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Units and Significant Figures
Published in Patrick F. Dunn, Fundamentals of Sensors for Engineering and Science, 2019
In 1670, a decimal system based on the length of one arc minute of the great circle of the earth was proposed by Gabriel Mounton. Jean Picard, in 1671, proposed that the length standard be defined as the length of a clock’s pendulum whose period was a specified time. It was not until 1790 when a commission appointed by the French Academy of Sciences developed and formalized a decimal-based system defining length, mass, and volume. The unit of length, the meter, equaled one ten-millionth of the distance from the north pole to the equator along the meridian of the earth running from Dunkerque, France, through Paris to Barcelona, Spain. The unit of mass, the gram, was defined in terms of a liquid volume, where one gram equaled the mass of one cubic centimeter of water at its temperature of maximum density. The unit of volume, the liter, equaled one cubic decimeter. This approach established mass and volume as supplementary units in terms of a base unit (the meter), which was to a physical standard (the earth’s circumference).
Units and Significant Figures
Published in Patrick F. Dunn, Michael P. Davis, Measurement and Data Analysis for Engineering and Science, 2017
Patrick F. Dunn, Michael P. Davis
In 1670, a decimal system based on the length of one arc minute of the great circle of the earth was proposed by Gabriel Mounton. Jean Picard, in 1671, proposed that the length standard be defined as the length of a clock’s pendulum whose period was a specified time. It was not until 1790 when a commission appointed by the French Academy of Sciences developed and formalized a decimal-based system defining length, mass, and volume. The unit of length, the meter, equaled one ten-millionth of the distance from the north pole to the equator along the meridian of the earth running from Dunkerque, France, through Paris to Barcelona, Spain. The unit of mass, the gram, was defined in terms of a liquid volume, where one gram equaled the mass of one cubic centimeter of water at its temperature of maximum density. The unit of volume, the liter, equaled one cubic decimeter. This approach established mass and volume as supplementary units in terms of a base unit (the meter), which was to a physical standard (the earth’s circumference).
Nanosensors for Industrial Applications
Published in Vinod Kumar Khanna, Nanosensors, 2021
The unit mIU/mL stands for milli-international units per milli-liter. The miU (milli-international unit) is 1/1000th of an international unit (IU), which is a unit for the amount of a substance (mass or volume). The mass or volume of a substance present in 1 IU varies with the substance and its biological activity. It is the amount agreed upon by scientists and doctors for easy comparison across substances. The mL (milli-liter) is unit of volume equal to 1/1000th of a liter. See also Section 9.2.7.
Charge transfer of CsMnFe-Prussian blue analogue induced by pressure and temperature
Published in Phase Transitions, 2022
Qinghang Zhang, Jiajun Mo, Yimin Xie, Yanfang Xia, Min Liu
Powder X-ray diffraction was performed at room temperature with the CsMn[Fe (CN)6]·xH2O samples treated by 0 Mpa and 40 Mpa (Figure 1). It is confirmed that the samples have a typical face-centered cubic (Fm-3 m) structure before and after pressure treatment, and the lattice constants are 10.504 Å and 10.499 Å fitted by the Bragg formula () to obtain. The unit cell volume was reduced by 1.6%. A structural transition of RbMn[Fe(CN)6] from the HT phase (F-43 m) to the LT phase (I-4m2) to the metastable phase (P-4n2) by pressure was reported by Y. Moritomo et al. [9]. The crossover pressure for the two-phase state structural transition is about 0.3 GPa and 1.8 GPa at 300 K, respectively. Some evidence suggests that the size of the alkali metal cation shows a negative correlation with the changes of the M-NC angle induced by pressure [18]. The radius of the Cs ion is larger than that of the Rb ion, and thus the pressure required to observe structural distortions in RbMn[Fe(CN)6] should be greater than 0.3 GPa or 1.8 GPa. In addition, the charge transfer phase transition between the HT and LT phases of CsMnFe-PBA was observed to induce no crystal structure transformation (Fm-3 m to Fm-3 m) and was accompanied only by a slight reduction in the lattice constant [7]. This explains why the new high-pressure phase, if any, does not occur at a low pressure of 40 MPa.
Band engineering of modified rhombohedral Cu4Mn2Te4: ab initio approach
Published in Philosophical Magazine, 2022
S. Priyadharshini, M. Sundareswari, E. Viswanathan, D. S. Jayalakshmi, M. Manjula
Volume optimisation is carried out for each of NM, FM, and AFM phases of rhombo Cu4Mn2Te4 by varying V/V0 from −10 to 10 in steps of 5. Here, V represents the reduced new unit cell volume and V0 represents the equilibrium unit cell volume at ambient condition. Total energy ‘E’ vs. ‘V/V0’ is fitted into the Birch Murnaghan Equation of states [51]. Volume optimisation curves of Cu4Mn2Te4 for NM, FM and AFM phases and comparative ‘E’ vs. ‘V/V0’ curves are shown in Figure 5(a) and 5(b). From Figure 5(b), it is inferred that Cu4Mn2Te4 (160_R3 m) compound energetically prefers the AFM phase, as this phase has the minimum total energy difference of 0.74973 Rydberg per formula unit, when compared to the corresponding NM phase. Table 6 (refer supplementary) shows the calculated values of lattice parameters (a and c), volume of rhombohedra unit cell, total energy, hydrostatic pressure, c/a ratio for various V/V0 at each of NM, FM and AFM phases of Cu4Mn2Te4 (160_R3m). Optimised Wyckoff positions of modified rhombo Cu4Mn2Te4 structure at ground state NM phase and AFM phase are calculated and are listed in Tables 5 and 10, respectively.
Influence of hydrogen on mechanical and thermodynamic properties of α-Nb5Si3 from first-principles calculations
Published in Philosophical Magazine, 2019
Yong Pan, Shuang Chen, Zhihang Shu
To reveal the H-doped mechanism, we further investigate the crystal structure of H-doped Nb5Si3. As listed in Table 1, the calculated lattice parameters of the parent Nb5Si3 are a = 6.601 Å and c = 11.949 Å, respectively, which are in good agreement with the theoretical results and experimental data [20,29]. When hydrogen is introduced, H-doping results in lattice expansion of the parent Nb5Si3 along the a- axis and c- axis because the calculated lattice parameters a-axis and c-axis of H-doped Nb5Si3 are larger than that of the parent Nb5Si3. The lattice expansion of H-doped Nb5Si3 is attributed to the discrepancy of the atomic radius because the atomic radius of hydrogen is close to the interstitial radius. This result is affirmed by the unit-cell volume. From Table 1, the calculated unit-cell volume of H-doped Nb5Si3 is slightly larger than that of the parent Nb5Si3. It is worth noticing that the calculated c- axis of H-ST(1) site is larger than that of other H-doped sites. However, the calculated a-axis of H-ST(3) site is larger than that of other H-doped sites. This discrepancy is related to the doped site, which is demonstrated by the chemical bonding and charge density.