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Influence of higher-order tunneling processes and a finite cooling rate

3 Influence of higher-order tunneling processes and a finite cooling rate [Pg.49]

In order to take into accoimt the cooling process we used the algorithm explained below. Tbe zero-time point is chosen as the time when the cooling process is started. The function n E,u,t) represents the difference in population of the TS energy states at any time t and no(E,T) means this difference in equilibrium (i- oo) at a temperature T. Analog to Eq. 11 the heat release can be written as  [Pg.49]

Note that the population difference n depends on E and u because the relaxation rates, that influence the relaxation of the TS, depend on these variables. As already described above, to obtain the function n we need to solve the differential equation given by Eq. 4. In general this is only possible by numerical methods. [Pg.50]

The time dependence of the temperature during the cooling process performed in this work can be well approximated by a linear function given by [Pg.50]

We assume that the sample is at t = 0 (/a) at T (To) /a is the time needed to cool the sample from T to To. The calculations have been done splitting the function T t)m.N steps of time At (Fig. 4.3). During the time At the temperature remains constant and n(E,u,t) shows an exponential behaviour given by Eq. 5 this is qualitatively shown in Fig. 4.3. To obtain the population difference at the time At cooling from Ti at t = 0 for a given E and u we calculate iteratively the value [Pg.50]




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Cooling process

Cooling rates

Cooling tunnels

Influence of Processing

Of higher-order

Order and As

Ordering processes

Process Tunnel

Processing rate

Rate of As

Rate processes

Tunneling process

Tunnelling, and

Tunnels and Tunnelling

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