
1. Introduction
2. Data Description
2.1. Simulated Diffraction Patterns
2.2. Cell Wall Templates
3. Methods
3.1. Dataset Generation
3.2. Validation
4. User Notes
4.1. Data Format
4.2. Recommended Applications
4.3. Assumptions and Considerations
4.4. Data Subsetting and Filtering
4.5. Analytical Method Development
4.6. Machine Learning Applications
4.7. Limitations
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
- Sisson, W. X-Ray Studies of Crystallite Orientation in Cellulose Fibers. Ind. Eng. Chem. 1935, 27, 51–56. [Google Scholar]
- Herzog, R.; Jancke, W. Röntgenspektrographische Beobachtungen an Zellulose. Z. Für Phys. 1920, 3, 196–198. [Google Scholar]
- Herzog, R.; Jancke, W.; Polanyi, M. Röntgenspektrographische Beobachtungen an Zellulose. II. Z. Für Phys. 1920, 3, 343–348. [Google Scholar]
- Preston, R. The fine structure of the wall of the conifer tracheid I. The X-ray diagram of conifer wood. Proc. R. Soc. Lond. Ser. B-Biol. Sci. 1946, 133, 327–348. [Google Scholar]
- Li, T.; Chen, C.; Brozena, A.; Zu, J. Developing fibrillated cellulose as a sustainable technological material. Nature 2021, 590, 47–56. [Google Scholar] [PubMed]
- Hall, J. Wood in an industrial world. Sci. Mon. 1948, 27, 398–405. [Google Scholar]
- Wang, J.; Wang, L.; Gardner, D.; Shaler, S.M.; Cai, Z. Towards a cellulose-based society: Opportunities and challenges. Cellulose 2021, 28, 4511–4543. [Google Scholar] [CrossRef]
- Sakurada, I.; Nukushina, Y.; Ito, T. Experimental determination of the elastic modulus of crystalline regions in oriented polymers. J. Polym. Sci. 1962, 57, 651–660. [Google Scholar]
- Matsuo, M.; Sawatari, C.; Iwai, Y.; Ozaki, F. Effect of Orientation Distribution and Crystallinity on the Measurement by X-ray Diffraction of the Crystal Lattice Moduli of Cellulose I and II. Macromolecules 1990, 23, 3266–3275. [Google Scholar]
- Nishino, T.; Takano, K.; Nakamae, K. Elastic modulus of the crystalline regions of cellulose polymorphs. J. Polym. Sci. Part B Polym. Phys. 1995, 33, 1647–1651. [Google Scholar]
- Rongpipi, S.; Ye, D.; Gomez, E.; Gomez, E. Progress and Opportunities in the Characterization of Cellulose—An Important Regulator of Cell Wall Growth and Mechanics. Front. Plant Sci. 2019, 9, 1894. [Google Scholar] [CrossRef]
- Salmén, L. Micromechanical understanding of the cell-wall structure. C. R. Biol. 2004, 327, 873–880. [Google Scholar] [CrossRef]
- Cave, I. Theory of X-ray Measurement of Microfibril Angle in Wood. For. Prod. J. 1966, 16, 37–42. [Google Scholar]
- Yamamoto, H.; Okuyama, T.; Yoshida, M. Method of Determining the Mean Microfibril Angle of Wood Over a Wide Range by the Improved Cave’s Method. Mokuzai Gakkaishi 1993, 39, 375–381. [Google Scholar]
- Verrill, S.; Kretschmann, D.; Herian, V.; Wiemann, M.; Alden, H. Concerns about a variance approach to X-ray diffractometric estimation of microfibril angle in wood. Wood Fiber Sci. 2011, 43, 153–168. [Google Scholar]
- Lichtenegger, H.; Reiterer, A.; Stanzl-Tschegg, S.; Fratzl, P. Comment about “The measurement of the micro-fibril angle in soft-wood” by K. M. Entwistle and N. J. Terrill. J. Mater. Sci. Lett. 2001, 20, 2245–2247. [Google Scholar]
- Wang, X.; Ma, J.; Xu, W.; Fei, B.; Lian, C.; Sun, F. Effect of bending on radial distribution density, MFA and MOE of bent bamboo. Sci. Rep. 2022, 12, 8610. [Google Scholar] [CrossRef]
- Cave, I.; Robinson, W. Interpretation of (002) diffraction arcs by means of a minimalist model. In Microfibril Angle in Wood; Butterfield, B.G., Ed.; Proceedings of the IAWA/IUFRO International Workshop on the Significance of Microfibril Angle to Wood Quality; University of Canterbury Press: Westport, New Zealand, 1997. [Google Scholar]
- Lichtenegger, H.; Müller, M.; Wimmer, R.; Fratzl, P. Microfibril Angles Inside and Outside Crossfields of Norway Spruce Tracheids. Holzforschung 2003, 57, 13–20. [Google Scholar]
- Kobayashi, K.; Hwang, S.W.; Okochi, T.; Lee, W.H.; Sugiyama, J. Non-destructive method for wood identification using conventional X-ray computed tomography data. J. Cult. Herit. 2019, 38, 88–93. [Google Scholar] [CrossRef]
- Donaldson, L.A. Wood cell wall ultrastructure the key to understanding wood properties and behaviour. IAWA J. 2019, 40, 645–672. [Google Scholar]
- Keplinger, T.; Wang, X.; Burgert, I. Nanofibrillated cellulose composites and wood derived scaffolds for functional materials. J. Mater. Chem. A 2019, 7, 2981–2992. [Google Scholar] [CrossRef]
- Yang, J.; Evans, R. Prediction of MOE of eucalypt wood from microfibril angle and density. Holz Als Roh- Und Werkst. 2003, 61, 449–452. [Google Scholar] [CrossRef]
- Meylan, B. Measurement of Microfibril Angle by X-Ray Diffraction. For. Prod. J. 1967, 17, 51–58. [Google Scholar]
- Evans, R. A variance approach to the X-ray diffractometric estimation of microfibril angle in wood. Appita J. 1999, 52, 283–289. [Google Scholar]
- Evans, R. Rapid scanning of microfibril angle in increment cores by X-ray diffractometry. In Microfibril Angle in Wood; Butterfield, B.G., Ed.; Proceedings of the IAWA/IUFRO International Workshop on the Significance of Microfibril Angle to Wood Quality; University of Canterbury Press: Westport, New Zealand, 1997. [Google Scholar]
- Eder, M.; Arnould, O.; William, J.; Dunlop, C.; Hornatowska, J.; Salmén, L. Experimental micromechanical characterisation of wood cell walls. Wood Sci. Technol. 2013, 45, 461–472. [Google Scholar] [CrossRef]
- Hein, P.; Lima, J. Relationships between microfibril angle, modulus of elasticity and compressive strength in Eucalyptus wood. Maderas. Cienc. Y Tecnol. 2012, 14, 267–274. [Google Scholar]
- Hein, P.; Lima, J.; Brancheriau, L. Correlations among microfibril angle, density, modulus of elasticity, modulus of rupture and shrinkage in 6-year-old Eucalyptus urophylla × E. grandis. Maderas. Cienc. Y Tecnol. 2013, 15, 171–182. [Google Scholar]
- Donaldson, L.; Singh, A. Formation and Structure of Compression Wood. In Cellular Aspects of Wood Formation; Fromm, J., Ed.; Springer-Verlag: Berlin/Heidelberg, Germany, 2013; pp. 225–256. [Google Scholar]
- Watanabe, U.; Norimoto, M.; Fujita, M.; Gril, J. Structural Variation of Tracheids in Norway Spruce (Picea abies [L.] Karst.). J. Wood Sci. 1998, 44, 9–14. [Google Scholar] [CrossRef]
- Sarén, M.; Serimaa, R.; Andersson, S.; Paakkari, T.; Saranpää, P.; Pesonen, E. Transverse shrinkage anisotropy of coniferous wood investigated by the power spectrum analysis. J. Struct. Biol. 2001, 136, 101–109. [Google Scholar] [CrossRef]
- Anagnost, S.; Mark, R.; Hanna, R. Variation of microfibril angle within individual tracheids. Wood Fiber Sci. 2002, 34, 337–349. [Google Scholar]
- Lichtenegger, H.; Reiterer, A.; Stanzl-Tschegg, S.; Fratzl, P. Variation of Cellulose Microfibril Angles in Softwoods and Hardwoods— A Possible Strategy of Mechanical Optimization. J. Struct. Biol. 1999, 128, 257–269. [Google Scholar]
- Evans, R.; Hughes, M.; Menz, D. Microfibril angle variation by scanning X-ray diffractometry. Appita J. 1999, 52, 363–367. [Google Scholar]
- Verrill, S.; Kretschmann, D.; Herian, V. JMFA—A Graphically Interactive Java Program that Fits Microfibril Angle X-ray Diffraction Data. In Res. Note FPL-RN-0283; U.S. Department of Agriculture, Forest Service, Forest Products Laboratory: Madison, WI, USA, 2001. [Google Scholar]
- Verrill, S.; Kretschmann, D.; Herian, V. JMFA 2—A Graphically Interactive Java Program that Fits Microfibril Angle X-ray Diffraction Data. In Res. Note FPL-RP-635; U.S. Department of Agriculture, Forest Service, Forest Products Laboratory: Madison, WI, USA, 2006. [Google Scholar]
- Sarén, M.; Serimaa, R. Determination of microfibril angle distribution by X-ray diffraction. Wood Sci. Technol. 2006, 40, 445–460. [Google Scholar]
- McKinney, W. Data structures for statistical computing in Python. SciPy 2010, 445, 51–56. [Google Scholar]
- Van Der Walt, S.; Colbert, S.C.; Varoquaux, G. The NumPy array: A structure for efficient numerical computation. Comput. Sci. Eng. 2011, 13, 22–30. [Google Scholar] [CrossRef]
- R Core Team. R: A Language and Environment for Statistical Computing; R Foundation for Statistical Computing: Vienna, Austria, 2023. [Google Scholar]
- Hastie, T.; Tibshirani, R.; Friedman, J. The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd ed.; Springer Science & Business Media: Berlin/Heidelberg, Germany, 2009. [Google Scholar]
- Abdi, H.; Williams, L.J. Principal component analysis. Wiley Interdiscip. Rev. Comput. Stat. 2010, 2, 433–459. [Google Scholar]
- Maaten, L.v.d.; Hinton, G. Visualizing data using t-SNE. J. Mach. Learn. Res. 2008, 9, 2579–2605. [Google Scholar]
- Jordan, M.I.; Mitchell, T.M. Machine learning: Trends, perspectives, and prospects. Science 2015, 349, 255–260. [Google Scholar]
- LeCun, Y.; Bengio, Y.; Hinton, G. Deep learning. Nature 2015, 521, 436–444. [Google Scholar]
- Virtanen, P.; Gommers, R.; Oliphant, T.E.; Haberland, M.; Reddy, T.; Cournapeau, D.; Burovski, E.; Peterson, P.; Weckesser, W.; Bright, J.; et al. SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nat. Methods 2020, 17, 261–272. [Google Scholar]
- Berens, P. CircStat: A MATLAB toolbox for circular statistics. J. Stat. Softw. 2009, 31, 1–21. [Google Scholar] [CrossRef]
- Mardia, K.V.; Jupp, P.E. Directional Statistics; John Wiley & Sons: Chichester, UK, 2000. [Google Scholar]
Parameter | Col. Name | Type | Range | Description |
---|---|---|---|---|
Pattern ID | id | Integer | Variable | ID for diffraction pattern |
Template | template | Integer | 1–3 | Cross-section shape type |
MFA | Float | 25.0°, 12.0°) | Mean microfibril angle | |
desMFA | Float | (5.0°, 20.0°) | MFA standard deviation | |
incli | Float | (0.0°, 10.0°) | Template rotation angle | |
omega | Float | (0.0°, 5.0°) | Mean forward/backward tilt | |
desv_omega | Float | (0.0°, 5.0°) | Forward/backward tilt standard deviation | |
rho | Float | (0°, 5.0°) | Mean lateral tilt | |
desv_rho | Float | (0°, 5.0°) | Lateral tilt standard deviation | |
VA MFA (Peak 1) | VA_MFA1 | Float | Variable | Variance approach MFA estimate for first peak |
VA MFA (Peak 2) | VA_MFA2 | Float | Variable | Variance approach MFA estimate for second peak |
Peak 1 Std Dev | desv1 | Float | Variable | Standard deviation of first diffraction peak |
Peak 2 Std Dev | desv2 | Float | Variable | Standard deviation of second diffraction peak |
Peak 1 Variance | var1 | Float | Variable | Variance of first diffraction peak |
Peak 2 Variance | var2 | Float | Variable | Variance of second diffraction peak |
Parameter | Column Name | Type | Range | Description |
---|---|---|---|---|
Pattern ID | id | Integer | Variable | ID for diffraction pattern |
Intensity Vector | 0.. 359 | Float Array | [0, max] | 360° azimuthal intensity profile |
ID | MFA | desMFA |
---|---|---|
72431 | 26.8° | 15.3° |
71946 | 28.0° | 17.6° |
21663 | 27.5° | 14.9° |
78119 | 27.8° | 18.8° |
71806 | 28.2° | 16.8° |
ID | MFA | desMFA |
---|---|---|
43056 | 27.7° | 12.6° |
29767 | 28.1° | 12.9° |
21145 | 28.3° | 13.2° |
14257 | 28.1° | 12.9° |
7068 | 27.9° | 11.8° |
ID | MFA | desMFA |
---|---|---|
78384 | 22.9° | 16.1° |
43178 | 22.0° | 14.0° |
55022 | 21.5° | 14.8° |
18541 | 22.0° | 14.5° |
13725 | 22.1° | 14.5° |
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Baettig, R.; Ingram, B. A Comprehensive Monte Carlo-Simulated Dataset of WAXD Patterns of Wood Cellulose Microfibrils. Data 2025, 10, 47. https://doi.org/10.3390/data10040047
Baettig R, Ingram B. A Comprehensive Monte Carlo-Simulated Dataset of WAXD Patterns of Wood Cellulose Microfibrils. Data. 2025; 10(4):47. https://doi.org/10.3390/data10040047
Chicago/Turabian StyleBaettig, Ricardo, and Ben Ingram. 2025. "A Comprehensive Monte Carlo-Simulated Dataset of WAXD Patterns of Wood Cellulose Microfibrils" Data 10, no. 4: 47. https://doi.org/10.3390/data10040047
APA StyleBaettig, R., & Ingram, B. (2025). A Comprehensive Monte Carlo-Simulated Dataset of WAXD Patterns of Wood Cellulose Microfibrils. Data, 10(4), 47. https://doi.org/10.3390/data10040047