Instant Access to the Journals You Need

for just $40 per month.

Start Your Free Trial

An integer programming approach to the phase problem for centrosymmetric structures

An integer programming approach to the phase problem for centrosymmetric structures

Abstract

The problem addressed in this paper is the determination of three-dimensional structures of centrosymmetric crystals from X-ray diffraction measurements. The `minimal principle' that a certain quantity is minimized only by the crystal structure is employed to solve the phase problem. The mathematical formulation of the minimal principle is a nonconvex nonlinear optimization problem. To date, local optimization techniques and advanced computer architectures have been used to solve this problem, which may have a very large number of local optima. In this paper, the minimal principle model is reformulated for the case of centrosymmetric structures into an integer programming problem in terms of the missing phases. This formulation is solvable by well established combinatorial optimization techniques that are guaranteed to provide the global optimum in a finite number of steps without explicit enumeration of all possible combinations of phases. Computational experience with the proposed method on a number of structures of moderate complexity is provided and demonstrates that the approach yields a fast and reliable method that resolves the crystallographic phase problem for the case of centrosymmetric structures.
Loading next page...
 
/lp/international-union-of-crystallography/an-integer-programming-approach-to-the-phase-problem-for-g4MC8z5zZu

You're reading a free preview. Subscribe to read the entire article.

And millions more from thousands of peer-reviewed journals, for only $40/month.

Start Your Free Trial

What content is in DeepDyve?

  • Read and share from thousands of the leading scholarly journals from Springer, Elsevier, Nature, IEEE, Wiley-Blackwell and more.
  • All the latest content is available, no embargo periods.

Rent Scholarly Articles?

  • Read the full article in your browser.
  • Access all of your rentals from the cloud anywhere you have an internet connection.
  • Beautiful reading experience – Full charts and figures, just like the PDF.
  • Read as much as you'd like - whenever you'd like.

Happy Users

“In one word renting from DeepDyve is FANTASTIC!!! ... 99% of the time I only need access to an article for a month or so, so renting the articles is perfect for me.”

Adam S.

“Thanks for a great service! For an unaffiliated science blogger like myself this is like a dream come true.”

Seppo P.

“Hi guys, I cannot tell you how much I love this resource. Incredible. I really believe you've hit the nail on the head with this site in regards to solving the research-purchase issue.”

Daniel C.

“Let me seize this opportunity and congratulate you on the service you are rendering to the scientific community.”

Joao B.