Force Plots Explained

A force plot is an observation of tip-sample interaction that provides information regarding the sample and tip. By way of analogy, suppose a materials researcher must determine how powerful two different types of magnets are. One magnet is made of iron, the other is a stronger, rare earth magnet.

A simple way of measuring each magnet’s strength would be to measure its pull upon a steel plate. For example, the researcher could hang each magnet from a simple spring scale, “zero” the scale, then lower the magnet toward a heavy steel plate. At regular distances from the plate, the amount of pull shown on the scale is recorded. At a particular height above the plate, each magnet is attracted strongly enough to attach itself to the plate. A plot of height, H, versus magnetic pull gives a comparative index of each magnet’s strength. Similarly, after attachment the researcher could pull each magnet away from the plate and measure the pulling force at regular intervals until the magnet breaks free. The pull-off point of each magnet gives an additional index of its holding strength. A representation of this setup during a lowering cycle of one magnet is illustrated below:

The pulling force is measured at 1 cm height intervals while the scale and magnet lower and lift in a controlled cycle. Figure 1, below, depicts a plot of this experiment with both magnets. The plot depicts each magnet’s attraction as it approaches the plate, and its tenacity when pulled off the plate. Assuming both magnets are the same size, this reveals information about each magnet’s strength. First, magnet #1 is weaker, attaching to the steel plate with 7 N of pulling force at 6 cm, and magnet #2 is stronger, attaching at 7 cm with 10 N.

Figure 1: Graph of pulling forces for two different magnets

This oversimplified model approximates activity between SPM tips and various materials. In reality, SPM force plots reveal far more. For example, by combining force curves at regularly spaced intervals across the sample you can obtain a force map of the sample’s electric properties, elastic modulus, and chemical bonding strengths.

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