In an IC engine, combustion was found to proceed during the expansion...
Lean mixture: Mixture which contains more air than the stoichiometric requirement. There is more oxygen than required to burn the amount of fuel completely; after combustion, there is excess oxygen in the exhaust gases.
Rich Mixture: Mixture which contains less air than the stoichiometric requirement. There is not enough air to completely burn the amount of fuel; after combustion, there is unburnt fuel in the exhaust gases.
Spark advance/Ignition Advance:
The purpose of the spark advance mechanism is to assure that under every condition of engine operation, ignition takes place at the most favorable instant in time, i.e., most favorable from the standpoint of engine power, fuel economy, and minimum exhaust dilution. By means of these mechanisms, the advance angle is accurately set so that ignition occurs before the TDC point of the piston.
Ignition timing is the correct instant for the introduction of a spark near the end of the compression stroke in the cycle. Several factors affect the ignition timing of an engine, like compression ratio, Engine speed, Engine load, Quality of fuel, Mixture strength, etc.
In the case of a rich mixture, the combustion rate is faster and less ignition advanced is required. And in the case of a lean mixture, the combustion rate will be slower, thus requiring more ignition advances.
When ignition occurs early in the compression stroke, the engine is said to be advanced. A retardation ignition takes place when the piston is just near the compression stroke.
If the ignition is advanced too much, it will be completed before the end of the compression stroke. Under these conditions, the crankshaft and connecting rod will have to push the piston upward, compressing the gases. In such a case, the force might not be sufficient to overcome the pressure and the engine would stop or stall.
If the ignition is retarded too much, the combustion of fuel will continue during the power stroke of the piston (Expansion stroke), and the maximum pressure will not be developed. Less work will be obtained from heat energy. Under these conditions, comparatively more exhaust gases will be going out of the engine cylinder overheating the exhaust valve.
Conclusion:
Rich Mixture with ignition advance: It can complete before the compression stroke
Weak Mixture without ignition advance: Combustion can be found to proceed during the expansion stroke
The rich mixture should have retarded ignition advance, and the lean mixture should have more ignition advance.