Lattice Constant Measurements Research Articles

Revision of JIS R7651: “Measurement of lattice constants and crystallite sizes of carbon materials”

Revision of JIS R7651: “Measurement of lattice constants and crystallite sizes of carbon materials”

Revision of JIS R7651: “Measurement of Lattice Constants and Crystallite Sizes of Carbon Materials”

Revision of JIS R7651: “Measurement of Lattice Constants and Crystallite Sizes of Carbon Materials”

Cd0.90Mn0.10Te single crystal for γ – Ray detector application: A comprehensive analysis of structural and compositional homogeneity

This study provides a comprehensive examination of the Cd0.90Mn0.10Te (CMT) single crystal in its role as a radiation detector. Covering aspects from the growth process to detector performance, the primary emphasis is placed on ensuring the uniformity of composition along the growth axis. A cost-effective custom-built vertical Bridgman (VB) setup is developed for the growth of highly homogeneous Cd0.90Mn0.10Te (CMT) single crystal. CMT single crystals of 10 mm diameter and 130 mm length with near uniform stoichiometry along the growth axis were grown using VB method. Laue diffraction confirms the single crystallinity of the grown crystal. The measured lattice constant is comparable to the theoretical value calculated using Vegard’s law. The two mode vibrations of the CdTe and MnTe sublattices were confirmed by Raman spectroscopy. The observed high optical transmittance in the mid-infra-red (IR) region and a nearly constant bandgap of ∼1.6 eV for the wafers taken at different locations along the growth axis reveals the IR transparency and compositional uniformity of the grown crystal. The energy dispersive X-ray spectroscopy proved that the elemental distribution is uniform in the grown crystal. The IR microscopic imaging shows Te inclusions with a number density in the range of ∼2.6–4.5 × 104 cm−2. The resistivity of the CMT crystal for all wafers was found to be in the order of 109 Ωcm. The γ–ray spectral resolution of ∼22 % of 59.5 keV irradiation from 241Am source is achieved.

Strain and atomic stacking of bismuth thin film in its quasi-van der Waals epitaxy on (111) Si substrate.

We report on the structural properties of Bi thin films grown on (111) Si substrates with a thickness of 22-30 BL. HRXRD and EBSD measurements show that these Bi films are mainly composed of twinning grains in the (0003) direction. The grain size can be as large as tens of microns. From a double-peak (01[Formula: see text]4) φ-scan, we found two pairs of twinning phases coexisting with a rotation angle of ~ 3.6°. We proposed a coincidence site lattice model based on preferential close-packed sites for Bi atoms on Si (111) surface to explain the coexistence of the rotation phases in the quasi-van der Waals epitaxy. From the measured lattice constants c and a of our samples, along with the data from the literature, we derived a c-a relation: (c-c0) = - 2.038(a-a0), where c0 and a0 are the values of bulk Bi. The normalized position of the second basis atom in the unit cell x, in these strained Bi films is found very close to that of bulk Bi, indicating that the strain does not disturb the Peierls distortion of the lattice. The fixed ratio of bilayer thickness to lattice constant c, reveals that the elastic properties of covalent-bonded bilayer dominate those of Bi crystal.

Metastable Phase Formation in Electrodeposited Co-Rich Co-Cu and Co-Ni Alloys

In a previous work [El-Tahawy et al., J. Magn. Magn. Mater. 560, 169660 (2022)], we reported that from a sulfate type bath, hcp-Co can be electrodeposited at high pH and low current density and investigated the structure and magnetoresistance (MR) characteristics of such hcp-Co electrodeposits. Based on this earlier work, Co-rich Co-Cu and Co-Ni alloy electrodeposits were prepared under the same conditions by adding varying amounts of CuSO4 and NiSO4, respectively, to the CoSO4 bath. According to the results of detailed structural studies by various X-ray diffraction (XRD) geometries, in both the Co-Cu and Co-Ni systems an hcp phase formed exclusively up to about 2 at% of the alloying element. Above this concentration, a significant fcc phase fraction appeared in Co-Cu and a minor fcc fraction in Co-Ni up to about 8 at%. This means that the destabilization effect of Cu on hcp-Co is higher than that of Ni. Although the reduction of the stability of hcp-Co with increasing Cu and Ni content is a well-known phenomenon, a quantitative comparison of this effect in Co-Cu and Co-Ni alloys is missing from the literature. The measured lattice constants are analyzed in comparison with Vegard’s law for the Co-Cu and Co-Ni element pairs deduced from data previously reported for the hcp and fcc phases of all three pure elements. For Co-rich Co-Ni alloys, the concentration dependence of the lattice parameters was found to follow Vegard’s law for both the hcp and fcc phases due to the miscibility of the two components. For the Co-rich Co-Cu alloys, the data indicate a positive deviation from Vegard’s law for both the hcp and fcc phases in agreement with the known similar behavior of fcc Co-Cu alloys for the whole composition range. The positive deviation from Vegard’s law in the Co-Cu system is due to the excess mixing volume required for solid solution alloy formation of these immiscible elements in either phases. The MR data are discussed in the light of the observed phases and of the MR parameters reported in our previous work on the hcp and fcc phases of pure Co.

A novel high entropy perovskite oxide with co-substitution in A and B sites (Ca1/3Sr1/3Ba1/3)(Y1/4Zr1/2Nb1/4)O3 design, synthesis and structural characterization

A novel high-entropy perovskite oxide (HEPO) (Ca1/3Sr1/3Ba1/3)(Y1/4Zr1/2Nb1/4)O3 (CSBYZN) was designed and synthesized by solid-state reaction method by the use of CaCO3, SrCO3, BaCO3, Y2O3, ZrO2 and Nb2O5. Due to the substitution of the cations at both the A and B sites, the configuration entropy of CSBYZN was higher than that of other HEPOs with only one Wyckoff site (A or B site) substituted with 5 elements. The crystal structure of CSBYZN was identified as a cubic structure of the Pm-3m space group by Rietveld refinement. The measured lattice constant a = 4.1242 Å is similar to the value obtained by using the empirical formula (acal = 4.1229 Å). It was proved that the lattice constant of HEPOs can be predicted by the empirical formula. This study provides a new thought for the design of novel HEPOs.

Linescan Lattice Microscopy: A Technique for the Accurate Measurement and Mapping of Lattice Spacing and Strain with Atomic Force Microscopy.

Lateral resolution and accuracy in scanning probe microscopies are limited by the nonideality of piezoelectric scanning elements due to phenomena including nonlinearity, hysteresis, and creep. By taking advantage of the well-established atomic-scale stick-slip phenomenon in contact-mode atomic force microscopy, we have developed a method for simultaneously indexing and measuring the spacing of surface atomic lattices using only Fourier analysis of unidirectional linescan data. The first step of the technique is to calibrate the X-piezo response using the stick-slip behavior itself. This permits lateral calibration to better than 1% error between 2.5 nm and 9 μm, without the use of calibration gratings. Lattice indexing and lattice constant determination are demonstrated in this way on the NaCl(001) crystal surface. After piezo calibration, lattice constant measurement on a natural bulk MoS2(0001) surface is demonstrated with better than 0.2% error. This is used to measure nonuniform thermal mismatch strain for chemical vapor deposition (CVD)-grown monolayer MoS2 as small as 0.5%. A spatial mapping technique for the lattice spacing is developed and demonstrated, with absolute accuracy better than 0.2% and relative accuracy better than 0.1%, within a map of 12.5 × 12.5 nm2 pixels using bulk highly oriented pyrolytic graphite (HOPG) and MoS2 as reference materials.

Crystalline growth and alloying of In[formula omitted]Ga[formula omitted]Sb films by electrodeposition onto liquid metal electrodes

Incorporating indium (In) atoms into the GaSb lattice provides broad tunability of the optical bandgap within the infrared spectral region. This research documents the first instance in the literature of electrochemical liquid–liquid–solid (ec-LLS) growth of a ternary semiconductor alloy. Indium content of deposited InxGa1−xSb samples was regulated by controlling the Ga/In ratio of the liquid metal electrode. All depositions were performed using a single-step growth method under ambient pressure at 90 ± 5 °C. X-ray diffraction analysis showed shifts of the (111) diffraction peaks toward the peak locations of cubic InSb for the x=0.50, 0.60, and 0.70 samples, indicating a consistent increase in lattice parameter. However, the x=0.28 and 0.41 samples displayed unexpected shifts toward larger angles, possibly due to increased presence of Ga vacancies and antisites caused by Ga-rich growth conditions, as well as insufficient mixing of the liquid metal electrode for x< 0.50. Optical bandgaps ranging from 0.594 to 0.707 eV were determined via the Tauc method and Kubelka–Munk theory applied to diffuse reflectance data, and showed general agreement with measured lattice constants. Data obtained in this research supports In incorporation into the GaSb lattice for samples with x≥ 0.50, but with significantly lower In compositions relative to the liquid metal electrode. No general trend was observed for average crystallite size as a function of In composition, likely due to inconsistencies in the film harvesting process. This research provides further support for ec-LLS as a semiconductor growth technique capable of crystalline growth and alloying of III-V semiconductors.

Metal-insulator transitions in epitaxial rocksalt-structure Cr1−x/2N1−xOx (001)

Substitutional replacement of N with O in epitaxial CrN(001) layers is achieved by reactive sputter deposition in a mixed ${\mathrm{N}}_{2}$ and $\mathrm{Ar}+{\mathrm{O}}_{2}$ atmosphere. O incorporation facilitates Cr vacancies, yielding a rocksalt-structure solid solution ${\mathrm{Cr}}_{1\ensuremath{-}x/2}{\mathrm{N}}_{1\ensuremath{-}x}{\mathrm{O}}_{x}$ with a single compositional parameter $x$ and a measured lattice constant that decreases from $a=0.4175$ to 0.4116 nm for $x=0$ to 0.59. First-principles calculations predict $da/dx=+0.0200$, \ensuremath{-}0.0018, and \ensuremath{-}0.0087 nm for $\mathrm{Cr}{\mathrm{N}}_{1\ensuremath{-}x}{\mathrm{O}}_{x}, {\mathrm{Cr}}_{1\ensuremath{-}x/3}{\mathrm{N}}_{1\ensuremath{-}x}{\mathrm{O}}_{x}$, and ${\mathrm{Cr}}_{1\ensuremath{-}x/2}{\mathrm{N}}_{1\ensuremath{-}x}{\mathrm{O}}_{x}$, respectively, and confirm, in combination with ion-beam compositional analyses and x-ray diffraction results, a vacancy concentration of $x/2$ per cation site. The room-temperature resistivity decreases by over two orders of magnitudes from $\ensuremath{\rho}=1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ to $7.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}\phantom{\rule{0.16em}{0ex}}\mathrm{\ensuremath{\Omega}}\phantom{\rule{0.16em}{0ex}}\mathrm{m}$ for $x=0--0.26$. This is accompanied by a transition from a negative to a positive temperature coefficient of resistivity, an increase in the Hall mobility from ${\ensuremath{\mu}}_{\mathrm{H}}=0.37$ to $1.7\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{2}/\mathrm{Vs}$, an increase in the carrier concentration $n=1.1\ifmmode\times\else\texttimes\fi{}{10}^{20}$ to $4.9\ifmmode\times\else\texttimes\fi{}{10}^{21}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$, and a decrease in the calculated band gap from 0.54 to 0 eV. However, $\ensuremath{\rho}$ increases again to $6.9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\phantom{\rule{0.16em}{0ex}}\mathrm{\ensuremath{\Omega}}\phantom{\rule{0.16em}{0ex}}\mathrm{m}$ for $x=0.34$ and to $g10\phantom{\rule{0.16em}{0ex}}\mathrm{\ensuremath{\Omega}}\phantom{\rule{0.16em}{0ex}}\mathrm{m}$ for $x\ensuremath{\ge}0.59$, with a corresponding drop in ${\ensuremath{\mu}}_{\mathrm{H}}$ and the opening of a gap. The maximum in the measured carrier density and conductivity at $x=0.26$ is attributed to a maximum in the density of states near the Fermi level, in perfect agreement with calculations using supercells with randomly distributed O substitutions and Cr vacancies that predict a maximum at $x=0.25\ifmmode\pm\else\textpm\fi{}0.05$. The measurements indicate insulator-to-metal and subsequent metal-to-insulator transitions at $x=0.04\ifmmode\pm\else\textpm\fi{}0.03$ and $0.30\ifmmode\pm\else\textpm\fi{}0.03$, respectively. The transition to metallic conduction is attributed to substitutional O on anion sites acting as donors, while the measured $n$ for $x=0.01--0.26$ quantitatively indicates charge compensation by cation vacancies that act as acceptors. The insulating properties at large $x$ are likely caused by increased electron correlation effects.

Facile synthesis of Ge1−xSnx nanowires

We report a facile one-pot solution phase synthesis of one-dimensional Ge1−xSnx nanowires. These nanowires were synthesized in situ via a solution-liquid-solid (SLS) approach in which triphenylchlorogermane was reduced by sodium borohydride in the presence of tin nanoparticle seeds. Straight Ge1−xSnx nanowires were obtained with an average diameter of 60 ± 20 nm and an approximate aspect ratio of 100. Energy-dispersive x-ray spectroscopy (EDX) and powder x-ray diffraction (PXRD) analysis revealed that tin was homogeneously incorporated within the germanium lattices at levels up to 10 at%, resulting in a measured lattice constant of 0.5742 nm. The crystal structure and growth orientation of the nanowires were investigated using high-resolution transmission electron microscopy (HRTEM). The nanowires adopted a face-centred-cubic structure with individual wires exhibiting growth along either the 〈111〉, 〈110〉 or 〈112〉 directions, in common with other group IV nanowires. Growth in the 〈112〉 direction was found to be accompanied by longitudinal planar twin defects.

Reciprocal Space Map Measurement of Ceramics Thin Films for Unequal Lattice Change at High Temperature

Ceria and zirconia are very important for their thermal, mechanical, and chemical stability, and their thin films have attracted much attention for applications such as buffer layers for growing electric devices, thermal-shield or optical coatings, corrosion-resistant coatings, oxygen sensors and ionic conductors for fuel cells. To investigate and control the thin film orientation and phase is important to improve those performances. In this study, the reciprocal space maps of CeO2/YSZ/Si(001) were obtained at high temperature by adding a heater to the sample stage. CeO2 and YSZ thin films were epitaxially grown samples. By measuring lattice constants at high temperature, it was conducted that axes of CeO2 and YSZ thin films parallel to the substrate surface showed smaller thermal coefficients than bulk reference and axes perpendicular to the surface showed larger thermal coefficients due to the underlayer and Si substrate. The distortion rate of the lattice of each film was small around at the film deposition temperature. And it could be controled the lattice parameter at the film surface by the film thickness. Therefore, when another thin film, for example, SrTiO3 is deposited on the CeO2 layer, the lattice change of CeO2 with increasing temperature may differ from that before depositing the top layer.

Growth of high-quality AlN films on sapphire substrate by introducing voids through growth-mode modification

We demonstrate the achieving of high-quality AlN films on flat sapphire substrate (FSS) by introducing voids during growth. Voids are embedded into AlN epilayers through a growth-mode transition from island growth to step flow growth. Such voids significantly facilitated the underlying dislocations annihilation as demonstrated by the transmission electron microscopy (TEM) image. For the 3 μm-thick AlN film grown on FSS, the full width at half maximum of the X-ray rocking curve was 57/260 arcsec for (0 0 2)/(1 0 2) reflection and a threading dislocation density of 1.7 × 108 cm−2 was determined from plain-view TEM image. Moreover, the voids provided an additional stress relief channel in the AlN film grown on FSS, resulting in a tensile stress comparable to that of grown on nano-patterned sapphire substrate (NPSS). The measured lattice constants and Raman shift of AlN-E2 (high) peak verified the 3 μm-thick AlN film grown on FSS is nearly stress free at room temperature. Taking advantages of the deliberately embedded voids, a crack-free and atomically flat AlN film was grown on FSS. The strategy put forward in this work to obtaining high-quality AlN films on FSS is much cost-efficient, which is believed to hold great promise for commercialization in AlN-based devices.

Computational characterization of the structural and mechanical properties of AlxCoCrFeNiTi1−x high entropy alloys

AlCoCrFeNiTi is one kind of high entropy alloys with potential applications in aerospace, electronics and machinery manufacturing, etc. Its microstructure, thermodynamic and mechanical properties vary with Al and Ti contents. The disordered structures of AlxCoCrFeNiTi1−x (x = 0–1.0) alloys were generated and screened with the special quasi-random method. First-principles calculations with the Perdew–Burke–Ernzerhof functional and projector-augmented wave potential were carried out to further identify the structures and assess their thermodynamic and mechanical properties. The measured lattice constants and observed phase transition from bcc to fcc with Ti addition and Al reduction were reproduced in the calculations. The predicted transition point is at the Al content of about 8 at%. The heat capacity of the bcc and fcc structures exhibit similar temperature dependence, matching well with the empirical Dulong-Petit Model and the quantum Debye Model. The elastic constants and elastic moduli vary with the phase structures and compositions. The studied AlxCoCrFeNiTi1−x alloys are predicted to possess good comprehensive mechanical performances, especially for x = 0.8 and 0.6 for the bcc structures and x = 0.5 for the fcc structures. The addition/reduction of Al atoms from the systems alters the electron localization/delocalization that has considerable influence on the interatomic interaction strength in the alloy systems.

Structural and magnetic studies on Co-Zn nanoferrite synthesized via sol-gel and combustion methods

Abstract Co–Zn nanocrystalline ferrites with chemical composition Co0:5Zn0:5Fe2O4 were synthesized by sol-gel and combustion methods. The sol-gel method was carried out in two ways, i.e. based on chelating agents PVA and PEG of high and low molecular weights. In auto-combustion method, the ratio of citric acid to metal nitrate was taken as 1:1, while in sol-gel method the chelating agents were taken based on oxygen balance. All the three samples were studied by thermogravimetric and differential thermal analysis for the identification of phase formation and ferritization temperature. The synthesized samples were characterized by powder X-ray diffraction and FT-IR spectroscopy without any thermal treatment. The measured lattice constants and observed characteristic IR absorption bands of the three samples are in good agreement with the reported values showing the formation of a cubic spinel structure. The crystallite sizes of all samples were determined using high intensity peaks and W-H plot. Size-Strain Plot method was also implemented since two of the samples showed low crystallite sizes. The least crystallite size (5.5 nm) was observed for the sample CZVP while the highest (23.8 nm) was observed for the sample CZCA. Cation distribution was proposed based on calculated and observed intensity ratios of selected planes from X ray diffraction data. All structural parameters were presented using experimental lattice constant and oxygen positional parameter, and they correlated with FT-IR results. Magnetic measurements were carried out using vibrating sample magnetometer at room temperature to obtain the characteristic parameters such as saturation magnetization, coercivity, remanence, squareness ratio and Bohr magnetons. Among all, the sample synthesized via citric acid autocombustion method displayed a remarkably higher magnetization of 53 emu/g and the remaining two samples displayed low magnetization values owing to their smaller crystallite sizes.

Energy-dispersive Laue experiments with X-ray tube and PILATUS detector: precise determination of lattice constants

A PILATUS detector in combination with a conventional sealed X-ray tube was used for the development of the energy-dispersive Laue diffraction technique, which can be applied for precise measurements of single-crystal lattice constants in transmission and reflection modes without moving the sample. Exploiting the ability of PILATUS detectors to suppress counting of X-ray photons below a certain energy threshold allows one to recover the wavelength of diffracted Bragg reflections, reconstruct the three-dimensional reciprocal-space pattern, index X-ray diffraction peaks, and find the orientation and lattice parameters of the crystal without any a priori information about the sample. By making some geometrical assumptions and using a set of fast in situ calibration procedures, it is possible to simultaneously refine lattice constants and hardware correction factors, which simplifies the sample preparation and measurement strategies. Several samples [silicon, quartz, fluorite (CaF2), o′-Al13Co4 quasicrystal approximant, Laves (MgZn2) and Bergman (Mg32(Al,Zn)49) phases] were studied with the developed technique, and 0.01 Å and 0.1° precisions were routinely reached for lattice vector lengths and angles, respectively. The use of the developed methods is only limited by the energy resolution of the PILATUS detector, where lattice vectors with &gt;27 Å length cannot be reliably resolved.

An Answer to the Structure of Carbon Cluster in Low-Temperature Aged Ferritic Low-Carbon Steel

The morphology and structure of carbon cluster in a low temperature aged low-carbon ferritic steel were examined by transmission electron microscopy and atomically-resolved scanning transmission electron microscopy. The needle-like carbon cluster was found parallel to direction to the matrix. The crystal structure of the carbon cluster was determined as martensite-like body-centered tetragonal structure via measurement of lattice constant of them, which suggested that the carbon cluster was supersaturated with carbon atoms occupying specific octahedral sites orderly. The carbon content of the carbon cluster was estimated as 0.11 mass%, five times larger than the solubility of carbon in the alloy.

Precise measurements of diamond lattice constant using Bond method

Precise lattice constant measurements based on the Bond method for various types of diamond were performed with a recently reported compensation technique. For the measurements, a calibrated Si single crystal was used as a reference; it was placed in a chamber whose temperature was carefully controlled below the standard deviation σ of ±0.1 °C, including thermo-couple fluctuation of ±0.06 °C for ±σ, X-ray wavelength calibration was performed using the monochromator temperature. A calibration was also carried out for the instrumental value depending on the Bragg angle and it was applied to the 004 diffraction peak of diamond. The lattice constant of high quality insulating undoped IIa type diamond was 3.567095 ± 0.000017 Å (±2σ), which was larger than the previous data derived without above mentioned calibrations. The measurements were carried out for various types of diamond including high pressure high temperature (HPHT) grown crystals as well as crystals grown by the chemical vapor deposition (CVD) method.

In Situ stress Measurements during Strained-Layer Electrodeposition

Enhanced catalytic activity has been demonstrated in elastically strained thin films, pseudomorphically grown on substrates with an appropriate lattice mismatch. The enhancement in catalytic activity is typically attributed to both electronic interactions and the epitaxial mismatch strain in the overlayer. The magnitude of the strain is often estimated from lattice-constant measurements using x-ray diffraction. An additional probe gaining popularity in electrochemistry involves the measurement of surface and growth stress using cantilever curvature. Cantilever curvature offers a nice complement to the direct strain measurementand can provide an in situ measurement while the strained layer is being formed. This talk will focus on the biaxial growth stress that develops during the self-terminated electrodeposition of ultrathin Pt films onto a variety of cantilever substrates that introduce different levels of misfit strain into the Pt. The cantilever was a borosilicate glass strip measuring 60 mm × 3 mm × 0.108 mm and was metallized on one side by electron beam evaporation, resulting in substrates with strong (111) crystallographic orientation. The electrolyte was 0.5 mol/L NaCl containing 3 mmol/L K2PtCl4. Deposition consisted of stepping the potential from the open circuit potential (~ -0.1V vs SSE) down to -1.2V for 10s and then back to -0.1V for another 30s, following the procedure established by Liu et al.1Figure 1 shows the stress response for Au, Pt and Ir substrates. Pt grown on Au exhibits considerable tensile stress, which is consistent with the +3.9% lattice mismatch between Au and Pt. In contrast, Pt deposition onto a Pt cantilever deposits homoepitaxially as an unstrained continuation of the substrate. The slight increase in stress with continued deposition is likely microstructural. Pt grown on Ir, with its -2.1% lattice misfit, initially exhibits compressive stress, before leveling off and turning tensile, similar to the growth of Pt on Pt. Although it is tempting to focus on lattice misfit as the primary source of stress, one must consider other contributions, such as step line tension associated with the growth of small islands, possible intermixing, and surface roughness. References Y. Liu, D. Gokcen, U. Bertocci and T. P. Moffat, Science 338, 1327 (2012). Figure 1

Spin-coating technique to investigate structural and optical properties of nano and micro cubic-like photonic LiNbO3 under annealing temperature effect

Lithium Niobate (LiNbO3) nano and micro structures are deposited on glass substrates by sol-gel method. The nanostructures are deposited at 3000 RPM for 30 s, and annealed at different temperatures, 400, 500 and 600 °C. These samples are characterized and analyzed by Scanning Electron Microscope (SEM), Atomic Force Microscopy (AFM), X-ray diffraction (XRD) and Ultra-Violet visible (UV–vis) spectrophotometer, respectively. The results show an importance of increasing the annealing temperatures, which indicate that the structure will be enhanced and more crystallize to become more regular. The measured lattice constants, energy gaps and refractive index give good accordance with the experimental results.

Experimental determination of thermal expansion of natural MoS2

We report helium diffraction from natural MoS2 single crystal. The high quality of the samples studied lead to the appearance of sharp and intense in-plane and out-of-plane diffraction peaks, with unusually low background. The pronounced out-of-plane features observed confirm the high corrugation of the 2D surface unit cell. The observation of diffraction features along the two main high symmetry directions allows determining the in-plane surface lattice constant with high accuracy. The measured lattice constant along and is Å. Within experimental error, the MoS2 lattice parameter was found to remain constant in the temperature range between 90 and 522 K, in good agreement with previously reported DFT based calculations.