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High P-T phase transitions and P-V-T equation of state of hafnium
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10.1063/1.4726211
/content/aip/journal/jap/111/11/10.1063/1.4726211
http://aip.metastore.ingenta.com/content/aip/journal/jap/111/11/10.1063/1.4726211

Figures

Image of FIG. 1.
FIG. 1.

P-T range surveyed in our experiment.

Image of FIG. 2.
FIG. 2.

Variation of c/a ratio of α-hafnium (hcp) unit cell with increasing pressure at two different temperatures.

Image of FIG. 3.
FIG. 3.

Representative x-ray diffraction patterns of our sample in several P-T regimes.

Image of FIG. 4.
FIG. 4.

Pressure-volume relation of α-phase hafnium at room temperature.

Image of FIG. 5.
FIG. 5.

Heat capacity of α-phase hafnium as functions of temperature at several pressures calculated from P-V-T EOS.

Image of FIG. 6.
FIG. 6.

Entropy of α-phase hafnium as functions of temperature at several pressures calculated from P-V-T EOS.

Image of FIG. 7.
FIG. 7.

P-V-T EOS molar volume calculation errors for the entire P-T range of our experiment.

Image of FIG. 8.
FIG. 8.

Comparison of literature reported data on thermal expansion of hafnium and data calculated using our P-V-T EOS. Literature data on thermal expansion of hafnium was included in our P-V-T EOS determination. Superscript (a) in the figure denotes the data points compiled from several literature sources.14,15,17,18

Image of FIG. 9.
FIG. 9.

For Group IVB transition metals, γ 0 and δ 0 are seen to decrease with increasing atomic number of element.

Image of FIG. 10.
FIG. 10.

The relationship between γ 0 and δ 0 is nearly δ 0 = 2 γ 0, which is consistent with previously reported trend.19

Tables

Generic image for table
Table I.

Equation of state parameters for α-phase of hafnium.

Generic image for table
Table II.

Bulk modulus (B 0), and derivative bulk modulus (B 0′), Grüneisen (γ 0) and Anderson-Grüneisen (δ 0) parameters of Group IVB transition metals (Figs. 9 and 10).

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/content/aip/journal/jap/111/11/10.1063/1.4726211
2012-06-15
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: High P-T phase transitions and P-V-T equation of state of hafnium
http://aip.metastore.ingenta.com/content/aip/journal/jap/111/11/10.1063/1.4726211
10.1063/1.4726211
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