You could apply ac-current to your 4-contact sample and measure ac-voltage at the same frequency by SR830. You will find principles of phase-sensitive detection in attached file.
Of course, formation of good ohmic contacts to your samples is very important.
Thanks Dear V. L. Gurtovoi for your answer. I have chemistry background so we have SR830 lock in amplifier in my lab but I do not know how can I connect it to measure the conductivity for my samples. P lease, if you have information about that help me.
You can do conductivity measurement for your four probe sample by SR 830. SR 830 has ac voltage source on its sine output. You can connect BNC cable on it. You can change this voltage source to current source by connecting a resistor. connect the hi and low part of this to the two metal pad of your sample. From this you will supply constant ac current on your sample. The inner two voltage probe pads, you should connect to the input of the SR830. Let choose differential mode of input. With this connection configuration, you can supply current on your sample and measure the voltage means you can measure the conductivity. I hope it will work for you.