JMFA—A Graphically 

Interactive Java Program 

That Fits Microfibril Angle 

X-ray Diffraction Data

Steve P. Verrill 

David E. Kretschmann 

Victoria L. Herian 

United States

Department of 

Agriculture 

Forest Service 

Forest 

Products 

Laboratory 

Research 

Note 

FPL−RN–0283 

μ

α

2θ

φ

Z

Y

X (90-θ)

b

p

Beam

002

101

Back plane

Specimen
Abstract 

Because much of our future timber resource is expected to 

come from short rotation plantations, we need to develop 

silvicultural practices that will improve the quality of the 

timber coming from these plantations. Short rotation plantations tend to produce timber with a higher percentage of 

juvenile wood, which has substantially lower mechanical 

property values than does mature wood. Measuring the 

microfibril angle (MFA) of wood gives important clues 

about the characteristics of the wood and can be used as a 

silvicultural tool to improve the quality of a plantation. In 

this report, we discuss a graphically interactive Java computer program that permits a user to estimate MFA from 

X-ray diffraction profiles. Given an MFA and a wood cell 

rotation pair (μ, α), this program makes use of Cave’s theory 

to predict the locations of the eight high intensity X-ray 

spots on the back plane. Nonlinear least squares techniques 

are then used to find the (μ, α) pair that yields a broadened 

form of the eight spots that best fits the empirical X-ray 

diffraction data. The program can be run as an applet over 

the World Wide Web, or it can be downloaded and run as an 

application on a user’s own machine. Because this program 

is based on a more complete physics model than earlier 

programs, we expect that it will yield more accurate MFA 

estimates. Preliminary comparisons of the new program’s 

MFA estimates with microscopy based estimates are encouraging. A complete evaluation of the accuracy of the program’s estimates will appear in a subsequent paper. 

Keywords: microfibril angle, X-ray diffraction, Java, 

interactive graphics, mechanical properties of wood, forest 

monitoring 

November 2001 

Verrill, Steve P.; Kretschmann, David E.; Herian, Victoria L. 2001. JMFA—

A graphically interactive Java program that fits microfibril angle X-ray 

diffraction data. Res. Note FPL-RN-0283. Madison, WI: U.S. Department 

of Agriculture, Forest Service, Forest Products Laboratory. 44 p. 

A limited number of free copies of this publication are available to the 

public from the Forest Products Laboratory, One Gifford Pinchot Drive, 

Madison, WI 53705–2398. This publication is also available online at 

www.fpl.fs.fed.us. Laboratory publications are sent to hundreds 

of libraries in the United States and elsewhere. 

The Forest Products Laboratory is maintained in cooperation with the 

University of Wisconsin. 

The United States Department of Agriculture (USDA) prohibits discrimination in all its programs and activities on the basis of race, color, national 

origin, sex, religion, age, disability, political beliefs, sexual orientation, or 

marital or familial status. (Not all prohibited bases apply to all programs.) 

Persons with disabilities who require alternative means for communication 

of program information (Braille, large print, audiotape, etc.) should contact 

the USDA’s TARGET Center at (202) 720–2600 (voice and TDD). To file a 

complaint of discrimination, write USDA, Director, Office of Civil Rights, 

Room 326-W, Whitten Building, 1400 Independence Avenue, SW, Washington, DC 20250–9410, or call (202) 720–5964 (voice and TDD). USDA is 

an equal opportunity provider and employer. 

Contents 

Page 

1 Introduction .....................................................................1 

 1.1 Background............................................................1 

 1.2 Importance of Microfibril Angle ...........................1 

 1.3 Methods of Measuring MFA .................................2 

2 The Program ....................................................................3 

 2.1 Heuristic Justification of Our Approach................3 

 2.2 Predicted Intensity .................................................6 

 2.3 The Applet.............................................................7 

 2.4 The Application ...................................................12 

3 Summary........................................................................14 

4 Acknowledgment...........................................................14 

5 References .....................................................................14 

6 Appendix—Cave’s Equation.........................................16 

 6.1 Derivation of Cave’s Equation ............................16 

 6.2 Relation Between φ and the Azimuthal Angle on 

 the Back Plane................................................17 

 6.3 Solution of Cave’s Equation................................18 

Figures...............................................................................21 
   	


  

 
  
 
 

 

  	

 	
 	


	
   	 

 



		  	 	


 	  
 	



 	


 	
 	
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