From an atomic stand point, T_{1} relaxation occurs when a precessing proton transfers energy with its surroundings as the proton relaxes back from higher energy state to its lower energy state. With T_{2} relaxation, apart from this energy transfer there is also dephasing and hence T_{2} is less than T_{1} in general. For solid suspensions, there are three independent relaxation mechanisms involved:-

- 1) Bulk fluid relaxation, which affects both T
_{1} and T_{2} relaxation. - 2) Surface relaxation, which affects both T
_{1} and T_{2} relaxation. - 3) Diffusion in the presence of the magnetic field gradients, which affects only T
_{2} relaxation.

These mechanisms act in parallel so that the net effects are given by Equation 5 and Equation 6

1
T
2
=
1
T
2,
bulk
+
1
T
2,
surface
+
1
T
2,
diffusion
1
T
2
=
1
T
2,
bulk
+
1
T
2,
surface
+
1
T
2,
diffusion
size 12{ { {1} over {T rSub { size 8{2} } } } = { {1} over {T rSub { size 8{2, ital "bulk"} } } } + { {1} over {T rSub { size 8{2, ital "surface"} } } } + { {1} over {T rSub { size 8{2, ital "diffusion"} } } } } {}

(5)
1
T
1
=
1
T
1,
bulk
+
1
T
1,
surface
1
T
1
=
1
T
1,
bulk
+
1
T
1,
surface
size 12{ { {1} over {T rSub { size 8{1} } } } = { {1} over {T rSub { size 8{1, ital "bulk"} } } } + { {1} over {T rSub { size 8{1, ital "surface"} } } } } {}

(6)The relative importance of each of these terms depend on the specific scenario. For the case of most solid suspensions in liquid, the diffusion term can be ignored by having a relatively uniform external magnetic field that eliminates magnetic gradients. Theoretical analysis has shown that the surface relaxation terms can be written as Equation 7 and Equation 8, where ρ = surface relaxivity and s/v = specific surface area.

1
T
1,
surface
=
ρ
1
(
S
V
)
particle
1
T
1,
surface
=
ρ
1
(
S
V
)
particle
size 12{ { {1} over {T rSub { size 8{1, ital "surface"} } } } =ρ rSub { size 8{1} } \( { {S} over {V} } \) rSub { size 8{ ital "particle"} } } {}

(7)
1
T
2,
surface
=
ρ
2
(
S
V
)
particle
1
T
2,
surface
=
ρ
2
(
S
V
)
particle
size 12{ { {1} over {T rSub { size 8{2, ital "surface"} } } } =ρ rSub { size 8{2} } \( { {S} over {V} } \) rSub { size 8{ ital "particle"} } } {}

(8)Thus one can use T_{1} or T_{2} relaxation experiment to determine the specific surface area. We shall explain the case of the T_{2} technique further as Equation 9.

1
T
2
=
1
T
2,
bulk
+
ρ
2
(
S
V
)
particle
1
T
2
=
1
T
2,
bulk
+
ρ
2
(
S
V
)
particle
size 12{ { {1} over {T rSub { size 8{2} } } } = { {1} over {T rSub { size 8{2, ital "bulk"} } } } +ρ rSub { size 8{2} } \( { {S} over {V} } \) rSub { size 8{ ital "particle"} } } {}

(9)One can determine T_{2} by spin-echo measurements for a series of samples of known S/V values and prepare a calibration chart as shown in Figure 6, with the intercept as 1T2,bulk1T2,bulk size 12{ { {1} over {T rSub { size 8{2, ital "bulk"} } } } } {} and the slope as
ρ2ρ2 size 12{ρ rSub { size 8{2} } } {}, one can thus find the specific surface area of an unknown sample of the same material.