How electrons outrun vibrating nuclei -- the X-ray movie

A crystal represents a regular array of atoms in space, a so-called lattice, which is held together by interactions between the electron clouds of neighboring atoms. While most electrons are tightly bound to the positively charged nuclei, the outermost valence electrons form chemical bonds to the next neighbors. Such bonds determine the distance between atoms in the crystal as well as basic properties such as mechanical stability or the electrical behavior.

In the crystal lattice, atoms are not at rest but perform vibrational motions around their equilibrium positions. The spatial elongation of the vibrating nuclei together with their core electrons is a tiny fraction -- typically less than 1 percent -- of the distance between neighboring atoms. With respect to the outer valence electrons, the situation is much less clear and their elongations have remained unknown in many cases. Measuring the motions of valence electrons in space and time is important for understanding their fundamental role for the crystal's static and dynamic electric properties.

To address this issue, Flavio Zamponi, Philip Rothhardt, Johannes Stingl, Michael Woerner, and Thomas Elsaesser built an x-ray "reaction microscope" which allows for an in situ imaging of moving electrons and atoms in crystalline materials. As they report in PNAS (doi/10.1073/pnas.1108206109) vibrations in the ionic crystal potassium dihydrogen phosphate (KDP) are kicked off by excitation with an optical pulse of 50 femtosecond duration (1 fs = 10^-15 seconds). The momentary position of atoms and electrons is measured with high spatial resolution by 100 fs hard x-ray pulses which are diffracted from the vibrating atoms. Measuring simultaneously many different x-ray diffraction peaks allows for reconstructing the momentary distances of atoms and in turn the three-dimensional distribution of electrons within the crystal. Taking x-ray snap shots at various delay times after initiating the vibrations creates a molecular movie according to the well known stroboscope effect.

It was a big surprise for the researchers that for a special kind of lattice vibrations (the so called soft mode of KDP) the involved valence electrons move a 30 times larger distance than the involved atoms (i.e. nuclei plus core electrons) when performing their oscillatory motion. Such a scenario is sketched in the electron density maps shown in Fig. 1. During the soft mode oscillation an electron initially residing on the phosphorus (P) atom moves to one of the neighboring oxygen (O) atoms (P-O bond length: 160 picometers (10^-12 m)) and returns to the P-atom after half the oscillation period. However, when measuring the positions of the involved atoms one finds that the latter move just a few picometers. This is very surprising, because according to textbook knowledge one expects the same motion as that of the nucleus for all electrons of an atom. To understand this unexpected large-amplitude motion of valence electrons, one has to consider the electric forces the oscillating ionic lattice exerts on the electrons during the soft mode vibration. Theories developed in the 1960's predicted such a behaviour which is now experimentally proven for the first time and determines the ultrahigh-frequency electric behavior of the material. In the attached movie, we show the iso-electron density surface of the phosphate ion during the soft mode oscillation in a KDP crystal.

The femtosecond x-ray powder diffraction method demonstrated here can be applied to many other systems in order to map ultrafast structure changes in physical and chemical processes.

Movie: http://www.fv-berlin.de/news/videos/x-ray-movie/view