Heat capacity and entropy of tungsten carbide

Andon, R. J. L.; Martin, John F.; Mills, Kenneth C.; Jenkins, T.R.

doi:10.1016/0021-9614(75)90241-4

Cited by 19 publications

(5 citation statements)

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“…The detailed information on their structure parameters and formation energies are listed in Table S2 in the SI. The calculated lattice constants of δ-WC and γ-WC by the PBE functional are in good agreement (maximum deviation being less than 3%) with the available experimental data. ,, The calculated formation energy of δ-WC at 0 K by the PBE functional is reasonably close to the experimentally reported standard enthalpy of formation of δ-WC at 298.15 K. , These results indicate the reliability of the PBE functional in the present study. In both δ-WC and L ′3-WC, the W atom is surrounded by six equidistant C atoms in a trigonal-prismatic coordination.…”

Section: Resultssupporting

confidence: 85%

Toward a Unified Understanding of W₂C Polymorphic Structures by First-Principles Calculations

Luo

Hou

Lin

et al. 2023

Crystal Growth & Design

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Tungsten subcarbide (W2C) is widely applied to industrial catalysts, military industries, and aerospace facilities because it possesses excellent high-temperature performance and superior mechanical properties. However, contradictory data on the crystal structure of W2C including its disordered and different ordered phases have been often reported in the literature, and atomic-scale understanding of W2C polymorphic structures has not yet reached a consensus. Based on the L′3-type lattice, we have performed first-principles calculations to study the stability of L′3-WC, the interaction of dilute carbon vacancies in L′3-WC, the stable ordered structures of W2C up to a unit cell containing ten formula units, and the phase transition among five stable ordered W2C structures. Our results indicate that carbon vacancies in L′3-WC can exhibit an attractive interaction, which provides an essential driving force to stabilize the ordered structures of W2C. The high-temperature disordered β-W2C with L′3-type lattice is more likely to be stabilized by configuration entropy. The stable ordered W2C structures are all extended in the ab plane of the L′3-type lattice rather than along the c axis and possess some specific distribution patterns of aggregate carbon vacancies. New ordered W2C structures with formation energies lower than those of β″-W2C and ε-W2C are found to be mechanically and dynamically stable. Carbon atom migration between the interlayers of the L′3-type lattice via a sequential mechanism is an energetically favorable pathway for the phase transition among different W2C modifications. Our results bring a deep insight into the understanding of the stable W2C polymorphic structures and would be very helpful to identify the ordered structures of highly nonstoichiometric tungsten carbide and other transition metal carbides in experiments.

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Section: Resultssupporting

confidence: 85%

Toward a Unified Understanding of W₂C Polymorphic Structures by First-Principles Calculations

Luo

Hou

Lin

et al. 2023

Crystal Growth & Design

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“…Specific-heat measurements, as a function of temperature (at temperatures >700 K), also are uncertain. [33][34][35] Values obtained by Andon et al 35 were applied at temperatures <300 K, and the formula that was recommended by Kubaschewski et al 36 was used at higher temperatures. The upper limit for hightemperature thermal expansion was calculated from Grüneisen's rule with the experimental isobaric specific heat.…”

Section: Moduli and Thermal Expansion Calculationsmentioning

confidence: 99%

Thermophysical Properties of α‐Tungsten Carbide

Reeber

Wang

1999

Journal of the American Ceramic Society

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Upper and lower bounds for the thermal expansion of polycrystalline tungsten carbide (␣-WC) are predicted at ultrahigh temperatures from low-temperature experimental data. The lower bound is obtained from an ␣ V K T V model, where ␣ V is the volume thermal expansion, K T the isothermal bulk modulus for a randomly oriented polycrystalline sample, and V the molar volume. For many materials, the ␣ V K T V product approaches a constant value that is similar to the specific heat at the highest temperatures. The upper bound uses Grü neisen's rule with a constant Grü neisen parameter ␥ at temperatures >1.3 D (where D is the Debye temperature) and experimental data below that temperature. Literature data for the thermophysical properties of ␣-WC have been reviewed and used in our ␣ V K T V model to calculate a lower bound for the thermal expansion at temperatures >2 D and to calculate the temperature dependence of the bulk modulus. The ultrahigh-pressure thermal expansion has been calculated from the lower bound. Model predictions of the thermophysical properties of WC are given for an extended temperature range.

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“…The smoothed specific heat capacity of the sample was corrected for the presence of 0.3310 g WC, 0.031 g Fe,C and 0.0021 g elemental carbon. For WC, the results of Andon et al [17] were used in the subambient temperature region. In the higher temperature region the heat capacity equation derived by Uhrenius [18] from the DSC results of Andon et al [17] and the drop calorimetric results of Chang [19] and Levinson [20] was used:…”

Section: Resultsmentioning

confidence: 99%

Heat capacity and thermodynamic properties of ditungsten carbide, W2C1−x, from 10 to 1000 K

et al. 1988

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Thermodynamic properties of tungsten carbide, W&s,,, have been derived from heat capacities measured by adiabatic calorimetry in the range 10-1000 K on a sample rich in this phase. The standard entropy of WzCo.s33 was found to be 75.80 J K-i mol-' at 298.15 K and 159.8 J K-i mol-' at 1000 K. Thermodynamic formation values for W&e.,,, were deduced from the reported coexistence of this phase with tungsten and tungsten monocarbide at about 1550 K.

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Heat capacity and entropy of tungsten carbide

Cited by 19 publications

References 5 publications

Toward a Unified Understanding of W₂C Polymorphic Structures by First-Principles Calculations

Toward a Unified Understanding of W₂C Polymorphic Structures by First-Principles Calculations

Thermophysical Properties of α‐Tungsten Carbide

Heat capacity and thermodynamic properties of ditungsten carbide, W2C1−x, from 10 to 1000 K

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Heat capacity and entropy of tungsten carbide

Cited by 19 publications

References 5 publications

Toward a Unified Understanding of W2C Polymorphic Structures by First-Principles Calculations

Toward a Unified Understanding of W2C Polymorphic Structures by First-Principles Calculations

Thermophysical Properties of α‐Tungsten Carbide

Heat capacity and thermodynamic properties of ditungsten carbide, W2C1−x, from 10 to 1000 K

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Toward a Unified Understanding of W₂C Polymorphic Structures by First-Principles Calculations

Toward a Unified Understanding of W₂C Polymorphic Structures by First-Principles Calculations