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Thermoelectric materials enable the conversion of a thermal gradient into electricity, making them candidates in applications such as waste heat recovery. Their efficiency is determined by key, often interdependent, electrical and thermal transport properties. Therefore, requiring complex optimisation of the chemical composition and synthesis process. In this thesis, I perform first-principles modelling of the thermoelectric properties of half-Heusler alloys focused on analysis of XNiSn (X = Ti, Zr, Hf) and Nb₁₋ₓCoSbySn₁₋y based compositions. Thermoelectric properties of complex defective supercells were performed using plane-wave DFT as implemented in CASTEP and by solving the phonon Boltzmann Transport equation and the modified Debye-Callaway model to estimate Kl . We successfully use the non-diagonal supercell method, phonon unfolding, and neutron weighting techniques to analyse vibrational spectra in defective half-Heuslers and compare against inelastic neutron scattering experiments performed with our collaborators. We determine that Ni interstitial vacancy clustering results in agreement with experiments. We find a reduction of the Kl in defective TiNi₁.₁₂₅Sn and establish importance of grain boundaries. We model the effect of interstitials on the electronic structure in n-type XNiSn (X = Ti, Zr, Hf) compositions. Interstitial Cu in TiNiSn has been experimentally observed to reduce Kl without impeding electron mobility [1]. A promising thermoelectric with a ZT value of 0.8 at 773K. The electronic structure is investigated using DFT and DFT+U, charged calculations, and meta-GGA treatment of the exchange and correlation, considering possible localisation effects. We determine the effect of X-site vacancies in defective n-type Nb₁₋ₓCoSbySn₁₋y compositions, tuned to lower the average electron count, mimicking the unique, closed shell 18-electron half-Heusler system. Results predict semi-conducting behaviour in correspondence with experiments. The calculations successfully model thermoelectric properties of stoichiometric and defective half-Heusler compositions in good agreement with experiments. This predictive power can be used in future research to aid in the optimisation of thermoelectric materials.

Organic semiconductors are materials that are promising for novel optoelectronic applications, such as more efficient solar cells and LEDs. The optoelectronic response of these materials is dominated by bound electron-hole pairs called excitons, which are often strongly affected by hundreds of possible molecular vibrations. Although quantum theory contains all the ingredients to describe these complex phenomena, in practice it is only possible to solve the corresponding equations in small systems with few vibrations. As a result, it has been common to assume weak exciton-vibration interactions and to employ perturbative approaches. Similarly, exciton-photon interactions have almost universally been treated in the so-called weak coupling regime. However, in recent years it has become increasingly clear that these approximations can break down in organic semiconductors, placing an important roadblock towards the novel energy-harvesting technologies that could be based on these materials. In this thesis we address this issue by developing methods to treat exciton-photon and exciton-vibration interactions, without relying on any approximation regarding their magnitude. We propose a first principles description of hybrid exciton-light (polariton) states that result from strong exciton-photon interactions. We discuss a method to treat strong exciton-vibration interactions, showing that the spatial extent of exciton states controls their magnitude. Subsequently, we present a beyond Born-Oppenheimer method based on tensor networks to study real-time exciton dynamics. By using these methods, we show how selective excitation of vibrational modes can enhance charge transfer. Moreover, through rigorous comparison to experiments, we highlight that tensor network methods are highly accurate, and we generate a `movie' of the photophysical process of singlet fission, which occurs during early light-harvesting by organic molecules and has the potential to increase solar cell efficiencies. Finally, we construct a singlet fission model including the effects of excess energy, vibrations and the solvent of molecules concurrently, demonstrating that the fission mechanism can be qualitatively changed in a controlled manner, allowing for its acceleration by an order of magnitude.

Optical frequency combs have resulted in significant advances in optical frequency metrology and found wide application to precise physical measurements and molecular fingerprinting. A direct analogue of frequency combs in the phononic or acoustic domain has not been reported to date. This thesis describes a series of results to provide the first clear evidence for the generation of phononic frequency combs in the domain of micromechanical resonators. These results are supported by a theoretical framework which was originally developed to predict the existence of such features of combs in physical systems described by Fermi-Pasta-Ulam dynamics. The phononic frequency combs is mediated by nonlinear coupling between a primary driven mode and one or more parametrically excited internal modes. We provide experimental evidence for the formation of such phononic frequency combs in systems comprising of 2 or more coupled modes, with results qualitatively consistent with previous numerical studies based on Fermi-Pasta-Ulam dynamics. Additionally, externally pumped comb processes are also reported. Through systematic experiments at different drive frequencies and amplitudes, we portray the well-connected processes of phononic frequency comb formation and define attributes to control their concomitant features. Further, the interplay between these new nonlinear resonances and the well-established Duffing phenomenon is also discussed. While the experimental verification of the existence of phononic frequency combs is of scientific interest, several potential engineering applications exist including the unique capability to track resonant frequency of a micromechanical resonator without the requirement for an external feedback loop to sustain oscillations at the resonant frequency. The initial experimental results also demonstrate that good short-term frequency stability may be obtained for such micromechanical resonators operated under ambient conditions.

This thesis presents work done on the calculation of the effects of anharmonic nuclear motion on the properties of solid materials from first principles. Such anharmonic effects can be significant in many cases. A vibrational self-consistent field (VSCF) method is used as the basis for these calculations, which is then improved and applied to a variety of solid state systems. Firstly, work done to improve the efficiency of the VSCF method is presented. The standard VSCF method involves using density functional theory (DFT) to map the Born-Oppenheimer (BO) energy surface that the nuclei move in, a computationally expensive process. It is shown that the accurate forces available in plane-wave basis DFT can be used to help map the BO surface more accurately and reduce the computational cost. This improved VSCF+f method is tested on molecular and solid hydrogen, as well as lithium and zirconium, and is found to give a speed-up of up to 40%. The VSCF method is then applied to two different systems of physical interest. It is first applied to the case of the neutral vacancy in diamond, in order to resolve a known discrepancy between harmonic ab initio calculations and experiment -- the former predict a static Jahn-Teller distortion, whilst the latter leads to a dynamic Jahn-Teller effect. By including anharmonic corrections to the energy and nuclear wavefunction, we show that the inclusion of these effects results in agreement between first-principles calculations and experiment for the first time. Lastly, the VSCF method is applied to barium titanate, a prototypical ferroelectric material which undergoes a series of phase transitions from around 400 K downwards. The nature of these phase transitions is still unclear, and understanding them is an active area of research. We describe the physics of the phase transitions of barium titanate, including both anharmonicity and the effect of polarisation caused by long wavelength vibrations, to help understand the important physics from first principles.

In this thesis, I report on the investigation of the low frequency vibrational modes in a number of different systems using ultrafast spectroscopic techniques. These consist of biological systems, including the enzyme, morphinone reductase (MR) and the related biomolecules, riboflavin (Rb) and flavin mononucleotide (FMN), as well as non-biological systems, including the semiconductor gallium nitride (GaN) and gold nanoparticles (Au NPs). The term low frequency refers to terahertz (THz) frequencies, where vibrational modes exist at the molecular level, with molecular rotations, lattice vibrations and inter- and intra-molecular vibrations occurring in the THz spectral range. These vibrational modes occur on sub-picosecond timescales and therefore ultrafast techniques utilising femtosecond laser pulses provide a means of studying these modes, and are employed throughout this thesis. The two ultrafast techniques of transient absorption (TA) spectroscopy and terahertz time-domain spectroscopy (THz-TDS) were used. Firstly, a high-repetition rate transient absorption (HRRTA) spectrometer was commissioned to perform pump-probe measurements with an ultraviolet pump and broadband visible probe. The performance of the HRRTA spectrometer was benchmarked using Au NPs and used to investigate the existence of a promoting vibration in MR contributing to the catalysis process, predicted to occur at THz frequencies. Weak oscillations were detected in the charge-transfer absorption band of MR bound to the non-reactive cofactor 1,4,5,6-tetra-hydro-nicotinamide adenine dinucleotide (NADH4), with a frequency of approximately 1.5 THz and provide evidence of the first direct observation of a promoting vibration in an enzyme. To complement the TA measurements, THz-TDS was also used to obtain direct measurements of the absorption at THz frequencies. Due to the challenge of studying water-based biological samples, an initial investigation was performed on a wurtzite GaN wafer, which exhibited optical phonon modes in the THz frequency range that were found to determine the dielectric response of the semi-insulating semiconductor wafer. Use of a non-polar m-plane wafer allowed the anisotropic nature to be observed and values of 9.22 ± 0.02 and 10.32 ± 0.03 for the static dielectric constants were obtained for the THz electric field polarised both perpendicular and parallel to the c-axis of the wurtzite GaN wafer, respectively. Finally, biological studies using THz-TDS were performed with measurements on Rb pellets and films revealing vibrational modes in the THz region. The sharp absorption features were not observed in FMN, despite a small difference in molecular content from Rb, and dehydration was required to reveal small amplitude absorption features. Final measurements on MR and MR-NADH4 films were carried out and evidence of absorption features in the THz frequency range were observed, however further work is required to determine the precise origin of these features.

Reliable, robust, efficient, and scalable light detectors operated at milli-Kelvin temperature that can resolve individual photons in a scintillation event are required by the cryogenic phonon-scintillation detectors (CPSD) for next generation rare-event search experiments. This thesis demonstrates a cryogenic detector with a scintillating crystal as the absorber, equipped with a Neutron Transmutation Doped Germanium (NTD-Ge) phonon sensor and a Hamamatsu R8520-06 photomultiplier tube (PMT) with platinum underlay as the light detector. The PMT is powered by a Cockcroft-Walton generator. In this experiment, two CPSD modules are successfully tested, one with CaWO4 and the other with CaMoO4 as the scintillating absorber. The detector modules were cooled down to ~ 18 milli- Kelvin inside a dilution refrigerator. The CPSD modules are demonstrated to be able to measure signals from the phonon channel and light channel simultaneously, which is critical for particle identification. The full-width-at-half-maximum (FWHM) energy resolutions at 122.1 keV for the phonon channel are 2.17 keV (1.8%) for CaWO4 and 0.97 keV (0.79%) for CaMoO₄. The FWHM resolutions at 122.1 keV γ excitation for the scintillation/photon channel are 19.9% for CaWO₄ and 29.7% for CaMoO₄. At milli-Kelvin temperatures, the dark count rate of the PMT is determined to be less than 5 Hz while the gain of the PMT is found to be 3.3 × 10E⁶. These characteristics of the CPSD in this work compare favourably to conventional CPSDs with cryogenic calorimeter-based light detectors currently deployed in cryogenic rare-event search experiments, especially in the energy region of interest for dark matter direct detection. The PMT is demonstrated to have low dark count rate and high gain at milli-Kelvin temperatures, thus it remains an effective single photon detector. From the radioactivity of a similar model of PMT as input to a Geant4 simulation, the radioactivity introduced by the PMT contributes only minorly (< 10%) to the overall radioactive background of a hypothetical CPSD module for WIMP searches. The CPSD module with PMT readout benefits a reliable, well-tested and commercially available apparatus, while the PMT as a photon detector at milli-Kelvin temperatures offers a much better time resolution than cryogenic light detectors, allowing to resolve individual photons. The technology in this study can potentially revolutionise the science reach of rare event search experiments using CPSD (e.g. the CRESST experiment), by offering an alternative light detector solution which is much more scalable and more consistent in performance than conventional CPSDs with cryogenic calorimeter-based light detectors, addressing two major issues that the present techniques face.

This dissertation reports the results of optical studies of epitaxial (e), polycrystalline (p) and amorphous (a) Ge2Sb2Te5 (GST) thin films. The dynamic properties of GST films in all three (e/p/a) phases were investigated by a time-resolved optical pump-probe technique in which a femtosecond pump pulse of 55 fs duration was used to excite the sample. The intensity and polarization of the reflected probe beam respectively provide information about the transient reflectance (R) and anisotropic reflectance (AR) induced in the sample, that in turn provide the information about the crystal structure, phonon spectrum, and ultimately phase transitions within the sample. The study of an epitaxial sample provides an opportunity to explore the character of the modes within the phonon spectrum. The epitaxial GST film was grown upon a homoepitaxial layer of GaSb grown upon a GaSb wafer. We observed a 6.7 THz coherent optical phonon (COP) in GaSb(001). The dependence of the signal strength upon the pump and probe polarization was explained in terms of a model that considered both Transient stimulated Raman Scattering (TSRS) and the action of a Surface Space-Charge (SSC) field. The presence of the 6.7 THz transverse COP in the AR channel and its four fold dependence on pump and probe polarization suggests a three-dimensional T2 character. The COP amplitude was maximum when the probe was polarized parallel to the cube edge (GaSb[100]) and the pump polarization was set parallel to a face diagonal (GaSb[110]). The results were fully understood using a microscopic model of selective bond breaking. The AR response of e-GST/GaSb(001) reveals the presence of a 3D 3.4 THz transverse optical phonon. The mode amplitude was independent of pump polarization indicating that the mode is excited by a SSC field. This SSC field could exist within the GST, if the distorted rock-salt structure of GST lacks inversion symmetry, or GaSb, which has the non-centrosymmetric zincblende structure, leading to impulsive excitation of phonons at the GST/GaSb interface. The mode in GST was inferred to be T2-like. The observation of a T2-like phonon mode confirms that GST is cubic in structure and challenges previous studies where 1D or 2D character was assigned to the 3.4 THz mode. While pump-probe measurements displayed the presence of a 3D 3.4 THz mode in the AR response of e-GST/GaSb(001), a 4.5 THz mode was observed in both R and AR channels for p-GST(37 nm)/Si(001) and a-GST(57 nm)/Si(001). The mode character was identified to be either of A or E type by comparing the frequency with frequencies reported in the literature. Additional Raman microscope measurements confirmed the presence of the modes observed in the pump-probe measurements and also revealed additional frequencies. The differences in the frequencies observed from the different samples are quite small suggesting the presence of similar bonds that are modified to some extent by the different structural environment found within each sample. After exposure to high pump fluence the original modes disappeared and were replaced by new modes with frequencies at 4.2 THz and 3.1 THz in e-GaSb, 4.2 THz in e-GST, 3.5 THz in p-GST and 3.6 THz in a-GST. The difference in the final frequencies observed for p and a-GST sample may result from the difference in stack structure affecting the time-dependent temperature profile in each sample. The dependence of the temperature profile on the sample stack was understood from an experimental study of the phase transition between the amorphous and crystalline states induced by exposure to a series of amplified laser pulses. The dependence of the crystalline area and its reflectivity upon the number of pulses and fluence was described using a simple algebraic model. The results justify the assumption of one-dimensional heat flow. The growth velocity of the crystalline region was calculated to be 7-9 m/s. Apparatus and methods were developed to extend the time-resolved optical studies described previously. Firstly, an apparatus was constructed for the measurement of the wavelength dependent sample reflectance with a white-light pulse. A reference arm was employed to allow normalization and hence removal of the intensity noise arising in the laser regenerative amplifier system. Secondly an electrical measurement apparatus was constructed to allow combined electro-optical measurements in future. Switching of GST vertical memory cells was successfully demonstrated. The cells were fabricated on a borosilicate substrate with TiW top and bottom electrodes. A DC voltage of 4.5 to 6 V was required to induce switching, while in pulsed measurements, the device demonstrated switching in response to a pulse with minimum duration of 100 ns.

A detailed understanding of fundamental material properties can be obtained through the study of atomic vibrations, performed experimentally with neutron scattering techniques and coupled with the two powerful new computational methodologies I have developed. The first approach involves phonon-based simulations of the pair distribution function - a histogram of localised atomic positions generated experimentally from total scattering data. This is used to reveal ordering behaviour, to validate interatomic models and localised structure, and to give insights into how far dynamic behaviour can be studied using total scattering techniques. Most importantly, the long-standing controversy over dynamic disorder in β-cristobalite is resolved using this technique. Inelastic neutron spectroscopy (INS) allows \emph{direct} study of vibrational modes through their interaction with the neutron beam, and is the experimental basis for the second strand of the new methodology. I have developed new simulation and refinement tools based on the next generation of spectrometers currently being commissioned at the ISIS pulsed neutron source. This allows a detailed powder spectroscopy study of cristobalite and vitreous silica demonstrating that the Bose peak and so-called 'fast sound' features can be derived from standard lattice dynamics in both the crystal and the amorphous counterpart, and allowing discussion of their origins. Given the controversy in the literature, this is a key result. The new methodology also encompasses refinement of interatomic models against powder INS data, with aluminium providing a successful test-case. A more complex example is seen in calcite, with experimental data collected during the commissioning of the new MERLIN spectrometer. Simulated one-phonon coherent INS spectra for the single crystal and powder (the latter including approximations to multi-phonon and multiple scatter) are fully convolved with experimental resolution functions. These are used in the analysis of the experimental data, yielding previously unpublished dispersion curves and soft mode information, as well as allowing the effectiveness of powder refinement of more complex materials to be assessed. Finally, I present further applications with technologically important materials - relaxor ferroelectrics and high temperature pnictide superconductors. The conclusions draw together the different strands of the work, discussing the importance of these new advances together with future developments and scientific applications.

This thesis is concerned with studying the fascinating quantum properties of real-world nanostructures embedded in a noisy condensed matter environment. The interaction with light is used for controlling and manipulating the quantum state of the systems considered here. In some instances, laser pulses also provide a way of actively probing and controlling environmental interactions. The first two research chapters assess two different ways of performing all-optical spin qubit gates in self-assembled quantum dots. The principal conclusion is that an `adiabatic' control technique holds the promise of achieving a high fidelity when all primary sources of decoherence are taken into account. In the next chapter, it is shown that an optically driven quantum dot exciton interacting with the phonons of the surrounding lattice acts as a heat pump. Further, a model is developed which predicts the temperature-dependent damping of Rabi oscillations caused by bulk phonons, finding an excellent agreement with experimental data. A different system is studied in the following chapter: two electron spin qubits with no direct interaction, yet both exchange-coupled to an optically active mediator spin. The results of this study show that these general assumptions are sufficient for generating controlled electron spin entanglement over a wide range of parameters, even in the presence of noise. Finally, the Radical Pair model of the avian compass is investigated in the light of recent experimental results, leading to the surprising prediction that the electron spin coherence time in this molecular system seems to approach the millisecond timescale.

This thesis deals with the development and application of Monte Carlo simulations to study electron transport in bulk GaN in the wurtzite crystal structure and the properties of field effect transistors made from the material. There is a particular emphasis on transport in the high electric field regime and transistors operating at high voltages. The simulation model includes five sets of non-parabolic conduction band valleys which can be occupied by electrons during high field transport. The effects on electron transport of impurities and the relevant phonon scattering mechanisms have been considered. Results for electron transport at both low and high electric field are presented and compared with the properties of GaN in the zincblende structure, of other group-III nitride semiconductors, and of GaAs. The dependence of the transport properties on the material parameters is discussed and also with regard to the temperature, donor concentration and electric field magnitude and direction. The transport properties of electrons in wurtzite GaN n+-i(n)-n+ diodes are also explored, including the effect of the upper valleys and the temperature on hot electron transport. Simulations have also been carried out to model the steady-state and transient properties of GaN MESFETs that have recently been the subject of experimental study. It has been suggested that traps have a substantial effect on the performance of GaN field effect transistors and we have developed a model of a device with traps to investigate this suggestion. The model includes the simulation of the capture and release of electrons by traps whose charge has a direct effect on the current flowing through the transistor terminals. The influence of temperature and light on the occupancy of the traps and the /- V characteristics are considered. It is concluded that traps are likely to play a substantial role in the behaviour of GaN field effect transistors. Further simulations were performed to model electron transport in AlGaN/GaN hetero-junction FETs. So called HFET structures with a 78 nm Alo.2Gao.8N pseudomorphically strained layer have been simulated, with the inclusion of spontaneous and piezoelectric polarization effects in the strained layer. The polarization effects are shown to not only increase the current density, but also improve the electron transport by inducing a higher electron density close to the positive charge sheet that occurs in the channel.

The structural and electronic properties of several candidate atomic scale wires are analysed. Three candidates are studied: the trans-polyacetylene molecule, the silicon line on the (001) face of cubic silicon carbide (the (nx2) series of reconstructions) and the indium chain on the (111) face of silicon carbide (the (4x1) reconstruction). We use the polyacetylene molecule as a test-bed for the techniques that we use to calculate transport properties in an empirically based tight-binding Hamiltonian (the SSH Hamiltonian). We calculate the transport properties of wires that show evidence of a strong coupling of the electronic degrees of freedom to the phonon degrees of freedom (Peierls distorted wires). The structure of the (nx2) series of silicon lines (composed of the (3x2) reconstruction which forms the line and the c(4x2) reconstruction which forms the surface the line resides on) axe modelled in a supercell geometry using ab initio plane-wave calculations in the Local-Density-Approximation and an ab initio Density Functional Theory based tight-binding technique. We found that the thermodynamically favoured model for the (3x2) reconstruction was the Two-Adlayer-Asymmetric-Dimer Model (with IML of Si adatoms) and the favoured model for the c(4x2) reconstruction is the Additional-Dimer- Row-Model (with 0.5ML of Si adatoms). In the tight-binding approximation the line was found to undergo a Peierls-like transition and holes are observed to form polaron-like defects. The transport properties of the line are also calculated. Finally we find which of the two models of the Si(111)-(4x1)-In reconstruction is thermodynamically favoured in a supercell geometry. We use ab initio plane wave techniques in the Local-Density-Approximation, and calculate and compare the electronic structure of the two models with respect to the characteristic energies for electron dispersion along and across the chain structures. We also consider the effects of electronic structure on the in-plane transport properties of the indium lines.

The polaron problem is studied, on an infinite lattice, using the continuous-time path-integral quantum Monte Carlo scheme The method is based on the Feynman technique to analytically integrate out the phonon degrees of freedom. The transformed problem is that of a single electron with retarded self-interaction in imaginary time. The Metropolis algorithm is used to sample an ensemble of electron trajectories with twisted (rather than periodic) boundary conditions in imaginary time, which allows dynamic properties of the system to by measured directly. The method is numerically "exact", in the sense that there are no systematic errors due to finite system size, trotter decomposition or finite temperature The implementation of the algorithm in continuous imaginary time dramatically increases computational efficiency compared with the traditional discrete imaginary time algorithms.

PVD hard ceramic coatings grown via the combined cathodic arc/unbalance magnetron deposition process were studied using Raman microscopy. Characteristic spectra from binary, multicomponent, multilayered and superlattice coatings were acquired to gain knowledge of the solid-state physics associated with Raman scattering from polycrystalline PVD coatings and to compile a comprehensive spectral database. Defect-induced first order scattering mechanisms were observed which gave rise to two pronounced groups of bands related to the acoustical (150-300cm[-1]) and optical (400-750cm[-1]) parts of the phonon spectrum. Evidence was gathered to support the theory that the optic modes were mainly due to the vibrations of the lighter elements and the acoustic modes due to the vibrations of the heavier elements within the lattice. A study into the deformation and disordering on the Raman spectral bands of PVD coatings was performed. TiAIN and TiZrN coatings were intentionally damaged via scratching methods. These scratches were then analysed by Raman mapping, both across and along, and a detailed spectral interpretation performed. Band broadening occurred which was related to "phonon relaxation mechanisms" as a direct result of the breaking up of coating grains resulting in a larger proportion of grain boundaries per-unit-volume. A direct correlation of the amount of damage with band width was observed. Band shifts were also found to occur which were due to the stresses caused by the scratching process. These shifts were found to be the largest at the edges of scratches. The Raman mapping of "droplets", a defect inherent to PVD deposition processes, found that higher compressive stresses and large amounts of disorder occurred for coating growth onto droplets. Strategies designed to evaluate the ability of Raman microscopy to monitor the extent of real wear on cutting tools were evaluated. The removal of a coating layer and subsequent detection of a base layer proved successful. This was then expanded to real wear situations in which tools were monitored after 3,6,12,64,120 and 130 minutes-in-cut. A PCA chemometrics model able to distinguish between component layers and oxides was developed. Raman microscopy was found to provide structural and compositional information on oxide scales formed on the surfaces of heat-treated coatings. Wear debris, generated as a consequence of sliding wear tests on various coatings, was also found to be primarily oxide products. The comparison of the oxide types within the debris to those formed on the surface of the same coating statically oxidised, facilitated a contact temperature during sliding to be estimated. Raman microscopy, owing to the piezo-spectroscopic effect, is sensitive to stress levels. The application of Raman microscopy for the determination of residual compressive stresses within PVD coatings was evaluated. TiAlN/VN superlattice coatings with engineered stresses ranging -3 to -11.3 GPa were deposited onto SS and HSS substrates. Subsequent Raman measurements found a correlation coefficient of 0.996 between Raman band position and stress (determined via XRD methods). In addition, there was also a similar correlation coefficient observed between hardness and Raman shift (cm-1). The application of mechanical stresses on a TiAlCrN coating via a stress rig was investigated and tensile and compressive shifts were observed.