04Dec 2014

Your fuel gauge indicator, whether it is in your smartphone, tablet or even electric vehicle, gives an indication of remaining charge in your battery. That indicator is universally given in percentage. It is assumed that at 100%, the battery is full, and at 0%, the battery is empty. But what is the definition of full and what is the definition of empty. That’s the topic of today’s post.

In an earlier post, I showed how the voltage across the terminals of an individual battery cell is really the composite voltage contributions of both electrodes, the anode as well as the cathode. The voltage contribution for each electrode varies with the fraction of lithium ions that are embedded inside the electrode. A user can only measure the composite voltage sum of the two electrodes when he or she measures the terminal voltage of the cell.

The first point to understand is the relationship between the fraction of lithium ions inside the electrode material vs. the notion of empty or full. When the graphite or carbon anode is completely devoid of lithium ions, the cell is truly empty. In other words, there are no available lithium ions and consequently, no “stored” charge. From that earlier post, one can see that the composite cell voltage can be very low, somewhere near 1V or even less. Cells never operate near that low voltage point. A truly empty battery cell has most likely incurred serious damage to its internal structure. If any of your lithium ion cells measure less than 2V, it is time to discard them. As a result, most battery cells consider a safe lowest operating voltage to be between 2.5V and 3.0V. This is the definition that one may get from the battery manufacturer. In practice, however, a smartphone will display 0% when the cell voltage is near 3.3V. This is because several electronics components, most notably the power amplifier for the radio, will not operate efficiently below 3.3V. Consequently, your mobile device shuts off at that low voltage threshold. This is the definition of zero as made by the mobile device maker. In either case, you will observe that the definition of empty is usually related to a low operating voltage threshold, and less so about being “empty.”

The chart below illustrates the dependence of voltage on the amount of charge taken out of the cell during discharge. When the battery is fully charged — to the far left of the chart — the voltage is at its maximum. As charge is slowly removed from the cell, the voltage declines. At some point near 3.6V, it begins to drop precipitously; in other words, one needs to take out only a small amount of charge before the voltage drops rapidly. The rate at which the voltage declines depends on the choice of material. The chart below shows the voltage dependence for a battery that is made with a carbon anode and a lithium-cobalt-oxide (LCO) alloy cathode. The battery nominally stores 3,000 mAh.

If you think about this chart for a brief moment, you will quickly realize that the area under the curve is the amount of energy stored in the battery — after all, energy is the product of charge and voltage.  So let’s compare this to NiMH batteries that have a nominal cell voltage of 1.2V. Which one has a higher energy density? Naturally, lithium-ion: by at least a factor of 3X.

What about the definition of the 100% point? Is the battery full and hence cannot accept more charge? Not really. The definition of 100% is simple: the terminal voltage of the battery has reached 4.35V (sometimes, it is 4.2V but more often in consumer devices, it is 4.35V). This voltage threshold is strictly due to safety. Above 4.35V, three unsafe mechanisms begin to take place. First, lithium plating occurs in lithium ion batteries that use a carbon-based anode. These lithium metal deposits can short the cell and cause a fire. Second, the electrolyte, being liquid or gel-based, deteriorates rapidly and decomposes. The electrolyte is the medium through which the lithium ions can travel from one electrode to the other. And finally, the structure of the cathode itself begins to change its material phase and it becomes unstable.

So there you have it, empty is really not empty, and full is really not full. Both limits are defined primarily on the basis of safety and practical utilization of the battery.