Grid not presenting data in colums used in HierarchicalDataTemplate

Question

I used a Grid to present a FileInDirNC type, but the ColumDefinitions doesn't seem to work?

I think it has something to do with HorizontalContentAlignment = "Stretch", but where is it needed? I want to left align the filenames and right align the dates in the Grid.

        <TreeView  Grid.Row="2" Grid.Column="3" ItemsSource="{Binding RootNC}" Style="{StaticResource TreeViewOrange}" AllowDrop="True"
            cal:Message.Attach="[Event Drop] = [Action FileDropped($eventArgs)]; [Event PreviewDragOver] = [Action FilePreviewDragEnter($eventArgs)]" Background="Transparent">
        <TreeView.Resources>
            <HierarchicalDataTemplate DataType="{x:Type Model:DirectoryNC}"
                                      ItemsSource="{Binding Children}">
                <TextBlock Text="{Binding DirectoryName}" />

            </HierarchicalDataTemplate>
            <HierarchicalDataTemplate DataType="{x:Type Model:FileInDirNC}">
                <Grid Margin="1" Background="{Binding CreationTime,Converter={StaticResource CreationTimeToBrushConverter}}" >
                    <Grid.ColumnDefinitions>
                        <ColumnDefinition Width="5*"/>
                        <ColumnDefinition Width="*"/>
                    </Grid.ColumnDefinitions>
                    <TextBlock Grid.Column ="0" Text="{Binding FileName}" Margin="5,0,20,0"  />
                    <TextBlock Grid.Column ="1" Text="{Binding CreationTime,StringFormat='{}{0:d/M/yyyy, hh:mm:ss}'}" FontSize="10" TextAlignment="Right"/>
                </Grid>
            </HierarchicalDataTemplate>
        </TreeView.Resources>
    </TreeView>

Kind Regards

Johan