diff --git a/ChangeLog.md b/ChangeLog.md
index 79c263f44..d45c023e5 100644
--- a/ChangeLog.md
+++ b/ChangeLog.md
@@ -9,12 +9,14 @@ and this project adheres to
 ### Added
 * `freud.diffraction.StaticStructureFactorDirect` class (unstable) can be used to compute the static structure factor S(k) by sampling reciprocal space vectors.
 * Python 3.10 is supported.
+* Hexatic, Translational, SolidLiquid, and LocalDescriptors handle cases with zero neighbors.
 
 ### Fixed
 * Added error checking for `r_min`, `r_max` arguments in `freud.density.RDF`, `freud.locality.NeighborList`, `freud.locality.NeighborQuery`, and `freud.density.LocalDensity` classes.
 * Doctests are now run with pytest.
 * Cleaned up tests for the static structure factor classes.
 * CMake build system only uses references to TBB target.
+* Translational returns `nan` when particles do not have neighbors.
 
 ## v2.7.0 -- 2021-10-01
 
diff --git a/cpp/order/HexaticTranslational.cc b/cpp/order/HexaticTranslational.cc
index 8f706158c..cb53abbc1 100644
--- a/cpp/order/HexaticTranslational.cc
+++ b/cpp/order/HexaticTranslational.cc
@@ -37,7 +37,14 @@ void HexaticTranslational<T>::computeGeneral(Func func, const freud::locality::N
             }
             if (normalize_by_k)
             {
-                m_psi_array[i] /= std::complex<float>(m_k);
+                if (total_weight == 0.)
+                {
+                    m_psi_array[i] /= std::complex<float>(0.);
+                }
+                else
+                {
+                    m_psi_array[i] /= std::complex<float>(m_k);
+                }
             }
             else
             {
diff --git a/freud/order.pyx b/freud/order.pyx
index cb838f739..598b03c78 100644
--- a/freud/order.pyx
+++ b/freud/order.pyx
@@ -284,6 +284,15 @@ cdef class Hexatic(_PairCompute):
         **2D:** :class:`freud.order.Hexatic` is only defined for 2D systems.
         The points must be passed in as :code:`[x, y, 0]`.
 
+    .. note::
+        The value of per-particle order parameter will be set to NaN for
+        particles with no neighbors. We choose this value rather than setting
+        the order parameter to 0 because in more complex order parameter
+        calculations, it is possible to observe a value of 0 for the
+        per-particle order parameter even with a finite number of neighbors.
+        If you would like to ignore this distinction, you can mask the output
+        order parameter values using NumPy: :code:`numpy.nan_to_num(particle_order)`.
+
     Args:
         k (unsigned int, optional):
             Symmetry of order parameter (Default value = :code:`6`).
@@ -421,6 +430,16 @@ cdef class Translational(_PairCompute):
     .. note::
         This class is slated for deprecation and will be removed in freud 3.0.
 
+    .. note::
+        The value of per-particle order parameter will be set to NaN for
+        particles with no neighbors. We choose this value rather than setting
+        the order parameter to 0 because in more complex order parameter
+        calculations, it is possible to observe a value of 0 for the
+        per-particle order parameter even with a finite number of neighbors.
+        If you would like to ignore this distinction, you can mask the output
+        order parameter values using NumPy: :code:`numpy.nan_to_num(particle_order)`.
+
+
     Args:
         k (float, optional):
             Normalization of order parameter (Default value = :code:`6.0`).
@@ -808,6 +827,15 @@ cdef class SolidLiquid(_PairCompute):
     the particle is considered solid-like. Finally, solid-like particles are
     clustered.
 
+    .. note::
+        The value of :math:`q_l(i, j)` will be set to NaN for
+        particles with no neighbors. We choose this value rather than setting
+        the order parameter to 0 because in more complex order parameter
+        calculations, it is possible to observe a value of 0 for the :math:`q_l(i, j)`
+        order parameter even with a finite number of neighbors.
+        If you would like to ignore this distinction, you can mask the output order
+        parameter values using NumPy: :code:`numpy.nan_to_num(particle_order)`.
+
     Args:
         l (unsigned int):
             Spherical harmonic quantum number l.
@@ -859,6 +887,7 @@ cdef class SolidLiquid(_PairCompute):
         self.thisptr.compute(nlist.get_ptr(),
                              nq.get_ptr(),
                              dereference(qargs.thisptr))
+        return self
 
     @property
     def l(self):  # noqa: E743
diff --git a/tests/test_environment_LocalDescriptors.py b/tests/test_environment_LocalDescriptors.py
index ca9dd453e..4837088fe 100644
--- a/tests/test_environment_LocalDescriptors.py
+++ b/tests/test_environment_LocalDescriptors.py
@@ -438,3 +438,13 @@ def test_query_point_ne_points(self):
                         "Failed for l={}, m={}, x={}, y = {}" "\ntheta={}, phi={}"
                     ).format(l, m, scipy_val, ld_val, theta, phi)
                     count += 1
+
+    def test_no_neighbors(self):
+        l_max = 8
+        box = freud.box.Box.cube(10)
+        points = [(0, 0, 0)]
+
+        ld = freud.environment.LocalDescriptors(l_max)
+        ld.compute((box, points), neighbors={"r_max": 1.25})
+        assert ld.num_sphs == 0
+        assert len(ld.sph) == 0
diff --git a/tests/test_order_Hexatic.py b/tests/test_order_Hexatic.py
index 9eadcb118..9b0dea66b 100644
--- a/tests/test_order_Hexatic.py
+++ b/tests/test_order_Hexatic.py
@@ -218,3 +218,13 @@ def test_repr_png(self):
         hop._repr_png_()
         hop.plot()
         plt.close("all")
+
+    def test_no_neighbors(self):
+        """Ensure that particles without neighbors are assigned NaN"""
+        box = freud.box.Box.square(10)
+        positions = [(0, 0, 0)]
+        hop = freud.order.Hexatic()
+        hop.compute((box, positions), neighbors={"r_max": 1.25})
+
+        assert np.all(np.isnan(hop.particle_order))
+        npt.assert_allclose(np.nan_to_num(hop.particle_order), 0)
diff --git a/tests/test_order_SolidLiquid.py b/tests/test_order_SolidLiquid.py
index b087e7494..9093d38f1 100644
--- a/tests/test_order_SolidLiquid.py
+++ b/tests/test_order_SolidLiquid.py
@@ -1,4 +1,5 @@
 import matplotlib
+import numpy as np
 import numpy.testing as npt
 import pytest
 
@@ -95,3 +96,17 @@ def test_attribute_access(self):
     def test_repr(self):
         comp = freud.order.SolidLiquid(6, q_threshold=0.7, solid_threshold=6)
         assert str(comp) == str(eval(repr(comp)))
+
+    def test_no_neighbors(self):
+        """Ensure that particles without neighbors are assigned NaN"""
+        box = freud.box.Box.cube(10)
+        positions = [(0, 0, 0)]
+        comp = freud.order.SolidLiquid(6, q_threshold=0.7, solid_threshold=6)
+        comp.compute((box, positions), neighbors=dict(r_max=2.0))
+
+        npt.assert_equal(comp.cluster_idx, np.arange(len(comp.cluster_idx)))
+        npt.assert_equal(comp.cluster_sizes, np.ones_like(comp.cluster_sizes))
+        assert comp.largest_cluster_size == 1
+        npt.assert_equal(comp.num_connections, np.zeros_like(comp.cluster_sizes))
+        assert np.all(np.isnan(comp.particle_harmonics))
+        npt.assert_equal(comp.ql_ij, [])
diff --git a/tests/test_order_Translational.py b/tests/test_order_Translational.py
index 8a571f43c..927a1bb17 100644
--- a/tests/test_order_Translational.py
+++ b/tests/test_order_Translational.py
@@ -40,3 +40,12 @@ def test_repr(self):
         with pytest.warns(FreudDeprecationWarning):
             trans = freud.order.Translational(4)
             assert str(trans) == str(eval(repr(trans)))
+
+    def test_no_neighbors(self):
+        box = freud.box.Box.square(10)
+        positions = [(0, 0, 0)]
+        trans = freud.order.Translational(4)
+        trans.compute((box, positions), neighbors={"r_max": 0.25})
+
+        assert np.all(np.isnan(trans.particle_order))
+        npt.assert_allclose(np.nan_to_num(trans.particle_order), 0)