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Fig. 9.10 The Hydrogen-Zirconium Phase Diagram

The P modification of metallic Zr is a high-temperature phase of cubic crystal structure. In hydrogen-free Zr, the a-Zr structure transforms to the P-Zr structure at 860oC. Addition of hydrogen stabilizes P-Zr at lower temperatures; at H/Zr = 0.54, P-Zr exists down to 550oC. Between 550 and 860oC, the upper phase boundary of the a-Zr phase is separated from the lower phase boundary of P-Zr by the two-phase metal zone labeled a+P in Fig. 9.9. The upper phase boundary of P-Zr and the lower phase boundary of the S-hydride are connected by the P+S two-phase region.

Each point in Fig. 9.10 has a corresponding equilibrium hydrogen pressure. This function, ph = f(T, H/Zr) can be thought of as a surface the space above the T-H/Zr plane. The dashed lines and curves in Fig. 9.10 represent projections of this surface on the T-H/Zr plane. These curves are analogous to the elevation contours on hikers' maps of wilderness areas. In Fig. 9.10, the dashed lines are called hydrogen isobars because they represent constant values of ph2.

In the three single-phase regions, the hydrogen isobars are sloped curves, indicating that pH is a function of both T and H/Zr; that is, the system has two degrees of freedom. In the a-Zr and P-Zr regions, horizontal isotherms cut through the hydrogen isobars at combinations of pH -H/Zr values that satisfy Sieverts' law, Eq (9.61) (ignoring the distinction between mole fraction and atom ratio as measures of hydrogen concentration2). Since the S-hydride is more ceramic-like than metallic, it need not follow Sieverts' law.

In the three two-phase zones, on the other hand, the hydrogen isobars are horizontal lines, indicating that pH is independent of H/Zr and a function of temperature only. The reason for this behavior is simple to understand: the H/Zr ratio in the two-phase regions refers to the mole-weighted average of the left and right hand phases (see the lever rule, Sect. 8.7). In moving along an isotherm in a two-phase region, the H/Zr ratios of the two phases present do not change; only the relative amounts of the two phases shift. At 500oC, for example, the hydrogen pressure in equilibrium with a-Zr with H/Zr = 0.04 is exactly the same as that in equilibrium with the S-hydride at H/Zr = 1.33.

Problem 9.13 shows how the H2/Zr equilibrium is applied in a laboratory device for measuring the hydrogen content of zirconium, which is important in nuclear fuels. Problem 9.14 analyzes the effect of other gas-phase reactions of a diatomic species on its dissolution in a metal.

2 The mole fraction and the hydrogen-to-zirconium atom ratio are related by xH = (H/Zr)/(1 + H/Zr)

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