Anomalous temperature behaviour of the shear elastic constant C44 in tantalum

Wałker, E.; Bujard, P.

doi:10.1016/0038-1098(80)90957-6

Cited by 48 publications

(34 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[17,18,19] The calculated thermal expansion coefficients of bcc Ta crystal are in good agreement with the experimental results expected for a higher temperature region than ;2000 K. For this higher temperature region, experimental results, by symbols 3, show the anomalous increase of the thermal expansion coefficients as increasing the temperature (which might be attributed to the extrinsic causes such as the oxidation of the specimen). Instead, the present SMM calculations of the thermal lattice expansion coefficients of bcc Ta crystal (solid curve) are in good agreement with the theoretical calculations of Reference 20, symbols s, using the anharmonic particle in a cell (PIC) model.…”

Section: A Thermodynamic Quantities Of Metalssupporting

confidence: 82%

Thermodynamic properties and phase diagram by the statistical moment and cluster variation methods: Application to pure metals and Ta-W alloys

Masuda‐Jindo

Hùng

Turchi

2006

Metall Mater Trans A

View full text Add to dashboard Cite

The thermodynamic quantities of metals and alloys are studied using the moment method in the quantum statistical mechanics, going beyond the quasi-harmonic (QH) approximations. Including the power moments of the atomic displacements up to the fourth order, the free energies and the related thermodynamic quantities are derived explicitly in closed analytic forms. The configurational entropy term is taken into account by coupling the moment expansion scheme with the cluster variation method (CVM). The energetics of the binary (TaW) alloys are treated within the framework of the firstprinciples tight-binding linear muffin-tin orbital (TB-LMTO) method coupled to the coherent potential approximation (CPA) and generalized perturbation method (GPM). The equilibrium phase diagrams are calculated for the refractory Ta-W bcc alloys. I. INTRODUCTIONTHE explicit analytic calculations of the thermodynamic quantities of metals and alloys are of great importance for the fundamental understanding of phase stabilities and phase transitions and also for the purpose of materials (alloy) designs. [1,2] However, they have been calculated so far extensively by using the molecular dynamics methods or the Monte Carlo simulations. [3,4] It is the purpose of the present article to study the thermodynamic quantities of metals and alloys using the moment method in the quantum statistical mechanics, hereafter referred to as the statistical moment method (SMM). [5,6] We first derive the Helmholtz free energy formula, C 5 E À TS, of metals and alloys using the fourth-order moment approximation, and then calculate the thermodynamic quantities, i.e., thermal lattice expansions, root-mean-square atomic displacements, specific heats, Grüneisen constants, elastic moduli, and melting temperatures. The application calculations using the SMM are performed for ordinary cubic metals and for the bcc alloys. Recently, much attention has been paid to alloy systems made of refractory metals of columns VB and VIB of the Periodic Table [7,8] and, in particular, Nb, Mo, Ta, and W, which display high melting temperature space and nuclear applications. In view of this, we calculate the equilibrium phase diagram of Ta-W alloys including the effects of thermal lattice vibrations. II. THEORYWe derive the thermodynamic quantities of metals and alloys, taking into account the higher order (fourth-order) anharmonic contributions in the thermal lattice vibrations going beyond the quasi-harmonic (QH) approximation. The basic equations for obtaining thermodynamic quantities are derived in the following manner: The equilibrium thermal lattice expansions are calculated by the force balance criterion and then the thermodynamic quantities are determined for the equilibrium lattice spacings. The anharmonic contributions to the thermodynamic quantities are given explicitly in terms of the power moments of the thermal atomic displacements.We consider a quantum system, which is influenced by supplemental forces a i in the space of the generalized coordinates q i . [5,6] The Hami...

show abstract

Section: A Thermodynamic Quantities Of Metalssupporting

confidence: 82%

Thermodynamic properties and phase diagram by the statistical moment and cluster variation methods: Application to pure metals and Ta-W alloys

Masuda‐Jindo

Hùng

Turchi

2006

Metall Mater Trans A

View full text Add to dashboard Cite

show abstract

“…A sample of these results for Ta is displayed in Fig. 6 and compared with available experimental data [23][24][25]. In this case, anharmonic effects are found to be small and the observed temperature dependence of the elastic moduli at ambient-pressure [23] is well described by both our quasi-harmonic and Monte Carlo methods.…”

Section: B Atomistically-informed Dd Simulations Of Plasticitymentioning

confidence: 69%

“…6 and compared with available experimental data [23][24][25]. In this case, anharmonic effects are found to be small and the observed temperature dependence of the elastic moduli at ambient-pressure [23] is well described by both our quasi-harmonic and Monte Carlo methods. Accurate experimental moduli are also known at very low pressure from ultrasonic measurements [24] and have recently been measured in the diamond-anvil cell (DAC) to 105 GPa with a stress/angle-resolved x-ray diffraction (SAX) technique [25].…”

Section: B Atomistically-informed Dd Simulations Of Plasticitymentioning

confidence: 71%

Robust quantum-based interatomic potentials for multiscale modeling in transition metals

et al. 2006

View full text Add to dashboard Cite

First-principles generalized pseudopotential theory (GPT) provides a fundamental basis for transferable multi-ion interatomic potentials in transition metals and alloys within density-functional quantum mechanics. In the central bcc metals, where multi-ion angular forces are important to materials properties, simplified model GPT or MGPT potentials have been developed based on canonical d bands to allow analytic forms and large-scale atomistic simulations. Robust, advanced-generation MGPT potentials have now been obtained for Ta and Mo and successfully applied to a wide range of structural, thermodynamic, defect and mechanical properties at both ambient and extreme conditions. Selected applications to multiscale modeling discussed here include dislocation core structure and mobility, atomistically informed dislocation dynamics simulations of plasticity, and thermoelasticity and high-pressure strength modeling. Recent algorithm improvements have provided a more general matrix representation of MGPT beyond canonical bands, allowing improved accuracy and extension to f-electron actinide metals, an order of magnitude increase in computational speed for dynamic simulations, and the development of temperature-dependent potentials.

show abstract

“…The linear temperature dependence is suggested by available P = 0 experimental data on G over the temperature range 0 ≤ T ≤ T m [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. This straight-line representation turns out to be quite accurate: the maximum deviation of the data from the corresponding fitted lines is ∼ 5 % for 21 of the 22 metals analyzed in [30].…”

Section: Experimental Verificationmentioning

confidence: 99%

“…The data run from T = 0 to T m for Al [5], Ar [6], Bi [7], Cd [8], Cs [9], Cu [10], In [11], K [12], Na [13], Nb [14], Ne [15], Pb [11], Sn [7], Ta [16], Te [17], Xe [18], and Zn [19].…”

Section: Introductionmentioning

confidence: 99%

Analytic model of the shear modulus at all temperatures and densities

2003

View full text Add to dashboard Cite

An analytic model of the shear modulus applicable at temperatures up to melt and at all densities is presented. It is based in part on a relation between the melting temperature and the shear modulus at melt. Experimental data on argon are shown to agree with this relation to within 1%. The model of the shear modulus involves seven parameters, all of which can be determined from zero-pressure experimental data. We obtain the values of these parameters for 11 elemental solids. Both the experimental data on the room-temperature shear modulus of argon to compressions of ∼ 2.5, and theoretical calculations of the zero-temperature shear modulus of aluminum to compressions of ∼ 3.5 are in good agreement with the model. Electronic structure calculations of the shear moduli of copper and gold to compressions of 2, performed by us, agree with the model to within uncertainties.

show abstract

Anomalous temperature behaviour of the shear elastic constant C44 in tantalum

Cited by 48 publications

References 11 publications

Thermodynamic properties and phase diagram by the statistical moment and cluster variation methods: Application to pure metals and Ta-W alloys

Thermodynamic properties and phase diagram by the statistical moment and cluster variation methods: Application to pure metals and Ta-W alloys

Robust quantum-based interatomic potentials for multiscale modeling in transition metals

Analytic model of the shear modulus at all temperatures and densities

Contact Info

Product

Resources

About