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Platinum Metals Rev., 2006, 50, (3), 118

doi:10.1595/147106706x129088

Crystallographic Properties of Platinum

NEW METHODOLOGY AND ERRATUM

  • J. W. Arblaster
  • Coleshill Laboratories,
  • Gorsey Lane, Coleshill, West Midlands B46 1JU, U.K.
  • Email: jwarblaster@aol.com
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Article Synopsis

Equations are given to represent the lattice parameter thermal expansion of platinum from 293.15 K to the melting point at 2041.3 K. This treatment is intended to supersede a combination of dilatometric equations with corrections for thermal vacancy effects.

In the review of the crystallographic properties of platinum by the present author (1), the high-temperature data were represented by expressions derived from precision dilatometric thermal expansion measurements (Equations (i) and (ii)). Above 1000 K temperature, not only did length change measurements derived from lattice parameter measurements fail to agree with one another, they also showed marked scatter around the dilatometric results. The length change measurements were therefore unsuitable for calculating the lattice parameter thermal expansion. This problem was addressed by correcting the dilatometric data for thermal vacancy effects (Equations (iii) and (iv)), based on the consistent set of thermal vacancy parameters given in Table I and explained in the original review (1).

High Temperature Dilatometric Thermal Expansion (293.15–2041.3 K)

  α* = 7.08788 × 10−6 + 1.04970 × 10−8 T

    − 2.00846 × 10−11T2 + 2.28200 × 10−14T3

    − 1.18453 × 10−17T4 + 2.37348 × 10−21T5 K−1    (i)

  δL/L293.15 K = 7.08788 × 10−6 + 5.24850 × 10−9 T2 − 6.69487 × 10−12 T3

    + 5.70500 × 10−15 T4 − 2.36906 × 10−18 T5

    + 3.95580× 10−22T6 − 2.39745 × 10−3        (ii)

Thermal Vacancy Corrections (1300–2041.3 K)

  α*(lattice) = α*(dilatometric) − (5841/T2) e(1.32 −17523/T) K−1   (iii)

  δa/a293.15 K = δL/L293.15 K − (1/3) e(1.32 − 17532/T)      (iv)

Note: in Equation (x) of Ref. (1), to which Equation (iv) corresponds, the second δ was incorrectly given as d.

On reflection, this procedure is cumbersome and might be considered unsatisfactory. It has therefore been replaced here by Equations (v) and (vi) which are based on a combination of Equations (i) and (iii), and which represent the lattice parameter thermal expansion from 293.15 K to the melting point at 2041.3 K. Equation (v) agrees with a combination of Equations (i) and (iii) to within 4 × 10−9 K−1 and to within ± 2 × 10−9 K−1 overall, well within the accuracy of Equation (i) of ± 2 × 10−8 K−1.

In Equations (i), (iii) and (v), α* is the thermal expansion coefficient relative to 293.15 K.

High Temperature Lattice Parameter Thermal Expansion (293.15–2041.3 K)

  α* = 7.03139 × 10−6 + 1.08937 × 10 −8 T

    − 2.10071 × 10−11T2 + 2.36623 × 10−14 T3

    − 1.20728 × 10−17T4 + 2.34219 × 10−21T5 K−1    (v)

  δa/a293.15 K = 7.03139 × 10−6 T + 5.44686 × 10−9T2 − 7.00236 × 10−12 T3

    + 5.91557 × 10−15 T4 − 2.41456 × 10−18 T5

    + 3.90366× 10−22T6 − 2.39164 × 10−3       (vi)

Table I

Thermal Vacancy Parameters for Platinum



ParameterSymbolValue


Thermal vacancy concentration at melting point cv 7 × 10−4
Enthalpy of monovacancy formation Hvf 1.51 eV
Entropy of monovacancy formation Svf 1.32k


Note: k is the Boltzmann constant, given at the time of publication of Reference (1) as 8.617385 × 10−5 eV K−1

Erratum

In the review (1), equations were given representing a precision relationship between thermal expansion and specific heat. However, the third equation on page 19 of (1) (at the top of the right-hand column) was incorrectly given. It should have read as in the Figure:

 

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Reference

  1.  J. W. Arblaster, Platinum Metals Rev., 1997, 41, (1), 12

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