NIST Standard Reference Database 30
Last Update to Data Content: 2002
"Thermophysical Properties of α-Tungsten Carbide," R.R. Reeber and K. Wang, Journal of the American Ceramic Society, Vol. 82 [1], pp. 129-135 (1999), published by American Ceramic Society.Language: English
"Tungsten carbide (α-WC) is an important industrial material that has a melting point >3000 K and hexagonal symmetry. ... Thermal expansion measurements and theory have been reviewed at low temperatures for α-WC. We have predicted the thermal expansion and bulk modulus over an extended temperature range, up to the melting point. In addition, we have used our lower-bound values to calculate the thermal expansion up to pressures of 150 GPa."
The authors cite K. Wang et al., J. Mater. Res., Vol. 11, 1800 (1996), and summarize the procedure as follows. "Upper and lower bounds for the thermal expansion of polycrystalline tungsten carbide (α-WC) are predicted at ultrahigh temperatures from low-temperature experimental data. The lower bound is obtained from an αVKTV model, where αV is the volume thermal expansion, KT the isothermal bulk modulus for a randomly oriented polycrystalline sample, and V the molar volume. For many materials, the αVKTV product approaches a constant value that is similar to the specific heat at the highest temperatures. The upper bound uses Gruneisen's rule with a constant Gruneisen parameter γ at temperatures >1.3ϑD (were ϑD is the Debye temperature) and experimental data below that temperature. Literature data for the thermophysical properties of α-WC have been reviewed and used in our αVKTV model to calculate a lower bound for the thermal expansion at temperatures >2ϑD 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."
| Temperature ( K ) | Bulk Modulus ( GPa ) |
|---|---|
| 50 | 442.83 |
| 100 | 442.82 |
| 150 | 442.80 |
| 200 | 442.70 |
| 250 | 442.44 |
| 298 | 442.02 |
| 300 | 442.00 |
| 350 | 441.36 |
| 400 | 440.53 |
| 450 | 439.53 |
| 500 | 438.38 |
| 550 | 437.09 |
| 600 | 435.67 |
| 650 | 434.15 |
| 700 | 432.54 |
| 750 | 430.84 |
| 800 | 429.07 |
| 850 | 427.23 |
| 900 | 425.33 |
| 950 | 423.39 |
| 1000 | 421.40 |
| 1100 | 417.29 |
| 1200 | 413.05 |
| 1300 | 408.70 |
| 1400 | 404.25 |
| 1500 | 399.73 |
| 1600 | 395.14 |
| 1700 | 390.49 |
| 1800 | 385.80 |
| 1900 | 381.06 |
| 2000 | 376.29 |
| 2200 | 366.65 |
| 2400 | 356.91 |
| 2600 | 347.09 |
| 2800 | 337.20 |
| 3000 | 327.26 |
| Axis | Temperature ( K ) | Axis Length ( Å ) |
|---|---|---|
| a | 50 | 2.90423 |
| a | 100 | 2.90438 |
| a | 150 | 2.90462 |
| a | 200 | 2.90495 |
| a | 250 | 2.90538 |
| a | 298 | 2.90585 |
| a | 300 | 2.90587 |
| a | 350 | 2.90641 |
| a | 400 | 2.90699 |
| a | 450 | 2.90761 |
| a | 500 | 2.90825 |
| a | 550 | 2.90892 |
| a | 600 | 2.90961 |
| a | 650 | 2.91032 |
| a | 700 | 2.91105 |
| a | 750 | 2.91179 |
| a | 800 | 2.91255 |
| a | 850 | 2.91331 |
| a | 900 | 2.91409 |
| a | 950 | 2.91488 |
| a | 1000 | 2.91567 |
| a | 1100 | 2.91728 |
| a | 1200 | 2.91891 |
| a | 1300 | 2.92056 |
| a | 1400 | 2.92223 |
| a | 1500 | 2.92391 |
| a | 1600 | 2.92560 |
| c | 50 | 2.83525 |
| c | 100 | 2.83536 |
| c | 150 | 2.83554 |
| c | 200 | 2.83580 |
| c | 250 | 2.83613 |
| c | 298 | 2.83651 |
| c | 300 | 2.83653 |
| c | 350 | 2.83698 |
| c | 400 | 2.83748 |
| c | 450 | 2.83801 |
| c | 500 | 2.83858 |
| c | 550 | 2.83917 |
| c | 600 | 2.83978 |
| c | 650 | 2.84040 |
| c | 700 | 2.84104 |
| c | 750 | 2.84168 |
| c | 800 | 2.84234 |
| c | 850 | 2.84300 |
| c | 900 | 2.84367 |
| c | 950 | 2.84434 |
| c | 1000 | 2.84502 |
| c | 1100 | 2.84638 |
| c | 1200 | 2.84776 |
| c | 1300 | 2.84915 |
| c | 1400 | 2.85055 |
| c | 1500 | 2.85196 |
| c | 1600 | 2.85337 |
| Crystal Cell System |
|---|
| hexagonal |
| Temperature ( K ) | Molar Volume ( cm3/mol ) | Density ( g cm-3 ) |
|---|---|---|
| 50 | 12.47 | 15.71 |
| 100 | 12.47 | 15.71 |
| 150 | 12.48 | 15.69 |
| 200 | 12.48 | 15.69 |
| 250 | 12.49 | 15.68 |
| 298 | 12.49 | 15.68 |
| 300 | 12.49 | 15.68 |
| 350 | 12.50 | 15.67 |
| 400 | 12.51 | 15.66 |
| 450 | 12.51 | 15.66 |
| 500 | 12.52 | 15.64 |
| 550 | 12.53 | 15.63 |
| 600 | 12.54 | 15.62 |
| 650 | 12.55 | 15.61 |
| 700 | 12.56 | 15.59 |
| 750 | 12.57 | 15.58 |
| 800 | 12.57 | 15.58 |
| 850 | 12.58 | 15.57 |
| 900 | 12.59 | 15.56 |
| 950 | 12.60 | 15.54 |
| 1000 | 12.61 | 15.53 |
| 1100 | 12.63 | 15.51 |
| 1200 | 12.65 | 15.48 |
| 1300 | 12.67 | 15.46 |
| 1400 | 12.70 | 15.42 |
| 1500 | 12.72 | 15.40 |
| 1600 | 12.74 | 15.37 |
| 1700 | 12.76 | 15.35 |
| 1800 | 12.78 | 15.33 |
| 1900 | 12.81 | 15.29 |
| 2000 | 12.83 | 15.27 |
| 2200 | 12.88 | 15.21 |
| 2400 | 12.93 | 15.15 |
| 2600 | 12.98 | 15.09 |
| 2800 | 13.03 | 15.03 |
| 3000 | 13.08 | 14.97 |
| Temperature ( K ) | Elastic Modulus ( GPa ) |
|---|---|
| 50 | 706.75 |
| 100 | 706.75 |
| 150 | 706.71 |
| 200 | 706.55 |
| 250 | 706.14 |
| 298 | 705.47 |
| 300 | 705.43 |
| 350 | 704.41 |
| 400 | 703.09 |
| 450 | 701.50 |
| 500 | 699.65 |
| 550 | 697.59 |
| 600 | 695.33 |
| 650 | 692.90 |
| 700 | 690.33 |
| 750 | 687.62 |
| 800 | 684.79 |
| 850 | 681.86 |
| 900 | 678.83 |
| 950 | 675.73 |
| 1000 | 672.55 |
| 1100 | 665.99 |
| 1200 | 659.23 |
| 1300 | 652.28 |
| 1400 | 645.18 |
| 1500 | 637.97 |
| 1600 | 630.64 |
| 1700 | 623.23 |
| 1800 | 615.73 |
| 1900 | 608.17 |
| 2000 | 600.56 |
| 2200 | 585.17 |
| 2400 | 569.63 |
| 2600 | 553.95 |
| 2800 | 538.17 |
| 3000 | 522.31 |
| Temperature ( K ) | Molar Heat Capacity ( J·mol-1 K-1 ) | Specific Heat ( J kg-1 K-1 ) |
|---|---|---|
| 50 | 3.12 | 15.9 |
| 100 | 13.11 | 66.9 |
| 150 | 20.48 | 104.6 |
| 200 | 26.47 | 135.1 |
| 250 | 31.47 | 160.7 |
| 298 | 35.36 | 180.5 |
| 300 | 35.52 | 181.4 |
| 350 | 38.66 | 197.4 |
| 400 | 40.84 | 208.5 |
| 450 | 42.45 | 216.7 |
| 500 | 43.71 | 223.2 |
| 550 | 44.74 | 228.4 |
| 600 | 45.60 | 232.8 |
| 650 | 46.35 | 236.6 |
| 700 | 47.02 | 240.1 |
| 750 | 47.62 | 243.1 |
| 800 | 48.17 | 245.9 |
| 850 | 48.68 | 248.5 |
| 900 | 49.16 | 251.0 |
| 950 | 49.62 | 253.3 |
| 1000 | 50.05 | 255.5 |
| 1100 | 50.85 | 259.6 |
| 1200 | 51.60 | 263.5 |
| 1300 | 52.30 | 267.0 |
| 1400 | 52.96 | 270.4 |
| 1500 | 53.59 | 273.6 |
| 1600 | 54.18 | 276.6 |
| 1700 | 54.74 | 279.5 |
| 1800 | 55.28 | 282.2 |
| 1900 | 55.79 | 284.8 |
| 2000 | 56.28 | 287.3 |
| 2200 | 57.18 | 291.9 |
| 2400 | 57.98 | 296.0 |
| 2600 | 58.70 | 299.7 |
| 2800 | 59.33 | 302.9 |
| 3000 | 59.88 | 305.7 |
| Temperature ( K ) | Thermal Expansion ( 10-6 K-1 ) |
|---|---|
| 50 | 2.25 |
| 100 | 3.56 |
| 150 | 5.51 |
| 200 | 7.37 |
| 250 | 8.92 |
| 298 | 10.10 |
| 300 | 10.17 |
| 350 | 11.17 |
| 400 | 11.96 |
| 450 | 12.60 |
| 500 | 13.12 |
| 550 | 13.55 |
| 600 | 13.91 |
| 650 | 14.22 |
| 700 | 14.50 |
| 750 | 14.74 |
| 800 | 14.96 |
| 850 | 15.15 |
| 900 | 15.34 |
| 950 | 15.51 |
| 1000 | 15.67 |
| 1100 | 15.98 |
| 1200 | 16.25 |
| 1300 | 16.51 |
| 1400 | 16.76 |
| 1500 | 17.00 |
| 1600 | 17.24 |
| 1700 | 17.47 |
| 1800 | 17.71 |
| 1900 | 17.95 |
| 2000 | 18.18 |
| 2200 | 18.67 |
| 2400 | 19.17 |
| 2600 | 19.70 |
| 2800 | 20.25 |
| 3000 | 20.82 |