Equilibrium is determined by finding chemical composition with minimum free energy. Method of steepest descent is applied to quadratic representation of free-energy surface. Solution is initiated by selecting arbitrary set of mole fractions, from which point on free-energy surface is computed

Brinkley, K. L.

Stroud, C. W.

English

NASA Technical Reports Server

October 1975 
•	 NASA TECH BRIEF 
Langley Research Center 
B75-10225 
L 
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Chemical Equilibrium of Ablation Materials
Including Condensed Species 
The problem: 
A method is needed to find the chemical-
equilibrium compositions of ablation materials, 
including condensed species. 
The solution: 
A computer program has been developed to 
calculate equilibrium compositions of multiphase 
systems.
point on the parabola closest to the minimum but 
yielding a set of positive mole fractions, provide a new 
set of mole fractions from which a new point on the 
energy surface is calculated. 
The procedure is repeated until the change in the 
set of mole fractions is less than a prescribed value 
(10-5, for example). The program may be applied to 
the calculation of chemical-equilibrium compositions 
of many ablation materials, particularly at tempera-
tures below 2,700 K. 
•	 How it's done: 
Equilibrium is determined by finding the chemical 	 Notes: 
composition with the minimum free energy. The	 1. The program is written entirely in FORTRAN IV, 
method of steepest descent is applied to a quadratic 	 presently for CDC 6000-series machines. 
representation of the free-energy surface. The solution	 2. Inquiries concerning this program should be 
is initiated by selecting an arbitrary set of mole 	 directed to: 
fractions, from which a point on the free-energy 	 COSMIC 
surface is computed.	 112 Barrow Hall 
An n-dimensional parabola (where n equals the 	 University of Georgia 
number of species) is fitted to the surface at the point 	 Athens, Georgia 30601 
corresponding to the initial selection of mole fractions 	 Reference: LAR- 11801 
and is oriented in the direction of steepest descent. 
The minimum of this parabola is obtained by using 	 Source: Columbus W. Stroud and 
Lagrangian multipliers to deal with the mass-balance 	 Kay L. Brinkley 
constraints. The coordinates of the minimum, or the 	 (LAR-11801) 
Categories: 04 (Materials) 
09 (Mathematics and 
Information Sciences) 
This document was prepared under the sponsorship of the National	 Government assumes any liability resulting from the use of the 
Aeronautics and Space Administration. Neither the United States 	 information contained in this document, or warrants that such use 
Government nor any person acting on behalf of the United States 	 will be free from privately owned rights.
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Chemical equilibrium of ablation materials including condensed species

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