Visualization of Structure-Property Relationships:
Spanning the Length Scales (nano to macro)

Submitted to the NSF Science and Engineering Visualization Challenge

March 3, 2003


R.D. Kriz*, A.A. Ray, J.T. Kelso, D. Farkas**, and R.E. Flanery Jr.***
***Oak Ridge National Laboratories, Oak Ridge, Tennesseee, and
**Department of Materials Science and Engineering,
*Department of Engineering Science and Mechanics,
Department of Computer Science
Virginia Tech
Blacksburg, Virginia

Description (100 words)

Recent development of networked collaborative immersive software [1-3] allows more accurate visual analysis of complex connected wave-velocity surfaces propagating through anisotropic crystals. Existing topologies, used for sub-classification within orthorhombic symmetry [4-6], were studied using these immersive tools. From Christoffel's equation the fourth order elastic stiffness tensor, Cijkl, uniquely defines these topologies where the collection of all wave speeds, v, (topology) and their vibration directions, ak, correspond to the wave propagation direction, nk, and color is defined by ak nk [7]. Together both topology and color uniquely represent Cijkl for Ca[HCOO]2. Insight occurs when the observer is "immersed" inside this crystal (nano-structure) and the wave velocity (macro-property) topology. Polar covalent bond orientations are seen to align along stiffer directions where faster longitudinal wave speeds appear as purple bulges.

Figure 1a. Nano-Macro Topology for Ca[HCOO]2 (landscape)/ (300dpi)

Figure 1b. Description of Nano-Macro Topology for Ca[HCOO]2 (landscape)/ (300dpi)


1. DIVERSE (2001):
2. DIVERSE Atomview (2002):
3. DIVERSE Collab Tools (2003):
4. Musgrave, M.J.P., "On an Elastodynamic Classification of Orthorhombic Media", Proc. R. Soc. Lond.
    A374, p. 401, 1981.
5. Ledbetter, H.M. and Kriz. R.D., "Elastic-Wave Surfaces in Solids", Physica Status Solidi, Vol.114,
    pp. 475-480, 1982.
6. Kriz, R.D., and Ledbetter, H.M., "Elastic Wave Surfaces in Anisotropic Media", Rheology of
    Anisotropic Materials
, C. Huet, D. Bourgoin, and S. Richemond, Eds., CEPADUES-Editions,
    Toulouse, France, pp. 79-91, 1986.
7. Kriz, R.D., Farkas, D. Batra, R.C., "NSF-Combined Research and Curriculum Development:
   Computer Simulation of Material Behavior -From Atomistic to The Continuum Level",
   Course Module: Introduction to Mechanical Behavior of Anisotropic Materials (2002):

Download Data files for Alpha-Ca[HCOO]2 (Alpha-Calciumformate)


Macro-Property Topology (Velocity Surface Glyph): Nano-Structure and Macro-Property Combined:
Email questions-comments to Dr. R.D. Kriz
Ronald D. Kriz, Resume/Vitae
College of Engineering
Virginia Tech
Revised March 3, 2003