Ball milling-induced reduction of MoS₂ with Al

Abstract

The ball milling-induced reduction of MoS₂ by Al has been investigated. Although this is a highly exothermic reaction that, based on its thermodynamic properties, should progress as a self-sustaining process, ignition could not be achieved by ball milling. In order to identify the reason, XRD, particle size distribution, SEM, and DTA measurements were carried out on a series of samples milled for different durations. It was found that the largest composite agglomerates broke up due to the presence of a fine dispersion of MoS₂ particles. SEM also revealed that the grains are packed rather loosely within the agglomerates. These results indicate that a self-sustaining process can take place only if large and well-compacted composite particles are present.

Appendix

The particle size distribution is characterized in Fig. 3 by plotting the volume fraction density (Q _log) as a function of the decadic logarithm of the particle diameter (log x.) From this graph, the volume fraction of particles between diameters x ₁ and x ₂,

P(x ₁ < x< x ₂), is obtained as the area under the curve between log x ₁ and log x ₂. If x ₂−x ₁ << x ₂,

$$ P(x_1 \, < \,x\, < \,x_2 )\, \approx \,Q_{\log } (\log \;x_2 - \log \;x_1 )\, = \,Q_{\log } \log (x_2 /x_1 ) $$

(A.1)

Although the proper variable of the horizontal axis is log x, it is usually labeled in terms of diameters. The logarithm is dimensionless, thus both P and Q _log can be expressed in percentages.

The quantity most often used to characterize the particle size distribution is the cumulative distribution F(x), defined as the volume fraction occupied by particles smaller than x. If an atom of the sample is chosen at random, F(x) gives the probability that it belongs to a particle smaller than x. As F is an integral quantity, it may hide some fine details of the particle size distribution. Q _log relates to F as follows:

The volume fraction of particles between diameters x ₁ and x ₂ is

$$ P(x_1 \, < \,x\, < \,x_2 )\, = \,F(x_2 ) - F(x_1 ). $$

(A.2)

If Δx = x ₂−x ₁ << x ₂,

$$ P(x_1 \, < \,x\, < \,x_2 )\, \approx \,Q(x_2 - x_1 ) = Q\Delta x{\hbox{,}} $$

(A.3)

where Q = dF/dx is the volume fraction density. The dimension of Q is 1/length. Q _log differs from Q, because its variable is log(x) rather than x. But Eq. (A.1) and (A.3) provide the same quantity, consequently

$$ Q\Delta x\,= \,Q_{\log} \log (1\, + \,\Delta x/x_1 )\, \approx \,Q_{\log} [\log (e)/x]\,\Delta x{\hbox{.}} $$

(A.4)

From here,

$$ Q_{\log} \, = \, Q x /{\log} (e)\, \approx \, 2.3 x \, Q \,{\hbox{ = }} \, {\hbox{2.3}}\, x \,{\hbox{d}} F / {\hbox{d}}x.$$

(A.5)