Session X36: Metallic Glasses and Quasicrystals

Local growth rules and kinetics for ordered icosahedral quasicrystals

Icosahedral quasicrystals (IQCs) with extremely high degrees of translational order have been produced in the lab and found in naturally occurring minerals. While the existence of IQCs is well established, questions remain about how IQCs form. We address the question of whether it is possible in principle for nucleation and growth dominated by local growth rules and kinetics to produce a {\em perfectly} ordered IQC. We find that it is possible to produce an IQC with a vanishing density of defects through a local growth algorithm for sequential, face-to-face addition of tiles of two different shapes to a growing cluster. The choice of how to add a tile at any selected vertex on the surface is based only on short-range information about tiles that share the vertex. The process is analogous to the Onoda growth rule for 2D Penrose tilings [Onoda et al., PRL 60, 2653 (1988)], but new subtleties emerge in three dimensions. The geometric features underlying this algorithm can inform analyses of experimental systems and numerical models that generate highly ordered quasicrystals.   

Low participation ratio vibrational modes in a limit-periodic structure

Motivated by the demonstration that patterned colloidal particles may form a limit-periodic phase\footnote{C.\ Marcoux, T.\ W.\ Byington, Z.\ Qian, P.\ Charbonneau, and J.\ E.\ S.\ Socolar, {\it Phys. Rev. E} {\bf 90}, 012136 (2014).}, we study the nature of vibrational modes in a toy model based on the Taylor-Socolar tiling. We consider a triangular lattice of identical point masses with nearest neighbors connected by springs of two different strengths, where the pattern of spring constants reflects the limit-periodic structure of the tiling. Using calculations of the phonon spectra for crystalline approximants to the limit-periodic structure, we identify several hierarchies of modes shared by the full limit-periodic system that have arbitrarily low participation ratios. We present a heuristic explanation of the existence of such modes, which are robust in the presence of vacancies and small amounts of disorder in the spring constants.   

Magnetism in the i-$R$-Cd ($R \quad =$ Y, Gd-Tm) binary quasicrystals

Progress in our understanding of the consequences of aperiodicity for physical phenomena such as the electronic, magnetic, and optical properties has recently seen a surge of activity and new results. A new family of i-$R$-Cd binary magnetic quasicrystals, exhibiting spin-glass-like behavior, and the closely related $R$Cd$_{\mathrm{6}}$ crystalline approximants , which manifest long-range magnetic order at low temperature, offer new opportunities for studies of the impact of aperiodicity on magnetic interactions in compounds that have similar local structures. I will discuss their magnetic behavior, as well as recent x-ray diffraction and elastic magnetic neutron scattering investigations that provide some insight into their structural and magnetic properties.   

Crystal electric field excitations in quasicrystal approximant TbCd$_6$ studied by inelastic neutron scattering

All of the known quasicrystals with local moments exhibit frustration and spin glass-like behavior at low temperature. The onset of the spin freezing temperature is believed to be affected by the crystal electric field (CEF) splitting of the local moments. The quasicrystal approximant TbCd$_6$ and its related icosahedral quasicrystal phase, i-Tb-Cd, form a set of model systems to explore how magnetism evolves from a conventional lattice (approximant phase) to an aperiodic quasicrystal. Though TbCd$_6$ shows long-range antiferromagnetic ordering ($T_N$ = 24 K), only spin glass like behavior is observed in i-Tb-Cd with a spin freezing temperature of $T_F$ = 6 K. To investigate further, we have performed inelastic neutron scattering measurements on powder samples of TbCd$_6$ and observed two distinct CEF excitations at low energies which points to a high degeneracy of the CEF levels related to the Tb surrounding with almost icosahedral symmetry.   

Magnetoresistance in i-R-Cd icosahedral quasicrystals (R=Y, Gd)

We use magnetoresistance (MR) to probe the electronic properties of the recently discovered binary quasicrystals (QCs) i-Gd-Cd and i-Y-Cd, with and without local magnetic moments, respectively. DC magnetization has revealed spin-glass freezing in i-Gd-Cd at a temperature $T_f = 4.6$~K. MR was measured at $1.6\leq T$(K)$\leq 300$ and in magnetic fields $H$ up to 12~T. %In the MR measurements, The most interesting behavior is observed in i-Gd-Cd, in which the MR exhibits thermo-magnetic history dependence at low $T$. In particular, there is a clear difference between the ZFC and FC values of the low-field positive MR. In contrast, the i-Y-Cd MR does not depend on magnetic history. The onset of the history dependent MR at $T\sim 20$~K~$>T_f$, when the QC with local magnetic moments is cooled in a high field of 12~T, may be related to the formation of magnetic clusters above $T_f$, as inferred from the magnetization and specific heat studies. Possible mechanisms responsible for the striking coupling between charge transport and local magnetic environment observed in the MR will be discussed.   

Predicting Novel Bulk Metallic Glasses via High- Throughput Calculations

Bulk metallic glasses (BMGs) are materials which may combine key properties from crystalline metals, such as high hardness, with others typically presented by plastics, such as easy processability[1]. However, the cost of the known BMGs poses a significant obstacle for the development of applications, which has lead to a long search for novel, economically viable, BMGs[2,3]. The emergence of high-throughput DFT calculations, such as the library provided by the AFLOWLIB consortium[4], has provided new tools for materials discovery. We have used this data to develop a new glass forming descriptor combining structural factors with thermodynamics in order to quickly screen through a large number of alloy systems in the AFLOWLIB database, identifying the most promising systems and the optimal compositions for glass formation. [1] M. F. Ashby, A. L. Greer. Scripta Mater. 54, 321 (2006). [2] A. Inoue Bulk Amorphous Alloys: Preparation and Fundamental Characteristics, Vol. 4. (Trans Tech Publications, Zurich, 1998). [3] T. Egami, Y. Waseda. J. Non-Cryst. Solids 64, 113 (1984). [4] S. Curtarolo et al. Comp. Mater. Sci. 58, 218 (2012).   

Stretched Exponential relaxation in pure Se glass.

A universal feature of glasses is the stretched exponential relaxation, f(t) $=$ exp[-t/$\tau $]$^{\mathrm{\beta }}$. The model of diffusion of excitations to randomly distributed traps in a glass by Phillips$^{\mathrm{1}}$ yields the stretched exponent $\beta =$ d[d$+$2] where d, the effective dimensionality. We have measured the enthalpy of relaxation $\Delta $H$_{\mathrm{nr}}$(t$_{\mathrm{w}})$ at T_{\mathrm{g}}$ of Se glass in modulated DSC experiments as glasses age at 300K and find $\beta\quad=$ 0.43(2) for t$_{\mathrm{w}}$ in the 0 \textless t$_{\mathrm{w}}$ \textless 8 months range. The observed $\beta $ is in harmony with the trap model. The result is consistent with the growth of interchain structural correlations mediated by both long range (van der Waals forces) and short-range (covalent) interactions. A striking consequence of this relaxation is a narrowing of the glass transition width from 7.1\textdegree C to 1.4\textdegree C, and the $\Delta $H$_{\mathrm{nr}}$ term increasing from 0.21 cal/gm to 0.92 cal/gm. In bulk Ge$_{\mathrm{x}}$Se$_{\mathrm{100-x}}$ glasses as x increases to 20{\%}, the length of the polymeric Se$_{\mathrm{n}}$ chains between the Ge-crosslinks decreases to n $=$ 2. and the striking relaxation effects nearly vanish.   

Low-temperature internal friction in quenched amorphous selenium films

Using ultra-high-quality-factor silicon mechanical resonators, we have measured the internal friction and shear modulus of amorphous selenium (a-Se) films at liquid helium temperatures. The glass transition temperature of selenium lies at a conveniently accessible $40-50^{\circ}$C, facilitating a series of in- and ex-situ annealing and quench cycles. The a-Se films exhibit the low-temperature internal friction plateau ($10^{-4} \leq Q^{-1} \leq 10^{-3}$) found in almost all amorphous solids, which is a result of (and direct measure of) a broad distribution of two-level tunneling systems (TLS), whose origin is still unknown. We find a clear correlation between the post-anneal quench rate and the value of this plateau. The implications of these observations for understanding the microscopic origin of TLS will be discussed. Principally, the observed changes in the internal friction plateau could show the way in which the density of TLS could be manipulated or suppressed in other amorphous systems.   

Non-Gaussian resistance noise in misfit layer compounds: Bi-Se-Cr

Misfit layer ternary compounds Bi-Se-Cr have been synthesized and structurally and magnetically characterized [1]. However, the nature of the magnetic ordering below the transition temperature remains debatable between ferromagnetic and spin-glass. These misfit layer compounds consist of two alternating chalcogenide layers of CrSe2 and BiSe along the c-axis. Whereas the a-axis is lattice matched, the lattice mismatch along the b-axis introduces non-periodic modulation of atomic position leading to quasi-crystalline order along the b-axis alone. We explore unconventional electrical transport properties in the noise spectrum of these compounds. After thinning down the compounds to nanoscale, Van der Pauw devices are fabricated with standard electron beam lithography process. Large resistance noise was observed at temperature below the Cure temperature. The magnitude of resistance noise is much greater than trivial intrinsic noises like thermal Johnson noise and increases as temperature decreases. The probability density function of the relative noise shows 2-4 peaks among different observations which indicate strong non-Gaussian statistic property suggesting glassy behaviors in this material. [1] S. M. Clarke and D. E. Freedman, Inorg. Chem. 54, 2765-2771 (2015)   

Synthesis, optical and thermal characterization of NaPO$_{3}$ glass.

We have synthesized the stoichiometric bulk glass by reacting equimolar amounts of Na$_{2}$CO$_{3}$ and P$_{2}$O$_{5}$, and handling the anhydrous starting materials and reacted product in a dry ambient environment. The bulk glass displays a T$_{g}$ of 306(2)\textdegree C and an enthalpy of relaxation of 0.26 cal/gm using MDSC. In a previous report a T$_{g}=$ 287\textdegree C was obtained$^{1}$ using DSC. The glass was crystallized and characterized by XRD and revealed a powder pattern that is in excellent agreement with the known structure (CSD 174021). Raman scattering of the glass revealed prominent modes of symmetric vibration of the PO$_{4}$ tetrahedra bearing P-O$_{br\, }$and$_{\, }$-P-O$_{ter}$ bonds near 684 cm$^{-1}$ and 1162 cm$^{-1}$ respectively. The integrated intensity ratio R of the 1162 cm$^{-1}$/684 cm$^{-1}$ modes is close to 1.0(1) in the crystal but increases to 1.4(1) in the glass reflecting the finite length of the P-O-P chains in the latter. The highest frequency mode is a weak feature near 1268 cm$^{-1}$, which coincides with the TO response in IR reflectivity of the glass, suggesting that it represents the TO mode of the NaPO$_{3}$ glass.   

Raman scattering and Medium Range Structure of (BaO)$_{\mathrm{x}}$(B$_{\mathrm{2}}$O$_{\mathrm{3}})_{\mathrm{100-x}}$-glasses.

In Raman scattering of titled glasses we observe a triad of modes (770 cm$^{\mathrm{-1}}$, 750 cm$^{\mathrm{-1}}$, 705 cm$^{\mathrm{-1}})$ on the low frequency side of the famous Boroxyl-Ring (BR) mode (808 cm$^{\mathrm{-1}})$ as the BaO content x increases in the 0 \textless x \textless 40{\%} range. Raman polarization experiments reveal that the triad of modes show a rather low depolarization ratio ($\rho $ \textless 0.25) suggesting that each mode results from a symmetric stretch of O atoms in mixed-3-member-rings, analogous to the BR-mode. In the 0 \textless x \textless 15{\%} range, the conspicuous absence of these mixed-ring modes is consistent with the composition range representing the immiscibility range. At x \textgreater 15{\%}, the 770 cm-1 mode scattering strength grows precipitously to show a maximum near x$_{\mathrm{c}} \quad =$20{\%}, consistent with presence of Ba-tetraborate structural grouping (SG). At x \textgreater 15{\%}, we also observe scattering strength of the 750 cm$^{\mathrm{-1}}$ mode to increase with x and show a maximum near x$_{\mathrm{c}} \quad =$ 33{\%}, consistent with formation of Ba-diborate SG. Finally, a mode near 705 cm$^{\mathrm{-1}}$, whose scattering strength increases linearly with x in the 15{\%} \textless x \textless 40{\%} range, we identify with Ba-metaborate SG. FTIR measurements permit a measurement of the B$_{\mathrm{4}}$/B$_{\mathrm{3}}$ fraction and also the LO-TO splittings.   

The effect of spherical inclusions in metallic glass nanowires under tensile test and its relation to atomic structure

The plastic behavior of crystalline metals is well understood. It is know that this regime is mainly mediated by nucleation and propagation of dislocations as well as by grain boundary sliding. In metallic glasses (MGs) the plastic behavior is quite different from their crystalline counterparts and a relationship between atomic-micro structure and properties remains one of the barriers that has hampered the progress to wide applications of MGs. In particular it would be desirable to have studies which directly relate the evolution of the shear bands (SBs) and glass matrix structure to each step of the applied strain, which would allow us to easily connect the evolution of the atomic structure to the stress-strain curve. Here we present a computational tensile test which shows the evolution of the atomic structure according to the strain is applied for a Cu$_{50}$Zr$_{50}$ metallic glass nanowire at 300 K with a Cu-Zr b2 inclusion in the center of the system with three different radius from 20 to 60 \AA. The system consists of a million atoms and the local structure is analyzed by means of the Voronoi polyhedral technique and the nucleation and propagation of SBs by monitoring the local atomic shear strain.