Table of Contents ECNDT '98 Session: Materials Characterization | Interpolation Method for Debye Temperature NDT DeterminationValentin D. VladimirovSofia University St. Kl. Ohridski Dept of Mineralogy, Petrology & Economic Geology 15 Tzar Osvoboditel, Sofia, 1000, Bulgaria E-mail: valentin@gea.uni-sofia.bg |
TABLE OF CONTENTS |
The Debye characteristic temperature () is one of the important characteristics of substance, which reflects its structure stability, the strength of bonds between its separate elements, structure defects availability (dislocations in crystalline structure of mineral grains, pores, microcracks) and its density (5). Hence, every alteration of external conditions of rock formation, as every event in its further geological history, leading to transformation of the structure, must evoke a change in the Debye characteristic temperature.
For the first time this notion was introduced by the German physicist Paul Debye to express the connection between heat capacity of poly-atomic solid and its elastic coefficient.
C_{v-} substance heat capacity, R- gas constant, T- absolute temperature.
The Debye temperature is constant for a given (present) substance, and defines the maximum frequency in the spectrum of particle vibration of the solid.
h- Planck's constant, k- Boltzman's constant, V_{max-} maximal frequency of vibration of solid.
The Debye theory gives possibility to calculate the characteristic temperature ( ,K) on the basis of data density () and velocities of longitudinal (V_{p}) and transversal (Vs_{1}, Vs_{2}) ultrasonic waves in the solid (1, 2, 4, 3):
where:
if Vs_{1} = Vs_{2}
M/P- mean atomic weight (M-molecular weight divided by the P-number of atoms), N - discrete point masses.
In case of silicate rocks - M/P=21
and for sulphide massive ores - M/P=40 then
Thus, Debye temperature calculation allows Dergachov and Starostin (1981) to estimate the formation and transformation conditions of rocks and ores.
According the regional metamorphism also changes the of rocks and differences of the Debye temperature between separated facieses of the metamorphic rocks are maximal, on middle level of metamorphism they are lower and in the very alternated rocks these differences are minimal.
From the other side the absolute value of Debye temperature increases according to the degree of increase of the thermodynamic conditions of metamorphism from the green schist up to the amphybolite and garnet facieses.
But when we investigate rocks of the area of endogenous massive ore deposits, always there are some ore components in them (pyrite, chalcopyrite, sphalerite etc.). That leads to the change of the M/P ratio. On the other hand the presence of the ore components leads to the increase of rock density approximately from 2.7 t/m³ for silicates, up to 4.7 t/m³ for massive sulphide ores. So the density increment will correspond to the increment of M/P ratio. In this connection with interpolation between values, calculated by both formulae (for rocks and massive ores), on the basis of density variations, we can determine a real value of the Debye temperature by the formula:
_{r}, _{r} - for rocks; _{o},_{o} - for ores.
If we change _{r} and _{o} with their mean values for rocks and sulphide ores ( _{r}=2.7 t/m³ and _{o} =4.7 t/m³) then we receive
Such a method of calculation for mineralised rocks, allows to determine that important parameter with 1% precision, for density variation of 0.1 t/m³. This is quite enough for geological interpretations. For comparison a table with the results of Debye temperature calculation (for pure rocks and ores, and for interpolated values also) are attached.
As the characteristic temperature of Debye is a most important characteristic of substance reflecting its structure, defects, stability of relationships and dislocations in the crystal lattice, pores and macrocracks and etc.. Its synonymous definition has a very important role.
Thus we offer a new method and a formula which unites the previous two, makes easier its application and increases its effectiveness.
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