Constitutive laws and crystal plasticity in diamond deformation have been the subjects of substantial interest since synthetic diamond was made in 1950's. To date, however, little is known quantitatively regarding its brittle-ductile properties and yield strength at high temperatures. Here we report, for the first time, the strain-stress constitutive relations and experimental demonstration of deformation mechanisms under confined high pressure. The deformation at room temperature is essentially brittle, cataclastic and mostly accommodated by fracturing on {111} plane with no plastic yielding at uniaxial strains up to 15%. At elevated temperatures of 1000°C and 1200°C diamond crystals exhibit significant ductile flow with corresponding yield strength of 7.9 and 6.3 GPa, indicating that diamond starts to weaken when temperature is over 1000°C. At high temperature the plastic deformation and ductile flow is meditated by the <110>{111} dislocation glide and a very active {111} micro-twinning.
We study the temperature and pressure dependence of phase evolution in the 0.5MgO-0.5Y2O3 nanocomposite system using a diamond anvil apparatus in conjunction with in situ synchrotron energy dispersive x-ray diffraction at 7 GPa hydrostatic pressure. At (298 K, 7.0 GPa), structural transformations in the Y2O3 phase are observed, giving rise to the co-existence of its cubic, hexagonal, and monoclinic polymorphs together with cubic MgO. An increase in temperature to 1273 K causes the crystallinity of the Y2O3 hexagonal and monoclinic phases to increase. Isothermal and isobaric hold at (1273 K, 7.0 GPa) for 60 min results in yttrium dissolution in cubic MgO, causing ∼1.0% expansive volumetric lattice strain despite the large differences in the ionic radii of the cations. Cooling the nanocomposite to (298 K, 0 GPa) after a 60 min soak yields four phase co-existence among cubic MgO and cubic, hexagonal, and monoclinic Y2O3. The residual MgO unit cell volume expansion is 0.69% at 298 K, indicating solid solution formation at room temperature despite large differences in the ionic radii of Mg2+ and Y3+. The macroscopic shrinkage due to densification is 3% by volume. Thermodynamic considerations suggest that the relative molar partial volume of Y3+ in MgO is a negative quantity, indicating that the partial molar volume of Y3+ in the solid solution is smaller than its molar volume in the pure state. Aging of the nanocomposites for 240 h does not change the observed 4 phase co-existence. We propose a crystallographic model in which the observed volumetric expansion of the MgO unit cell is primarily attributed to two hydrostatic expansive strain components accompanying solid solution formation: (i) Coulomb repulsion among O2− ions in the immediate vicinity of Mg2+ vacancies, and (ii) misfit strain due to differences in ionic radii upon Y3+ substitution on Mg2+ sites.
A comparative phase transition study of nanocrystalline and micro-TiO2 has been conducted under high pressure–temperature (P–T) conditions using energy-dispersive synchrotron x-ray diffraction (XRD). Our study reveals that on compression at room temperature, the micro-tetragonal anatase-type TiO2 started to transform to the orthorhombic columbite-type TiO2 near 1.6 GPa. In contrast, we did not observe this phase transition in nano-anatase at pressures of up to 8.5 GPa. At 8.5 GPa, by applying moderate heat, both samples were transformed completely to columbite-type TiO2 almost simultaneously, indicating that heat treatment could significantly expedite this phase transition. These columbite-type TiO2 phases were quenchable because after cooling them to room temperature and decompressing them to 2.0 GPa, the XRD patterns displayed no changes in comparison with those collected at 8.6 GPa and 1270 K. At 2 GPa, we heated the specimens again, and the rutile-type TiO2 started to emerge around 970 K. This phase was also quenchable after cooling and releasing pressure to ambient conditions. The grain size effects on the phase transition were discussed based on the kinetics mechanism. This study should be of considerable interest to the fields of materials science and condensed matter.
The elastic properties of jarosite were investigated using synchrotron X-ray diffraction coupled with a multi-anvil apparatus at pressures up to 8.1 GPa. With increasing pressure, the c dimension contracts much more rapidly than a, resulting in a large anisotropy in compression. This behavior is consistent with the layered nature of the jarosite structure, in which the (001) [Fe(O,OH)6]/[SO4] sheets are held together via relatively weak K-O and hydrogen bonds. Fitting of the measured unit-cell parameters to the second-order Birch-Murnaghan equation of state yielded a bulk modulus of 55.7 ± 1.4 GPa and zero-pressure linear compressibilities of 3.2 × 10-3 GPa-1 for the a axis and 13.6 × 10-3 GPa-1 for the c axis. These parameters represent the first experimental determination of the elastic properties of jarosite.
We have conducted synchrotron x-ray diffraction studies on high purity zirconium metal at pressures $(P)$ up to $17\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$ and temperatures $(T)$ up to $973\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. Unit cell volumes $(V)$ were derived from the refinements of x-ray diffraction data for the $\ensuremath{\alpha}$, $\ensuremath{\beta}$, and $\ensuremath{\omega}$ phases of zirconium and fitted to a Birch-Murnaghan equation of state with the pressure derivative of the bulk modulus, $K_{0}{}^{\ensuremath{'}}$, fixed at 4.0. The derived thermoelastic parameters for $\ensuremath{\alpha}$ zirconium are isothermal bulk modulus ${K}_{0}=92(3)\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$, temperature derivative of bulk modulus ${(\ensuremath{\partial}K∕\ensuremath{\partial}T)}_{P}=\ensuremath{-}2.3(8)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}∕\mathrm{K}$, volumetric thermal expansivity ${\ensuremath{\alpha}}_{T}=a+bT$ with $a=1.5(\ifmmode\pm\else\textpm\fi{}0.8)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\phantom{\rule{0.3em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$ and $b=1.7(\ifmmode\pm\else\textpm\fi{}1.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}\phantom{\rule{0.3em}{0ex}}{\mathrm{K}}^{\ensuremath{-}2}$, and the pressure derivative of thermal expansion ${(\ensuremath{\partial}\ensuremath{\alpha}∕\ensuremath{\partial}P)}_{T}=\ensuremath{-}2.7(9)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}\phantom{\rule{0.3em}{0ex}}{\mathrm{GPa}}^{\ensuremath{-}1}\phantom{\rule{0.2em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$. For the $\ensuremath{\beta}$ phase we obtained an isothermal bulk modulus of ${K}_{T}=66(3)\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$ at $973\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and a unit-cell volume of $V(973\phantom{\rule{0.3em}{0ex}}\mathrm{K})=47.7(3)\phantom{\rule{0.3em}{0ex}}{\mathrm{\AA{}}}^{3}$ at ambient pressure. For the $\ensuremath{\omega}$ zirconium we obtained ${K}_{0}=90(5)\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$. Within the experimental errors, the ${K}_{0}$ values we determined for the $\ensuremath{\alpha}$ and $\ensuremath{\omega}$ phases and volumetric thermal expansion for the $\ensuremath{\alpha}$ phase are in agreement with previous experimental results, whereas all other thermoelastic parameters represent the first determinations for the three crystalline phases of zirconium metal.
Pressure-induced first-order phase transition often involves spatial disruption around the nucleus of a new phase, due to the inherent volume change. Atomic relaxations during this process produce lattice strain that in turn affects the nucleation kinetics and dynamics of transition, especially in nanoparticles. However, it is difficult to experimentally measure the lattice strain of materials, leading to many unsettled questions regarding size-dependent phenomena in nanomaterials at pressure. Here we present a method to determine the lattice strain of nanoparticles during first-order phase transitions using the pressure-volume data. A case study of nano-${\mathrm{Ho}}_{2}{\mathrm{O}}_{3}$ with multiple pressure-induced phase transitions is systematically performed to reveal the critical role of lattice strain in the size-dependent phase selection and amorphization. A phenomenological model is also given to describe the metastability of intermediate phases and size-tunable phase evolution during the nucleation of new phases at pressure.
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