High-pressure equation of state for Nb with a helium-pressure medium: Powder x-ray diffraction experiments

High-pressure powder x-ray diffraction experiments have been carried out on Nb at room temperature up to $134\mathrm{GPa}$ with a He-pressure medium and $145\mathrm{GPa}$ with an alcohol-water pressure medium. Nb remains in the bcc structure to the highest pressure investigated. The bulk modulus and its pressure derivative have been determined from the data with the He medium as $B_0=168\left(4\right)\mathrm{GPa}$ and $B_0^{\prime }=3.4\left(3\right)$. No anomaly is found in the equation of state of Nb to be connected with the electronic topological transitions, which were inferred from the anomalies in the superconducting transition temperature under pressure. The origin of the asymmetric broadening of the diffraction peaks is discussed.

Figure 1

Powder x-ray diffraction patterns of Nb at high pressures taken with the He pressure medium in two different runs. The x-ray wavelength was $0.6174\mathrm{\AA }$. Diffraction peaks from the Re gasket are indicated.

Figure 2

Powder x-ray diffraction patterns of Nb at high pressures taken with the MEW pressure medium. The x-ray wavelength was $0.6180\mathrm{\AA }$.

Figure 3

Relative change of the $d$ spacings of Nb as a function of pressure with a He (open symbols) and a MEW (solid symbols) pressure medium. Circles, triangles, and squares indicate the 110, 200, and 211 reflections, respectively. The experimental errors in $d∕d_0$ and pressure are smaller than the size of the symbols.

Figure 4

Ruby luminescence spectra taken with the He pressure medium. Luminescence peaks other than $R_1$ and $R_2$ are getting strong at high pressures.

Figure 5

The gamma plot for Nb with a He pressure medium at $71.5\mathrm{GPa}$. The lattice parameters $a_m$ calculated from each reflection are plotted as a function of 3 $(1-3{\sin }^2\theta )\Gamma \left(hkl\right)$. See text for the detailed explanation.

Figure 6

Pressure-volume relationship of Nb. Different symbols show different experimental runs in the present experiments. Solid symbols are the best data, which are used to obtain the bulk modulus. The solid curve is a fit with the Burch-Murnaghan EOS with $B_0=168\mathrm{GPa}$ and $B_0^{\prime }=3.4$. The dashed curve is the shock compression data reduced to $T=0\mathrm{K}$ (Ref. 5). The inset shows an enlarged plot at low pressures.

Figure 7

Bulk modulus $B_0$ and its pressure derivative $B_0^{\prime }$ for Nb. Solid and open circles indicate the present results for pressure range $0–72\mathrm{GPa}$, and $0–134\mathrm{GPa}$, respectively. The large ellipsoid, which encloses the solid and open circles, indicates the probable range of the values $B_0$ and $B_0^{\prime }$ determined in the present experiments. Previous experimental and theoretical data are shown by solid squares.

Figure 8

The 110 diffraction peak of Nb at $51.8\mathrm{GPa}$ taken with the MEW pressure medium. Background intensity is subtracted. The positions of peak intensity $x_P$ and the centroid $x_C$ are indicated by solid and dashed vertical lines, respectively. The integral width $\beta$ is also indicated. The asymmetric peak profile is evident, if one compares the observed profile (open circles) with a fit with a Gaussian function (solid curve). The x-ray wavelength was $0.6180\mathrm{\AA }$.

Figure 9

The asymmetry parameter $A$ as a function of the uniaxial stress component $t$ for the data taken with the MEW pressure medium. See text for the explanation of $A$.