Dr. Cahn died March 14 at 88. (Courtesy of National Institute of Standards and Technology)

John W. Cahn, who fled Nazi Germany as a boy and became a foremost thinker in materials science — the field of study focused on the understanding and improvement of metals and other substances that form the physical foundations of everyday life — died March 14 at a retirement community in Seattle. He was 88.

The cause was leukemia, said his son Andy Cahn.

Dr. Cahn spent decades as a scientist specializing in metallurgy at the National Institute of Standards and Technology in Gaithersburg, Md. He received some of the most prestigious honors in his field, including a 1998 National Medal of Science, awarded to him by President Bill Clinton, and the Kyoto Prize for advanced technology in 2011.

The honors recognized Dr. Cahn’s wide-ranging discoveries related to the ways molecules interact — and how those interactions help create the properties, such as strength or slickness, that make some substances more useful than others.

“John’s developments in the theory and models of materials have given scientists tools to understand and make new materials ranging from metals to plastics to ceramics and glass,” Frank W. Gayle, a former chief of the metallurgy division of NIST’s Material Measurement Laboratory, said when Dr. Cahn received the Kyoto Prize.

“For instance,” Gayle continued, “your smartphone or laptop computer might contain 100 different materials, and John’s work has probably influenced the understanding and development of half of those.”

Dr. Cahn’s name was immortalized in the Cahn-Hilliard equation, a mathematical description co-created with British metallurgist John E. Hilliard. The equation explained how dissimilar materials such as oil and water, in perhaps the most basic example, distance themselves from one another in a process called phase separation.

Dr. Cahn was concerned not with oil and water but rather with metal alloys, said Sharon Glotzer, a former NIST staff scientist and professor at the University of Michigan. Example of alloys include steel and brass — mixtures of two or more metals that combine to form a substance that is stronger or otherwise superior to its component parts.

Beyond materials science, the equation has been used in population studies to explain why people may gravitate toward already populous areas rather than disperse more evenly across a wider area. It has also been applied to the study of the cosmos to explain how galaxies were formed.

In the 1980s, Dr. Cahn assisted a colleague, Israeli scientist Dan Shechtman, with the discovery of the quasi-crystal, a particle described by NIST as “an arrangement of atoms thought to be forbidden by nature.” Rather than displaying repeating patterns, as do the crystals that form snowflakes or rock candy, quasi-crystals show non-repeating patterns.

“We inherited that catalogue of crystals from the early 19th century,” Dr. Cahn told the New York Times in 1985, “and the whole subject has long been considered closed. There was nothing more to be done but classify crystals according to pigeonholes. When Shechtman first showed me his discovery, I told him to go away, that it couldn’t be. But to his credit, he didn’t. Despite the objections of nearly all scientists, he patiently and obstinately kept at it. He was a real hero.”

Shechtman received the Nobel Prize in chemistry in 2011.

In an interview, Carol A. Handwerker, a professor in the school of materials engineering at Purdue University in Indiana, credited Dr. Cahn with bringing a “mathematical and physics-based rigor” to his science.

“The advancement of materials science and engineering as an exact and unified science,” she once wrote in a tribute to him, “owes a large measure of its success to John Cahn.”

Hans Werner Cahn was born to a Jewish family in Cologne, Germany, on Jan. 9, 1928. His mother was an X-ray technician, and his father was a lawyer who had opposed the Nazis in the years before Adolf Hitler became chancellor in 1933.

That year, a fellow lawyer stopped the elder Cahn on his way to work and warned him that the SS had come to arrest him. He returned home, collected his wife and children, and escaped to the Black Forest.

The Cahns moved throughout Europe and eventually to Amsterdam, where Dr. Cahn began his schooling, according to a biographical sketch.

In 1939, the family immigrated to the United States, where Dr. Cahn became known as John. Most of his family, including relatives in Germany and those who had decided to wait out the war in Holland, perished in the Holocaust.

The Cahns settled in New York City. Dr. Cahn became a U.S. citizen in 1945 and served in the Army in Japan in the aftermath of World War II. He received a bachelor’s degree in chemistry from the University of Michigan in 1949 and a Ph.D in physical chemistry from the University of California at Berkeley in the early 1950s.

He was a researcher for General Electric in Schenectady, N.Y., and taught at MIT before joining what was then the National Bureau of Standards in 1977. He later became a senior fellow in the materials science and engineering laboratory.

Dr. Cahn lived for many years in Bethesda, Md., before moving to Seattle in 2007. He was an affiliate professor at the University of Washington.

Survivors include his wife of 65 years, the former Anne Hessing, of Seattle; three children, Martin Cahn of Seattle, Andy Cahn of Kenmore, Wash., and Lorie Cahn of Jackson, Wyo.; a sister; and six grandchildren.

Dr. Cahn was credited with weaving mathematics into science to help explain phenomena such as the tendency of water to form beads on slick surfaces such as a newly waxed car. At times, particularly in applications of the Cahn-Hilliard equation, Dr. Cahn said that he was surprised by the discoveries his work begot.

“Having been the father of this equation, it really is very similar to being a father, because it has a life of its own,” he once told an interviewer for NIST. “I long ago lost the ability to keep guiding it. It’s just going, and I’m very proud of it, but it’s on its own.”