• Phonon dispersion curves and atomic mean square displacement for several fcc and bcc materials

      Pinnegar, C. Robert.; Department of Physics (Brock University, 1995-07-09)
      The atomic mean square displacement (MSD) and the phonon dispersion curves (PDC's) of a number of face-centred cubic (fcc) and body-centred cubic (bcc) materials have been calclllated from the quasiharmonic (QH) theory, the lowest order (A2 ) perturbation theory (PT) and a recently proposed Green's function (GF) method by Shukla and Hiibschle. The latter method includes certain anharmonic effects to all orders of anharmonicity. In order to determine the effect of the range of the interatomic interaction upon the anharmonic contributions to the MSD we have carried out our calculations for a Lennard-Jones (L-J) solid in the nearest-neighbour (NN) and next-nearest neighbour (NNN) approximations. These results can be presented in dimensionless units but if the NN and NNN results are to be compared with each other they must be converted to that of a real solid. When this is done for Xe, the QH MSD for the NN and NNN approximations are found to differ from each other by about 2%. For the A2 and GF results this difference amounts to 8% and 7% respectively. For the NN case we have also compared our PT results, which have been calculated exactly, with PT results calculated using a frequency-shift approximation. We conclude that this frequency-shift approximation is a poor approximation. We have calculated the MSD of five alkali metals, five bcc transition metals and seven fcc transition metals. The model potentials we have used include the Morse, modified Morse, and Rydberg potentials. In general the results obtained from the Green's function method are in the best agreement with experiment. However, this improvement is mostly qualitative and the values of MSD calculated from the Green's function method are not in much better agreement with the experimental data than those calculated from the QH theory. We have calculated the phonon dispersion curves (PDC's) of Na and Cu, using the 4 parameter modified Morse potential. In the case of Na, our results for the PDC's are in poor agreement with experiment. In the case of eu, the agreement between the tlleory and experiment is much better and in addition the results for the PDC's calclliated from the GF method are in better agreement with experiment that those obtained from the QH theory.
    • Phonon spectra and temperature variation of thermodynamic properties of fcc metals via Finnis-Sinclair type many body potentials: Sutton-Chen and improved Sutton-Chen models

      Januszko, Aistis; Department of Physics (Brock University, 2014-06-06)
      Volume(density)-independent pair-potentials cannot describe metallic cohesion adequately as the presence of the free electron gas renders the total energy strongly dependent on the electron density. The embedded atom method (EAM) addresses this issue by replacing part of the total energy with an explicitly density-dependent term called the embedding function. Finnis and Sinclair proposed a model where the embedding function is taken to be proportional to the square root of the electron density. Models of this type are known as Finnis-Sinclair many body potentials. In this work we study a particular parametrization of the Finnis-Sinclair type potential, called the "Sutton-Chen" model, and a later version, called the "Quantum Sutton-Chen" model, to study the phonon spectra and the temperature variation thermodynamic properties of fcc metals. Both models give poor results for thermal expansion, which can be traced to rapid softening of transverse phonon frequencies with increasing lattice parameter. We identify the power law decay of the electron density with distance assumed by the model as the main cause of this behaviour and show that an exponentially decaying form of charge density improves the results significantly. Results for Sutton-Chen and our improved version of Sutton-Chen models are compared for four fcc metals: Cu, Ag, Au and Pt. The calculated properties are the phonon spectra, thermal expansion coefficient, isobaric heat capacity, adiabatic and isothermal bulk moduli, atomic root-mean-square displacement and Gr\"{u}neisen parameter. For the sake of comparison we have also considered two other models where the distance-dependence of the charge density is an exponential multiplied by polynomials. None of these models exhibits the instability against thermal expansion (premature melting) as shown by the Sutton-Chen model. We also present results obtained via pure pair potential models, in order to identify advantages and disadvantages of methods used to obtain the parameters of these potentials.
    • Phonon spectra and thermal properties of some fcc metals using embedded-atom potentials /

      Bian, Qiuping.; Department of Physics (Brock University, 2005-06-15)
      By employing the embedded-atom potentials of Mei et ai.[l], we have calculated the dynamical matrices and phonon dispersion curves for six fee metals (Cu,Ag,Au,Ni,Pd and Pt). We have also investigated, within the quasiharmonic approximation, some other thermal properties of these metals which depend on the phonon density of states, such as the temperature dependence of lattice constant, coefficient of linear thermal expansion, isothermal and adiabatic bulk moduli, heat capacities at constant volume and constant pressure, Griineisen parameter and Debye temperature. The computed results are compared with the experimental findings wherever possible. The comparison shows a generally good agreement between the theoretical values and experimental data for all properties except the discrepancies of phonon frequencies and Debye temperature for Pd, Pt and Au. Further, we modify the parameters of this model for Pd and Pt and obtain the phonon dispersion curves which is in good agreement with experimental data.
    • Phonon spectra and thermodynamic properties of rare gas solids based on empirical and semi-empirical (ab initio) two-body potentials : a comparative study /

      Fekete, Gary.; Department of Physics (Brock University, 2007-06-01)
      We study the phonon dispersion, cohesive and thermal properties of raxe gas solids Ne, Ar, Kr, and Xe, using a variety of potentials obtained from different approaches; such as, fitting to crystal properties, purely ab initio calculations for molecules and dimers or ab initio calculations for solid crystalline phase, a combination of ab initio calculations and fitting to either gas phase data or sohd state properties. We explore whether potentials derived with a certain approaxih have any obvious benefit over the others in reproducing the solid state properties. In particular, we study phonon dispersion, isothermal ajid adiabatic bulk moduli, thermal expansion, and elastic (shear) constants as a function of temperatiue. Anharmonic effects on thermal expansion, specific heat, and bulk moduli have been studied using A^ perturbation theory in the high temperature limit using the neaxest-neighbor central force (nncf) model as developed by Shukla and MacDonald [4]. In our study, we find that potentials based on fitting to the crystal properties have some advantage, particularly for Kr and Xe, in terms of reproducing the thermodynamic properties over an extended range of temperatiures, but agreement with the phonon frequencies with the measured values is not guaranteed. For the lighter element Ne, the LJ potential which is based on fitting to the gas phase data produces best results for the thermodynamic properties; however, the Eggenberger potential for Ne, where the potential is based on combining ab initio quantum chemical calculations and molecular dynamics simulations, produces results that have better agreement with the measured dispersion, and elastic (shear) values. For At, the Morse-type potential, which is based on M0ller-Plesset perturbation theory to fourth order (MP4) ab initio calculations, yields the best results for the thermodynamic properties, elastic (shear) constants, and the phonon dispersion curves.
    • Planar Topological Defects in Unconventional Superconductors

      Przedborski, Michelle; Department of Physics (Brock University, 2013-09-12)
      In this work, we consider the properties of planar topological defects in unconventional superconductors. Specifically, we calculate microscopically the interaction energy of domain walls separating degenerate ground states in a chiral p-wave fermionic superfluid. The interaction is mediated by the quasiparticles experiencing Andreev scattering at the domain walls. As a by-product, we derive a useful general expression for the free energy of an arbitrary nonuniform texture of the order parameter in terms of the quasiparticle scattering matrix. The thesis is structured as follows. We begin with a historical review of the theories of superconductivity (Sec. 1.1), which led the way to the celebrated Bardeen-Cooper- Schrieffer (BCS) theory (Sec. 1.3). Then we proceed to the treatment of superconductors with so-called "unconventional pairing" in Sec. 1.4, and in Sec. 1.5 we introduce the specific case of chiral p-wave superconductivity. After introducing in Sec. 2 the domain wall (DW) model that will be considered throughout the work, we derive the Bogoliubov-de Gennes (BdG) equations in Sec. 3.1, which determine the quasiparticle excitation spectrum for a nonuniform superconductor. In this work, we use the semiclassical (Andreev) approximation, and solve the Andreev equations (which are a particular case of the BdG equations) in Sec. 4 to determine the quasiparticle spectrum for both the single- and two-DW textures. The Andreev equations are derived in Sec. 3.2, and the formal properties of the Andreev scattering coefficients are discussed in the following subsection. In Sec. 5, we use the transfer matrix method to relate the interaction energy of the DWs to the scattering matrix of the Bogoliubov quasiparticles. This facilitates the derivation of an analytical expression for the interaction energy between the two DWs in Sec. 5.3. Finally, to illustrate the general applicability our method, we apply it in Sec. 6 to the interaction between phase solitons in a two-band s-wave superconductor.
    • Preparation of Single Crystal Molybdenum Bronzes and Polycrystalline Rubidium Molybdenum Oxide

      Hicks, Darren; Department of Physics
      Lithium purple bronze (LiPB) Li0.9Mo6O17 was studied extensively in the 1980’s and has recently regained interest in the research community. The mechanism for the metal-insulator (M/I) transition at ∼25 K and superconductivity at ∼2 K is still unknown. The temperature gradient flux technique has been used to grow single crystal LiPB. A large superconducting LiPB single crystal was grown (di- mensions: 4.7×3.0×1.2 mm3) and characterized and will be referred to throughout this work as ‘I33sc2’. For the non-superconducting single crystal oriented along the b-crystallographic axis, we found the maximum value of the energy gap to be 2 meV±0.1 meV at 9.16 K, which is different from the accepted literature value of ∼1 meV at 5-6 K [1,2]. Furthermore, heavier alkali metals (Na, K and Rb) were used in the temperature gradient flux technique. Small lilac brown single crystals were found in all three growths. In particular, the rubidium growth yielded polyhedral (denoted as ‘POLY’, having approximate dimensions: 0.5 × 0.3 × 0.3 mm3) and small bar shaped (denoted as ‘SBAR’, having approximate dimensions: 1×0.1×0.1 mm3) lilac brown single crystals which exhibited anomalous properties in the re- sistivity and specific heat. The anomalous properties include a M/I transition at 250 K and a small phase transition in the resistivity at 94 K. These lilac brown single crystals were studied with powder X-ray diffraction (XRD) and match very closely with molybdenum dioxide MoO2, however with slightly larger ‘a’ and ‘b’ lattice parameters. These lilac brown crystals are being further characterized with single crystal XRD. Polycrystalline rubidium molybdenum dioxide Rb0.03MoO2−δ was then grown to further understand what rubidium doping (if any) these lilac brown single crystals have. The resistivity of polycrystalline Rb0.03MoO2−δ has a M/I transition at 250 K, similar to the lilac brown single crystals, but lacks a phase transition at 94 K. Unlike the lilac brown single crystals, the slope of the M/I transition at 250 K is strongly affected by thermal cycling. Furthermore, poly- crystalline Rb0.03MoO2−δ shows signs of a small superconducting volume fraction. This material is under further investigation.
    • Preparation of SrMgx-Ru1-xO3 thin films by pulsed laser deposition /

      Yazdanian, Mohammad Mehdi.; Department of Physics (Brock University, 2004-07-14)
      SrMg^Rui-iOa thin films were made by using pulsed laser deposition on SrTiOa (100) substrates in either O2 or Ar atmosphere. The thin films were characterized by x-ray diffraction, energy dispersive x-ray microanalysis, dc resistivity measurement, and dc magnetization measurement. The effect of Mg doping was observed. As soon as the amount of Mg increased in SrMg-cRui-iOa thin films, the magnetization decreased, and the resistivity increased. It had little effect on the Curie temperature (transition temperature). The magnetization states of SrMgiRui-iOa thin films, for x < 0.15, are similar to SrRuOs films. X-ray diffraction results for SrMga-Rui-iOa thin films made in oxygen showed that the films are epitaxial. The thin films could not be well made in Ar atmosphere during laser ablation as there was no clear peak of SrMg^Rui-iOa in x-ray diffraction results. Substrate temperatures had an effect on the resistivity of the films. The residual resistivity ratios were increased by increasing substrate temperature. It was observed that the thickness of thin films are another factor for film quality: Thin films were epitaxial, but thicker films were not epitaxial.
    • Pressure dependence of spin fluctuations in metallic glasses Zrâ â Niâ â ,Zrâ â (Nix/Feâ â â -x)â â and /Zrx/feâ â â -x

      Hamed, Fathalla A.; Department of Physics (Brock University, 1991-07-09)
      The superconducting transition temperature Tc of metallic glasses ZrxFelOO-x (x=80, 75), Zr75(NixFelOO-x)25 (x=75, 50, 25), and CU2SZr75 were measured under quasi-hydrostatic pressure up to 8 OPa (80kbar). The volume (pressure) dependence of the electron-phonon coupling parameters Aep for CU25Zr75 was calculated using the McMillan equatio11. Using this volume dependence of Aep and the modified McMillan equation which incorporates spin-fluctuations, the volume dependence of the spin fluctuation parameter, Asf, was determined in Zr75Ni25, ZrxFelOO-x , a11d Zr75(NixFelOO-x)25. It was found that with increasing pressure, spinfluctuations are suppressed at a faster rate in ZrxFe lOO-x and Zr75(NixFelOO-x)25, as Fe concentration is increased. The rate of suppression of spin-fluctuations with pressure was also found to be higher in Fe-Zr glasses than in Ni-Zr glasses of similar composition.
    • Pressure dependence of superconducting properties of MgB2 /

      Ploczek, Henrich.; Department of Physics (Brock University, 2003-07-14)
      We prepared samples of MgB2 and ran sets of experiments aimed for investigation of superconducting properties under pressure. We found the value of pressure derivative of the transition temperature -1.2 ± 0.05 K/GPa. Then, using McMillan formula, we found that the main contribution to the change of the transition temperature under the pressure is due to the change in phonon frequencies. Griineisen parameter was calculated to be 7g = 2.4. Our results suggest that MgB2 is a conventional superconductor.
    • Pressure dependence of superconductivity in amorphous Ni x Zr 100-x alloys

      Mahini Abyaneh, Fariba.; Department of Physics (Brock University, 1988-10-02)
      Pressure variations of the superconducting transition temperature Ic of a series of amorphous NixZr 1 OO-x alloys have been studied under quasmydrostatic pressures upto 8 G Pa. For amorphous samples having Ni-concentration less than 40%, i)Tc/dP is positive in sign and it decreases non linearly with increase in I. whereasdTcldP is negative in sign for Ni concentration of 45%. Comparison with the Hall coefficient (I) and the thermoelectric power (2) results for the same amorphous alloys leads to the conclusion that s-d hybridization nature of the d-band (Nil plays a central role in the sign reversal behaviour. Application of pressures greater than 2 G Pa to Ni20ZrgO led to the formation of a new phase, w-Zr. which retains its form after the pressure is released.
    • Properties of NaxCoO2 /

      Jalili, Helia.; Department of Physics (Brock University, 2005-06-29)
      Polycrysttdline samples of NaiCoOa were prepared using the "Rapid heat-up" method. One set of samples was annealed in flowing O2, while the other set in flowing Argon. X-Ray diffraction measurements indicated a stable phase of Nao.7Co02 mixed with C03O4 for all the samples even though they differed in concentration of Na. Argon annealed samples were insulators, whereas the ones annealed in O2 were metallic. Most of the measurements were performed on the sample Nao.7Co02, because it is the host compound for the superconductor sample Nao.35Co02-H20. Magnetization measurement showed that the magnetic moment decreased with increasing sodium concentration. This is due to the existence of C03O4 in samples with Na^ 0.7. As sodium concentration decreases, the magnetic moment increases due to the increasing concentration of C03O4 and its large magnetic moment. Magnetization measurements showed that the magnetic moment of Nao.7Co02 is field-dependent in low fields eind field-independent in fields higher than 100 G. Resistivity changes with temperature (dp/dT) increased with increasing Na concentration. Also resistivity measurements were performed under different hydrostatic pressures on Nao.7Co02. Two transitions were observed; one at a temperature Ti ~20 K and the other at T2 ^280 K, the transition at Ti has a magnetic origin and the one at T2 is a structiural transition. It was noticed that pressure aJfects resistivity of the sample. At higher pressures resistivity changes faster with temperature. Magnetoresistance measurement showed a small change in the resistivity, especially at lower temperatures. A novel layered superconductor Nao.35Co02H20 was prepared using de-intercalation of Na from the host compound Nao.7Co02. FVom the temperature dependence of the magnetization, the superconducting transition temperature and lower critictil field have been estimated as Tc=4.12 K and Hci=66 G, respectively.
    • Pulsed laser deposition of YBa2Cu3O7-[delta]/PrBa2Cu3O7-[delta] /

      Recker, Stephanie J.; Department of Physics (Brock University, 1998-05-21)
      The process of depositing thin films by the use of pulsed laser deposition (PLD) has become a more widely used technique for the growth of substances in a thin film form. Pulsed laser deposition allows for the stoichiometric film growth of the target which is of great significance in the deposition of High Temperature Superconducting materials. We will describe a system designed using an excimer laser and vaccum chamber in which thin films and superlattices of YBa2Cuj07_i, PrBa2Cu307_i, and YBajCujOr-j/ PrBajCusOr-^ were deposited on SrTiOs. Results of resistivity measurements using the four probe technique will be shown.
    • Quantum Monte Carlo study of electrostatic polarizabilities of H and He atoms /

      Hornik, Miroslav.; Department of Physics (Brock University, 2001-07-14)
      The infinitesimal differential quantum Monte Carlo (QMC) technique is used to estimate electrostatic polarizabilities of the H and He atoms up to the sixth order in the electric field perturbation. All 542 different QMC estimators of the nonzero atomic polarizabilities are derived and used in order to decrease the statistical error and to obtain the maximum efficiency of the simulations. We are confident that the estimates are "exact" (free of systematic error): the two atoms are nodeless systems, hence no fixed-node error is introduced. Furthermore, we develope and use techniques which eliminate systematic error inherent when extrapolating our results to zero time-step and large stack-size. The QMC results are consistent with published accurate values obtained using perturbation methods. The precision is found to be related to the number of perturbations, varying from 2 to 4 significant digits.
    • Resistivity of Single Crystal Molybdenum Dioxide

      BAUER, KURTIS; Department of Physics
      The chemical vapour transport method was used to grow molybdenum oxide single crystals so that their electrical properties could be analyzed. Satisfactory single crystal samples of MoO2 and Mo4O11 were grown successfully using I2 as a transport agent. Crystal growths using TeCl4 as a transport agent were also performed, though with mixed results. This approach yielded MoO2, MoO3, and Mo9O26, but this produced samples of a quality not suitable for single crystal analysis. Measurements performed on these samples yielded unique results, due to their mixed oxide nature, but as the composition of each sample was inconsistent, even between crystals from the same growth, little can be said about them definitively. Rubidium doped single crystal growths were also attempted, to build on previous polycrystalline Rb doped sample research, however no growths successfully included measurable amounts of Rb. While resistivity and heat capacity measurements performed on MoO2 did identify a phase transition in the area of 267K reported by other researchers, there was however no evidence found to support a reported 220K electronic transition [1]. In Mo4O11 two previously identified 109K and 30K charge density wave transitions were observed in the DC resistivity. When AC resistivity measurements were performed the 30K transition was not apparent. Instead, a divergence of the cooling and warming curves not seen in the DC experiments occurred above 200K, with previously unseen peaks appearing at 285K and 250K when cooling from 400K.
    • Rotation-electronic interaction in the 3p-complex Rydberg state of water

      Hussain, Syed Mohammad Javed.; Department of Physics (Brock University, 1979-07-09)
      An energy theory is formulated for the rotational energy levels in a p-complex Rydberg state of an asymmetric top molecule of symmetry C2v. The effective Hamiltonian used consists of the usual rigid rotor Hamiltonian augmented with terms representing electronic spin and orbital angular momentum effects. Criteria for assigning symmetry species to the rotational energy levels, following Houganfs scheme that uses the full molecular group,are established and given in the form of a table. This is particularly suitable when eigenvectors are calculated on a digital computer. Also, an intensity theory for transitions to the Rydberg p-complex singlet states is presented and selection rules in terms of symmetry species of energy states are established. Finally, applications to HpO and DpO are given.
    • Set-up and evaluation of a mid-infrared reflectometer and investigation of the optical properties of doped tin telluride

      Hawesa, Halima.; Department of Physics (Brock University, 1998-07-09)
      A system comprised of a Bomem interferometer and a LT3-110 Heli-Tran cryostat was set up to measure the reflectance of materials in the mid-infrared spectral region. Several tests were conducted to ensure the consistency and reliability of the system. Silicon and Chromium, two materials with well known optical properties were measured to test the accuracy of the system, and the results were found to be in good agreement with the literature. Reflectance measurements on pure SnTe and several Pb and Mn-doped alloys were carried out. These materials were chosen because they exhibit a strong plasma edge in the mid infrared region. The optical conductivity and several related optical parameters were calculated from the measured reflectance. Very low temperature measurements were carried out in the far-infrared on Sn9SMn2Te, and the results are indicative of a spin glass phase at 0.8 K. Resistivity measurements were made at room temperature. The resistivity values were found, as expected, to decrease with increasing carrier concentration and to increase with increasing manganese concentration.
    • Simultaneous extraction of order parameters and orientational distribution fuctions from 31[superscript]P NMR spectra of magnetically partially oriented phospholipid bilayers

      Paul, Launy C.; Department of Physics (Brock University, 1996-07-09)
      Order parameter profiles extracted from the NMR spectra of model membranes are a valuable source of information about their structure and molecular motions. To al1alyze powder spectra the de-Pake-ing (numerical deconvolution) ~echnique can be used, but it assumes a random (spherical) dist.ribution of orientations in the sample. Multilamellar vesicles are known to deform and orient in the strong magnetic fields of NMR magnets, producing non-spherical orientation distributions. A recently developed technique for simultaneously extracting the anisotropies of the system as well as the orientation distributions is applied to the analysis of partially magnetically oriented 31p NMR spectra of phospholipids. A mixture of synthetic lipids, POPE and POPG, is analyzed to measure distortion of multilamellar vesicles in a magnetic field. In the analysis three models describing the shape of the distorted vesicles are examined. Ellipsoids of rotation with a semiaxis ratio of about 1.14 are found to provide a good approximation of the shape of the distorted vesicles. This is in reasonable agreement with published experimental work. All three models yield clearly non-spherical orientational distributions, as well as a precise measure of the anisotropy of the chemical shift. Noise in the experimental data prevented the analysis from concluding which of the three models is the best approximation. A discretization scheme for finding stability in the algorithm is outlined
    • Specific heat of UPdâ Siâ

      Startseva, Tatiana.; Department of Physics (Brock University, 1994-07-09)
      The specific heat of single-crystal U Pd2 Si2 has been studied using both the step heating and continious heating methods for the temperature range 2 to 250 K. Successive phase transitions at Tl = 136I< and T2 = 108I< are reported, which are consistent with current publications. The transition at 40K, which was previously reported, has not been detected. Recent published elastic neutron scattering data, magnetic susceptibility and resistivity results suggest that U Pd2 Si2 may be a heavy fermion compound, however, the electronic specific heat coefficient I (= 18.97 ;~), obtained from the specific heat Cv measurements, is smaller than that of the conventional heavy fermion system. The Debye temperature of U Pd2Si2 is found to be 116.55K. The possibility is discussed that the maximum in CIT in the low-temperature range 2 to 4K corresponds to Schottky anomaly induced by localized magnetic impurities .
    • Study of colossal magnetoresistance and pressure effects in La2/3Ca1/3MnO2 thin films /

      Roch, Tomás.; Department of Physics (Brock University, 1998-05-21)
      The main purpose of this thesis is to study properties of La2/3Cai/3Mn03, both polycrystalline ceramics and thin films. This material has striking related electrical and magnetic properties. Thin films show colossal negative magnetoresistance (CMR) near transition from an insulating to a metallic state accompanied closely by transition from a paramagnetic to a ferromagnetic state. The double exchange mechanism (DE) and the Jahn-Teller deformations play an important role in CMR effect. Applied pressure has a very similar effect as does an applied magnetic field, except, at low temperatures (T<Tc) the field suppresses the resistivity more than pressure. In our study we performed x-ray diffraction analysis, resistivity and magnetization measurements, as well as measurements of resistivity under applied pressure. The origin of strong resistivity change at low temperatures can be explcdned by the intergranular spin-dependent scattering of DE electrons. Oxygen stoichiometry plays an important role in the magnitude and position of MR(T) maximum. The distortions of structure and Mn-O-Mn bonds in applied pressure axe discussed. The fabrication of La2/3Cai/3Mn03 thin films by pulsed laser deposition was successfully developed. The films grown on (100) SrTiOs substrate are c-axis oriented and exhibit negative magnetoresistance Ap/p(H) of over 400% at 245°C and 4200% at 90 K.
    • Study of heat capacity measurement methods for small samples

      Rogge, Ronald B.; Department of Physics (Brock University, 1990-07-09)
      Methods of measuring specific heats of small samples were studied. Three automated methods were explored, two of which have shown promising results. The adiabatic continuous heating method, has provided smooth well behaved data but further work is presently underway to improve on the results obtained so far . The decay method has been success fully implemented demonstrating reasonable agreement with accepted data for a copper test sample.