diff --git a/openmc/data/function.py b/openmc/data/function.py
index 751f6cdb57..b0390d19cd 100644
--- a/openmc/data/function.py
+++ b/openmc/data/function.py
@@ -544,7 +544,7 @@ class Combination(EqualityMixin):
         self._operations = operations
 
 
-class Sum(EqualityMixin):
+class Sum(Function1D):
     """Sum of multiple functions.
 
     This class allows you to create a callable object which represents the sum
diff --git a/openmc/data/thermal.py b/openmc/data/thermal.py
index 6cf5a4e9e1..3d5f2df64e 100644
--- a/openmc/data/thermal.py
+++ b/openmc/data/thermal.py
@@ -701,7 +701,7 @@ class ThermalScattering(EqualityMixin):
                 energy = ace.xss[idx + 1: idx + 1 + n_energy]*EV_PER_MEV
                 P = ace.xss[idx + 1 + n_energy: idx + 1 + 2 * n_energy]
                 coherent_xs = CoherentElastic(energy, P*EV_PER_MEV)
-                coherent_dist = CoherentElasticAE(xs)
+                coherent_dist = CoherentElasticAE(coherent_xs)
 
                 # Coherent elastic shouldn't have angular distributions listed
                 n_mu = ace.nxs[6] + 1
diff --git a/openmc/data/thermal_angle_energy.py b/openmc/data/thermal_angle_energy.py
index b7ca349f12..1f37863ea0 100644
--- a/openmc/data/thermal_angle_energy.py
+++ b/openmc/data/thermal_angle_energy.py
@@ -2,6 +2,7 @@ import numpy as np
 
 from .angle_energy import AngleEnergy
 from .correlated import CorrelatedAngleEnergy
+import openmc.data
 
 
 class CoherentElasticAE(AngleEnergy):
@@ -33,25 +34,37 @@ class CoherentElasticAE(AngleEnergy):
     def __init__(self, coherent_xs):
         self.coherent_xs = coherent_xs
 
-    def to_hdf5(self, group, xs_group=None):
+    def to_hdf5(self, group):
         """Write coherent elastic distribution to an HDF5 group
 
-        .. versionchanged:: 0.13.1
-            The *xs_group* argument was added.
-
         Parameters
         ----------
         group : h5py.Group
             HDF5 group to write to
-        xs_group : h5py.Group, optional
-            Group containing 'xs' dataset
 
         """
         group.attrs['type'] = np.string_('coherent_elastic')
-        if xs_group is not None:
-            group['coherent_xs'] = xs_group['xs']
-        else:
-            group['coherent_xs'] = group.parent['xs']
+        self.coherent_xs.to_hdf5(group, 'coherent_xs')
+
+    @classmethod
+    def from_hdf5(cls, group):
+        """Generate coherent elastic distribution from HDF5 data
+
+        .. versionadded:: 0.13.1
+
+        Parameters
+        ----------
+        group : h5py.Group
+            HDF5 group to read from
+
+        Returns
+        -------
+        openmc.data.CoherentElasticAE
+            Coherent elastic distribution
+
+        """
+        coherent_xs = openmc.data.CoherentElastic.from_hdf5(group['coherent_xs'])
+        return cls(coherent_xs)
 
 
 class IncoherentElasticAE(AngleEnergy):
@@ -255,7 +268,7 @@ class MixedElasticAE(AngleEnergy):
         """
         group.attrs['type'] = np.string_('mixed_elastic')
         coherent_group = group.create_group('coherent')
-        self.coherent.to_hdf5(coherent_group, group.parent)
+        self.coherent.to_hdf5(coherent_group)
         incoherent_group = group.create_group('incoherent')
         self.incoherent.to_hdf5(incoherent_group)