Title  : INT 96-41 -- SSR 96-15 Theoretical and Numerical Investigations of
         Relaxation in Metastable System
Type   : International Document
NSF Org: SBE / INT
Date   : December 2, 1996
File   : int9641

The National Science Foundation's offices in Tokyo and in Paris periodically
report on developments abroad that are related to the Foundation's mission.
These documents present facts for the use of NSF program managers and policy
makers; they are not statements of NSF policy.

The National Science Foundation's (NSF) Tokyo Office periodically receives and
disseminates reports on research developments in Japan that are related to the
Foundation's mission. Many of these reports are prepared by NSF-sponsored
researchers currently working in Japan.  These reports provide information for
use by the global science and engineering community.

Special Scientific Report #96-15 (November 21, 1996)

The following report was prepared by Dr. Per Arne Rikvold, Department of
Physics, and Center for Materials Research and Technology, and Supercomputer
Computations Research Institute, Florida State University, Tallahassee, Fl
32306.  Dr. Rikvold recently completed a 3.5 month research visit to the
Department of Fundamental Sciences, Kyoto University, Kyoto, Japan.  At Kyoto
University, Dr. Rikvold worked collaboratively with Professor Hiroyuki Tomita.
Dr. Rikvold received an NSF-Center for Global Partnership (CGP) Fellowship to
support his visit to Japan.  Dr. Rikvold has returned to the U.S. and can be
reached via email at:  rikvold@scri.fsu.edu.

        Theoretical and Numerical Investigations of Relaxation in Metastable
        Systems

This project supported Professor Per Arne Rikvold of the Physics Depart-ment,
Center for Materials Research and Technology, and Supercomputer Computations
Institute at Florida State University to spend the period from April 1 through
July 9, 1996, in the Department of Fundamental Sciences, Faculty of Integrated
Human Studies, Kyoto University. During the visit he studied nonequilibrium
statistical-mechanics aspects of metastable phases of matter in the group of
Professor Hiroyuki Tomita.

Metastable phases are ubiquitous in nature and include such familiar examples
as the diamond phase of carbon, supercooled water, and permanent magnets. Drs.
Rikvold and Tomita have both previously studied this common but as-yet
ill-understood state of matter, using analytical and numerical methods.

By bringing together researchers from the U.S. and Japan working on the
nonequilibrium statistical mechanics of metastability, the project enhanced
the research in this area in both countries. The U.S. scientist had the
opportunity to become familiar with the work performed at Kyoto University and
several other public and private universities in Japan, while informing
Japanese researchers of recent results of U.S. research.  Therefore, this
project fulfilled the objectives of the Program in its exchange and transfer
of scientific knowledge through international collaboration.

TECHNICAL INFORMATION

The work described here was supported by NSF Grant INT-9512679, NSF-CGP
Science Fellowship Program: Theoretical and Numerical investigations of
Relaxation in Metastable Systems ($18,401 for the period 3/1/96 through
8/31/96).  The work was performed in the group of Professor Hiroyuki Tomita,
Department of Fundamental Sciences, Faculty of Integrated Human Studies, at
Kyoto University in Japan.  It concentrated on investigations of the modes of
phase separation and decay of metastable phases by analytic and computational
methods. Applications were considered to magnetic, electrochemical, and
metallurgical systems.

The citations refer to the list of publications acknowledging NSF support
through this project, which is arranged chronologically within each of the
groups Published, Accepted, Submitted, and In Preparation.

Research on Metastability and Dynamics of Phase Transitions

Studies of metastability and dynamics of phase transitions were performed with
collaborators in Japan, Canada, Denmark, and the U.S. Work concentrated on
two-dimensional kinetic Ising models (with Glauber and Metropolis dynamics).

In collaboration with Dr. H. L. Richards at the University of Tokyo, and
colleagues at FSU and in Denmark, work was completed on a study of the
influence of long-range antiferromagnetic interactions on the decay of
metastability [1]. A study of the effects of boundary conditions in such
systems was started with the same collaborators [3,4].

Despite its simplicity and obvious approximations, "Avrami's law" of
metastable decay (also known as the Kolmogorov-Johnson-Mehl-Avrami, or KJMA,
theory) is a surprisingly accurate model for the time evolution of the order
parameter during the decay of metastable phases in a wide range of systems,
from magnetism and electrochemistry to food science and astrophysics.  I have
therefore undertaken a careful investigation of the time development of the
magnetization, the structure factor, and the spatial correlation and
connectedness functions in two-dimensional kinetic Ising systems, comparing
Monte Carlo simulation results with the predictions of the KJMA theory.  The
purpose of the study is to obtain a better understanding of the limits of
applicability of this simple and useful approximate theory.  A full paper on
this topic, large portions of which were written at Kyoto University and with
valuable advice from Professor Tomita, is close to completion [6].

With collaborators at McGill University in Canada I continued work on the
detailed statistical features of the scattering intensity from phase
separating binary alloys. The study was inspired by speckle patterns observed
in coherent synchrotron X-ray diffraction from phase-separating Cu3Au; similar
to laser speckle, but with time- and wavevector dependent intensity
correlations.  Our study revealed a new scaling regime for the two-time
intensity-intensity correlation function. Numerical results are included in a
conference proceeding paper [2]. The study reveals a number of new questions
in connection with the phase separation dynamics, and two large theoretical
papers are in preparation [7,8].  These papers will also include an exact
result for the asymptotic scaling function for the intensity correlation
function, which I derived during my visit to Kyoto University. This is an area
where Japanese researchers, notably Professor Tomita and Professor Kyozi
Kawasaki (formerly of Kyushu University, presently of Chubu University), have
been in the forefront of research for many years. The advice and suggestions
of these and other Japanese colleagues have been invaluable for the success of
this investigation.

A small paper with applications to electrochemical adsorption problems was
also conceived and is presently in the final draft stage [5].

Research Visits and Invited Talks

With Kyoto as my base, I was able to travel to exchange information with
colleagues at a number of Japanese public and private universities. During my
visit I gave a total of ten lectures, seven on decay of metastable phases and
three on theoretical modeling of electrochemical adsorption:

     Classical Decay of Metastable Phases:

1.  May 8, 1996: Department of Fundamental Sciences, Faculty of Integrated
Human Studies, Kyoto University, Kyoto.

2.  May 14, 1996: Department of Natural Science and Mathematics, Chubu
University, Kasugai, Aichi-ken.

3.  May 16, 1996: Department of Physics, Faculty of Science, Keio University,
Yokohama.

4.  June 13, 1996:  Department of Physics, Faculty of Science, The University
of Tokyo, Tokyo.

5.  June 14, 1996:  Department of Physics, Faculty of Science, Tokyo
Metropolitan University, Tokyo.

6.  June 18, 1996:  Department of Physics, Faculty of Science, Tohoku
University, Sendai.

7.  July 2, 1996:  Department of Earth and Space Science, Faculty of Science,
Osaka University, Osaka.

     Modeling of Phase Transitions in Electrochemical Adsorption:

1.  May 17, 1996:  Department of Chemistry, Faculty of Science, Keio
University, Yokohama.

2.  June 4, 1996:  Department of Energy Applications Engineering, Faculty of
Engineering, Kyoto University, Kyoto.

3.  June 17, 1996:  ERATO/JRDC Electrochemiscopy Project, Department of
Applied Chemistry, Faculty of Engineering, Tohoku University, Sendai, Japan.

Development of Human Resources.

The visit enabled me to continue my collaboration with my former graduate
student, Howard L. Richards, who is presently a postdoc with Professor Masuo
Suzuki at The University of Tokyo, supported by the private Inoue Foundation
for Science. I believe postdoctoral experience in Japan is an extremely
important component of the drive to strengthen the scientific and cultural
ties between the U.S. and Japan, and I will continue to try to place students
in Japan for postdoctoral experience whenever possible.

I also would like to add to this report that I find the support network for
U.S. researchers in Japan that has been set up by the NSF's Tokyo office is a
very valuable source of moral and practical support, especially for young
researchers.

Publications Acknowledging NSF Support from this grant

     Published:

1.  "Analytical and Computational Study of Magnetization Switching in Kinetic
Ising Systems with Demagnetizing Fields. H.L. Richards, P.A. Rikvold, and M.A.
Novotny, Phys. Rev. B 54, 4113-4127 (1996).

     Accepted for Publication:

2.  "Numerical Simulations of Scattering Speckle from Phase Ordering Systems.
G.Brown, P.A. Rikvold, and M.Grant, preprints FSU-SCRI-96-50 and
cond-mat/9606151, Physica A.

3.  "Magnetization Switching in Nanoscale Ferromagnetic Grains: Simulations
with Heterogeneous Nucleation."  M.Kolesik, H.L. Richards, M.A. Novotny, P.A.
Rikvold, and P.-A. Lindgrd, preprints FSU-SCRI-96C-99 and cond-mat/9609056,
submitted for the Proceedings of the 1996 Conference on Magnetism and Magnetic
Materials, to be published in J. Appl. Phys.

   Submitted:

4.  "Effects of Boundary Conditions on Magnetization Switching in Kinetic
Ising Models of Nanoscale Ferromagnets." H.L. Richards, M.Kolesik, P.-A.
Lindgrd, M.A. Novotny, and P.A. Rikvold, preprints FSU-SCRI-96-117 and
cond-mat/9611054, submitted to Phys. Rev. B.

   In Preparation:

5.  "Lattice-Gas Models of Electrochemical Adsorption: Static and Dynamic
Aspects.  P.A. Rikvold, A.Wieckowski, and R.A. Ramos, to be submitted to Mat.
Res. Soc. Symp. Proc. Ser.

6.  "Order parameter, Correlations, and Connectedness during the Decay of a
Metastable Phase. R.A. Ramos, S.W. Sides, P.A. Rikvold and M.A. Novotny,  to
be submitted to J. Chem. Phys.

7.  "Scattering Speckle from Phase Ordering Systems.'' G.Brown, P.A. Rikvold,
B.Morin, M.Sutton,  and M.Grant, to be submitted to Phys. Rev. E.

8.  "Universality in Phase Ordering Systems.  G.Brown, P.A. Rikvold, and
M.Grant, to be submitted to Phys. Rev. E.

Published Abstracts and Titles Acknowledging NSF Support Through this Grant

a.  "Phase Transitions in Electrochemical Adsorption. P.A. Rikvold and
A.Wieckowski, Program for the 1996 American Chemical Society National Meeting,
Orlando, FL, August, 1996. Invited talk.

b.  "Lattice-Gas Models of Electrochemical Adsorption: Static and Dynamic
Aspects.  P.A. Rikvold, A.Wieckowski, and R.A. Ramos, Program for the 1996
Materials Research Society Fall Meeting, Boston, MA, December, 1996.