Grain size dependence of elastic anomalies accompanying the α–β phase transition in polycrystalline quartz

Abstract

The effects of grain size on the elastic properties of quartz through the α–β phase transition have been investigated by resonant ultrasound spectroscopy. It is found that there are three regimes, dependent on grain size, within which elastic properties show different evolutions with temperature. In the large grain size regime, as represented by a quartzite sample with ∼100–300 µm grains, microcracking is believed to occur in the vicinity of the transition point, allowing grains to pull apart. In the intermediate grain size regime, as represented by novaculite (1–5 µm grain size) and Ethiebeaton agate (∼120 nm grain size), bulk and shear moduli through the transition follow closely the values expected from averages of single crystal data. The novaculite sample, however, has a transition temperature ∼7 °C higher than that of single crystal quartz. This is assumed to be due to the development of internal pressure arising from anisotropic thermal expansion. In the small grain size region, agates from Mexico (∼65 nm) and Brazil (∼50 nm) show significant reductions in the amount of softening of the bulk modulus as the transition point is approached from below. This is consistent with a tendency for the transition to become more second order in character. The apparent changes towards second order character do not match quantitative predictions for samples with homogeneous strain across elastically clamped nanocrystals, however. Some of the elastic variations are also due to the presence of moganite in these samples. True ‘nanobehaviour’ for quartz in ceramic samples thus appears to be restricted to grain sizes of less than ∼50 nm.

Elastic and anelastic relaxation behaviour of perovskite multiferroics I: PbZr0.53Ti0.47O3 (PZT)–PbFe0.5Nb0.5O3 (PFN)

“…From considerations of the phase diagram, the pattern is expected to be that of a tricritical transition. The steep and nonlinear stiffening with falling temperature below T c is characteristic of tricritical character, as seen, for example, in association with tilting transitions in SrZrO 3 [129], KMnF 3 [130,131], BaCeO 3 [132] and quartz [125]. Also as expected in this context, there is a correlation between the magnitudes of the reduction in f 2 , measuring softening of the shear modulus, and the magnitudes of the tetragonal shear strains.…”

“…The high-temperature (HT) RUS measurements were performed after the low temperature (LT) measurements and the larger samples from the LT measurements were subdivided in-between these two experiments and hence the lower masses in Table 2 for the HT experiments. The instrument used for measurements above room temperature has been described by McKnight et al [125] and uses Stanford electronics [126]. Temperature was determined with a thermocouple 4 (453.6 K).…”

Elastic and anelastic relaxations accompanying relaxor ferroelectric behaviour of Ba6GaNb9O30 tetragonal tungsten bronze from resonant ultrasound spectroscopy

“…Again the sample was excited at frequencies between 0.1 and 1.2 MHz with 65,000 data points per spectrum. The head assembly was held vertically in a helium-flow cryostat in an atmosphere of few millibars of He to facilitate heat transfer, as described previously by McKnight et al [60,61]. Sequences of spectra were collected during cooling and heating between *300 and *10 K, and a period of 20 min was allowed for thermal equilibration at each temperature before data collection.…”

Strain behavior and lattice dynamics in Ni50Mn35In15

“…In the hightemperature instrument, the sample sits lightly between the tips of alumina rods which protrude into a horizontal Netzsch 1600 °C resistance furnace. The piezoelectric transducers are at the other end of the rods, outside the furnace [19]. In the lowtemperature instrument the sample sits directly between the transducers and is suspended in an atmosphere of a few mbars of helium gas, within a helium flow cryostat [20].…”