NOTICE: Due to a lapse in annual appropriations, most of this website is not being updated. Learn more.
Form submissions will still be accepted but will not receive responses at this time. Sections of this site for programs using non-appropriated funds (such as NVLAP) or those that are excepted from the shutdown (such as CHIPS and NVD) will continue to be updated.
An official website of the United States government
Here’s how you know
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
Secure .gov websites use HTTPS
A lock (
) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.
A Phase Field Model of the Premelting of Grain Boundaries in Pure Materials
Published
Author(s)
A E. Lobkovsky, James A. Warren
Abstract
We present a phase field model of solidification which includes the effects of the crystalline orientation in the solid phase. This model describes grain boundaries as well as solid-liquid boundaries within a unified framework. With an appropriate choice of coupling of the phase field variable to the gradient of the crystalline orientation variable in the free energy, we find that high angle boundaries undergo a premelting transition. As the melting temperature is approached from below, low angle grain boundaries remain narrow. The width of the liquid layer at high angle grain boundaries diverges logarithmically.
Citation
A Phase Field Model of the Premelting of Grain Boundaries in Pure Materials
crystalline orientation, grain boundaries, melting, phase field model, pure materials, solid-liquid boundaries
Citation
Lobkovsky, A.
and Warren, J.
(2001),
A Phase Field Model of the Premelting of Grain Boundaries in Pure Materials, A Phase Field Model of the Premelting of Grain Boundaries in Pure Materials, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=853036
(Accessed October 8, 2025)