First principles calculation of the elastic constants of intermetallic compounds: metastable Al3Li

1991 ◽  
Vol 6 (2) ◽  
pp. 324-329 ◽  
Author(s):  
X-Q. Guo ◽  
R. Podloucky ◽  
A.J. Freeman
Keyword(s):  
Young’S Modulus ◽  
Elastic Constants ◽  
First Principles ◽  
Local Density ◽  
Young's Modulus ◽  
Poisson Ratio ◽  
First Principles Calculation ◽  
Full Potential ◽  
A Value ◽  
Experimental Values

We report first principles local density calculations for the metastable Al3Li intermetallic compound with cubic L12 crystal structure using the full-potential linearized augmented plane wave method. From the second derivative of the total energy as a function of volume, and generated tetragonal and trigonal lattice distortions, the elastic constants C11, C12, and C44 were derived yielding C11 = 158 GPa, C12 = 29.4 GPa, and C44 = 57.7 GPa. Because of the very high Young's modulus (E = 141 GPa) compared, for example, to pure Al (E = 66 GPa), it is suggested that Al3Li plays an important role in strengthening the Al–Li alloys. The calculated Young's modulus appears in good agreement with experimental estimates when the experimental values are extrapolated to 0 K. Although the Young's modulus of Al3Li is increased in comparison to Al, the calculated bulk modulus is decreased to a value of 72 GPa as compared to pure Al (82 GPa), in agreement with experiment. As a result, the Poisson ratio is reduced to ŝ = 0.173 as compared to the value 1/3 for an isotropic medium. Because of this and the high Young's modulus, the calculated Debye temperature ΘD at 0 K amounts to 672 K, which is substantially larger than ΘD for Al, which is about 400 K.

Tension-induced mechanical properties of stanene

2016 ◽  
Vol 30 (12) ◽  
pp. 1650146 ◽  
Author(s):  
Lele Tao ◽  
Chuanghua Yang ◽  
Liyuan Wu ◽  
Lihong Han ◽  
Yuxin Song ◽  
...  
Keyword(s):  
Young’S Modulus ◽  
Elastic Constants ◽  
First Principles ◽  
Young's Modulus ◽  
Poisson Ratio ◽  
Group Iv ◽  
First Principles Calculations ◽  
Stress Strain Relation ◽  
Group Iv Elements ◽  
Internal Atom

In this paper, elastic properties of stanene under equiaxial or uniaxial tensions along armchair and zigzag directions are investigated by first-principles calculations. The stress–strain relation is calculated and the relaxation of the internal atom positions is analyzed. The high-order elastic constants are calculated by fitting the polynomial expressions. The Young’s modulus and Poisson ratio of the stanene is calculated to be 24.14 N/m and 0.39 N/m, respectively. The stanene exhibits lower Young’s modulus than those of the proceeding group IV elements, which is attributed to the smaller [Formula: see text]–[Formula: see text] bond energy in stanene than those of silicene and germanene. Calculated values of ultimate stresses and strains, second-order elastic constants (SOCEs) and the in-plane Young’s modulus are all positive. It proves that stanene is mechanically stable.

Elastic constants of inflated lobes of dog lungs

1976 ◽  
Vol 40 (4) ◽  
pp. 508-513 ◽  
Author(s):  
S. J. Lai-Fook ◽  
T. A. Wilson ◽  
R. E. Hyatt ◽  
J. R. Rodarte
Keyword(s):  
Bulk Modulus ◽  
Young’S Modulus ◽  
Elastic Constants ◽  
Young's Modulus ◽  
Poisson Ratio ◽  
Inflation Pressure ◽  
Initial State ◽  
Volume Curve ◽  
Pressure Volume Curve ◽  
Indentation Tests

The elastic constants of dog lungs were determined at various degrees of inflation. In one set of experiments, the lobes were subjected to deformations that approximated the conditions of uniaxial loading. These data, together with the bulk modulus data obtained from the local slope of the pressure-volume curve, were used to determine the two elastic moduli that are needed to describe small nonuniform deformations about an initial state of uniform inflation. The bulk modulus was approximately 4 times the inflation pressure, and Young's modulus was approximately 1.5 times the inflation pressure. In a second set of experiments, lobes were subjected to indentation tests using cylindric punches 1–3 cm in diameter. The value for Young's modulus obtained from these data was slightly higher, approximately twice the inflation pressure. These experiments indicate that the lung is much more easily deformable in shear than in dilatation and that the Poisson ratio for the lung is high, approximately 0.43.

scholarly journals The Elastic Constants of the Single Crystal of the Mg-Zn-Zr-REM Alloy from the Data of the Elastic Anisotropy and the Texture of the Polycrystalline Sheet

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
S. V. San’kova ◽  
N. M. Shkatulyak ◽  
V. V. Usov ◽  
N. A. Volchok
Keyword(s):  
Single Crystals ◽  
Young’S Modulus ◽  
Elastic Constants ◽  
Elastic Anisotropy ◽  
Young's Modulus ◽  
Rare Earth Metals ◽  
Alloy Sheet ◽  
Pole Figures ◽  
Integral Characteristics ◽  
Experimental Values

The measuring of the constants of single-crystals requires the availability of crystals of relatively big size. In this paper the elastic constants of the single crystals of magnesium alloy with zinc, zirconium, and rare earth metals (REM) were determined by means of the experimental anisotropy of Young’s modulus and integral characteristics of texture (ICT), which were found from pole figures. Using these constants the anisotropy of Young’s modulus of alloy sheet ZE10 was calculated. Deviation of calculated values from experimental values did not exceed 2%.

Calculation of the parameters of mechanical properties of the heart muscle

2020 ◽  
Vol 12 ◽  
pp. 42-52
Author(s):  
S. A. Muslov ◽  
◽  
A. I. Lotkov ◽  
S. D. Arutyunov ◽  
T. M. Albakova ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Young’S Modulus ◽  
Elastic Constants ◽  
Heart Muscle ◽  
Human Heart ◽  
Young's Modulus ◽  
Experimental Values ◽  
Two Parameter

A review of studies of the mechanical properties of human and animal heart tissues has been performed. Based on literature data, a form of approximating function is found for the dependence of the Young’s modulus of the ventricles of the human heart on the magnitude of the deformation. The average values of the Young’s modulus and other elastic constants were calculated and compared with the known experimental values. The coefficients C1 and C2 of the two-parameter hyperelastic myocardial Mooney-Rivlin model are calculated.

Effect of Ce Substitution on Mechanical and Thermal Properties of Tetragonal YSZ: First-Principles Calculations

2015 ◽  
Vol 1120-1121 ◽  
pp. 73-84
Author(s):  
Lei Jin ◽  
Pei Zhong Li ◽  
Guo Dong Zhou ◽  
Wei Gao ◽  
Jiang Ning Ma ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Thermal Properties ◽  
Sound Velocity ◽  
Young’S Modulus ◽  
Elastic Constants ◽  
First Principles ◽  
Density Functional ◽  
Young's Modulus ◽  
Mechanical And Thermal Properties ◽  
Ce Substitution

The effect of impurity Ce on the mechanical and thermal properties of tetragonal ZrO2 stabilized by rare earth element Y (YSZ) have been studied using first principles density functional theory within generalized gradient approximation (GGA) for the exchange correlation potential. The predicted elastic constants indicate that YSZ and Ce doped YSZ (CeYSZ) are mechanically stable structures. And then the numerical estimates of bulk modulus, shear modulus, Young’s modulus, Poisson’s ratio, sound velocity and minimum thermal conductivity were performed using the calculated elastic constants and analyzed for the first time. The values of sound velocity from different orientations are also reported. The agreement between the results of the available experiments and our calculations was satisfactory. Our calculated results indicate that Young’s modulus, hardness, mean sound velocity and minimum thermal conductivity of YSZ can be decreased by Ce substitution. The reasons are from the “softened” Ce-O bond strength using bond population and relative volume change under external hydrostatic pressure. Chemical bonding nature was also analyzed from the density of states and electron density difference.

First-Principles Calculation of the Work Functions for the High-Index Copper Surfaces

2003 ◽  
Vol 10 (02n03) ◽  
pp. 207-211 ◽  
Author(s):  
I. G. Kim ◽  
B. C. Lee ◽  
J. I. Lee
Keyword(s):  
Local Density ◽  
High Index ◽  
First Principles Calculation ◽  
Full Potential ◽  
Kelvin Probe ◽  
Generalized Gradient ◽  
Copper Surfaces ◽  
Work Functions ◽  
Anisotropy Model ◽  
Experimental Values

We calculated the work functions (WFs) for the high-index copper surfaces, (112), (321), and (413), as well as the low-index surfaces, (111), (100), and (110), using the full-potential linearized augmented plane wave (FLAPW) method within both the local density approximation (LDA) and the generalized gradient approximation (GGA). It is found that the GGA lowers rigidly the WFs about 0.46–0.49 eV from the values obtained by the LDA, for all the surfaces, and the experimental values for low-index surfaces are in between the calculated values by the LDA and GGA. It is also found that the WF does not decrease further, for the surfaces with higher indices than (112). This result is different from that of the recent measurements by the Kelvin probe technique [Appl. Phys. Lett.79, 4337 (2001)], which shows a linear dependence of WF on the atomic packing density. The result of our calculation is consistent with the WF anisotropy model, which was recently applied to tungsten surfaces.

Elastic Constants and Related Properties of the Group III-Nitrides

1995 ◽  
Vol 395 ◽  
Author(s):  
Kwiseon Kim ◽  
Walter R. L. Lambrecht ◽  
B. Segall
Keyword(s):  
Elastic Constants ◽  
First Principles ◽  
Bond Angle ◽  
Local Density ◽  
Group Iii Nitrides ◽  
Internal Displacement ◽  
Orbital Method ◽  
Model Parameters ◽  
Full Potential ◽  
Group Iii

ABSTRACTThe elastic constants of the Group-III nitrides, c-BN, AlN and GaN were calculated from first-principles using the full-potential linear muffin-tin orbital method and local density approximation. The relation between the elatic constants in zincblende and wurtzite is studied by means of a tensor coordinate transformation approach. The latter combined with a correction for the internal displacement of the rotated tetrahedra is found to provide good results for the Ch11Ch12 and Ch44 but not for Ch13 and Ch33. These two require explicit calculations involving distortions along the c-axis. The calculations also provide information on the transverse optical phonons. By deriving Keating model parameters we show that BN is much stiffer against bond-angle distortions than the other nitrides.

scholarly journals Insight into Physical and Thermodynamic Properties of X3Ir (X = Ti, V, Cr, Nb and Mo) Compounds Influenced by Refractory Elements: A First-Principles Calculation

Crystals ◽  
2019 ◽  
Vol 9 (2) ◽  
pp. 104 ◽  
Author(s):  
Dong Chen ◽  
Jiwei Geng ◽  
Yi Wu ◽  
Mingliang Wang ◽  
Cunjuan Xia
Keyword(s):  
Thermodynamic Properties ◽  
First Principles ◽  
Density Functional ◽  
Local Density ◽  
First Principles Calculation ◽  
Generalized Gradient ◽  
Functional Theory ◽  
Debye Temperatures ◽  
Experimental Parameters ◽  
Experimental Values

The effects of refractory metals on physical and thermodynamic properties of X3Ir (X = Ti, V, Cr, Nb and Mo) compounds were investigated using local density approximation (LDA) and generalized gradient approximation (GGA) methods within the first-principles calculations based on density functional theory. The optimized lattice parameters were both in good compliance with the experimental parameters. The GGA method could achieve an improved structural optimization compared to the LDA method, and thus was utilized to predict the elastic, thermodynamic and electronic properties of X3Ir (X = Ti, V, Cr, Nb and Mo) compounds. The calculated mechanical properties (i.e., elastic constants, elastic moduli and elastic anisotropic behaviors) were rationalized and discussed in these intermetallics. For instance, the derived bulk moduli exhibited the sequence of Ti3Ir < Nb3Ir < V3Ir < Cr3Ir < Mo3Ir. This behavior was discussed in terms of the volume of unit cell and electron density. Furthermore, Debye temperatures were derived and were found to show good consistency with the experimental values, indicating the precision of our calculations. Finally, the electronic structures were analyzed to explain the ductile essences in the iridium compounds.

Elastic Constants of A Laves Phase Compound: C15 NbCr2

1996 ◽  
Vol 460 ◽  
Author(s):  
Alim Ormeci ◽  
F. Chu ◽  
John M. Wills ◽  
S. P. Chen ◽  
R. C. Albers ◽  
...  
Keyword(s):  
Single Crystal ◽  
Elastic Constants ◽  
Energy Method ◽  
First Principles ◽  
Elastic Moduli ◽  
Full Potential ◽  
Self Consistent ◽  
Phase Compound ◽  
Direction Dependence ◽  
Experimental Values

ABSTRACTThe single-crystal elastic constants of C15 NbCr2 have been computed by using a first-principles, self-consistent, full-potential total energy method. From these single-crystal elastic constants the isotropie elastic moduli are calculated using the Voigt and Reuss averages. The calculated values are in fair agreement with the experimental values. The implications of the results are discussed with regards to Poisson's ratio and the direction dependence of Young's modulus.

First-Principles Calculations of Thermoelectric PbSe2 Compound to Predict its Elastic Properties

2019 ◽  
Vol 956 ◽  
pp. 46-54
Author(s):  
Jia Fu ◽  
Tian Hou ◽  
Jing Rui Chen
Keyword(s):  
Young’S Modulus ◽  
Elastic Properties ◽  
First Principles ◽  
Elastic Anisotropy ◽  
Young's Modulus ◽  
Poisson Ratio ◽  
Structural Parameters ◽  
Homogenization Method ◽  
Parameter Method ◽  
G Ratio

The influencing effect of pressure on structural stability and elastic properties of PbSe2 compound is mainly investigated by first-principles method and homogenization method of the Y parameter. The optimized structural parameters at zero pressure are a=b=6.446Å, c=7.887Å (GGA method) and a=b=6.316Å, c=7.651Å (LDA method), which has good agreement with the experimental and theoretical values. Our calculated lattice parameters and Se-Se bond length are in excellent agreement with experimental data. PbSe2 compound is energetically stable with a good alloying ability. The elastic constants are calculated, and then the bulk modulus, shear modulus, Young’s modulus, Poisson’s ratio and anisotropy factor are determined. Besides, Y parameter method is used to investigate changes of the Poisson ratio, Young’s and shear moduli of PbSe2 within different normal orientation crystal planes. Results show that: 1) Young’s modulus is about 48.37 GPa from GGA and 58.87 GPa from LDA by Reuss-Voigt-Hill estimation, which is averaged about 53.62 GPa; 2) The PbSe2 compound is ductile according to B/G ratio. The universal anisotropic index AU shows that PbSe2 exhibits a fairly high elastic anisotropy.

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