The nature of negative linear expansion in layer crystals C,Bn, GaS,GaSe and InSe

Experimental investigations of thermal expansion parallel and perpendicular to the layers plane of layer crystals GaS, GaSe and InSe are described. The obtained results are analized together with known thermal expansion data on graphite, C, and boron nitride, BN. Theoretical calculations of linear expansion coefficients are carried out on the basis of the model of highly anisotropic crystal. It is shown, that the negative thermal expansion in the layer plane, typical of layer crystals, is due to “bending” waves, acoustic waves propagating in the layer plane and polarized perpendicular to this plane (TA_⊥ mode)     

Thermal properties of K<Subscript>3</Subscript>Li<Subscript>2−<Emphasis Type="Italic">x</Emphasis></Subscript>Nb<Subscript>5+<Emphasis Type="Italic">x</Emphasis></Subscript>O<Subscript>15±δ</Subscript> crystals

The unit-cell parameters of the nonlinear crystal K₃Li_2?xNb_5+xO_15±δ were measured with x-ray diffraction in the temperature region 80–300 K. The room-temperature parameters of the crystal of this composition are a=12.599±0.001 and c=4.018±0.001 Å. The temperature dependences of the thermal expansion coefficients (TECs) along the [100] and [001] crystallographic directions were determined. A small TEC anisotropy was established. The specific heat of this crystal was measured using adiabatic calorimetry in the temperature interval 80–300 K. The experimental data on the specific heat were used to calculate the changes in the thermodynamic functions.     

Thermal expansion property of anomalous magnetic alloy Fe70Al30

D0₃-type Fe₇₀Al₃₀ shows a transition from ferromagnetism to spin glass with anomalous slow spin dynamics below 170 K. Furthermore, it shows a structural transition from D0₃ to body-centered cubic (BCC) at 823 K. In this article, the relationship between the magnetic properties, thermal expansion coefficient (TEC), and crystal structure transition of D0₃-type Fe₇₀Al₃₀ is discussed. Below 170 K, TEC decreases with temperature, accompanied by a decrease in the Fe moments. In the ferromagnetic state between 170 K and the Curie temperature (T_C), TEC increases gradually with temperature. Above T_C, TEC increases rapidly. These temperature variations of TEC could be connected to the high-spin/low-spin transition and thermal spin fluctuations. During transition from D0₃ to disordered BCC at 823 K, TEC shows discontinuous behavior, similar to a first-order transformation. With further increase in temperature, TEC becomes constant. This implies that the phase transition from D0₃ to disordered BCC is accompanied by a change in spin fluctuation.     

Thermal expansion of niobium diselenide in the basal plane at low temperatures

The thermal expansion of a high-quality 2H-NbSe₂ single crystal is precisely measured in the basal plane and the temperature range 5.7–50 K. An anomaly of the thermal expansion in the basal plane is detected, and it is found to be caused by a superconducting transition. The change in thermal expansion coefficient α _ab is used to calculate the pressure derivative of the critical temperature (dT _c /dp _ab ) = (19.0 ± 2.0) × 10^?9 K/Pa, and this derivative agrees well with the reported data. An additional anomaly, which indicates a phase transition, is also detected in the pretransition range. The nature of the detected phase transition is discussed.     

Potential and restriction of high resolution,high energy photoemission in 400–8,000 eV for studying strongly correlated electron systems

InSe and InSe:Er single crystals were grown by using the Bridgman–Stockbarger method. The absorption measurements were carried out for voltage U=0 and U=30 V states of InSe and InSe:Er samples in the temperature range of 10–320 K with a step of 10 K. The absorption edge shifted towards longer wavelengths and the intensity of the absorption spectra decreased under a 5.90 kV/cm electric field. The same binding energy values for InSe and InSe:Er were calculated as 22.2 and 14.2 meV at U=0 and U=30 V, respectively. The steepness parameters and Urbach energies for InSe and InSe:Er samples increased with increasing sample temperature in the range of 10–320 K. An applied electric field caused a shift and a decrease of the intensity of the absorption spectra and an increase in the Urbach energy and steepness parameters. The shift of the absorption edge can be explained on the basis of the Franz–Keldysh effect or thermal heating of the sample under the electric field. PACS 71.20.Nr     

Absorption measurements in InSe:Ho single crystal under an electric field

InSe:Ho single crystal was grown by Bridgman-Stockberger method. Electric field effects on the absorption measurements have been investigated as a function of temperature in InSe:Ho single crystal. The absorption edge shifted towards longer wavelengths and a decrease of intensity in absorption spectra occurred under an electric field of 7.5 kV/cm. Using absorption measurements, steepness parameter and Urbach energy were calculated under electric field. Applied electric field caused an increase in the Urbach energy. At 10 K and 320 K, the first exciton energies were calculated as 1.322 and 1.301 eV for zero voltage and 1.245 and 1.232 eV for applied electric field, respectively.     

Size- and Temperature-Dependent Thermal Expansion Coefficient of a Nanofilm

The thermal expansion coefficient （TEC） of an ideal crystal is derived by using a method of Boltzmann statistics. The Morse potential energy function is adopted to show the dependence of the TEC on the temperature. By taking the effects of the surface relaxation and the surface energy into consideration, the dimensionless TEC of a nanofilm is derived. It is shown that with decreasing thickness, the TEC can increase or decrease, depending on the surface relaxation of the nanofilm.     

Surface relaxation and thermal expansion for the (001) face of α-Fe and Cu

The surface relaxation and the near-surface enhancement of thermal expansion have been calculated for the (001) face of a bcc crystal, α-Fe, and an fcc crystal, Cu. The calculations make use of the anharmonic perturbation formalism of Dobrzynski and Maradudin; the results for certain equal-time vibrational correlation functions which arise in this formalism are also presented. The crystal potential is described in terms of several kinds of short-range empirical interatomic potentials, such as have been used in studies of defects in bulk; in the near-surface region, the effects of surface redistribution of the electron distribution are modelled by the addition of a simple surface Madelung (SSM) force. The effect of the SSM force is to limit severely the usual outward relaxation driven by short-range interatomic potentials. For Fe(001), the five and one-half percent outward static relaxation driven by the short-range potentials acting alone is changed to a one percent inward static relaxation when the SSM force is incorporated; for Cu(001), the comparable change is from a one percent outward relaxation to a one-half percent outward relaxation. On the other hand, the SSM force makes only a small effect on the surface-enhanced thermal expansion coefficients (STEC) for interplanar spacings. The STEC for the outermost spacing is between 2.5. and 3.0 times of that for the bulk at the Debye temperature for both Fe(001) and Cu(001); for the second interplanar spacing, the STEC is smaller than 1.5 times of that of the bulk at the Debye temperature. The ratios of the near-surface mean-square amplitudes (MSA) to those of the bulk at high temperatures are, for Fe(001), about 1.75 for z-components (normal to surface) and 1.55 for x-components (parallel to surface) in the surface layer; for Cu(001), about 1.95 for z-components and 1.30 for x-components. The interplanar correlation functions, while smaller than the MSA on an absolute scale, do show considerable surface-enhancement, particularly for the zz-compoments. For example, the zz-correlation between an atom in the outermost layer and its nearest neighbor in the next layer is nearly twice the comparable bulk correlation above the Debye temperature for both Fe(001) and Cu(001).     

Thermal expansion near plane and stepped surfaces

A theory of the thermal expansion of the plane and (11n) stepped surfaces of fcc crystals is presented. The temperature dependent relaxations arise from cubic anharmonic terms in the crystal potential energy. We show that the thermal expansion depends on the positions of the atoms with respect to the steps and is greatest for the atom of the upper corner. The knowledge of these new atomic positions at each temperature allows us to calculate new atomic force constants and then new vibrational properties at this temperature. The application is made for a Ni crystal for which we give the corrections, due to the thermal expansion, on the mean square displacements of stepped surface atoms. The variation with temperature of the optical modes due to a light monolayer is also presented.     

Thermal expansion of (Sr<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>La<Subscript>x</Subscript>)<Subscript>3</Subscript>Ru<Subscript>2</Subscript>O<Subscript>7</Subscript> single crystals at low temperatures

For single-crystal samples of the (Sr_1?xLa_x)₃Ru₂O₇ ruthenates, the temperature dependence of the thermal expansion coefficient α(T)) is measured in the range 4.2–80 K. The effect of magnetic fields H ≤ 3.5 T on thermal expansion is analyzed. It is found that the (Sr_1?xLa_x)₃Ru₂O₇ ruthenates exhibit an anomalous (negative) thermal expansion coefficient in the temperature range T ≤ 18 K. The position and width of the anomaly revealed in the temperature dependence of the thermal expansion coefficient α(T)) depend substantially on the magnetic field. The origin of the thermal expansion anomaly in ruthenates, the correlation of this anomaly with the stability of the crystal lattice, and the common nature of the anomalies in the thermal properties of ruthenates and high-temperature superconductors are discussed.     

Low temperature pressure dependence of the muon hyperfine fields in iron,cobalt and nickel

The pressure dependence of the μ⁺ local magnetic fields in polycrystalline Fe and Ni and a Co single crystal has been measured at 77 K, up to 0.7 GPa, using a He gas high pressure setup. The pressure derivatives dlnB_μ/dP in units of mT/GPa are +4.4±1.0 (Fe), -0.7±1.1 (Co) and +0.63±0.10 (Ni). From these values the hyperfine field volume derivatives are deduced. Using these values together with previously determined room temperature derivatives the thermal expansion part of the temperature dependence of the hyperfine field can be calculated. The remaining explicit temperature dependence below 300 K, which deviates markedly from the temperature dependence of the bulk magnetization, is discussed.     

Application of Mythen detector: In-situ XRD study on the thermal expansion behavior of metal indium

A Mythen detector has been equipped at the beamline 4B9A of Beijing Synchrotron Radiation Facility (BSRF), which is expected to enable BSRF to perform time-resolved measurement of X-ray diffraction (XRD) full-profiles. In this paper, the thermal expansion behavior of metal indium has been studied by using the in-situ XRD technique with the Mythen detector. The indium was heated from 303 to 433 K with a heating rate of 2 K/min. The in-situ XRD full-profiles were collected with a rate of one profile per 10 seconds. Rietveld refinement was used to extract the structural parameters. The results demonstrate that these collected quasi-real-time XRD profiles can be well used for structural analysis. The metal indium was found to have a nonlinear thermal expansion behavior from room temperature to the melting point (429.65 K). The a-axis of the tetragonal unit cell expands with a biquadratic dependency on temperature, while the c-axis contracts with a cubic dependency on temperature. By the time-resolved XRD measurements, it was observed that the [200] preferred orientation can maintain to about 403.15 K. While (110) is the last and detectable crystal plane just before melting of the polycrystalline indium foil. This study is not only beneficial to the application of metal indium, but also exhibits the capacity of in-situ time-resolved XRD measurements at the X-ray diffraction station of BSRF.     

X-ray diffraction investigation of the thermochromic phase transition in an [NH2(C2H5)2]2CuCl4 crystal

The unit cell parameters of an [NH₂(C₂H₅)₂]₂CuCl₄ crystal are determined using x-ray diffraction analysis, and the thermal expansion coefficients along the principal crystallographic directions are calculated in the temperature range 100–330 K. The behavior of the intensities of the diffraction reflections from the (100), (010), and (001) crystallographic planes is studied in the vicinity of the thermochromic phase transition temperature. The occurrence of a first-order phase transition in the [NH₂(C₂H₅)₂]₂CuCl₄ crystal at T ≈ 324 K is confirmed experimentally.     

The Debye-Waller factor in helium scattering by a crystalline surface

On the dense face of a metallic crystal or the (001) face of lithium fluoride, the distance between nearest neighbours is of the same order of magnitude as the helium diameter. The hypothesis of simultaneous interaction between incident helium atoms of thermal kinetic energy and surface atoms belonging to a surface unit cell is therefore introduced. Then the exponent of the Debye-Waller factor contains mean square and mean correlated displacement between atoms of the cell. This gives for the (00) peak an apparent surface Debye temperature Θ_sa higher than the corresponding value usually deduced for instance from LEED measurements. For the (001) face of copper the calculated value is: 323 < Θ_sa < 354 K according to the value ascribed to bulk Debye temperature. On this face, recent experimental results show that helium atoms are coherently scattered in the specular (00) peak. From its intensity analysis is deduced an attractive well depth of 0.009 ± 0.002 eV and Θ_s = 370 ± 10 K, very close to the calculated result. The simultaneous interaction implies that the one phonon exchange can only take place with phonons of long wavelength. This theoretical expectation seems to be in qualitative agreement with experimental data.     

Thermal Expansion of Co2MAl (M = Ti,V, Cr,Mn, Fe,Ni) Band Ferromagnets

Physics of the Solid State - The thermal expansion coefficient (TEC) of Co2MAl (M = Ti, V, Cr, Mn, Fe, Ni) band ferromagnets is measured in the temperature interval of 80–900 K. The...     

Specific features in thermal expansion of <Emphasis Type="Italic">R</Emphasis>Fe<Subscript>11</Subscript>Ti single crystals

Thermal expansion and its anomalies in the vicinity of spin-reorientation phase transitions in single crystals of RFe₁₁Ti (R=Y, Tb, Dy, Ho, and Er) compounds are investigated by the tensometric technique in the temperature range 77–400 K. The temperature dependences of the thermal expansion coefficient α(T) are obtained. It is found that the YFe₁₁Ti and HoFe₁₁Ti uniaxial magnetic materials exhibit pronounced anomalies in the α coefficient at T=200 and 290 K. For the TbFe₁₁Ti single crystal, the α coefficient is close to zero in the vicinity of the spin-reorientation phase transition (at T=325 K). For the DyFe₁₁Ti single crystal, which is characterized by two spin-reorientation phase transitions (at T=120 and 250 K), no features in the α(T) dependence are revealed in the region of the low-temperature spin-reorientation phase transition. In the ErFe₁₁Ti single crystal, the specific feature of thermal expansion is observed at T ～ 220 K.     

The sound velocity, internal friction, and thermal expansion in a single crystal of La0.85Sr0.15MnO3

The results are given of the investigation of the temperature dependence of the sound velocity v, internal friction Q ^?1, and thermal expansion ΔL/L of a single crystal of La_0.85Sr_0.15MnO₃ in the temperature range from 5 to 400 K. Clearly defined singularities of the elastic properties at a temperature of charge ordering T _co≈200 K are revealed. The results of X-ray diffraction studies performed at room temperature are used to determine the orientations and estimate the sizes of twins. The correlation between magnetic and structure inhomogeneities is established. Based on the results of analysis of the temperature dependence of internal friction and thermal expansion, an assumption is made of the presence in a single crystal of La_0.85Sr_0.15MnO₃ of a structural transition in the temperature range from 15 to 60 K that has not been observed previously.     

Positrons and electron-irradiation induced defects in the layered semiconductor InSe

The positron annihilation characteristics of the layered semiconductor InSe have been investigated. No evidence for low temperature positron trapping is found in as-grown and heavily deformed InSe. The temperature dependence of the S-parameter in these sample exhibits an increase rate in good agreement with the linear expansion coefficient along the c-axis. The positron lifetime spectra of electron-irradiated 0.01% Sn-doped InSe show a long-lifetime component of 336 ps which is tentatively attributed to positrons trapped at isolated In vacancies. Isochronal annealing experiments performed on these samples show that the recovery of the positron lifetime measured at 77K is accomplished in two stages. The first, starting after annealing at 150K, could be induced by the formation of complexes (V_In-Sn_In). The second stage, observed at temperatures T375K, is attributed to the dissociation of these complexes and subsequent annealing of the In vacancies.     

Effective mass calculation for InSe, InSe:Er crystals

Undoped indium selenide (InSe) and Er doped InSe single crystals were grown by Bridgman–Stockberger method. The InSe crystals both undoped and doped Er had no cracks or voids on the surface. No polishing or cleaning treatments were carried out on the cleaved faces of these samples because of the natural mirror-like cleavage faces. The absorption measurements were carried out in the temperature range 10–320 K and the external electric field effect on the absorption measurements is investigated. The absorption edge shifted towards to the longer wavelengths under an electric field as 6 kV/cm. Using the electric field shifting, effective mass values are calculated.     

Magnetization reorientation in HoCo2

In order to confirm the magnetization reorientation in HoCo₂, torque measurements have been performed at various temperatures on a spherical single crystal, in the (001) and (011) planes. The easy magnetization direction is the [110] axis at 4.2 K and the [100] axis above 16 K. Furthermore, between 11 K and 16 K, the easy magnetization direction rotates progressively within the (001) plane. These results agree with the magnetization measurements and can be interpreted by a crystal field model.