The relative emission per ion and the lifetime have been obtained as a function of Tb concentration for the

{}^{5}D_{4}

{}^{7}F_{J}

transitions in

{(Y_{1 - x} {Tb}_{x})}_{3} {Al}_{5} O_{12}

crystals. At 297 °K both are concentration independent for

x < 0.3

and decrease as

x^{4.6 \pm 0.2}

for

x > 0.4

up to about a factor

10^{2}

for

{Tb}_{3}

{Al}_{5}

O_{12}

. From the time dependence of the intrinsic

{Tb}_{3}

{Al}_{5}

O_{12}

luminescence the initial nonexponential portion of the decay is shown to be consistent with direct dipolar transfer to nonradiative sinks. The later part of the decay is exponential and involves resonant

{Tb}^{3 +}

{Tb}^{3 +}

migration to the sinks. The direct transfer is found to be relatively temperature insensitive, but migration is not. There is little migration at low temperatures but for

T > 8 °

K, where the higher-energy

{}^{5}D_{4}

levels begin to be populated, the migration rate increases rapidly. The temperature dependence of the migration constant

D

was calculated using the level populations and oscillator strengths. The migration contribution to the exponential decay is proportional to

D^{\frac{3}{4}}

indicating the

{Tb}^{3 +}

{Tb}^{3 +}

transfer also involves dipolar interactions. Impurity-perturbed

{Tb}^{3 +}

emission is observed for

T < 12 °

K. These ions are mainly populated by direct dipole transfer from the intrinsic ions. Multiple-ion-decay processes involving the deexcitation of an ion in the

{}^{5}D_{4}

state and the simultaneous excitation of three or more neighboring

{Tb}^{3 +}

ions are shown to be negligible at low temperatures.

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