Nuclear relaxation time in absence of a magnetic field It seems that after reading about how MRI scans work, and it appears that I had a misconception of what T1 relaxation times mean.  From what I think I understand now, the T1 relaxation time refers to the time it takes for nuclei to realign with an applied static magnetic field.  What I'm curious about is what determines and what is used to refer to the time for the alignment of hydrogen protons within a magnetic field to become disordered after this static magnetic field is turned off/removed?
 A: IN a molecular structure, nuclei are in constant rotational and vibrational motion, and create a magnetic field.
The magnetic field caused by thermal motion of the nuclei within the lattice is called the lattice field.
This lattice field of a nucleus with lower energy can interact with the lattice field of a nucleus with higher energy, thus distributing the energy.
Now if there is a radiofrequency pulse, it is dissipated as increased rotation and vibration in the lattice (increasing temperature).
Spin-lattice relaxation is when the spins give the energy (they gained from the FR pulse) back to the lattice, restoring equilibrium. The same is for when the spins have been altered by an external magnetic field.


The relaxation time, T1 (the average lifetime of nuclei in the higher energy state) is dependent on the gyromagnetic ratio of the nucleus and the mobility of the lattice.  As mobility increases, the vibrational and rotational frequencies increase, making it more likely for a component of the lattice field to be able to stimulate the transition from high to low energy states. However, at extremely high mobilities, the probability decreases as the vibrational and rotational frequencies no longer correspond to the energy gap between states.


https://en.wikipedia.org/wiki/Spin%E2%80%93lattice_relaxation
The answer to your question is, that the T1 rate depends on the:


*

*gyromagnetic ratio of the nucleus

*mobility of the lattice
The question after the comments is about when the static magnetic field is removed.


When the exciting RF field is switched off, the protons tend to returned to their lower energy state. This "relaxation" back to a state where their spins are parallel to the static magnetic field produces a small amount of RF radiation which is detected as the NMR signal. Two different time constants for decay are typically observed.
    The longer of the two time constants is usually labeled T1 and is associated with the decay of the field component that is parallel to the applied static magnetic field B0. This field direction is usually taken to define the z-axis of the system. This time constant is sometimes called the longitudinal time constant. It is also called the spin-lattice relaxation time. Since the magnetic potential energy is proportional to the projection along this axis, a change in the magnetization along this axis involves the exchange of energy. This implies that the spin has interacted with its environment.


http://hyperphysics.phy-astr.gsu.edu/hbase/Nuclear/spinrel.html


The name spin-lattice relaxation refers to the process in which the spins give the energy they obtained from the RF pulse back to the surrounding lattice, thereby restoring their equilibrium state. The same process occurs after the spin energy has been altered by a change of the surrounding static magnetic field (e.g. prepolarization by or insertion into high magnetic field) or if the nonequilibrium state has been achieved by other means (e.g. hyperpolarization by optical pumping).


So basically this is the answer to your question, it is the same process for when you remove the static magnetic field, of course the value of T1 can be different for RF pulses and static magnetic fields. 
