Journal articles: 'Vegard’s Law'

1

Denton, A. R., and N. W. Ashcroft. "Vegard’s law." Physical Review A 43, no. 6 (March 1, 1991): 3161–64. http://dx.doi.org/10.1103/physreva.43.3161.

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AGUILAR CRUZ, K. A., J. J. MEDEL JUÁREZ, M. T. ZAGACETA ÁLVAREZ, R. PALMA OROZCO, F. CABALLERO-BRIONES, and J. L. FERNÁNDEZ-MUÑOZ. "MODELING OF THE CHEMICAL X-PARAMETER IN PSEUDOBINARY ALLOYS FROM THE SHIFT OF THE X-RAY BRAGG ANGLE: APPLICATION TO CUBIC BaxSr1-xTiO3 FILMS." Digest Journal of Nanomaterials and Biostructures 15, no. 1 (January 2020): 33–40. http://dx.doi.org/10.15251/djnb.2020.151.33.

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Pseudobinary alloys of the type AxB1-xC are expected to obey the Vegard’s law that states a linear relationship between the chemical parameter x and the lattice parameter. However, in many cases, deviations from the Vegard’s are found, and the calculation of x requires compositional characterization, often complicated in the presence of secondary phases of the same material. In the present work, 𝐵𝑎𝑥𝑆𝑟(1−𝑥)𝑇𝑖𝑂3 (BSTO) films were deposited by RF co-sputtering from 𝐵𝑎𝑇𝑖𝑂3 and 𝑆𝑟𝑇𝑖𝑂3 targets to obtain differently 𝐵𝑎⁄𝑆𝑟 ratios considering the different RF-power applied to each target. We describe a mathematical model based on the Boltzmann equation to calculate the 𝑥 parameter of the cubic phase of the BSTO films in the 0 ≤ 𝑥 ≤ 1 range. That was made by following the 2𝜃 diffraction angular shift of the plane (111) upon the increase of substitutional Ba2+ in the pseudobinary alloy, as a function of the RF applied power and fitting the interplanar distances and lattice parameter in the alloys were calculated onto the fitted sigmoid trajectory. The model showed the region where the lattice parameter a vs x obeys the Vegard’s law and correctly fitted “a” in the entire 0<x<1 range. The model can be applicable to other pseudobinary systems with deviations from the Vegard’s law, from a simple X-ray diffraction analysis, providing fast chemical information, complementary with further compositional characterization.

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Khavrov, G. D., V. V. Kaminski, N. V. Sharenkova, and A. A. Vinogradov. "Features of the Implementation of the Vegard’s Law in Thin Films of Rare Earth Elements Compounds." Key Engineering Materials 822 (September 2019): 795–800. http://dx.doi.org/10.4028/www.scientific.net/kem.822.795.

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In this work, the fulfillment of Vegard's law in thin polycrystalline films Sm1-xGdxS and Sm1-xEuxS, obtained by the method of explosive evaporation of the powder in vacuum, is investigated. It is shown that compliance with the Vegard law in the manufacture of thin-film structures based on Sm1-xEuxS solid solutions is possible only with the same technological parameters of film deposition, in particular, the substrate temperature. In the case of the Sm1-xGdxS solid solutions, the law is observed only in the metal phase of the solid solutions, with x> 0.12.

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Magomedov, M. N. "On Deviations from Vegard’s Law at Increasing Pressure in Alloys." Inorganic Materials 56, no. 9 (September 2020): 903–8. http://dx.doi.org/10.1134/s0020168520090125.

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Adarakatti, Shashidhar N., Veeresh S. Pattar, Prashant K. Korishettar, Bhagyashri V. Grampurohit, Ravindra G. Kharabe, Akshay B. Kulkarni, Shridhar N. Mathad, Chidanandayya S. Hiremath, and Rangappa B. Pujar. "Synthesis, Structural and Electrical Studies of Li-Ni-Cu Nano Ferrites." Acta Chemica Iasi 26, no. 1 (July 1, 2018): 1–12. http://dx.doi.org/10.2478/achi-2018-0001.

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Abstract Li-Ni ferrite has gained great scientific elicit owing to of its unparalleled properties and applications. The copper doped Li-Ni ferrite has been synthesized by sucrose method. The structure was characterized by X-ray diffraction, which has confirmed the formation of single-phase spinel structure. X-ray diffraction and FTIR data reveals the formation of cubic structure phase. Unit cell parameters vary with copper content; overall variation of the unit cell parameters obeys Vegard’s law. The main absorption bands of spinel ferrite have appeared through IR absorption spectra recorded in the range of 300–700 cm−1. The copper concentration dependence of lattice parameters obeys Vegard’s law. DC electrical resistivity of the prepared samples decreases with increasing in the temperature which shows the semiconducting behaviour of all nano ferrites. The most prominent influence copper doping on the electrical properties of Li-Ni ferrites has been reported.

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Li, Wei, Markus Pessa, and Jari Likonen. "Lattice parameter in GaNAs epilayers on GaAs: Deviation from Vegard’s law." Applied Physics Letters 78, no. 19 (May 7, 2001): 2864–66. http://dx.doi.org/10.1063/1.1370549.

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Prasad, Raj Kumar, and Parmanand Mahto. "Lattice Distortion in Zn1-x Mx O(M=V,Mn) and Vegard’s Law." Indian Journal of Applied Research 3, no. 5 (October 1, 2011): 40–41. http://dx.doi.org/10.15373/2249555x/may2013/183.

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Liou, B. T., S. H. Yen, and Y. K. Kuo. "Vegard’s law deviation in band gap and bowing parameter of AlxIn1-xN." Applied Physics A 81, no. 3 (August 2005): 651–55. http://dx.doi.org/10.1007/s00339-004-2711-1.

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Domashevskaya, É. P., P. V. Seredin, É. A. Dolgopolova, I. E. Zanin, I. N. Arsent’ev, D. A. Vinokurov, A. L. Stankevich, and I. S. Tarasov. "Vegard’s law and superstructural phases in AlxGa1−x As/GaAs(100) epitaxial heterostructures." Semiconductors 39, no. 3 (March 2005): 336–42. http://dx.doi.org/10.1134/1.1882797.

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Rackham, Jonathan C., Bin Zou, and Michelle A. Moram. "Towards Two-Dimensional Oxides for Optoelectronic Applications." MRS Advances 3, no. 3 (2018): 147–51. http://dx.doi.org/10.1557/adv.2018.219.

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ABSTRACTPreliminary thin films of barium zirconate-titanate (BZT) are grown by pulsed laser deposition from bulk ceramic targets on magnesium oxide (001) substrates. Growth conditions are optimized for film crystallinity and thick (100 nm) films are deposited. These films are seen to be growing with a cube-on-cube epitaxial relation. The lattice constant of the alloy follows Vegard’s law as expected but shows a reasonable amount of non-linearity in the relation between band gap and composition.

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11

Guerra, Jorge Andres, Anja Winterstein, Oliver Erlenbach, Gonzalo Gálvez, Francisco De Zela, Roland Weingärtner, and Albrecht Winnacker. "Determination of the Optical Bandgap of Thin Amorphous (SiC)_1-x(AlN)_x Films." Materials Science Forum 645-648 (April 2010): 263–66. http://dx.doi.org/10.4028/www.scientific.net/msf.645-648.263.

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Amorphous wide bandgap semiconductor thin films of the pseudobinary compound (SiC)1-x(AlN)x were grown by radio frequency dual magnetron sputtering on CaF2, MgO and glass substrates. We performed isochronical annealing steps up to 500°C. The optical bandgap is determined for each composition from spectroscopic transmission measurement in two different ways: according to Tauc and using the (αhν)2 plot. The dependence of the optical bandgap on the composition x can be described by Vegard’s empirical law for alloys.

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Lee, Soonil, and Clive A. Randall. "A modified Vegard’s law for multisite occupancy of Ca in BaTiO3–CaTiO3 solid solutions." Applied Physics Letters 92, no. 11 (March 17, 2008): 111904. http://dx.doi.org/10.1063/1.2857475.

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13

Lambregts, Marsha J., and Steve Frank. "Application of Vegard’s law to mixed cation sodalites: a simple method for determining the stoichiometry." Talanta 62, no. 3 (February 27, 2004): 627–30. http://dx.doi.org/10.1016/j.talanta.2003.09.007.

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14

Banik, Soma, P. K. Mukhopadhyay, A. M. Awasthi, and S. R. Barman. "Structural Studies on Mn Excess and Ga Deficient Ni-Mn-Ga." Advanced Materials Research 52 (June 2008): 109–14. http://dx.doi.org/10.4028/www.scientific.net/amr.52.109.

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We report the structural studies on Mn excess and Ga deficient Ni2Mn1+zGa1-z specimens with z= 0, 0.05, 0.1, 0.15, 0.2 and 0.25. The crystal structure at room temperature was determined by the x-ray diffraction (XRD). Rietveld analysis has been performed to obtain the lattice parameters. For z= 0, 0.05 and 0.1, a cubic austenitic phase is observed. For 0.15≤ z ≤0.25, a tetragonal martensitic phase is obtained, whose lattice constant c increases and a decreases linearly with increasing z following Vegard’s law. Phase coexistence is observed for z= 0.15, confirming the first-order nature of the martensitic transition.

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Wang, Yi Ping, Sergiu Levcenco, Dumitru O. Dumcenco, Ying Sheng Huang, Ching Hwa Ho, and Kwong Kau Tiong. "Composition Dependent Band Gaps of Single Crystal Cu₂ZnSn(S_xSe_1-x)₄ Solid Solutions." Solid State Phenomena 194 (November 2012): 139–43. http://dx.doi.org/10.4028/www.scientific.net/ssp.194.139.

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Single crystals of Cu2ZnSn(SxSe1-x)4(CZTSSe) solid solutions have deen grown by chemical vapor transport technique using ICl3as a transport agent. Analyzing the X-ray diffraction patterns reveal that the as-grown CZTSSe solid solutions are crystallized in kesterite structure and the lattice parameters are determined. The S contents of the obtained crystals are estimated by Vegard’s law. The composition dependent band gaps of CZTSSe solid solutions are studied by electrolyte electroreflectance (EER) techniques. The band gaps of CZTSSe are evaluated by a lineshape fit of the EER spectra and are found to increase almost linearly with the increase of S content.

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Becerra, A., and M. Pekguleryuz. "Effects of lithium, indium, and zinc on the lattice parameters of magnesium." Journal of Materials Research 23, no. 12 (December 2008): 3379–86. http://dx.doi.org/10.1557/jmr.2008.0414.

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The lattice parameters of magnesium solid-solution alloys with lithium, indium, and/or zinc have been determined via x-ray diffraction (XRD). Li decreased the axial ratio (c/a) of Mg from 1.624 to 1.6068 within 0–16 at.% Li. Indium increased the c/a of Mg to 1.6261 with increasing In toward 3.3 at.% while Zn showed no effect on c/a in the 0.2–0.7 at.% range. The effects were explained by electron overlap through the first Brillouin zone and by Vegard’s Law. A relationship was determined between electron concentration (e/a) and c/a as c/a = −15.6(e/a)2 + 60(e/a) − 55.8.

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17

Bocchi, C., S. Franchi, F. Germini, A. Baraldi, R. Magnanini, D. De Salvador, M. Berti, and A. V. Drigo. "Influence of As incorporation on the deviation from Vegard’s law in the AlxGa1−xSb/GaSb system." Journal of Applied Physics 89, no. 8 (April 15, 2001): 4676–78. http://dx.doi.org/10.1063/1.1357460.

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18

Foronda, Humberto M., Baishakhi Mazumder, Erin C. Young, Matthew A. Laurent, Youli Li, Steven P. DenBaars, and James S. Speck. "Analysis of Vegard’s law for lattice matching InxAl1−xN to GaN by metalorganic chemical vapor deposition." Journal of Crystal Growth 475 (October 2017): 127–35. http://dx.doi.org/10.1016/j.jcrysgro.2017.06.008.

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19

AHAMED, M. I., K. S. KUMAR, E. E. ANAND, and A. SIVARANJANI. "OPTICAL ATTENUATION MODELLING OF PbSexS1-x QUANTUM DOTS WITH VEGARD'S LAW AND BRUS EQUATION USE." Journal of Ovonic Research 16, no. 4 (July 2020): 245–52. http://dx.doi.org/10.15251/jor.2020.164.245.

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Lead Selenide Sulphide (PbSeS) nanomaterial, a chalcogenide semiconductor which has maximum radiation attenuation can be tuned for required wavelength in the range from ultraviolet to infrared. Hence it has received much interest among researchers. Further, the electronical and optical properties of PbSeS Quantum Dots were modeled by Brus Equation, Vegard’s law and Interpolation principle calculations. Therefore, in this paper, we have studied the progress and structural parameters of PbSeS at different energy band gap and wavelength. The obtained results confirms that the attenuation of radiation versus wavelength is inversely proportional to the bandgap and also the mole fraction of lead increases with decrease in energy band gap. These findings confirm the quantum effects of the material and which can be utilized in solar cell and optoelectronics applications. The results are compared with available experimental data that supports the validity of the model reported.

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20

Dubey, Ritu, and Nikita Persai. "Theoretical Analysis of Semiconducting Sm1-xEuxS under Pressure." Circulation in Computer Science SED2017, no. 01 (April 9, 2017): 8–10. http://dx.doi.org/10.22632/sed-2017-ccs425.

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We have investigated the phase transition pressure and associated volume collapse in Sm1–XEuXS alloy (0≤x≤1) which shows transition from discontinuous to continuous as x is reduced. The calculated results from present approach are in good agreement with experimental data available for the end point members (x=0 and x=1). The results for the alloy counter parts are also in fair agreement with experimental data generated from the vegard’s law. An improved interaction potential model has been developed which includes coulomb, three body interaction, polarizability effect and overlap repulsive interaction operative up to second neighbor ions. It is found that the inclusion of polarizability effect has improved our results.

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Bhardwaj, Purvee. "Structural elastic and thermal properties of SrxCd1−x O mixed compounds — a theoretical approach." Materials Science-Poland 32, no. 3 (September 1, 2014): 350–57. http://dx.doi.org/10.2478/s13536-013-0197-2.

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AbstractIn the present paper, the structural and mechanical properties of alkaline earth oxides mixed compound SrxCd1−x O (0 ≤ x ≤ 1) under high pressure have been reported. An extended interaction potential (EIP) model, including the zero point vibrational energy effect, has been developed for this study. Phase transition pressures are associated with a sudden collapse in volume. Phase transition pressure and associated volume collapses [ΔV (Pt)/V(0)] calculated from this approach are in good agreement with the experimental values for the parent compounds (x = 0 and x = 1). The results for the mixed crystal counterparts are also in fair agreement with experimental data generated from the application of Vegard’s law to the data for the parent compounds.

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22

Tamura, Shota, Tsutomu Mashimo, Kenta Yamamoto, Zhazgul Kelgenbaeva, Weijan Ma, Xuesong Kang, Michio Koinuma, Hiroshi Isobe, and Akira Yoshiasa. "Synthesis of Pd-Fe System Alloy Nanoparticles by Pulsed Plasma in Liquid." Nanomaterials 8, no. 12 (December 18, 2018): 1068. http://dx.doi.org/10.3390/nano8121068.

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We synthesized Pd-Fe series nanoparticles in solid solution using pulsed plasma in liquid with Pd-Fe bulk mixture electrodes. The Pd-Fe atomic percent ratios were 1:3, 1:1, and 3:1, and the particle size was measured to be less than 10 nm by high-resolution transmission electron microscopy (HR-TEM). The nanoparticles showed face-centered cubic structure. The lattice parameter increased with increasing Pd content and followed Vegard’s law, and energy-dispersive X-ray spectra were consistent with the ratios of the starting samples, which showed a solid solution state. The solid solution structure and local structure were confirmed by HR-TEM and X-ray absorption fine structure.

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23

Wang, S. Z., S. F. Yoon, W. J. Fan, W. K. Loke, T. K. Ng, and S. Z. Wang. "The role of nitrogen-nitrogen pairs in the deviation of the GaAsN lattice parameter from Vegard’s law." Journal of Applied Physics 96, no. 4 (August 15, 2004): 2010–14. http://dx.doi.org/10.1063/1.1767614.

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24

Dang, Bo, Zengyun Jian, and Junfeng Xu. "Effect of phosphorus on the density and molar volume of Al–Si alloy without solidification shrinkage." International Journal of Materials Research 112, no. 10 (October 1, 2021): 782–86. http://dx.doi.org/10.1515/ijmr-2021-8286.

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Abstract The Al–Si alloys exhibit many unique properties, but not enough work has been dedicated to their thermophysical properties. In this work, the effect of phosphorus modifier on the density, molar volume and solidification shrinkage rate of Al-25% Si alloys was investigated by using the indirect Archimedes method. The results show that both density–temperature and molar volume–temperature curves show three inflection points: the liquidus temperature point, the eutectic transformation starting point and the finishing point. The density of the solidus linearly decreases and that of the liquidus linearly increases with phosphorus modifier content. Compared with Vegard’s law, the molar volumes show a negative deviation. Finally, the solidification shrinkage rate is calculated from the densities of solidus and liquidus.

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25

Hunter, B. A., C. J. Howard, and D. J. Kim. "Neutron Diffraction Study of Tetragonal Zirconias containing Tetravalent Dopants." Australian Journal of Physics 51, no. 3 (1998): 539. http://dx.doi.org/10.1071/p97060.

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In tetragonal zirconia, the cation is coordinated by two interpenetrating tetrahedra of oxygen ions, implying two different cation-oxygen bond lengths. Neutron powder diffraction was used to study tetragonal ZrO2–2 mol% Y2O3 incorporating various amounts of the different tetravalent ions Ge, Ti, Sn and Ce. Precise and accurate values for the lattice parameters and the variable oxygen position parameter have been obtained, and from these the bond lengths derived. The results are compared with those from an earlier X-ray and Raman study on the same materials. Of interest are the confirmation of the increase in cell volume occurring when Zr is replaced by the smaller Sn ion, and the observation of departures from Vegard’s law in the case of substitution of Zr by Ti.

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26

Singh, Anita, Ekta Sharma, and Umesh Kumar Sakalle. "Structural Properties of CaS_1-xSe_x Mixed Crystal under High Pressure." Advanced Materials Research 1047 (October 2014): 51–59. http://dx.doi.org/10.4028/www.scientific.net/amr.1047.51.

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The mixed ionic crystals are formed by the mixing of pure components and are truly crystalline and their lattice constants change linearly with concentration from one pure member to another. The present work is intended to investigate structural properties of CaS1-xSexunder high pressure. The structural properties of mixed compound CaS1-xSex(0≤x≤1) under high pressures have been evaluated using three body potential model (TBPM). This interaction potential has been calculated by using three model parameters. For this mixed compound, the experimental data has been generated by the application of Vegard’s law to experimental values available for pure end-point members.The Structure of CaS and CaSe has been Rock Salt (B1) at ambient pressure and with increasing pressure Rock Salt (B1) structure undergo a transition in Cesium Chloride (B2) at 40GPa and 38 GPa respectively and CaS1-xSexunder goes Rock Salt to Cesium Chloride (B1→B2) structure. The difference in phase transition pressure in end-point members is low. In the present work we have investigated structural properties at high pressure for five different concentration x (x=0, 0.25, 0.50, 0.75, 1) for CaS1-xSex. Phase transition pressure and relative volume collapse at different phase transition pressure for different values of x has been calculated. Predicted phase transition pressure and relative volume collapse are found in good agreement with experimental and other theoretical data. Linear variation of phase transition pressure and lattice constant of different composition show that Vegard’s law is valid for this alloy. We have evaluated the phase transition pressure from graphical analysis where the Gibb’s free energy difference ΔG [G(B1)-G(B2)] have been plotted against pressure (P) for CaS1-xSexfor different concentration x. The pressure at which ΔG approaches zero corresponds to phase –transition pressure (Pt). The relative volume changes, ΔV(Pt)/V(0), associated with the above mentioned compression have also been computed and plotted against pressure to get the phase diagram for CaS1-xSexin different concentration.

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27

Chelli, S., S. Touam, L. Hamioud, H. Meradji, S. Ghemid, and F. El Haj Hassan. "Ab-initio study of structural, elastic, electronic and thermodynamic properties of BaxSr1−xS ternary alloys." Materials Science-Poland 33, no. 4 (December 1, 2015): 879–86. http://dx.doi.org/10.1515/msp-2015-0108.

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AbstractThe structural, elastic, electronic and thermodynamic properties of BaxSr1−xS ternary alloys have been investigated using the full-potential (linearized) augmented plane wave method. The ground state properties, such as lattice constant, bulk modulus and elastic constants, are in good agreement with numerous experimental and theoretical data. The dependence of the lattice parameters, bulk modulus and band gap on the composition x was analyzed. Deviation of the lattice constant from Vegard’s law and the bulk modulus from linear concentration dependence (LCD) was observed. The microscopic origins of the gap bowing were explained by using the approach of Zunger et al. The thermodynamic stability of BaxSr1−xS alloy was investigated by calculating the excess enthalpy of mixing, ΔHm and the calculated phase diagram showed a broad miscibility gap with a critical temperature.

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28

Nakamura, Yuiga, Naoyuki Shibayama, Akiko Hori, Tomonori Matsushita, Hiroshi Segawa, and Takashi Kondo. "Crystal Systems and Lattice Parameters of CH3NH3Pb(I1–xBrx)3 Determined Using Single Crystals: Validity of Vegard’s Law." Inorganic Chemistry 59, no. 10 (March 18, 2020): 6709–16. http://dx.doi.org/10.1021/acs.inorgchem.9b03421.

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29

Lee, S., H. Miyazaki, S. D. Mahanti, and S. A. Solin. "Composition-drivenc-axis expansion of intercalated layered solids: 1D non–Vegard’s-law behavior in a 2D solid solution." Physical Review Letters 62, no. 26 (June 26, 1989): 3066–69. http://dx.doi.org/10.1103/physrevlett.62.3066.

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30

Ashrafi, A. B. M. Almamun, and Yusaburo Segawa. "Determination of Mg composition in Mg[sub x]Zn[sub 1−x]O alloy: Validity of Vegard’s law." Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures 23, no. 5 (2005): 2030. http://dx.doi.org/10.1116/1.2050653.

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31

Hossain, Shahzad, Mohammad Kamrul Hasan, S. K. Md Yunus, A. K. M. Zakaria, Tapash Kumar Datta, and Abul Kalam Azad. "Synthesis and Investigation of the Structural Properties of Al³⁺ Doped Mg Ferrites." Applied Mechanics and Materials 789-790 (September 2015): 48–52. http://dx.doi.org/10.4028/www.scientific.net/amm.789-790.48.

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The polycrystalline ferrites of MgAlxFe2-xO4 (0.0≤x≤0.4) were prepared by the conventional solid state ceramic method. The specimens were sintered at 13500C and X-ray diffraction experiments were done at room temperature which showed single phased cubic spinel structure. The lattice parameters were determined from the XRD data using Nelson-Riley extrapolation method and found to decrease with increasing Al concentration obeying Vegard’s law. The cation distribution and oxygen position parameters have also been determined by refining the data using the RIETAN-2000 in the Rietveld method which reveals that the samples possess cubic symmetry corresponding to the space group Fd-3m. The X-ray density and bulk density of each sample were calculated using the lattice parameters. The porosity has been determined from X-ray density (ρx) and bulk density (ρB) and it changes monotonically with Al content.

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32

Milanova, M., V. Donchev, S. Georgiev, K. Kirilov, and P. Terziyska. "Effect of growth temperature on nitrogen incorporation into GaAsN during liquid-phase epitaxy." Journal of Physics: Conference Series 2240, no. 1 (March 1, 2022): 012047. http://dx.doi.org/10.1088/1742-6596/2240/1/012047.

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Abstract We studied the growth temperature effect on nitrogen incorporation into GaAsN layers grown by liquid-phase epitaxy (LPE). The growth of dilute nitrides at nearly equilibrium conditions during LPE presents several major challenges: low solubility of nitrogen in Ga-melt, small incorporation efficiency in the solid and high volatility of nitrogen. GaAsN layers are grown from three different initial epitaxy temperatures: 580 °C, 680 °C and 780° C using GaN powder in the melt as a source of nitrogen. The N content in GaAsN is estimated from X-ray diffraction curves applying Vegard’s law. The local microstructure and surface morphology of the grown layers are studied by Fourier-transform infrared spectroscopy and atomic force microscopy measurements, respectively. The absorption edge and the composition dependence of the effective band gap are determined by employing optical transmission and surface photovoltage spectroscopies.

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33

Chettri, Dhanu, Khomdram Jolson Singh, Manish Mathew, and Nikhil Deep Gupta. "A novel numerical approach for the calculation of refractive index of Wurtzite InxGa1−xN." International Journal of Modern Physics B 32, no. 28 (November 7, 2018): 1850315. http://dx.doi.org/10.1142/s0217979218503150.

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Accurate values of refractive indices for In[Formula: see text]Ga[Formula: see text]N alloy as a function of indium mole fraction play a vital role in the modeling of In[Formula: see text]Ga[Formula: see text]N-based optoelectronics devices. This work extensively investigated, analyzed and derived a conclusive numerical approach to calculate the refractive index of In[Formula: see text]Ga[Formula: see text]N over a wide wavelength as a function of indium mole fraction based on Vegard’s law. The model is based on the fact that there is a strong correlation between the mole fraction (x) and the refractive index of ternary alloys A[Formula: see text]B[Formula: see text]C. An excellent agreement is observed between the computed values and experimental data which proves the effectiveness of our numerical approach.

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34

Боднарь, И. В. "Теплопроводность твердых растворов Cu-=SUB=-2-=/SUB=-ZnGe-=SUB=-1-x-=/SUB=-Sn-=SUB=-x-=/SUB=-Se-=SUB=-4-=/SUB=-." Физика и техника полупроводников 54, no. 2 (2020): 113. http://dx.doi.org/10.21883/ftp.2020.02.48888.9265.

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Abstract Cu_2ZnGeSe_4 and Cu_2ZnSnSe_4 and Cu_2ZnGe_1 –_ x Sn_ x Se_4-alloy crystals are grown by the Bridgman method (vertical variant). The composition and structure of the crystals are determined. It is established that both the initial compounds and their alloys crystalize with the formation of tetragonal structure. The unit-cell parameters a and c of the crystals are calculated, and the dependences of these parameters on the composition of the alloys are constructed. It is shown that, under variations in the composition parameter x , the parameters a and c vary in accordance with Vegard’s law. The thermal conductivity of the Cu_2ZnGeSe_4 and Cu_2ZnSnSe_4 compounds and Cu_2ZnGe_1 –_ x Sn_ x Se_4 alloys is measured in the temperature range 300–600 K. It is found that the thermal conductivity varies with x , with a minimum for the medium composition.

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35

Jahan, Nusrat, Faruque-uz-Zaman Chowdhury, and A. K. M. Zakaria. "Structural and electrical properties of chromium substituted nickel ferrite by conventional ceramic method." Materials Science-Poland 34, no. 1 (March 1, 2016): 185–91. http://dx.doi.org/10.1515/msp-2016-0028.

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AbstractPolycrystalline Cr substituted Ni ferrites [NiCrxFe2−xO4(0.0 ≤ x ≤ 1.0)] were synthesized by conventional ceramic method and sintered at 1350 °C in air. X-ray diffraction (XRD) patterns showing sharp peaks confirmed the formation of single phase cubic spinel structure. The lattice parameters of the samples were determined from the XRD data using Nelson-Riley extrapolation technique. They were found to decrease with increasing Cr concentration obeying Vegard’s law. X-ray density, bulk density and porosity were also calculated from the XRD data. The variation of DC resistivity with temperature was measured by two-probe method. The DC resistivity was found to decrease with increasing temperature indicating the semiconducting nature of the samples. Activation energy was calculated from the Arrhenius plot. AC resistivity, dielectric constant and loss tangent were measured in the frequency range of 1 kHz to 120 MHz at room temperature.

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Kong, Liang, Junqiu Guo, Joshua W. Makepeace, Tiancun Xiao, Heather F. Greer, Wuzong Zhou, Zheng Jiang, and Peter P. Edwards. "Rapid synthesis of BiOBrxI1-x photocatalysts: Insights to the visible-light photocatalytic activity and strong deviation from Vegard’s law." Catalysis Today 335 (September 2019): 477–84. http://dx.doi.org/10.1016/j.cattod.2019.02.013.

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Gultekin, A., P. Pashaei, Z. Khan, M. K. Ozturk, M. Tamer, and Y. Bas. "DFT and X-RAY study of structural, electronic, elastic and optical properties in Be1–XZnXS alloys depending on vegard’s law." International Journal of Computational Methods and Experimental Measurements 3, no. 4 (December 31, 2015): 340–49. http://dx.doi.org/10.2495/cmem-v3-n4-340-349.

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Zaman, Abid, Neeraj Kumar Shukla, Asad Ali, Aiyeshah Alhodaib, Vineet Tirth, Zahraa Hashim Kareem, Abdullah Hasan Jabbar, et al. "Effect of Cr Doping on the Structural, Optical and Dielectric Properties of MoO3 Microrods Synthesized by Sol-Gel Auto Combustion Method." Crystals 12, no. 9 (September 5, 2022): 1259. http://dx.doi.org/10.3390/cryst12091259.

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In the present work, pure and Cr-doped MoO3 microrods were successfully prepared through the sol gel auto combustion method. The phase evaluation and microstructural, dielectric, and optical properties of synthesized samples were investigated by using X-ray diffraction (XRD), scanning electron microscopy (SEM), energy dispersive spectroscopy (EDS), and an impedance analyzer (1 MHz–3 GHz). All the samples showed hexagonal structure with space group (P63). According to Vegard’s law, lattice parameters increase with the increase in chromium (Cr3+) contents. In addition, the Williamson–Hall (W–H) plot was drawn for evaluating the micro-strain (εW-H) and crystallite size (DW-H) parameters. From microstructural analysis it was found that the size of microrods increased along with Cr3+ contents. Decreasing band gap energy was observed (from 2.98 to 2.71 eV) with increasing Cr3+ contents. The variation of the dielectric constant and tangent loss of MoO3 microrods with respect to frequency were analyzed.

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Osman, Nafisah, Nurul Waheeda Mazlan, Oskar Hasdinor Hassan, and Zakiah Mohamed. "The Impact of Zr Substitution on the Crystal Structure of Yb Doped BaCeO₃ Solid Solution Prepared by a Sol-Gel Method." Solid State Phenomena 317 (May 2021): 412–16. http://dx.doi.org/10.4028/www.scientific.net/ssp.317.412.

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A modified sol-gel method using metal nitrate salts was adopted to synthesis proton conductor of Ba(Ce1-xZrx)0.95Yb0.05O2.975 where x=0.2, 0.3, 0.4, 0.5 and 0.6 ceramic powders. The aim of this work is to study the crystal structure of Yb-doped barium cerate solid solution at different Zr concentrations. The powder was calcined at 1100°C for 12 hours and pressed at 5 tons to become a pellet by a dry pressing technique. The pellet was sintered at 1400°C in air for 6 hours and ground to powder form prior to the X-ray diffraction measurement. The raw diffraction data of the sample at room temperature was analyzed using Rietveld refinement method in X’pert Highscore software. Cubic crystal structure was observed by software with goodness of fit in average 2.82. Phase formation, structure analysis and the empirical rule which holds the linear relation between lattice parameters at different Zr concentrations using Vegard’s Law were also presented and discussed.

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Singh, Ashish Kumar, Jahnvi Tiwari, Ashish Yadav, and Rakesh Kumar Jha. "Analysis of Si/SiGe Heterostructure Solar Cell." Journal of Energy 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/946406.

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Sunlight is the largest source of carbon-neutral energy. Large amount of energy, about 4.3 × 1020 J/hr (Lewis, 2005), is radiated because of nuclear fusion reaction by sun, but it is unfortunate that it is not exploited to its maximum level. Various photovoltaic researches are ongoing to find low cost, and highly efficient solar cell to fulfil looming energy crisis around the globe. Thin film solar cell along with enhanced absorption property will be the best, so combination of SiGe alloy is considered. The paper presented here consists of a numerical model ofSi/Si1-xGexheterostructure solar cell. The research has investigated characteristics such as short circuit current density (Jsc), generation rate (G), absorption coefficient (α), and open circuit voltage (Voc) with optimal Ge concentration. The addition of Ge content to Si layer will affect the property of material and can be calculated with the use of Vegard’s law. Due to this, short circuit current density increases.

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Dippong, Thomas, Erika Andrea Levei, Iosif Grigore Deac, Ioan Petean, and Oana Cadar. "Dependence of Structural, Morphological and Magnetic Properties of Manganese Ferrite on Ni-Mn Substitution." International Journal of Molecular Sciences 23, no. 6 (March 13, 2022): 3097. http://dx.doi.org/10.3390/ijms23063097.

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This paper presents the influence of Mn2+ substitution by Ni2+ on the structural, morphological and magnetic properties of Mn1−xNixFe2O4@SiO2 (x = 0, 0.25, 0.50, 0.75, 1.00) nanocomposites (NCs) obtained by a modified sol-gel method. The Fourier transform infrared spectra confirm the formation of a SiO2 matrix and ferrite, while the X-ray diffraction patterns show the presence of poorly crystalline ferrite at low annealing temperatures and highly crystalline mixed cubic spinel ferrite accompanied by secondary phases at high annealing temperatures. The lattice parameters gradually decrease, while the crystallite size, volume, and X-ray density of Mn1−xNixFe2O4@SiO2 NCs increase with increasing Ni content and follow Vegard’s law. The saturation magnetization, remanent magnetization, squareness, magnetic moment per formula unit, and anisotropy constant increase, while the coercivity decreases with increasing Ni content. These parameters are larger for the samples with the same chemical formula, annealed at higher temperatures. The NCs with high Ni content show superparamagnetic-like behavior, while the NCs with high Mn content display paramagnetic behavior.

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Rahmoune, M., A. Chahed, A. Amar, H. Rozale, A. Lakdja, O. Benhelal, and A. Sayede. "The effect of pressure and alloying on half-metallicity of quaternary Heusler compounds CoMnYZ (Z = Al, Ga, and In)." Materials Science-Poland 34, no. 4 (December 1, 2016): 905–15. http://dx.doi.org/10.1515/msp-2016-0120.

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AbstractIn this work, first-principles calculations of the structural, electronic and magnetic properties of Heusler alloys CoMnYAl, CoMnYGa and CoMnYIn are presented. The full potential linearized augmented plane waves (FP-LAPW) method based on the density functional theory (DFT) has been applied. The structural results showed that CoMnYZ (Z = Al, Ga, In) compounds in the stable structure of type 1+FM were true half-metallic (HM) ferromagnets. The minority (half-metallic) band gaps were found to be 0.51 (0.158), 0.59 (0.294), and 0.54 (0.195) eV for Z = Al, Ga, and In, respectively. The characteristics of energy bands and origin of minority band gaps were also studied. In addition, the effect of volumetric and tetragonal strain on HM character was studied. We also investigated the structural, electronic and magnetic properties of the doped Heusler alloys CoMnYGa1−xAlx, CoMnYAl1−xInx and CoMnYGa1−xInx (x = 0, 0.25, 0.5, 0.75, 1). The composition dependence of the lattice parameters obeys Vegard’s law. All alloy compositions exhibit HM ferromagnetic behavior with a high Curie temperature (TC).

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Deubner, H. Lars, Jascha Bandemehr, Antti J. Karttunen, and Florian Kraus. "A brief visit to the BeCl2/ZnCl2 system and the prediction of a new polymorph of ZnCl2." Zeitschrift für Naturforschung B 75, no. 5 (May 26, 2020): 491–96. http://dx.doi.org/10.1515/znb-2020-0023.

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AbstractReactions of zinc chloride with beryllium chloride in the molar ratios of 1:1 and 3:2 at T = 300°C in sealed ampoules lead to the formation of the two compounds Be1−xZnxCl2 (x = 0.563(2) and 0.489(3), respectively). Their composition and crystal structures were evidenced by single crystal X-ray structure analysis. Both compounds crystallize isotypic to β-BeCl2 in the tetragonal space group I41/acd, No. 142, tI96, with a = 10.7548(1), c = 19.4656(5) Å, V = 2251.50(7) Å3, Z = 32 at T = 100 K for the first and a = 10.7511(3), c = 19.2335(10) Å, V = 2223.1(2) Å3, Z = 32 at T = 100 K for the second compound. The positions of the Be atoms are mixed-occupied by Zn atoms. The compounds were additionally characterized by powder X-ray diffraction and infrared spectroscopy. Plots according to Vegard’s law allowed for extrapolation towards a neat ZnCl2 phase that would crystallize in the β-BeCl2 structure, which is the ZnI2 structure type. Quantum chemical calculations have confirmed that such a ZnCl2 modification would represent a true local minimum.

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Emanuel Thomet, Jonathan, Aman Kamlesh Singh, Mélanie Nelly Rouèche, Nils Toggwyler, Franz-Josef Haug, Gabriel Christmann, Sylvain Nicolay, et al. "Bandgap engineering of indium gallium nitride layers grown by plasma-enhanced chemical vapor deposition." Journal of Vacuum Science & Technology A 40, no. 6 (December 2022): 063102. http://dx.doi.org/10.1116/6.0002039.

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This paper reports on the fabrication of In[Formula: see text]Ga[Formula: see text]N (InGaN) layers with various compositions ranging from InN to GaN using a cost-effective low-temperature plasma-enhanced chemical vapor deposition (PECVD) method and analyzes the influence of deposition parameters on the resulting films. Single-phase nanocrystalline InGaN films with crystallite size up to 30 nm are produced with deposition temperatures in the range of 180–250 [Formula: see text]C using the precursors trimethylgallium, trimethylindium, hydrogen, nitrogen, and ammonia in a parallel-plate type RF-PECVD reactor. It is found that growth rate is a primary determinant of crystallinity, with rates below 6 nm/min producing the most crystalline films across a range of several compositions. Increasing In content leads to a decrease in the optical bandgap, following Vegard’s law, with bowing being more pronounced at higher growth rates. Significant free-carrier absorption is observed in In-rich films, suggesting that the highly measured optical bandgap (about 1.7 eV) is due to the Burstein–Moss shift.

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Ono, Satoshi, Yudai Hanaoka, Isao Matsui, Yorinobu Takigawa, Tokuteru Uesugi, and Kenji Higashi. "Influence of Impurities on Mechanical Properties of Electrodeposited Bulk Nanocrystalline Al." Advanced Materials Research 922 (May 2014): 574–79. http://dx.doi.org/10.4028/www.scientific.net/amr.922.574.

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Effect of typical impurities such as Fe, S, and Cl on mechanical properties of Al electrodeposited from a dimethylsulfone bath (DMSO2bath) were studied. Electrodeposition from a DMSO2bath was conducted to produce the bulk specimens with 0.08–0.24 at.% Fe, 0.47–0.84 at.% S, and 0.59–1.06 at.% Cl, varying the purity of aluminum chloride and current density. Decreasing the current density increased S contents and Cl contents, while the purity of aluminum chloride had no effect on chemical composition of the electrodeposits. The grain sizes were approximately 40–70 nm for Al electrodeposited from a DMSO2bath. The grain sizes decreased with increase in S contents and Cl contents. The electrodeposited bulk nanocrystalline Al exhibited hardness values of 1.56–1.92 GPa. These values were higher than predicted values based on Hall–Petch equation of pure Al. Lattice parameter of samples was less than pure Al. According to Vegard’s law, Fe solute decreases the lattice parameter of Al. These results indicated that the hardness of the electrodeposited bulk nanocrystalline Al was affected by the reduction in the grain size and solid solution strengthening from the Fe contaminant.

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M V, Santhosh Kumar, A. Alhadhrami, Shankarmurthy G J, M. G. Thriveni, and B. M. Prasanna. "Influence of divalent metal ion (Zn²⁺) on magnetic properties, curie temperature and DC electrical properties in Ce³⁺ substituted Ni-Zn ferrites." Physica Scripta 97, no. 1 (January 1, 2022): 015807. http://dx.doi.org/10.1088/1402-4896/ac4771.

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Abstract Nanoparticles of Ni1−xZnxCe0.1Fe1.9O4 ferrite substituted with Zn2+ ion concentrations (0.0, 0.2, 0.4, 0.6, 0.8 & 1.0) have been synthesised via aqueous citrate precursor auto combustion method. The obtained Powder x-ray diffraction data suggests a good crystalline phase; the crystallite size exists in the range of 14 ∼ 38 nm. The lattice constant of samples increases with Zn2+ concentration. It validates Vegard’s law and the decreasing trends in porosity of the samples were identified. The inhomogeneity in the grains was confirmed from FE-SEM. The EDS spectrogram attributes the good stoichiometry in the product. The Thermogravimetric analysis reveals that the crystallization occurred within the temperature 800 °C. The high-temperature DC conductivity of the samples shows that NTC behaviour. The Curie temperature and activation energy are estimated and the activation energy of carriers are found to be more at the paramagnetic region. The magnetic saturation (‘Ms*’) has maximum for Zn2+ = 0.2 (57.7 emu g−1) and coercive field (Hc) related with a radius of occupancy of Zn2+ ion validates the relation H c ∝ 1 r and also, the value of the remanence ratio suggests that isotropic magnetization took place in the heterogeneous material.

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Suri, Gurpreet Singh. "Synthesis and Structural Characterisation of Yttrium-Doped α-Zirconium Phosphate." ChemEngineering 5, no. 4 (December 2, 2021): 83. http://dx.doi.org/10.3390/chemengineering5040083.

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There has been a considerable amount of interest in the ion-exchange properties of layered zirconium phosphates. Potential applications in the remediation of nuclear waste have renewed interest in these inorganic materials, due to their high stability under the acidic conditions typically found in legacy waste pools. It has been well documented that the substitution of metals with different ionic radii into the frameworks of inorganic materials can alter the chemical properties including ion-exchange selectivity. The work presented here focusses on the synthesis and characterisation of yttrium-doped α-zirconium phosphates which are reported for the first time. Two different synthetic methods were used, reflux and hydrothermal syntheses, and the products were characterised by various methods such as powdered X-ray diffraction, MAS-NMR and scanning electron microscopy. It was found that up to 15% of zirconium could be replaced by yttrium before any noticeable impurity phases could be observed. Rietveld refinement from the doping showed that the products did not obey the Vegard’s law. However, the ion-exchange results clearly showed enhanced capacities and selectivity towards Co2+ ions for the substituted materials.

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Shih, Yu-Tai, Yu-Ching Tsai, and Der-Yu Lin. "Synthesis and Characterization of CuIn1−xGaxSe2 Semiconductor Nanocrystals." Nanomaterials 10, no. 10 (October 19, 2020): 2066. http://dx.doi.org/10.3390/nano10102066.

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In this paper, the synthesis and characterization of CuIn1−xGaxSe2 (0 ≤ x ≤ 1) nanocrystals are reported with the influences of x value on the structural, morphological, and optical properties of the nanocrystals. The X-ray diffraction (XRD) results showed that the nanocrystals were of chalcopyrite structure with particle size in the range of 11.5–17.4 nm. Their lattice constants decreased with increasing Ga content. Thus, the x value of the CuIn1−xGaxSe2 nanocrystals was estimated by Vegard’s law. Transmission electron microscopy (TEM) analysis revealed that the average particle size of the nanocrystals agreed with the results of XRD. Well-defined lattice fringes were shown in the TEM images. An analysis of the absorption spectra indicated that the band gap energy of these CuIn1−xGaxSe2 nanocrystals was tuned from 1.11 to 1.72 eV by varying the x value from 0 to 1. The Raman spectra indicated that the A1 optical vibrational mode of the nanocrystals gradually shifted to higher wavenumber with increasing x value. A simple theoretical equation for the A1 mode frequency was proposed. The plot of this equation showed the same trend as the experimental data.

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Hussain, A., S. Akbar Tahir, N. Ahmad, M. Hashim, A. Bashir Ziya, and S. Noreen. "A study on microstructure and magnetic properties of nanostructured CoxNi1-xMn0.5Fe1.5O4(x=0,0.25,0.5,0.75,1) spinel ferrites." Revista Mexicana de Física 67, no. 3 May-Jun (April 30, 2021): 527. http://dx.doi.org/10.31349/revmexfis.67.527.

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A low-temperature synthesis of novel nanostructured CoxNi1-xMn0.5Fe1.5O4(x=0,0.25,0.5,0.75,1) ferrites was carried out by sol-gel auto-combustion technique. The obtained nanostructured ferrites were investigated by employing the techniques of powder X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), energy dispersive X-ray spectroscopy (EDX) and vibrating sample magnetometry (VSM). The XRD diffractograms of the prepared ferrites revealed the formation of a spinel phase with face centered cubic (fcc) structure belonging to Fd- m space group. The average lattice parameter ‘a’ of ferrites exhibited a rise versus a rise in Co2+ concentration in accordance with the Vegard’s law. The SEM investigation of NiMn0.5Fe1.5O4 powder revealed an existence of octahedral-shaped morphology of ferrite grains. The TEM investigation of NiMn0.5Fe1.5O4 powder showed nanostructures of ferrite particles with sizes consistent with the crystallite sizes as estimated by Debye-Scherer’s formula. An EDX spectrum of NiMn0.5Fe1.5O4 powder confirmed its elemental composition. The M-H hysteresis loops recorded by VSM at room temperature revealed a dependence of coercivity (Hc), maximum magnetization (Mmax) and retentivity (Mr) on Co2+concentration. Due to the shape dependence of M-H loops on Co2+ concentration in compounds enabled their candidature for applications in memory devices and magnetic sensors.

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Kurbatkina, V. V., E. I. Patsera, T. A. Sviridova, P. A. Loginov, D. A. Sidorenko, A. S. Kolva, and E. A. Levashov. "Preparation, structure and properties of digoride’s solid solutions (Hf1 – хTaх)B2." Perspektivnye Materialy 1 (2023): 55–65. http://dx.doi.org/10.30791/1028-978x-2023-1-55-65.

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Porous sinters of solid solutions were obtained from the elements by the SHS method and then crushed in a ball mill to a fraction of d50 < 10 µm. Single-phase (Hf1 – хTах)B2 solid solutions with a wide range of compositions were obtained by a hot pressing. Detailed investigations of structure and properties were carried out. The plotted lattice parameters vs. solid solution stoichiometry diagrams confirmed the Vegard’s law. SEM, TEM, and EDX structural analysis demonstrated the existence of a HfВ2 – TaB2 single-phase solution region. The structure of samples (lamellas) of (Hf0.8Ta0.2)B2 and (Hf0.6Ta0.4)B2 solid solutions was analyzed by TEM. It has been established that with an increase in the content of tantalum, the size of subgrains decreases to 0.2 – 1 µm. This correlates with the CSR size determined by the X-ray diffraction method. Studies of mechanical properties of single-phase solid solutions have shown that (Hf0.8Ta0.2)B2 and (Hf0.6Ta0.4)B2 possessed extremely high hardness of 63–70 GPa and elastic modulus of 550 – 587 GPa. Electrical resistance dependence on temperature was investigated, values of heat capacity, thermal diffusivity and thermal conductivity coefficients were determined in a wide range of (Hf 1 – xTax)B2 solid solution compositions.

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Journal articles on the topic 'Vegard’s Law'

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