Phase transitions, strain, elasticity and anelastic phenomena in minerals and technological materials

 

My long standing interests relate to the role of strain and elastic relaxations in minerals and technological materials. These play a fundamental role in determining the nature, mechanisms and thermodynamic character of phase transitions and in controlling the mixing behaviour of oxide and silicate solid solutions. Phase transitions are by definition collective phenomena. Some local instability in the atomic or electronic configuration of a structure develops correlations over a significant length scale, macroscopic symmetry is broken and a new long-range order is established. The most overt and predictable evidence for this is typically the development of both symmetry-breaking and non-symmetry breaking spontaneous strains. It is well known that coupling of a driving order parameter with strain suppresses fluctuations, promotes mean field behaviour and leads to strong coupling between multiple order parameters in systems with more than one instability. From the perspective of potential device applications it is also well known that thin film properties can be engineered by imposing a strain from the substrate. In addition, the unique properties of nanomaterials can arise from suppression of strain relaxation with reducing grain size.

 

1. Strain measurements.

The High Resolution Powder Neutron Diffractometer at ISIS provides the highest resolution data in the world for routine lattice parameter determinations as a function of temperature. In combination with group theoretical treatment of strain/order parameter coupling, symmetry-adapted spontaneous strains extracted from these reveal the pattern of order parameter variations in materials with multiple phase transitions. For example, the Pnm21 structure of manganite perovskites which display Colossal Magnetoresistance (CMR) contains separate order parameters with the symmetry of irreducible representations M3+, R4+, G3+, Eps2 of space group Pm-3m. These correspond physically to two different octahedral tilt systems, two different Jahn-Teller ordering schemes and charge order/Zener polaron ordering, respectively. The incommensurate phase of Pr0.48Ca0.52MnO3, is stabilized predominantly by linear-quadratic coupling of Jahn-Teller order with the order parameter, coupling with the tilt order parameters is critical to stability, and the overall behaviour is consistent with a Landau tricritical transition. (Acta Cryst. 2009, B 65, 134-146, 147-159; Acta Cryst. 2010, B66, 40-50; Phys. Rev. B 2009, 80, 214101; Phys. Rev. B 2010, 82, 094101).

 

2. Elasticity measurements by Resonant Ultrasound Spectroscopy (RUS)

With funding from NERC (NE/B505738/1) and in collaboration with T.W.Darling (Univ. of Nevada, Reno) two RUS instruments for RUS have been built in Cambridge. The low temperature system uses an AS Scientific Orange Cryostat for measurements in the temperature range ~5-320 K (± ~0.1 K). In the high temperature system (295-1600 K), the sample is held between the tips of horizontal alumina rods protruding into a tube furnace. DRS Modulus II electronics are used for routine data collection. Software to drive the cryostat, furnace and RUS electronics has been produced in-house to allow fully automated data collection. Stanford electronics have subsequently been added to the high temperature instrument.

 

Cambridge low temperature RUS head, showing a sample cut in the shape of a rectangular parallelepiped with dimensions ~3x4x5 mm3. The sample is held lightly across a pair of corners or a pair of faces between two piezoelectric transducers, one of which is used to scan in frequency between ~0.1 and ~3 MHz and the second to detect acoustic resonances which are excited at particular frequencies. Resonance peaks with frequency f in the spectrum are predominantly due to shearing modes and are constrained by individual elastic constants or combinations of elastic constants whose absolute values scale with f2. A direct measure of acoustic dissipation in the sample is given by the inverse mechanical quality factor, Q-1, which depends on the peak width at half height, Df, according to Q-1 = Df/f. For a polycrystalline sample, shear and bulk moduli are obtained by fitting the frequencies of ~10-20 peaks. Single crystal elastic constants can also be obtained

 

One recent outcome is the characterisation of "superattenuation", i.e. extreme damping, due to the high mobility of ferroelastic twin walls in LaAlO3 under externally applied stress between the transition point, 817 K, and a freezing temperature of ~600 K. Softening of the elastic constants conforms to Landau theory, but Brillouin spectroscopy has also revealed a dynamic central peak attributed to phonon density fluctuations down to ~170 K below Tc. LaAlO3 is one of the most important single crystal substrates in current use for supporting thin films with many different ferroelectric, electrical and electronic properties. (Instruments: Am. Min. 2007, 92, p1665, J. Phys.: Cond. Matt. 2008, 20, 075229. Application to LaAlO3: J. Phys.: Cond. Matt. 2010, 22, 035403, 035404, 035405, 035406).

 

3. Elasticity and anelasticity in Earth Sciences (supported by NERC: NE/F017081/1).

The internal structure of the earth is known through comparisons of seismic velocities from geophysics with velocities of mineral assemblages at high P and T. Anelastic processes cause attenuation, depending explicitly on the mechanical quality factor Q. Much less is known about these, though they are important because they give independent evidence for the temperature profile through the earth. By the use of analogue materials such as BaCeO3, LaCoO3, analcite and CaCl2, the physics of geologically relevant acoustic loss mechanisms associated with phase transitions and with other relaxation processes is being determined, including the influence of twin walls in perovskites, motion of protons, magnetic ordering, and the high/spin low spin transition of Fe2+ in (Mg,Fe)O and (Mg,Fe)SiO3. RUS (~0.1-1 MHz) is being combined with dynamical mechanical analysis (~0.1-100 Hz) to develop "anelasticity maps" analogous to Ashby maps for plastic deformation mechanisms. (J. Phys.: Cond. Matt. 2010, 22, 295401; Phys. Rev. B 2010, 82, 014113).

 

4. Elasticity and anelasticity in Materials Physics.

Establishment of the RUS facility in Cambridge has led to a number of collaborative efforts with materials physics/chemistry groups in Cambridge (metallic glasses, multiferroics, relaxors, manganites, pnictides), Spain (multiferroics, relaxors) and Australia (piezoelectrics, ferroelectrics, multiferroics). Phase transitions which give rise to the physical properties of interest and the dynamic properties of transformation microstructures leave characteristic patterns of elastic softening or stiffening and acoustic dissipation. For example, shown below is a stack of RUS spectra though the Pnma to incommensurate transition in Pr0.48Ca0.52MnO3. Also shown is the variation of the shear modulus, G, and anelastic dissipation, Q-1, extracted from the spectra. The transition can be understood in terms of pseudoproper ferrelastic softening and stiffening due to coupling of a tetragonal shear strain with a Jahn-Teller order parameter which transforms according to the symmetry of the irrep of space group Pmm. This order parameter couples with the symmetry breaking order parameter, which is related to irrep Eps2. Acoustic dissipation below the transition point (high Q-1) is due to mobility of incommensurate antiphase boundaries under applied shear stress. (Phys. Rev. B, in press).

 

Stack of RUS spectra from Pr0.48Ca0.52MnO3 between 295 K (top spectrum) and 10 K (bottom spectrum). The incommensurate phase transition is clearly marked by a change in temperature dependence of resonance frequencies at 237 K and by changes in peak widths

Variations of shear modulus (G) and dissipation (expressed as Q-1) extracted from the RUS spectra. The minimum in G occurs just below the incommensurate transition point, Tc, but there is no anomaly associated with the antiferromagnetic ordering transition (TN). There is significant dissipation due to domain wall motion below Tc but this freezes out at ~75 K. The fit to the Debye peak at ~75 K gives an activation energy of ~0.07 eV and a relaxation time, to, of ~10-12 s, consistent with kinetic control by polarons.

 

 

Enquiries

I welcome opportunities to develop further collaborative ventures in aspects of strain and elasticity that arise in Earth Sciences, Solid State Chemistry, Solid State Physics, Materials Science, Engineering or Biomaterials. Anyone who would like to make elasticity measurements in my Resonant Ultrasound Spectroscopy lab should feel free to contact me at any time. I also welcome enquiries from potential students and post-docs.


Publications: 2006-Present

Last updated on 22-Oct-10 15:39