Driving force for diffusion and Fick s laws of diffusion

Transcription

1 Driving force for diffusion and Fick s laws of diffusion In the last lecture, it is eplained that diffusion of elements between different blocks is possible because of difference in chemical potential of a elements. We also have shown that even if there is concentration/composition difference between blocks, diffusion may not happen because of absence of difference in chemical potentials. On the other, we have eplained before the Fick s laws of diffusion with respect to concentration profile only. So we rather need more fundamental relations to relate flu because of diffusion. We will see now that the concentration gradient not necessarily eplains the direction of diffusing elements.

2 d L where L and L are the phenomenological constants Let us consider again a complete solid solution system and the couple between rich an rich. Since diffuse down the chemical potential gradient from to, the flu of,, with respect to phenomenological point of view can be written as d L Since diffuse down the chemical potential gradient from to, the flu of, with respect to phenomenological point of view can be written as

3 Note that these relations are developed based on the facts that happens in reality. Means it has been seen that the flu is negative proportional to the chemical potential gradient. If there is a continuous variation of chemical potential gradient with the change in position that is concentration/composition, flu also will vary accordingly. henomenological constants are also not the same everywhere, which will be clear at later stage when we shall relate these constants with the diffusion coefficients. reviously, we have seen that according to Fick s fist law D D D D d d d d This implies that Fick s law holds in this case, which states that diffusion occurs down the concentration gradient.

4 1 2 Now let us consider a system with miscibility gap. If we anneal two block with any compositions at temperature, T 2, the eplanation of the diffusion process will be similar as eplained before. However, if we couple two blocks with the composition of and, which are inside the miscibility gap, different situation will happen. From the slopes taken at and, we find G 1 G 2 < and > T 1 That means, the chemical potential of is less in rich alloy, compared to the lean alloy,. t 0 Similarly, the chemical potential of is higher in lean alloy, compared to the rich alloy,. t t

5 If we couple blocks of and then the average free energy of the system is, let say, R depending on the relative amounts of and. However, since the system always tries to decrease free energy, it will try to reach to the lowest free energy and. That means rich alloy should increase the content of and the rich alloy should increase the content of. G G 1 2 From the chemical potential point of view also it must be clear that will diffuse out of the lean alloy towards and will diffuse out of the lean alloy towards. The direction of elements is just opposite compared to the previous eample eplained. Since elements diffuse up the concentration gradient instead of down the concentration gradient, it is called uphill diffusion.

6 In terms of chemical potential gradient d D D d D D ; d L d L Since diffuse from to and and diffuse from to In terms of concentration gradient It can be seen that negative sign is not present in the Fick s first law for this case. This equation with negative sign is used to derive relations at later stage. That is why diffusion coefficient shows the negative sign when system shows uphill diffusion.

7 In previous slides we have shown diffusion of elements because of chemical potential driving forces. However, diffusion occurs even without the presence of thermodynamical driving force or any other driving forces. For eample, in pure material, where there are no forces present but atoms still to jump to another position. In a low melting point material, like in Sn or b, jump of atoms possible even at room temperature. However, jump of atoms in this case is completely random. resence of driving forces rather make net flu of atoms to a particular direction. To test the possibility of diffusion without any driving forces tracer diffusion eperiments are conducted. Radiotracer elements which has one or two neutron mass difference are deposited on a material of the same element and then annealed at elevated temperature.

8 oncentration of these tracer elements can be measured at different depths even in low concentration because of radiation of different rays. s shown in a schematic figure, these tracer elements diffuse inside the material. Since both are pure elements there is no chemical potential difference. These tracer elements are used to trace the diffusion of elements. There will be very small gain (increase in entropy) because of spreading of these tracer elements. If we do not use the tracer elements we will not be able to detect the jump of atoms.

9 + - roduct layer - In electronics industry, flip chip or wire bondings are used to join chip to chip or chip to board. In flip chip bonding, u, u, Ni etc. underbump metallization layers are joined with Sn based solder. t the interface intermetallic compounds grow. Further during usage electrons also flow. So there is both chemical potential and electrical potential as driving forces. This is also true for wire bonding where u or u wires are bonded on l pad.

10 Oidation of metal Ni NiO Ni Ni e 1/2O 2 +2e O -2 Ni +2 + O -2 NiO Ni +2 2e Since the product oide layer has Ni and O ions, Ni can diffuse only after dissociating electron. oth diffuse separately to the other interface. First oygen ions are produced and then oide layer is formed after combination with Ni ions. Diffusion starts because of chemical potential gradient but electrical potential gradient also comes into the picture Since the diffusion of metal ion and electrons are coupled, it is called coupled diffusion process.