We are trying to measure the adhesion force between 48 Mm silica
beads and silica substrate , and based on the theoretical model the expected
value of adhesion is around 10 micro N , so what is the proper type
of cantilever should we use???

You should choose a cantilever that is sensitive as possible, but does not cause the deflection measurement to saturate or become non-linear.

The force is the spring constant times the deflection sensitivity times the detector voltage (F=K*Sd*V). If we know K for a given probe type and we know the approximate Sd (this depends on probe type, head, microscope type, and laser spot position), we can calculate the approximate detector voltage. For best linearity the detector voltage should be in the range -2V to +2V (the system can measure up to +/-12V, but it is less linear, so accuracy will usually be less).

For example, some ballpark numbers for the Multimode are:

F (nN)

K (N/m)

~Sd (nm/V)

V

Probe

10000

350

75

0.380952

DNISP-HS

10000

150

75

0.888889

DNISP

10000

150

30

2.222222

TAP525A

10000

48

50

4.166667

LTESPA

Based on that I'd start with a TAP525A probe and see how it works.

You should choose a cantilever that is sensitive as possible, but does not cause the deflection measurement to saturate or become non-linear.

The force is the spring constant times the deflection sensitivity times the detector voltage (F=K*Sd*V). If we know K for a given probe type and we know the approximate Sd (this depends on probe type, head, microscope type, and laser spot position), we can calculate the approximate detector voltage. For best linearity the detector voltage should be in the range -2V to +2V (the system can measure up to +/-12V, but it is less linear, so accuracy will usually be less).

For example, some ballpark numbers for the Multimode are:

F (nN)

K (N/m)

~Sd (nm/V)

V

Probe

10000

350

75

0.380952

DNISP-HS

10000

150

75

0.888889

DNISP

10000

150

30

2.222222

TAP525A

10000

48

50

4.166667

LTESPA

Based on that I'd start with a TAP525A probe and see how it works.

This may be a bit out of the topic but I would also like to inquire what suggestions you may have for measurements of elastic modulus for ceramic samples with roughness of 0.4-2 microns..