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Stress Analysis by Powder Diffraction

The symmetry of snowflakes that Kepler found so intriguing continues to be an inspiration to crystallographers. This was eloquently demonstrated in the presentation by A. Janner at the IUCr special symposium "New Trends in Small Moiety Crystallography" that was part of the 1994 ACA meeting in Atlanta. Janner mapped hexagons and hexagrams on snowflakes as part of his superb exposition of a common symmetry approach encompassing commensurate and incommensurate crystals. (Illustration courtesy of A. Janner)

The long tradition of using X-ray diffraction to study metals in Czechoslovakia was described in an article by N. Ganev and I. Kraus in the IUCr Commission on Powder Diffraction Newsletter No. 10. Excerpts from that articlefollow.

In 1931 P. Skulari and V. Miklenda alerted the Czechoslovak scientific community to the application of X-ray radiation to the measurement of the properties of metals with the publication of "Materials Testing by Means of X-rays". The first measurement of residual stress by means of X-rays in Czechoslovakia was probably performed by a woman (A. Kochanovska) investigating the origin of cracking in the covers of bullet shells. Subsequent studies were made of forged aluminum and heat treated iron and steel.

At present extensive experimental stress analysis is conducted at the Faculty of Nuclear Sciences and Physical Engineering (FNSPE) of the Czech Technical University of Prague. Over the course of the past 30 years, Czech crystallographers have examined properties of sintered carbides of the WC-Co system, properties of nickel powder and carbonyl iron powders, oxide films on zirconium alloys, Cr-Ni steel of turbocompressor rotor blades, and countless other industrial materials. They have conducted stress measurements on pipes, axles, landing gear, and steam generators. Recent interest has focused on the surface qualities of solids related to brittleness and fatigue fracture. No other analytical technique permits analysis of nonuniform stress fields as efficiently as X-ray diffraction. Destructive diffraction stress analysis is achieved by removal of layers of material by grinding or by chemical or electrolytic etching. Electrolytic polishing introduces the least additional stress in the material under study.

" ... crystals as big as cathedral pillars, delicate as mildew and sharp as needles ... "

X-ray determination and analysis of nonuniform residual stress provides new details of the structure of polycrystalline materials and the mechanisms of plastic deformation. Nonhomogeneous stress has been detected In FNSPE studies of surface layers of pure iron, carbon steels subjected to laser heat treatment, steel samples hardened in electron beams, the surface of a unidirectionally ground martensitic steel, and in Al alloys.

X-ray stress measurement, study of textures, and qualitative and quantitative phase analysis are the most important applications of X-ray diffraction methods in the Czech and Slovak Republic today. In 1988 and 1990, two monographs on X-ray stress measurement appeared in Czechoslovakia: I. Kraus and V. V. Trofimov, Rentgenova tenzometrie (X-ray Tensometry), Academia, Prague 1988; I. Kraus, Rentgenografie nehomogennich napetovych poli (X-ray Stress Analysis of Nonuniform Stress Fields), Academia, Prague 1990.

In a second article in the same newsletter, I. Kraus eloquently describes the origins of crystallography in 16th century Czechoslovakia. In his encyclopedia of minerals written in 1556, Georgius Agricola delineated the properties of minerals, including color, density, transparency, lustre, and shape. He described not only well ordered forms but dendrites and whiskers and included technical instructions on how to artificially produce some crystals. In January of 1611 during a visit to Prague, Johann Kepler composed a dissertation on hexagonal snow. Kepler observed that no snowflake consists of five or seven points and speculated about the relationship between that observation and the close packing of spheres. He observed, "The treasure of secrets in nature is inexhaustible, its riches are undescribable. Whoever brings something new from it to the daylight has achieved no more than showing the way to others for further investigation."

K. Capek, a famous Czech writer offered the following comments on the nature of crystals, "There are crystals as big as cathedral pillars, delicate as mildew, and sharp as needles; plain, blue, green like nothing in the world, of fiery colors or black; mathematical, perfect, like the contrivances of queer and bewildered sages. Number and fantasy, law and abundance are the feverish forces of nature; not sitting down beneath a green tree, but creating crystals and ideas denotes becoming as nature; creating laws and forms; penetrating matter with glowing flashes of divine computation."

Kraus concludes, "The science of Crystals was founded in Bohemia more than 450 years ago. Now, near the end of the 20th century, the study of crystals is not only an occupation but also the very raison d'êum;tre for scholars and researchers in several dozens of laboratories in universities, academy, and industry throughout this country in the heart of Europe."

N. Ganev and I. Kraus