We report the results of highly sensitive transmission X-ray scattering measurements performed at the Advanced Photon Source, Argonne National Laboratory, on nearly fully dense high-purity amorphous-silicon (a-Si) samples for the purpose of determining their degree of hyperuniformity. A perfectly hyperuniform structure has complete suppression of infinite-wavelength density fluctuations, or, equivalently, the structure factor S(q→0) = 0; the smaller the value of S(0), the higher the degree of hyperuniformity. Annealing was observed to increase the degree of hyperuniformity in a-Si where we found S(0) = 0.0075 (±0.0005), which is significantly below the computationally determined lower bound recently suggested by de Graff and Thorpe [de Graff AMR, Thorpe MF (2010) Acta Crystallogr A 66(Pt 1):22-31] based on studies of continuous random network models, but consistent with the recently proposed nearly hyperuniform network picture of a-Si. Increasing hyperuniformity is correlated with narrowing of the first diffraction peak and extension of the range of oscillations in the pair distribution function.A fter more than a half century of theoretical efforts and increasingly precise measurements, understanding the atomicscale structure of disordered solids remains an outstanding challenge (1). Interest in this area continues unabated, as the link between structure and physical properties is key to the design of functional materials.In this paper, we examine the behavior of the structure factor S(q) in the infinite-wavelength (q→0) limit for high-purity amorphous silicon (a-Si) to determine its degree of hyperuniformity. The structure factor S(q) is given bysin θ, N is the number of atoms, R j and R k are their positions, λ is the X-ray wavelength, and 2θ is the scattering angle. By definition, a perfectly hyperuniform structure has infinitewavelength density fluctuations that are completely suppressed and, hence, its structure factor S(q→0) = 0 (2). In general, the value S(q→0) measures the degree of hyperuniformity.Ordered solids such as crystalline and quasicrystalline materials are trivially perfectly hyperuniform. Although liquids are nonhyperuniform, it is possible to have isotropic disordered solid structures that are perfectly hyperuniform (2). This special class includes "maximally random jammed" (MRJ) packings of equalsized spheres, for which it has been shown that S(q→0) vanishes linearly with q (3). Moreover, one can explicitly construct a wide class of disordered hyperuniform point patterns using a "collective-coordinate" approach (4).Determining where amorphous silicon falls in this spectrum was motivated by recent research on hyperuniform disordered photonic materials that exhibit complete (both polarizations and all directions) and sizable photonic band gaps (5). Florescu et al.(5) have argued that the existence of photonic bandgaps in disordered photonic solids may be explained using theoretical ideas similar to those introduced by Weaire and Thorpe to explain the electronic bandgap in amorphous semicondu...

We present a thermodynamic study of the phase diagram of single-crystal Ba 1−x K x Fe 2 As 2 using specific-heat measurements. In zero-magnetic field a clear step in the heat capacity of ⌬C / T c = 0.1 J / mol K 2 is observed at T c Ϸ 34.6 K for a sample with x = 0.4. This material is characterized by extraordinarily high slopes of the upper critical field of 0 ‫ץ‬ H c2 c / ‫ץ‬T = −6.5 T / K and 0 ‫ץ‬ H c2 ab / ‫ץ‬T = −17.4 T / K and a surprisingly low anisotropy of ⌫ ϳ 2.6 near T c . A consequence of the large field scale is the effective suppression of superconducting fluctuations. Using thermodynamic relations we determine Ginzburg-Landau parameters of c ϳ 100 and ab ϳ 260 identifying Ba 1−x K x Fe 2 As 2 as extreme type II. The large value of the normalized discontinuity of the slopes of the specific heat at T c , ͑T c / ⌬C͒⌬͑dC / dT͒ T c ϳ 6, indicates strong-coupling effects in Ba 1−x K x Fe 2 As 2 .

We present heat-capacity measurements of the upper critical fields of single-crystal NdFeAsO 1−x F x . In zero-magnetic field a clear step in the heat capacity is observed at T c Ϸ 47 K. In fields applied perpendicular to the FeAs layers the step broadens significantly whereas for the in-plane orientation the field effects are small. This behavior is reminiscent of the CuO 2 -high-T c superconductors and is a manifestation of pronounced fluctuation effects. Using an entropy conserving construction we determine the transition temperatures in applied fields and the upper critical-field slopes of ‫ץ‬H c2 c / ‫ץ‬T = −0.72 T / K and ‫ץ‬H c2 ab / ‫ץ‬T = −3.1 T / K. Zerotemperature coherence lengths of ab Ϸ 3.7 nm and c Ϸ 0.9 nm and a modest superconducting anisotropy of ϳ 4 can be deduced in a single-band model.