Chair for Multicomponent Materials

Metallic glasses and glass forming melts – diffusion and glass transition

Metallic glasses and particularly the multicomponent bulk metallic glasses are very interesting engineering materials. They are stronger than most steels and can be molded like plastics. In addition, they exhibit intriguing functional properties. During recent years, advanced multicomponent glass forming alloys with excellent glass forming ability also received much attention in the glass community as model systems for studying the glass transition, which is currently a very active research topic in physics. The attraction of metallic glass formers also for researchers working on ceramic or molecular glasses or on the dynamics of liquids and melts lies in their simple structure being made up of spherical atoms without or with relatively weak directional bonding, rotational degrees of freedom, or side chains, for instance. The glass forming ability of multicomponent metallic glass formers neither arises from strong directed covalent bonding, as in the traditional oxide glasses or amorphous semiconductors, nor does it arise from structural asymmetry, as in single component molecular glass formers, but it is due to dynamic asymmetry which mainly originates from size disparity and short-range order. Additional thermodynamic aspects and the “confusion principle also play a role.

While our early work (see below) aimed at clarifying the diffusion mechanisms in the glassy state, more recent work was focused on the glass transition upon undercooling glass forming metallic melts. Recently, we reported radiotracer diffusivities and viscosity data in the equilibrium liquid state of a bulk metallic glass forming Zr46.75Ti8.25Cu7.5Ni10Be27.5 melt (Vitreloy 4) far above the liquidus temperature. The results suggest that, in these Zr-based metallic glass forming systems, diffusion and viscous flow start to develop solid-like, i.e., energy-landscape-controlled, features already in the stable liquid state more than 300 K above the mode coupling temperature Tc. This is attributed to Zr atoms forming relatively long lasting temporary bonds in the melts compared to the other atoms. 

In previous investigations in a Pd43Cu27Ni10P20 melt, we were able, for the first time, to measure a complete set of diffusivity data for all components over the whole relevant temperature range. While a vast decoupling of more than 4 orders of magnitude was observed between the diffusivity of Pd and of the smaller components, at the glass transition temperature, the diffusivities of all components merge close to the critical temperature Tc of mode coupling theory (Fig. 1). For Pd, the Stokes-Einstein relation was found to hold in the whole range investigated encompassing more than 14 orders of magnitude suggesting the formation of a slow subsystem (Fig. 2) as a key to glass formation in systems with dynamic asymmetry. For comparison, in simple liquids and melts, the Stokes-Einstein relation holds for all components. Here viscous flow and diffusion of all components proceeds via the same mechanism of uncorrelated binary collision, and all components have almost identical diffusivities.


Fig. 1 Arrhenius plot for diffusion in liquid Pd43Cu27Ni10P20 alloys. Shown are diffusivities of the radiotracers 103Pd, 32P, 57Co, and 51Cr. Dashed lines display quasieutectic melting temperature Tm and critical temperature Tc of the mode coupling theory, determined from quasielastic neutron scattering.



Fig. 2  Sketch of a metallic glass forming Pd43Cu27Ni10P20 melt consisting of palladium, copper, nickel, and phosphorous atoms, where the relatively large palladium atoms form an immobile framework before the melt solidifies. Thus the other atoms are restricted to cages within the framework.


Selected publications on diffusion and glass transition in glass forming metallic melts
Basuki, S. Y.; Yang, F.; Gill, E.; Rätzke, K.; Meyer, A.; Faupel, F.; Atomic dynamics in Zr-based glass forming alloys near the liquidus temperature, PHYSICAL REVIEW B 95,024301 (2017) .

Basuki, S.W.; Bartsch, A.; Yang, F.; Rätzke, K.; Meyer, A.; Faupel, F.: Decoupling of component diffusion in a glass forming Zr46.75Ti8.825Cu7.5Ni10Be27.5 melt far above the liquidus temperature, Physical Review Letters 113 (2014) 165901.

Faupel, F.; Rätzke, K.; Gojdka, B.: Metallische Gläser - hart im Nehmen und extrem vielseitig, Welt der (2010) Lizenz: CC 2.0 by-nc-nd.

Bartsch, A.; Rätzke, K.; Meyer, A.; Faupel, F.: Dynamic Arrest in Multicomponent Glass-Forming Alloys, Physical Review Letters Vol. 104 Nr.19 (2010) PRL 104, 195901.

Bartsch, A.; Rätzke, K.; Faupel, F.: Codiffusion of 32P and 57Co in glass-forming Pd43Cu27Ni10P20 alloy and its relation to viscosity, Applied Physics Letters 89(12) (2006) 121917/1-121917/3.


Earlier work on diffusion mechanisms in metallic glasses and supercooled melts

In our early work, which meanwhile found its way into textbooks, we studied the mechanism of diffusion in the glassy and deeply supercooled liquid state. Based on radiotracer measurements of the isotope effect and the pressure dependence of diffusion we showed that diffusion in the glassy state is typically a highly collective hopping mechanism involving a large number of atoms. This was later confirmed by molecular dynamics simulations. We further showed that a similar solid-like collective hopping mechanism also holds for the deeply supercooled liquid state below the critical temperature Tc of the mode coupling theory.  In the glassy state, we also performed intensive work on structural relaxation based on diffusion measurements and positron annihilation spectroscopy.

Selected publications


Diffusion in metallic glasses and supercooled melts
F. Faupel, W. Frank, M.-P. Macht, H. Mehrer, V. Naundorf, K. Rätzke, H. R. Schober, S. K. Sharma, and H. Teichler, Review of Modern Physics 75, 237 (2003).

Zöllmer, V.; Rätzke, K.; Faupel, F.; and Meyer, A.: Diffusion in a metallic melt at the critical temperature of mode coupling theory, Physical Review Letters 90(19) (2003) 195502/1-195502/4.

Heesemann, A.; Zöllmer, V.; Rätzke, K.; Faupel, F.: Evidence of highly collective Co diffusion in the whole stability range of Co-Zr glasses, Physical Review Letters 84(7) (2000) 1467-1470.

Klugkist, P.; Rätzke, K.; Faupel, F.: Evidence of defect-mediated Zirconium self-diffusion in amorphous Co92Zr8, Physical Review Letters 81 (1998) 614.

Ehmler, H.; Heesemann, A.; Rätzke, K.; Faupel, F.; Geyer, U.: Mass dependence of diffusion in a supercooled metallic melt, Physical Review Letters 80 (1998) 4919.

Klugkist, P.; Rätzke, K.; Rehders, S.; Troche, P.; Faupel, F.: Activation volume of 57Co diffusion in amorphous Co81Zr19,Physical Review Letters 80(15) (1998) 3288-3291.

Rätzke, K.; Hüppe, P.-W.; Faupel, F.: Transition from single-jump type to highly cooperative diffusion during structural relaxation of a metallic glass, Phys. Rev. Lett. 68 (1992) 2347.

Faupel, F.; Hüppe, P.-W.; Rätzke, K.: Pressure dependence and isotope effect of self diffusion in a metallic glass, Physical Review Letters 65(10) (1990) 1219-22.

Structural relaxation

Evensen, Z.; Koschine, T.; Wei, S.; Gross, O.; Bednarcik, J.; Gallino, I.; Kruzic, J.J.; Rätzke, K.; Faupel, F.; Busch, R.; The effect of low-temperature structural relaxation on free volume and chemical short-range ordering in a Au49Cu26.9Si6.3Ag5.5Pd2.3 bulk metallic glass, Scripta Materialia 103 (2015) 14-17.

Rehmet, A.; Günther-Schade, K.; Rätzke, K.; Geyer, U.; Faupel, F.: Quenching rate dependence of free volume in a Zr-Cu-Ni-Ti-Be glass as probed by positron annihilation lifetime spectroscopy, Physica Status Solidi A: 201(3) (2004) 467-470.

Zöllmer, V.; Ehlmer, H.; Rätzke, K.; Troche, P.; Faupel, F.: Isotope effect of Co diffusion in thin amorphous Co51Zr49 layers during structural relaxation, Europhysics Letters 51(1) (2000) 75-81.

Nagel, C.; Rätzke, K.; Schmidtke, E.; Faupel, F.; Ulfert, W.: Positron annihilation studies of free volume changes in the bulk metallic glass Zr65Al7.5Ni10Cu17.5 during structural relaxation and at the glass transition, Physical Review 60(13)(1999) 9212-9215.

Nagel, C.; Rätzke, K.; Schmidtke, E.; Wolff, J.; Faupel, F.; Geyer, U.: Free volume changes in the bulk metallic glass Zr46.7Ti8.3Cu7.5Ni10Be27.5 and the undercooled liquid, Physical Review 57(17) (1998) 10224-10227.